A massive Feynman integral and some reduction relations for Appell functions

NASA Astrophysics Data System (ADS)

Shpot, M. A.

2007-12-01

New explicit expressions are derived for the one-loop two-point Feynman integral with arbitrary external momentum and masses m12 and m22 in D dimensions. The results are given in terms of Appell functions, manifestly symmetric with respect to the masses mi2. Equating our expressions with previously known results in terms of Gauss hypergeometric functions yields reduction relations for the involved Appell functions that are apparently new mathematical results.

Dynamic technique for measuring adsorption in a gas chromatograph

NASA Technical Reports Server (NTRS)

Deuel, C. L.; Hultgren, N. W.; Mobert, M. L.

1973-01-01

Gas-chromatographic procedure, together with mathematical analysis of adsorption isotherm, allows relative surface areas and adsorptive powers for trace concentrations to be determined in a few minutes. Technique may be used to evaluate relative surface areas of different adsorbates, expressed as volume of adsorbent/gram of adsorbate, and to evaluate their relative adsorptive power.

What is rate? Does context or representation matter?

NASA Astrophysics Data System (ADS)

Herbert, Sandra; Pierce, Robyn

2011-12-01

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students' expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.

Mathematics of gravitational lensing: multiple imaging and magnification

NASA Astrophysics Data System (ADS)

Petters, A. O.; Werner, M. C.

2010-09-01

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

NASA Technical Reports Server (NTRS)

Arnold, S. M.; Tan, H. Q.; Dong, X.

1989-01-01

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Learning to teach mathematics with technology: A survey of professional development needs, experiences and impacts

NASA Astrophysics Data System (ADS)

Bennison, Anne; Goos, Merrilyn

2010-04-01

The potential for digital technologies to enhance students' mathematics learning is widely recognised, and use of computers and graphics calculators is now encouraged or required by secondary school mathematics curriculum documents throughout Australia. However, previous research indicates that effective integration of technology into classroom practice remains patchy, with factors such as teacher knowledge, confidence, experience and beliefs, access to resources, and participation in professional development influencing uptake and implementation. This paper reports on a large-scale survey of technology-related professional development experiences and needs of Queensland secondary mathematics teachers. Teachers who had participated in professional development were found to be more confident in using technology and more convinced of its benefits in supporting students' learning of mathematics. Experienced, specialist mathematics teachers in large metropolitan schools were more likely than others to have attended technology-related professional development, with lack of time and limited access to resources acting as hindrances to many. Teachers expressed a clear preference for professional development that helps them meaningfully integrate technology into lessons to improve student learning of specific mathematical topics. These findings have implications for the design and delivery of professional development that improves teachers' knowledge, understanding, and skills in a diverse range of contexts.

Spectral Analysis: From Additive Perspective to Multiplicative Perspective

NASA Astrophysics Data System (ADS)

Wu, Z.

2017-12-01

The early usage of trigonometric functions can be traced back to at least 17th century BC. It was Bhaskara II of the 12th century CE who first proved the mathematical equivalence between the sum of two trigonometric functions of any given angles and the product of two trigonometric functions of related angles, which has been taught these days in middle school classroom. The additive perspective of trigonometric functions led to the development of the Fourier transform that is used to express any functions as the sum of a set of trigonometric functions and opened a new mathematical field called harmonic analysis. Unfortunately, Fourier's sum cannot directly express nonlinear interactions between trigonometric components of different periods, and thereby lacking the capability of quantifying nonlinear interactions in dynamical systems. In this talk, the speaker will introduce the Huang transform and Holo-spectrum which were pioneered by Norden Huang and emphasizes the multiplicative perspective of trigonometric functions in expressing any function. Holo-spectrum is a multi-dimensional spectral expression of a time series that explicitly identifies the interactions among different scales and quantifies nonlinear interactions hidden in a time series. Along with this introduction, the developing concepts of physical, rather than mathematical, analysis of data will be explained. Various enlightening applications of Holo-spectrum analysis in atmospheric and climate studies will also be presented.

Handbook for Spoken Mathematics: (Larry's Speakeasy).

ERIC Educational Resources Information Center

Chang, Lawrence A.; And Others

This handbook is directed toward those who have to deal with spoken mathematics, yet have insufficient background to know the correct verbal expression for the written symbolic one. It compiles consistent and well-defined ways of uttering mathematical expressions so listeners will receive clear, unambiguous, and well-pronounced representations.…

Laser Atmospheric Propagation Kinetics

DTIC Science & Technology

1975-07-01

the available data. Section III also describes the mathematical model used to calculate the relaxation of the vibrational degrees of freedom in...has been used. This relation is derived in Appendix C, 11 -30- ---— ^^^^UM^ MUfi L^^MAamMMWaaMbAaMMMMMAMÜMMMM MMUMfa*,«« M^Mi mmm \\i •s T...is when the change in the optical path length is of the order of \\/2-n. Mathematically , this is expressed by the formula t vf (n - l)4jrdx = O

Mathematical expressions using fringe projections for transparent objects

NASA Astrophysics Data System (ADS)

Su, Wei-Hung; Cheng, Chau-Jern

2017-08-01

A setup using fringe projection techniques to perform 3D profile measurements for transparent objects is presented. The related mathematical equations are derived as well. A fringe pattern is illuminated onto the transparent object. Fringes passing through the inspected object are then projected onto a screen. A CCD camera is employed to record the transmitted fringes on the screen. Fringe on the screen are deformed by the refractive index and the surface structure, and therefore are desirable to describe the shape of the inspected sample.

A Conversion Tool for Mathematical Expressions in Web XML Files.

ERIC Educational Resources Information Center

Ohtake, Nobuyuki; Kanahori, Toshihiro

2003-01-01

This article discusses the conversion of mathematical equations into Extensible Markup Language (XML) on the World Wide Web for individuals with visual impairments. A program is described that converts the presentation markup style to the content markup style in MathML to allow browsers to render mathematical expressions without other programs.…

Online handwritten mathematical expression recognition

NASA Astrophysics Data System (ADS)

Büyükbayrak, Hakan; Yanikoglu, Berrin; Erçil, Aytül

2007-01-01

We describe a system for recognizing online, handwritten mathematical expressions. The system is designed with a user-interface for writing scientific articles, supporting the recognition of basic mathematical expressions as well as integrals, summations, matrices etc. A feed-forward neural network recognizes symbols which are assumed to be single-stroke and a recursive algorithm parses the expression by combining neural network output and the structure of the expression. Preliminary results show that writer-dependent recognition rates are very high (99.8%) while writer-independent symbol recognition rates are lower (75%). The interface associated with the proposed system integrates the built-in recognition capabilities of the Microsoft's Tablet PC API for recognizing textual input and supports conversion of hand-drawn figures into PNG format. This enables the user to enter text, mathematics and draw figures in a single interface. After recognition, all output is combined into one LATEX code and compiled into a PDF file.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bialynicki-Birula, Iwo

Quantum mechanical uncertainty relations for the position and the momentum and for the angle and the angular momentum are expressed in the form of inequalities involving the Renyi entropies. These uncertainty relations hold not only for pure but also for mixed states. Analogous uncertainty relations are valid also for a pair of complementary observables (the analogs of x and p) in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Renyi entropies. The mathematical proofs of all the inequalities discussed in this paper can be found in Phys. Rev. A 74, No. 5more » (2006); arXiv:quant-ph/0608116.« less

Middle-School Mathematics Teachers' Beliefs in NCTM's Vision

ERIC Educational Resources Information Center

Perrin, John Robert

2012-01-01

This study examined the extent to which seventh- and eighth-grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in…

The Effects of Expressive Writing on General and Mathematics Anxiety for a Sample of High School Students

ERIC Educational Resources Information Center

Hines, Claudia L.; Brown, Nina W.; Myran, Steve

2016-01-01

Ninety-three (n = 93) students in grades 9-12 who failed the Virginia Standards of Learning mathematics test were placed into experimental and control groups. Pre and posttest measures for general and mathematics anxiety, and physical symptoms of stress were administered. The Expressive Writing intervention was used with both groups where the…

Correction of the wavefront using the irradiance transport equation

NASA Astrophysics Data System (ADS)

García, M.; Granados, F.; Cornejo, A.

2008-07-01

The correction of the wavefront in optical systems implies the use of wavefront sensors, software, and auxiliary optical systems. We propose evaluated the wavefront using the fact that the wavefront and its intensity are related in the mathematical expression the irradiance transport equation (ITE)

Students' Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin's Symbolic Forms

ERIC Educational Resources Information Center

Becker, Nicole; Towns, Marcy

2012-01-01

Undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. Here we present the findings of a study that examines student understanding of mathematical expressions, including partial derivative expressions, in two undergraduate physical chemistry courses.…

Math expression retrieval using an inverted index over symbol pairs

NASA Astrophysics Data System (ADS)

Stalnaker, David; Zanibbi, Richard

2015-01-01

We introduce a new method for indexing and retrieving mathematical expressions, and a new protocol for evaluating math formula retrieval systems. The Tangent search engine uses an inverted index over pairs of symbols in math expressions. Each key in the index is a pair of symbols along with their relative distance and vertical displacement within an expression. Matched expressions are ranked by the harmonic mean of the percentage of symbol pairs matched in the query, and the percentage of symbol pairs matched in the candidate expression. We have found that our method is fast enough for use in real time and finds partial matches well, such as when subexpressions are re-arranged (e.g. expressions moved from the left to the right of an equals sign) or when individual symbols (e.g. variables) differ from a query expression. In an experiment using expressions from English Wikipedia, student and faculty participants (N=20) found expressions returned by Tangent significantly more similar than those from a text-based retrieval system (Lucene) adapted for mathematical expressions. Participants provided similarity ratings using a 5-point Likert scale, evaluating expressions from both algorithms one-at-a-time in a randomized order to avoid bias from the position of hits in search result lists. For the Lucene-based system, precision for the top 1 and 10 hits averaged 60% and 39% across queries respectively, while for Tangent mean precision at 1 and 10 were 99% and 60%. A demonstration and source code are publicly available.

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

The initial response of secondary mathematics teachers to a one-to-one laptop program

NASA Astrophysics Data System (ADS)

Zuber, Edward Nordin; Anderson, Judy

2013-06-01

Studies of one-to-one programs consistently report lower use of laptops in mathematics classrooms compared to other subjects but do not elaborate reasons for these observations. This mixed-method study investigated the experiences and beliefs of 28 mathematics teachers at five secondary schools during the second year of the New South Wales Digital Education Revolution laptop program. While some mathematics teachers planned for students to use their laptops up to once a week, most reported less frequent use in the classroom. Teachers were grouped into categories "Non Adopters," "Cautious Adopters," and "Early Adopters" according to reported classroom use of laptops, then analysed for differences in confidence, knowledge, and beliefs relating to technology for teaching and learning mathematics. A prevalent belief limiting laptop use is that students authentically learn mathematics only using pen and paper. Cautious Adopters and Non Adopters expressed beliefs that laptops exacerbate classroom management problems, especially for lower-achieving students. In the context of ability-streamed classes these beliefs effectively ruled out use of laptops for entire classrooms.

Experimental investigation and application of the equilibrium rutile + orthopyroxene = quartz + ilmenite

USGS Publications Warehouse

Hayob, J.L.; Bohlen, S.R.; Essene, E.J.

1993-01-01

Equilibria in the Sirf (Silica-Ilmenite-Rutile-Ferrosilite) system: {Mathematical expression} have been calibrated in the range 800-1100?? C and 12-26 kbar using a piston-cylinder apparatus to assess the potential of the equilibria for geobarometry in granulite facies assemblages that lack garnet. Thermodynamic calculations indicate that the two end-member equilibria involving quartz + geikielite = rutile + enstatite, and quartz + ilmenite = rutile + ferrosilite, are metastable. We therefore reversed equilibria over the compositional range Fs40-70, using Ag80Pd20 capsules with {Mathematical expression} buffered at or near iron-wu??stite. Ilmenite compositions coexisting with orthopyroxene are {Mathematical expression} of 0.06 to 0.15 and {Mathematical expression} of 0.00 to 0.01, corresponding to KD values of 13.3, 10.2, 9.0 and 8.0 (??0.5) at 800, 900, 1000 and 1100?? C, respectively, where KD=(XMg/XFe)Opx/(XMg/XFe)Ilm. Pressures have been calculated using equilibria in the Sirf system for granulites from the Grenville Province of Ontario and for granulite facies xenoliths from central Mexico. Pressures are consistent with other well-calibrated geobarometers for orthopyroxeneilmenite pairs from two Mexican samples in which oxide textures appear to represent equilibrium. Geologically unreasonable pressures are obtained, however, where oxide textures are complex. Application of data from this study on the equilibrium distribution of iron and magnesium between ilmenite and orthopyroxene suggests that some ilmenite in deep crustal xenoliths is not equilibrated with coexisting pyroxene, while assemblages from exposed granulite terranes have reequilibrated during retrogression. The Sirf equilibria are sensitive to small changes in composition and may be used for determination of activity/composition (a/X) relations of orthopyroxene if an ilmenite model is specified. A symmetric regular solution model has been used for orthopyroxene in conjunction with activity models for ilmenite available from the literature to calculate a/X relations in orthopyroxene of intermediate composition. Data from this study indicate that FeSiO3-MgSiO3 orthopyroxene exhibits small, positive deviations from ideality over the range 800-1100??C. ?? 1993 Springer-Verlag.

Expressions Module for the Satellite Orbit Analysis Program

NASA Technical Reports Server (NTRS)

Edmonds, Karina

2008-01-01

The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.

On some stochastic formulations and related statistical moments of pharmacokinetic models.

PubMed

Matis, J H; Wehrly, T E; Metzler, C M

1983-02-01

This paper presents the deterministic and stochastic model for a linear compartment system with constant coefficients, and it develops expressions for the mean residence times (MRT) and the variances of the residence times (VRT) for the stochastic model. The expressions are relatively simple computationally, involving primarily matrix inversion, and they are elegant mathematically, in avoiding eigenvalue analysis and the complex domain. The MRT and VRT provide a set of new meaningful response measures for pharmacokinetic analysis and they give added insight into the system kinetics. The new analysis is illustrated with an example involving the cholesterol turnover in rats.

VERTICAL INTEGRATION OF THREE-PHASE FLOW EQUATIONS FOR ANALYSIS OF LIGHT HYDROCARBON PLUME MOVEMENT

EPA Science Inventory

A mathematical model is derived for areal flow of water and light hydrocarbon in the presence of gas at atmospheric pressure. Closed-form expressions for the vertically integrated constitutive relations are derived based on a three-phase extension of the Brooks-Corey saturation-...

Some Learning Problems Concerning the Use of Symbolic Language in Physics.

ERIC Educational Resources Information Center

De Lozano, Silvia Ragout; Cardenas, Marta

2002-01-01

Draws the attention of teachers of basic university physics courses to student problems concerning the interpretation of the symbolic language used in physics. Reports specific difficulties found in the first physics course related to different kinds of statements expressed in the mathematical language. (Contains 15 references.) (Author/YDS)

Planned Contrasts: An Overview of Comparison Methods.

ERIC Educational Resources Information Center

Chatham, Kathy

Contrasts or comparisons can be used to investigate specific differences between means. Contrasts, as explained by B. Thompson (1985, 1994) are coding vectors that mathematically express hypotheses. The most basic categories of contrasts are planned and unplanned. The purpose of this paper is to explain the relative advantages of using planned…

Technical Report for Contract N00039-82-C-0235, 15 November 1981-30 September 1983

DTIC Science & Technology

1983-09-30

Management of Data, Ann Arbor, Rich., June 1982. -. 2 ’’.’ , . .. ’,, .* ,° • ,"%,.° % °%" ° %- " "%" . . ." " -.. . . ,.%. Interactive Mathematical ...developed and implemented a hierachical representation for mathematical expres- sioms that includes display position, expression dimensions, font...etc) in internal forms are accepted and converted to box frames which can be displayed. 2. Strophe’s representation of mathematical expressions is

Designing Mathematical Learning Environments for Teachers

ERIC Educational Resources Information Center

Madden, Sandra R.

2010-01-01

Technology use in mathematics often involves either exploratory or expressive modeling. When using exploratory models, students use technology to investigate a premade expert model of some phenomena. When creating expressive models, students have greater flexibility for constructing their own model for investigation using objects and mechanisms…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Early Mathematics Fluency with CCSSM

ERIC Educational Resources Information Center

Matney, Gabriel T.

2014-01-01

To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…

Expanding Audio Access to Mathematics Expressions by Students with Visual Impairments via MathML. Research Report. ETS RR-17-13

ERIC Educational Resources Information Center

Frankel, Lois; Brownstein, Beth; Soiffer, Neil

2017-01-01

This report describes the pilot conducted in the final phase of a project, Expanding Audio Access to Mathematics Expressions by Students With Visual Impairments via MathML, to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low…

CBM Reading, Mathematics, and Written Expression at the Secondary Level: Examining Latent Composite Relations Among Indices and Unique Predictions With a State Achievement Test

PubMed Central

Codding, Robin S.; Petscher, Yaacov; Truckenmiller, Adrea

2015-01-01

A paucity of research has examined the utility of curriculum-based measurement (CBM) for data-based decision making at the secondary level. As schools move to multitiered systems of service delivery, it is conceivable that multiple screening measures will be used that address various academic subject areas. The value of including different CBM indices measures is not well understood. The purpose of this study was to (a) examine the relationship among a variety of reading, writing, and mathematics CBM indices administered to 249 seventh-grade students; (b) investigate amount and patterns of growth; and (c) examine predictive validity to a high-stakes state test using latent factor analysis and multiple indicator growth models. Results indicated strong correspondence among CBM types for fall static scores but weak relationships among slopes. Different patterns of growth were yielded for CBM writing than for CBM reading and mathematics. Findings from this study suggested that although reading, mathematics, and writing CBM were independently and moderately related to both English Language Arts and Math test scores, reading was the strongest predictor when all 3 CBM constructs were considered jointly. PMID:26347201

CBM Reading, Mathematics, and Written Expression at the Secondary Level: Examining Latent Composite Relations Among Indices and Unique Predictions With a State Achievement Test.

PubMed

Codding, Robin S; Petscher, Yaacov; Truckenmiller, Adrea

2015-05-01

A paucity of research has examined the utility of curriculum-based measurement (CBM) for data-based decision making at the secondary level. As schools move to multitiered systems of service delivery, it is conceivable that multiple screening measures will be used that address various academic subject areas. The value of including different CBM indices measures is not well understood. The purpose of this study was to (a) examine the relationship among a variety of reading, writing, and mathematics CBM indices administered to 249 seventh-grade students; (b) investigate amount and patterns of growth; and (c) examine predictive validity to a high-stakes state test using latent factor analysis and multiple indicator growth models. Results indicated strong correspondence among CBM types for fall static scores but weak relationships among slopes. Different patterns of growth were yielded for CBM writing than for CBM reading and mathematics. Findings from this study suggested that although reading, mathematics, and writing CBM were independently and moderately related to both English Language Arts and Math test scores, reading was the strongest predictor when all 3 CBM constructs were considered jointly.

Mathematical model of the solar radiation force and torques acting on the components of a spacecraft

NASA Technical Reports Server (NTRS)

Georgevic, R. M.

1971-01-01

General expressions for the solar radiation force and torques are derived in the vectorial form for any given reflecting surface, provided that the reflecting characteristics of the surface, as well as the value of the solar constant, are known. An appropriate choice of a spacecraft-fixed frame of reference leads to relatively simple expressions for the solar radiation forces and torques in terms of the functions of the sun-spacecraft-earth angle.

Mother and Child Emotions during Mathematics Homework

ERIC Educational Resources Information Center

Else-Quest, Nicole M.; Hyde, Janet S.; Hejmadi, Ahalya

2008-01-01

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the…

Automatic Semantic Generation and Arabic Translation of Mathematical Expressions on the Web

ERIC Educational Resources Information Center

Doush, Iyad Abu; Al-Bdarneh, Sondos

2013-01-01

Automatic processing of mathematical information on the web imposes some difficulties. This paper presents a novel technique for automatic generation of mathematical equations semantic and Arabic translation on the web. The proposed system facilitates unambiguous representation of mathematical equations by correlating equations to their known…

WISC-IV Intellectual Profiles in Italian Children With Specific Learning Disorder and Related Impairments in Reading, Written Expression, and Mathematics.

PubMed

Poletti, Michele

2016-01-01

The fifth edition of theDiagnostic and Statistical Manual of Mental Disordersgrouped specific learning disabilities in the single diagnostic category of specific learning disorder (SLD), with specifiers for impairments in reading, written expression, and mathematics. This study aimed at investigating the intellectual profile, assessed with the fourth edition of theWechsler Intelligence Scale for Children(WISC-IV), of 172 children with a diagnosis of SLD, compared to 74 clinical referral controls. WISC-IV intellectual functioning in children with SLD was characterized by a significant discrepancy between general ability and cognitive proficiency (General Ability Index [GAI] > Cognitive Proficiency Index [CPI]), and worse performances on the Similarities, Digit Span, Letter-Number Sequencing, and Coding subtests, supporting models of multiple cognitive deficits at the basis of neurodevelopmental disorders as SLD. GAI was the best and more conservative measure provided by the WISC-IV to identify intellectual functioning in children with SLD, and the intellectual discrepancy between GAI and CPI could be considered a "cognitive sign" for the presence of SLD in a single diagnostic category. Cognitive deficits differed in subtypes of impairment (reading, written expression, and mathematics), supporting their distinction for empirical, educational, and rehabilitative purposes. These findings need further replication in larger samples and in comparison to typically developing children. © Hammill Institute on Disabilities 2014.

From rational numbers to algebra: separable contributions of decimal magnitude and relational understanding of fractions.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2015-05-01

To understand the development of mathematical cognition and to improve instructional practices, it is critical to identify early predictors of difficulty in learning complex mathematical topics such as algebra. Recent work has shown that performance with fractions on a number line estimation task predicts algebra performance, whereas performance with whole numbers on similar estimation tasks does not. We sought to distinguish more specific precursors to algebra by measuring multiple aspects of knowledge about rational numbers. Because fractions are the first numbers that are relational expressions to which students are exposed, we investigated how understanding the relational bipartite format (a/b) of fractions might connect to later algebra performance. We presented middle school students with a battery of tests designed to measure relational understanding of fractions, procedural knowledge of fractions, and placement of fractions, decimals, and whole numbers onto number lines as well as algebra performance. Multiple regression analyses revealed that the best predictors of algebra performance were measures of relational fraction knowledge and ability to place decimals (not fractions or whole numbers) onto number lines. These findings suggest that at least two specific components of knowledge about rational numbers--relational understanding (best captured by fractions) and grasp of unidimensional magnitude (best captured by decimals)--can be linked to early success with algebraic expressions. Copyright © 2015 Elsevier Inc. All rights reserved.

Staircase Methods of Sensitivity Testing,

DTIC Science & Technology

1946-03-21

Mathematical Preliminaries ............. 32 b. Outline of the Investigation ..... .......... 35 8. The Possible Adjustments ...... ............... .. 36 9...bh Ar’Lied MathematIcs Pa-nel. ZCC, uU, -. for one decermntation !f tie per centtage point and the average nmber ee exp-li.-n. required far one such...accuracy per explosion. 32. II. TECOI4ICPJJ 7. Introduction. a. Some Mathematical Preliminaries. Expressed mathematically , the problem of sensitivity

The Value of Emoticons in Investigating Student Emotions Related to Mathematics Task Negotiation

ERIC Educational Resources Information Center

D'Agostin, Fabio

2014-01-01

"Emoticons" are simple face icons expressing common feelings such as happiness, interest and boredom and are popularly used in electronic communication. Emoticons were utilised in this study as experience sampling devices. Year 10 students selected emoticons to indicate their emotional states at set intervals during classroom tasks.…

Characterizing Student Expectations: A Small Empirical Study

ERIC Educational Resources Information Center

Warwick, Jonathan

2016-01-01

This paper describes the results of a small empirical study (n = 130), in which undergraduate students in the Business Faculty of a UK university were asked to express views and expectations relating to the study of a mathematics. Factor analysis is used to identify latent variables emerging from clusters of the measured variables and these are…

Urban stormwater capture curve using three-parameter mixed exponential probability density function and NRCS runoff curve number method.

PubMed

Kim, Sangdan; Han, Suhee

2010-01-01

Most related literature regarding designing urban non-point-source management systems assumes that precipitation event-depths follow the 1-parameter exponential probability density function to reduce the mathematical complexity of the derivation process. However, the method of expressing the rainfall is the most important factor for analyzing stormwater; thus, a better mathematical expression, which represents the probability distribution of rainfall depths, is suggested in this study. Also, the rainfall-runoff calculation procedure required for deriving a stormwater-capture curve is altered by the U.S. Natural Resources Conservation Service (Washington, D.C.) (NRCS) runoff curve number method to consider the nonlinearity of the rainfall-runoff relation and, at the same time, obtain a more verifiable and representative curve for design when applying it to urban drainage areas with complicated land-use characteristics, such as occurs in Korea. The result of developing the stormwater-capture curve from the rainfall data in Busan, Korea, confirms that the methodology suggested in this study provides a better solution than the pre-existing one.

The Negative Sign and Exponential Expressions: Unveiling Students' Persistent Errors and Misconceptions

ERIC Educational Resources Information Center

Cangelosi, Richard; Madrid, Silvia; Cooper, Sandra; Olson, Jo; Hartter, Beverly

2013-01-01

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential…

University of Chicago School Mathematics Project (UCSMP) Algebra. WWC Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

Quantify spatial relations to discover handwritten graphical symbols

NASA Astrophysics Data System (ADS)

Li, Jinpeng; Mouchère, Harold; Viard-Gaudin, Christian

2012-01-01

To model a handwritten graphical language, spatial relations describe how the strokes are positioned in the 2-dimensional space. Most of existing handwriting recognition systems make use of some predefined spatial relations. However, considering a complex graphical language, it is hard to express manually all the spatial relations. Another possibility would be to use a clustering technique to discover the spatial relations. In this paper, we discuss how to create a relational graph between strokes (nodes) labeled with graphemes in a graphical language. Then we vectorize spatial relations (edges) for clustering and quantization. As the targeted application, we extract the repetitive sub-graphs (graphical symbols) composed of graphemes and learned spatial relations. On two handwriting databases, a simple mathematical expression database and a complex flowchart database, the unsupervised spatial relations outperform the predefined spatial relations. In addition, we visualize the frequent patterns on two text-lines containing Chinese characters.

E-Coli and Other Problems

ERIC Educational Resources Information Center

Scott, Paul

2009-01-01

In applied mathematics particularly, one is interested in modeling real life situations; that is why, one tries to express some actual phenomenon mathematically, and then uses mathematics to determine future outcomes. It may be that one actually wishes to change the future outcome. Mathematics will not do this, but at least it tells one what to…

The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations

ERIC Educational Resources Information Center

Tristanti, Lia Budi; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muskar, Makbul

2016-01-01

This study discusses the construction of deductive warrant derived from inductive warrant in mathematical argumentations expressed by pre-service teacher. In completing a mathematics task, a problem solver needs argumentation to determine, reveal, and support a reasonable solution. A mathematical argumentation can be analyzed by Toulmin scheme…

Mathematics Teacher-Candidates' Performance in Solving Problems with Different Representation Styles: The Trigonometry Example

ERIC Educational Resources Information Center

Dündar, Sefa

2015-01-01

Using multiple representations of a problem can reveal the relationship between complex concepts by expressing the same mathematical condition differently and can contribute to the meaningful learning of mathematical concepts. The purpose of this study is to assess the performances of mathematics teacher-candidates on trigonometry problems…

24 CFR 51.103 - Criteria and standards.

Code of Federal Regulations, 2010 CFR

2010-04-01

... decibels to sound levels in the night from 10 p.m. to 7 a.m. Mathematical expressions for average sound..., as indicated in § 51.106(a)(3). Methods for assessing the contribution of loud impulsive sounds to day-night average sound level at a site and mathematical expressions for determining whether a sound...

Missing Dimensions of Mathematics Instruction.

ERIC Educational Resources Information Center

Meyer, Walter

1995-01-01

Emphasizes how to express the breadth of mathematics itself. Addresses other missing dimensions which make mathematics attractive to a larger number of students by making it appear less isolated and more tied to thoughts and experiences that students find familiar and congenial. (ASK)

Discretization of Gene Expression Data Unmasks Molecular Subgroups Recurring in Different Human Cancer Types.

PubMed

Beleut, Manfred; Soeldner, Robert; Egorov, Mark; Guenther, Rolf; Dehler, Silvia; Morys-Wortmann, Corinna; Moch, Holger; Henco, Karsten; Schraml, Peter

2016-01-01

Despite the individually different molecular alterations in tumors, the malignancy associated biological traits are strikingly similar. Results of a previous study using renal cell carcinoma (RCC) as a model pointed towards cancer-related features, which could be visualized as three groups by microarray based gene expression analysis. In this study, we used a mathematic model to verify the presence of these groups in RCC as well as in other cancer types. We developed an algorithm for gene-expression deviation profiling for analyzing gene expression data of a total of 8397 patients with 13 different cancer types and normal tissues. We revealed three common Cancer Transcriptomic Profiles (CTPs) which recurred in all investigated tumors. Additionally, CTPs remained robust regardless of the functions or numbers of genes analyzed. CTPs may represent common genetic fingerprints, which potentially reflect the closely related biological traits of human cancers.

Mathematical Description of THE Traction Characteristics of the Driving Devices at Spatial Stiffness Compensators of the Vibration Isolation Installations

NASA Astrophysics Data System (ADS)

Gurova, E. G.

2016-08-01

During the researches the mathematical description of the traction characteristics of the stiffness compensators of the vibration isolation devices, relatively of the each axis, has been done. Representation of the compensators properties considers the variable load, thereby provide the wide enough spectrum of the action of the suggested vibration isolators. The derived expressions are valid for all three axes of space at the different stiffnesses, i.e. basic basic and two compensating. The research was supported by the scholarships of Russian Federation President for young scientists №184 from 10th of March 2015.

A formulation of the foundations of genetics and evolution.

PubMed

Bahr, Brian Edward

2016-05-01

This paper proposes a formulation of theories of the foundations of genetics and evolution that can be used to mathematically simulate phenotype expression, reproduction, mutation, and natural selection. It will be shown that Mendelian inheritance can be mathematically simulated with expressions involving matrices and that these expressions can also simulate phenomena that are modifications to Mendel's basic principles, like alleles that give rise to quantitative effects and traits that are the expression of multiple alleles and/or multiple genetic loci. Copyright © 2016 Elsevier Inc. All rights reserved.

The energy spectrum of a microchannel multiplier with two microchannel plates in the chevron assembly

NASA Astrophysics Data System (ADS)

Kosulya, A. V.; Verbitskii, V. G.

2017-11-01

A mathematical model of the response of a microchannel multiplier based on two microchannel plates in the chevron assembly has been considered. Analytical expressions relating the parameters of input and output signals have been obtained. The geometry of the chevron unit has been determined, and it has been optimized.

Make Your Own Paint Chart: A Realistic Context for Developing Proportional Reasoning with Ratios

ERIC Educational Resources Information Center

Beswick, Kim

2011-01-01

Proportional reasoning has been recognised as a crucial focus of mathematics in the middle years and also as a frequent source of difficulty for students (Lamon, 2007). Proportional reasoning concerns the equivalence of pairs of quantities that are related multiplicatively; that is, equivalent ratios including those expressed as fractions and…

Signifying the Accumulation Graph in a Dynamic and Multi-Representation Environment

ERIC Educational Resources Information Center

Yerushalmy, Michal; Swidan, Osama

2012-01-01

The present study focuses on the accumulation process involved in the integration of a single-variable function. Observing the work of two high-school calculus students who had not yet learned any other integral-related ideas, we analyze the emergence of the semiotic relationship between personal and mathematical meanings, as expressed through the…

To Solve or Not to Solve, that Is the Problem

ERIC Educational Resources Information Center

Braiden, Doug

2011-01-01

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

Computer Solution of the Two-Dimensional Tether Ball: Problem to Illustrate Newton's Second Law.

ERIC Educational Resources Information Center

Zimmerman, W. Bruce

Force diagrams involving angular velocity, linear velocity, centripetal force, work, and kinetic energy are given with related equations of motion expressed in polar coordinates. The computer is used to solve differential equations, thus reducing the mathematical requirements of the students. An experiment is conducted using an air table to check…

Linguistic Documentation of Metal System

DTIC Science & Technology

1978-05-01

of the set- theoretical operations intersection, union , and complement. These are used to express relations which may hold between the values of...means of the set-theoretical operations union , intersection, and difference. Union is represented by "+M, intersection by ".", and difference by...RAILway RELigion = RELIGion RHETorical RUGby SCIENTific SCULPture SKIing ... SOCIOLOGY SPINning SPORT STATistics ■ MATHematics STock

Loving and Hating Mathematics: Challenging the Myths of Mathematical Life

ERIC Educational Resources Information Center

Hersh, Reuben; John-Steiner, Vera

2010-01-01

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. "Loving and Hating…

Error propagation in eigenimage filtering.

PubMed

Soltanian-Zadeh, H; Windham, J P; Jenkins, J M

1990-01-01

Mathematical derivation of error (noise) propagation in eigenimage filtering is presented. Based on the mathematical expressions, a method for decreasing the propagated noise given a sequence of images is suggested. The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of the final composite image are compared to the SNRs and CNRs of the images in the sequence. The consistency of the assumptions and accuracy of the mathematical expressions are investigated using sequences of simulated and real magnetic resonance (MR) images of an agarose phantom and a human brain.

Prediction of Layer Thickness in Molten Borax Bath with Genetic Evolutionary Programming

NASA Astrophysics Data System (ADS)

Taylan, Fatih

2011-04-01

In this study, the vanadium carbide coating in molten borax bath process is modeled by evolutionary genetic programming (GEP) with bath composition (borax percentage, ferro vanadium (Fe-V) percentage, boric acid percentage), bath temperature, immersion time, and layer thickness data. Five inputs and one output data exist in the model. The percentage of borax, Fe-V, and boric acid, temperature, and immersion time parameters are used as input data and the layer thickness value is used as output data. For selected bath components, immersion time, and temperature variables, the layer thicknesses are derived from the mathematical expression. The results of the mathematical expressions are compared to that of experimental data; it is determined that the derived mathematical expression has an accuracy of 89%.

Exploring grade 3 teachers' resistance to `take up' progressive mathematics teaching roles

NASA Astrophysics Data System (ADS)

Westaway, Lise; Graven, Mellony

2018-03-01

This article addresses the question: Why teachers of mathematics have yet to `take up' progressive roles? Drawing on the philosophy of critical realism and its methodological equivalent, social realism, we analyse interview and observation data of four grade 3 teachers, with the view to identifying the mechanisms conditioning the expression of teachers' identities. In so doing, we show how post-apartheid changes in systemic roles of teachers create contradictory tensions for teachers as these bring their own mathematical learning and teaching experiences into contradiction with the new post-apartheid roles they are mandated to enact. We examine how this contradiction, together with beliefs about mathematics, pedagogy and learners, is expressed in the teaching of grade 3 mathematics. We maintain that the complementarity between teachers' beliefs and old systemic roles provides an explanation for why teachers of grade 3 mathematics have yet to `take-up' progressive roles. The implications point to the need for teacher development that creates enablers that lead to changes in classroom practices that align with policy-designated, progressive roles in teaching mathematics.

Study ethnomathematics of aboge (alif, rebo, wage) calendar as determinant of the great days of Islam and traditional ceremony in Cirebon Kasepuhan Palace

NASA Astrophysics Data System (ADS)

Syahrin, Muhammad Alfi; Turmudi, Puspita, Entit

2016-02-01

This research attempts to show about the relationship between mathematics and culture. Paradigm that emerged currently, that mathematics is an abstract concept and difficult, therefore mathematics is not favored by most students. In the reality, indirectly mathematics is present in a culture of a society. Ethnomathematics study is a study to examine how does a group of people in a particular culture understand, express, and use the concepts and practices of culture that depicted mathematically. This research was conducted in Cirebon precisely in Kasepuhan Palace, which was in RW 04, Kasepuhan village, Lemah Wungkuk district, Cirebon city, West Java. The focus of the study and research purposes was the application of aboge (alif rebo wage) calendar as the calculation of days and the calendar rules determine the time of days, great days of Islam and traditional ceremony in Kasepuhan Palace. Qualitative methods with the principles of ethnography such as studies in ethnomathematics i.e observation, interviews, documentation and fieldnotes were used in this research. The findings of this ethnomathematics study show that the determining great days of Islam and the days of palace traditional ceremony have a close relationship with the counts and principles in mathematics. This study provides recommendations that mathematics is closely related to culture due to ethnomathematics.

Two-dimensional dispersion of magnetostatic volume spin waves

NASA Astrophysics Data System (ADS)

Buijnsters, Frank J.; van Tilburg, Lennert J. A.; Fasolino, Annalisa; Katsnelson, Mikhail I.

2018-06-01

Owing to the dipolar (magnetostatic) interaction, long-wavelength spin waves in in-plane magnetized films show an unusual dispersion behavior, which can be mathematically described by the model of and and refinements thereof. However, solving the two-dimensional dispersion requires the evaluation of a set of coupled transcendental equations and one has to rely on numerics. In this work, we present a systematic perturbative analysis of the spin wave model. An expansion in the in-plane wavevector allows us to obtain explicit closed-form expressions for the dispersion relation and mode profiles in various asymptotic regimes. Moreover, we derive a very accurate semi-analytical expression for the dispersion relation of the lowest-frequency mode that is straightforward to evaluate.

The Great Mathematician Project

ERIC Educational Resources Information Center

Goldberg, Sabrina R.

2013-01-01

The Great Mathematician Project (GMP) introduces both mathematically sophisticated and struggling students to the history of mathematics. The rationale for the GMP is twofold: first, mathematics is a uniquely people-centered discipline that is used to make sense of the world; and second, students often express curiosity about the history of…

Type Specialization in Aldor

NASA Astrophysics Data System (ADS)

Dragan, Laurentiu; Watt, Stephen M.

Computer algebra in scientific computation squarely faces the dilemma of natural mathematical expression versus efficiency. While higher-order programming constructs and parametric polymorphism provide a natural and expressive language for mathematical abstractions, they can come at a considerable cost. We investigate how deeply nested type constructions may be optimized to achieve performance similar to that of hand-tuned code written in lower-level languages.

Complex compatible taper and volume estimation systems for red and loblolly pine

Treesearch

John C. Byrne; David D. Reed

1986-01-01

Five equation systems are described which can be used to estimate upper stem diameter, total individual tree cubic-foot volume, and merchantable cubic-foot volumes to any merchantability imit (expressed in terms of diameter or height), both inside and outside bark. The equations provide consistent results since they are mathematically related and are fit using stem...

MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics

ERIC Educational Resources Information Center

Lalingkar, Aparna; Ramnathan, Chandrashekar; Ramani, Srinivasan

2015-01-01

The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…

Mathematics Diagnostic Testing in Engineering: An International Comparison between Ireland and Portugal

ERIC Educational Resources Information Center

Carr, M.; Fidalgo, C.; Bigotte de Almeida, M. E.; Branco, J. R.; Santos, V.; Murphy, E.; Ní Fhloinn, E.

2015-01-01

Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into…

Maths Games: A Universal Design Approach to Mathematical Reasoning

ERIC Educational Resources Information Center

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia E.

2017-01-01

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

Emotion and Disaffection with School Mathematics

ERIC Educational Resources Information Center

Lewis, Gareth

2013-01-01

This paper reports some initial findings from research designed to understand more deeply the motivational and emotional landscape of disaffection with school mathematics. A context is described in which there has been significant concern expressed about a number of aspects of mathematics education, but where affect is seen as salient to these…

Dynamics of Longitudinal Impact in the Variable Cross-Section Rods

NASA Astrophysics Data System (ADS)

Stepanov, R.; Romenskyi, D.; Tsarenko, S.

2018-03-01

Dynamics of longitudinal impact in rods of variable cross-section is considered. Rods of various configurations are used as elements of power pulse systems. There is no single method to the construction of a mathematical model of longitudinal impact on rods. The creation of a general method for constructing a mathematical model of longitudinal impact for rods of variable cross-section is the goal of the article. An elastic rod is considered with a cross-sectional area varying in powers of law from the longitudinal coordinate. The solution of the wave equation is obtained using the Fourier method. Special functions are introduced on the basis of recurrence relations for Bessel functions for solving boundary value problems. The expression for the square of the norm is obtained taking into account the orthogonality property of the eigen functions with weight. For example, the impact of an inelastic mass along the wide end of a conical rod is considered. The expressions for the displacements, forces and stresses of the rod sections are obtained for the cases of sudden velocity communication and the application of force. The proposed mathematical model makes it possible to carry out investigations of the stress-strain state in rods of variable and constant cross-section for various conditions of dynamic effects.

Structural equation modeling assessing relationship between mathematics beliefs, teachers' attitudes and teaching practices among novice teachers in Malaysia

NASA Astrophysics Data System (ADS)

Borhan, Noziati; Zakaria, Effandi

2017-05-01

This quantitative study was conducted to investigate the perception level of novice teachers about mathematics belief, teachers' attitude towards mathematics and teaching practices of mathematics in the classroom. In addition, it also aims to identify whether there is a correspondence model with the data obtained and to identify the relationship between the variables of beliefs, attitudes and practices among novice teachers in Malaysia. A total of 263 primary novice teachers throughout the country were involved in this study were selected randomly. Respondents are required to provide a response to the questionnaire of 66 items related to mathematics beliefs, attitudes and practices of the teaching mathematics. There are ten sub-factors which have been established in this instrument for three major constructs using a Likert scale rating of five points. The items of the constructs undergo the exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) procedure involve of unidimensionality test, convergent validity, construct validity and discriminant validity. Descriptive statistics were used to describe the frequency, percentage, the mean and standard deviation for completing some research questions that have been expressed. As for inferential statistical analysis, the researchers used structural equation modeling (SEM) to answer the question of correspondents model and the relationship between these three variables. The results of the study were found that there exist a correspondence measurement and structural model with the data obtained. While the relationship between variable found that mathematics beliefs have a significant influence on teachers' attitudes towards mathematics as well as the relationship between the attitudes with teaching practices. Meanwhile, mathematics belief had no significant relationship with mathematics teaching practices among novice teachers in Malaysia.

Scientific Assistant Virtual Laboratory (SAVL)

NASA Astrophysics Data System (ADS)

Alaghband, Gita; Fardi, Hamid; Gnabasik, David

2007-03-01

The Scientific Assistant Virtual Laboratory (SAVL) is a scientific discovery environment, an interactive simulated virtual laboratory, for learning physics and mathematics. The purpose of this computer-assisted intervention is to improve middle and high school student interest, insight and scores in physics and mathematics. SAVL develops scientific and mathematical imagination in a visual, symbolic, and experimental simulation environment. It directly addresses the issues of scientific and technological competency by providing critical thinking training through integrated modules. This on-going research provides a virtual laboratory environment in which the student directs the building of the experiment rather than observing a packaged simulation. SAVL: * Engages the persistent interest of young minds in physics and math by visually linking simulation objects and events with mathematical relations. * Teaches integrated concepts by the hands-on exploration and focused visualization of classic physics experiments within software. * Systematically and uniformly assesses and scores students by their ability to answer their own questions within the context of a Master Question Network. We will demonstrate how the Master Question Network uses polymorphic interfaces and C# lambda expressions to manage simulation objects.

RF multicoupler design techniques to minimize problems of corona, multipaction, and stability

NASA Technical Reports Server (NTRS)

Hurley, H. S.; Kozakoff, D. J.

1971-01-01

A mathematical expression was derived describing multipacting and corona effects in a coaxial cavity. Both mechanical and electrical design techniques were investigated to minimize the susceptibility of coaxial cavity to corona and multipacting-type breakdown. To assist in the design of a multicoupler free from corona and multipactor breakdown, a flow chart obtained from the derived mathematical expression is included.

Atmospheric refraction effects on baseline error in satellite laser ranging systems

NASA Technical Reports Server (NTRS)

Im, K. E.; Gardner, C. S.

1982-01-01

Because of the mathematical complexities involved in exact analyses of baseline errors, it is not easy to isolate atmospheric refraction effects; however, by making certain simplifying assumptions about the ranging system geometry, relatively simple expressions can be derived which relate the baseline errors directly to the refraction errors. The results indicate that even in the absence of other errors, the baseline error for intercontinental baselines can be more than an order of magnitude larger than the refraction error.

Science Education - Deja Vu Revised.

ERIC Educational Resources Information Center

Walsh, John

1982-01-01

Summarizes views expressed and issues raised at the National Convocation on Precollege Education in Mathematics and Science and another meeting to establish a coalition of affiliates for science and mathematics education. (DC)

Note-Taking in a Mathematics Classroom

ERIC Educational Resources Information Center

Hoong, Leong Yew; Guan, Tay Eng; Seng, Quek Khiok; Fwe, Yap Sook; Luen, Tong Cherng; Toh, Wei Yeng Karen; Chia, Alexander; Teck, Ong Yao

2014-01-01

The authors are a team of teachers and teacher educators who are deeply interested in helping mathematically-challenged students improve in their learning of mathematics. In Singapore, depending on their performance at the end of a nationwide Year 6 examination, students are channelled into three ability streams for Years 7 to 10: Express (60%),…

A Snowflake Project: Calculating, Analyzing, and Optimizing with the Koch Snowflake.

ERIC Educational Resources Information Center

Bolte, Linda A.

2002-01-01

Presents a project that addresses several components of the Algebra and Communication Standards for Grades 9-12 presented in Principles and Standards for School Mathematics (NCTM, 2000). Describes doing mathematical modeling and using the language of mathematics to express a recursive relationship in the perimeter and area of the Koch snowflake.…

Building Conceptual Understanding in a Remedial College Mathematics Classroom: A Study of Effectiveness

ERIC Educational Resources Information Center

Bachman, Rachel Marie

2013-01-01

This study investigated the effectiveness of two remedial mathematics courses that aimed to (a) present topics conceptually, (b) construct adequate schemata, and (c) introduce students to the culture of mathematics. The topics covered during the two courses were word problems, equivalence, variables and expressions, equations and inequalities, and…

Promoting the Understanding of Mathematics in Physics at Secondary Level

ERIC Educational Resources Information Center

Thompson, Alaric

2016-01-01

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

Fifty Years of A-Level Mathematics: Have Standards Changed?

ERIC Educational Resources Information Center

Jones, Ian; Wheadon, Chris; Humphries, Sara; Inglis, Matthew

2016-01-01

Advanced-level (A-level) mathematics is a high-profile qualification taken by many school leavers in England, Wales, Northern Ireland and around the world as preparation for university study. Concern has been expressed in these countries that standards in A-level mathematics have declined over time, and that school leavers enter university or the…

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Fitting relationship between the beam quality β factor of high-energy laser and the wavefront aberration of laser beam

NASA Astrophysics Data System (ADS)

Ji, Zhong-Ye; Zhang, Xiao-Fang

2018-01-01

The mathematical relation between the beam quality β factor of high-energy laser and the wavefront aberration of laser beam is important in beam quality control theory of the high-energy laser weapon system. In order to obtain this mathematical relation, numerical simulation is used in the research. Firstly, the Zernike representations of typically distorted atmospheric wavefront aberrations caused by the Kolmogoroff turbulence are generated. And then, the corresponding beam quality β factors of the different distorted wavefronts are calculated numerically through fast Fourier transform. Thus, the statistical distribution rule between the beam quality β factors of high-energy laser and the wavefront aberrations of the beam can be established by the calculated results. Finally, curve fitting method is chosen to establish the mathematical fitting relationship of these two parameters. And the result of the curve fitting shows that there is a quadratic curve relation between the beam quality β factor of high-energy laser and the wavefront aberration of laser beam. And in this paper, 3 fitting curves, in which the wavefront aberrations are consisted of Zernike Polynomials of 20, 36, 60 orders individually, are established to express the relationship between the beam quality β factor and atmospheric wavefront aberrations with different spatial frequency.

Diderot: a Domain-Specific Language for Portable Parallel Scientific Visualization and Image Analysis.

PubMed

Kindlmann, Gordon; Chiw, Charisee; Seltzer, Nicholas; Samuels, Lamont; Reppy, John

2016-01-01

Many algorithms for scientific visualization and image analysis are rooted in the world of continuous scalar, vector, and tensor fields, but are programmed in low-level languages and libraries that obscure their mathematical foundations. Diderot is a parallel domain-specific language that is designed to bridge this semantic gap by providing the programmer with a high-level, mathematical programming notation that allows direct expression of mathematical concepts in code. Furthermore, Diderot provides parallel performance that takes advantage of modern multicore processors and GPUs. The high-level notation allows a concise and natural expression of the algorithms and the parallelism allows efficient execution on real-world datasets.

Analysing the lack of Demand Organisation

NASA Astrophysics Data System (ADS)

Boxer, Philip; Cohen, Bernard

1998-07-01

We seek to develop means of intervention in Enterprises that will enable them to react in an effective, sustainable and timely fashion to changes in the ways that markets and demand are organized; that is, to act strategically. We take an enterprise to be some entity that seeks to provide its clients with services that they value while maintaining its ability to do so in the face of changes in the demands of its clients and in the resources at its disposal. The services that clients value form around what the organization of their demands lack. The concept of strategy therefore rests on critically evaluating the ontology and semantics of the Enterprise in relation to these holes in demand organization. We access ontology and semantics by constructing and manipulating hypothetical, first-order, mathematical models of the Enterprise's services and of its value-adding processes. Because an enterprise is an anticipatory system, its semantic domain must include representations of the enterprise's model of itself and of the market and demand organizations within which it competes. First-order (set) theory provides adequate expressive power here, but alternative, higher order, mathematical frameworks, such as Dubois' hyperincursion, provide inadequate power, particularly in relation to the analysis of the properties of emergence. Knowing exactly why and where this mathematical lack manifests in the analysis process enables effective collaboration between systems analysts and psychoanalysts, and suggest directions for mathematical research.

"A Bad Head for Maths"? Constructions of Educability and Mathematics in Adult Students' Narrative Life Histories

ERIC Educational Resources Information Center

Siivonen, Päivi

2013-01-01

The article focuses on the social differences of educability constructed in Finnish general upper secondary school adult graduates' narratives on mathematics. Social class, gender, and age intertwine in the narratives that express the adult students' worries about their ability and competence to study and learn mathematics. Social differences of…

Factors influencing undergraduates' self-evaluation of numerical competence

NASA Astrophysics Data System (ADS)

Tariq, Vicki N.; Durrani, Naureen

2012-04-01

This empirical study explores factors influencing undergraduates' self-evaluation of their numerical competence, using data from an online survey completed by 566 undergraduates from a diversity of academic disciplines, across all four faculties at a post-1992 UK university. Analysis of the data, which included correlation and multiple regression analyses, revealed that undergraduates exhibiting greater confidence in their mathematical and numeracy skills, as evidenced by their higher self-evaluation scores and their higher scores on the confidence sub-scale contributing to the measurement of attitude, possess more cohesive, rather than fragmented, conceptions of mathematics, and display more positive attitudes towards mathematics/numeracy. They also exhibit lower levels of mathematics anxiety. Students exhibiting greater confidence also tended to be those who were relatively young (i.e. 18-29 years), whose degree programmes provided them with opportunities to practise and further develop their numeracy skills, and who possessed higher pre-university mathematics qualifications. The multiple regression analysis revealed two positive predictors (overall attitude towards mathematics/numeracy and possession of a higher pre-university mathematics qualification) and five negative predictors (mathematics anxiety, lack of opportunity to practise/develop numeracy skills, being a more mature student, being enrolled in Health and Social Care compared with Science and Technology, and possessing no formal mathematics/numeracy qualification compared with a General Certificate of Secondary Education or equivalent qualification) accounted for approximately 64% of the variation in students' perceptions of their numerical competence. Although the results initially suggested that male students were significantly more confident than females, one compounding variable was almost certainly the students' highest pre-university mathematics or numeracy qualification, since a higher percentage of males (24%) compared to females (15%) possessed an Advanced Subsidiary or A2 qualification (or equivalent) in mathematics. Of particular concern is the fact that undergraduates based in Health and Social Care expressed significantly less confidence in their numeracy skills than students from any of the other three faculties.

Methods for Quantum Circuit Design and Simulation

DTIC Science & Technology

2010-03-01

cannot be deter- mined given the one output. Reversible gates, expressed mathematically, are unitary matrices. 16 3.3.1 PAULI Gates/Matrices Three...common single-qubit gates are expressed mathematically as Pauli matrices, which are 2x2 matrices. A 2x2 quantum gate can be applied to a single quantum...bit (a 2x1 column vector). The Pauli matrices are expressed as follows: X =   0 1 1 0   Y =   0 −i i 0   Z =   1 0 0 −1   (3.10) where i

Research on the correlation between corona current spectrum and audible noise spectrum of HVDC transmission line

NASA Astrophysics Data System (ADS)

Liu, Yingyi; Zhou, Lijuan; Liu, Yuanqing; Yuan, Haiwen; Ji, Liang

2017-11-01

Audible noise is closely related to corona current on a high voltage direct current (HVDC) transmission line. In this paper, we measured a large amount of audible noise and corona current waveforms simultaneously based on the largest outdoor HVDC corona cage all over the world. By analyzing the experimental data, the related statistical regularities between a corona current spectrum and an audible noise spectrum were obtained. Furthermore, the generation mechanism of audible noise was analyzed theoretically, and the related mathematical expression between the audible noise spectrum and the corona current spectrum, which is suitable for all of these measuring points in the space, has been established based on the electro-acoustic conversion theory. Finally, combined with the obtained mathematical relation, the internal reasons for these statistical regularities appearing in measured corona current and audible noise data were explained. The results of this paper not only present the statistical association regularities between the corona current spectrum and the audible noise spectrum on a HVDC transmission line, but also reveal the inherent reasons of these associated rules.

Working memory and language: skill-specific or domain-general relations to mathematics?

PubMed

Purpura, David J; Ganley, Colleen M

2014-06-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills. Copyright © 2014 Elsevier Inc. All rights reserved.

CBM Reading, Mathematics, and Written Expression at the Secondary Level: Examining Latent Composite Relations among Indices and Unique Predictions with a State Achievement Test

ERIC Educational Resources Information Center

Codding, Robin S.; Petscher, Yaacov; Truckenmiller, Adrea

2015-01-01

A paucity of research has examined the utility of curriculum-based measurement (CBM) for data-based decision making at the secondary level. As schools move to multitiered systems of service delivery, it is conceivable that multiple screening measures will be used that address various academic subject areas. The value of including different CBM…

Preservice Elementary Mathematics Teachers' Level of Relating Mathematical Concepts in Daily Life Contexts

ERIC Educational Resources Information Center

Akkus, Oylum

2008-01-01

The purpose of this study was to investigate preservice elementary mathematics teachers' ability of relating mathematical concepts and daily life context. Two research questions were set; what is the preservice elementary mathematics teachers' level of relating mathematical concepts and daily life context regarding to their education year and…

Mathematics Teachers' Perceptions of Their Students' Mathematical Competence: Relations to Mathematics Achievement, Affect, and Engagement in Singapore and Australia

ERIC Educational Resources Information Center

Areepattamannil, Shaljan; Kaur, Berinderjeet

2013-01-01

This study, drawing on data from the Trends in International Mathematics and Science Study (TIMSS) 2011, examined whether mathematics teachers' perceptions of their students' mathematical competence were related to mathematics achievement, affect toward mathematics, and engagement in mathematics lessons among Grade 8 students in Singapore and…

Student difficulties regarding symbolic and graphical representations of vector fields

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke

2017-12-01

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.

The reality of Mathematics

NASA Astrophysics Data System (ADS)

Ligomenides, Panos A.

2009-05-01

The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.

A Cognitive Analysis of Developmental Mathematics Students' Errors and Misconceptions in Real Number Computations and Evaluating Algebraic Expressions

ERIC Educational Resources Information Center

Titus, Freddie

2010-01-01

Fifty percent of college-bound students graduate from high school underprepared for mathematics at the post-secondary level. As a result, thirty-five percent of college students take developmental mathematics courses. What is even more shocking is the high failure rate (ranging from 35 to 42 percent) of students enrolled in developmental…

What is the uncertainty principle of non-relativistic quantum mechanics?

NASA Astrophysics Data System (ADS)

Riggs, Peter J.

2018-05-01

After more than ninety years of discussions over the uncertainty principle, there is still no universal agreement on what the principle states. The Robertson uncertainty relation (incorporating standard deviations) is given as the mathematical expression of the principle in most quantum mechanics textbooks. However, the uncertainty principle is not merely a statement of what any of the several uncertainty relations affirm. It is suggested that a better approach would be to present the uncertainty principle as a statement about the probability distributions of incompatible variables and the resulting restrictions on quantum states.

Development of Contextual Mathematics teaching Material integrated related sciences and realistic for students grade xi senior high school

NASA Astrophysics Data System (ADS)

Helma, H.; Mirna, M.; Edizon, E.

2018-04-01

Mathematics is often applied in physics, chemistry, economics, engineering, and others. Besides that, mathematics is also used in everyday life. Learning mathematics in school should be associated with other sciences and everyday life. In this way, the learning of mathematics is more realstic, interesting, and meaningful. Needs analysis shows that required contextual mathematics teaching materials integrated related sciences and realistic on learning mathematics. The purpose of research is to produce a valid and practical contextual mathematics teaching material integrated related sciences and realistic. This research is development research. The result of this research is a valid and practical contextual mathematics teaching material integrated related sciences and realistic produced

New method for calculating a mathematical expression for streamflow recession

USGS Publications Warehouse

Rutledge, Albert T.

1991-01-01

An empirical method has been devised to calculate the master recession curve, which is a mathematical expression for streamflow recession during times of negligible direct runoff. The method is based on the assumption that the storage-delay factor, which is the time per log cycle of streamflow recession, varies linearly with the logarithm of streamflow. The resulting master recession curve can be nonlinear. The method can be executed by a computer program that reads a data file of daily mean streamflow, then allows the user to select several near-linear segments of streamflow recession. The storage-delay factor for each segment is one of the coefficients of the equation that results from linear least-squares regression. Using results for each recession segment, a mathematical expression of the storage-delay factor as a function of the log of streamflow is determined by linear least-squares regression. The master recession curve, which is a second-order polynomial expression for time as a function of log of streamflow, is then derived using the coefficients of this function.

Sensorimotor coordination and the structure of space.

PubMed

McCollum, Gin

2003-01-01

Embedded in neural and behavioral organization is a structure of sensorimotor space. Both this embedded spatial structure and the structure of physical space inform sensorimotor control. This paper reviews studies in which the gravitational vertical and horizontal are crucial. The mathematical expressions of spatial geometry in these studies indicate methods for investigating sensorimotor control in freefall. In freefall, the spatial structure introduced by gravitation - the distinction between vertical and horizontal - does not exist. However, an astronaut arriving in space carries the physiologically-embedded distinction between horizontal and vertical learned on earth. The physiological organization based on this distinction collapses when the strong otolith activity and other gravitational cues for sensorimotor behavior become unavailable. The mathematical methods in this review are applicable in understanding the changes in physiological organization as an astronaut adapts to sensorimotor control in freefall. Many mathematical languages are available for characterizing the logical structures in physiological organization. Here, group theory is used to characterize basic structure of physical and physiological spaces. Dynamics and topology allow the grouping of trajectory ranges according to the outcomes or attractors. The mathematics of ordered structures express complex orderings, such as in multiphase movements in which different parts of the body are moving in different phase sequences. Conditional dynamics, which combines dynamics with the mathematics of ordered structures, accommodates the parsing of movement sequences into trajectories and transitions. Studies reviewed include those of the sit-to-stand movement and early locomotion, because of the salience of gravitation in those behaviors. Sensorimotor transitions and the conditions leading to them are characterized in conditional dynamic control structures that do not require thinking of an organism as an input-output device. Conditions leading to sensorimotor transitions on earth assume the presence of a gravitational vertical which is lacking in space. Thus, conditions used on earth for sensorimotor transitions may become ambiguous in space. A platform study in which sensorimotor transition conditions are ambiguous and are related to motion sickness is reviewed.

Modeling the plant-soil interaction in presence of heavy metal pollution and acidity variations.

PubMed

Guala, Sebastián; Vega, Flora A; Covelo, Emma F

2013-01-01

On a mathematical interaction model, developed to model metal uptake by plants and the effects on their growth, we introduce a modification which considers also effects on variations of acidity in soil. The model relates the dynamics of the uptake of metals from soil to plants and also variations of uptake according to the acidity level. Two types of relationships are considered: total and available metal content. We suppose simple mathematical assumptions in order to get as simple as possible expressions with the aim of being easily tested in experimental problems. This work introduces modifications to two versions of the model: on the one hand, the expression of the relationship between the metal in soil and the concentration of the metal in plants and, on the other hand, the relationship between the metal in the soil and total amount of the metal in plants. The fine difference of both versions is fundamental at the moment to consider the tolerance and capacity of accumulation of pollutants in the biomass from the soil.

On Boundaries of the Language of Physics

NASA Astrophysics Data System (ADS)

Kvasz, Ladislav

The aim of the present paper is to outline a method of reconstruction of the historical development of the language of physical theories. We will apply the theory presented in Patterns of Change, Linguistic Innovations in the Development of Classical Mathematics to the analysis of linguistic innovations in physics. Our method is based on a reconstruction of the following potentialities of language: analytical power, expressive power, integrative power, and explanatory power, as well as analytical boundaries and expressive boundaries. One of the results of our reconstruction is a new interpretation of Kant's antinomies of pure reason. If we relate Kant's antinomies to the language, they retain validity.

Mathematics Self-Related Beliefs and Online Learning

ERIC Educational Resources Information Center

Ichinose, Cherie; Bonsangue, Martin

2016-01-01

This study examined students' mathematical self-related beliefs in an online mathematics course. Mathematical self-related beliefs of a sample of high school students learning mathematics online were compared with student response data from the 2012 Programme for International Student Assessment (PISA). The treatment group reported higher levels…

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Signs of In/Equality: A History of Representation and Reform in Elementary School Mathematics from the 1950s to the Present

ERIC Educational Resources Information Center

Diaz, Jennifer DeNet

2014-01-01

This study begins with the assumption that the equal sign (=) in elementary school mathematics is not merely a symbol of mathematical logic. Rather, as the equal sign (=) appears in the school math curriculum, it orders children's thinking about equality by assigning identities to things of the world--as expressions of equivalences and…

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Mathematics-Related Emotions among Finnish Adolescents across Different Performance Levels

ERIC Educational Resources Information Center

Holm, Marja Eliisa; Hannula, Markku Sakari; Björn, Piia Maria

2017-01-01

This study examined the relation of mathematics performance and gender with seven mathematics-related emotions (enjoyment, pride, anger, anxiety, shame, hopelessness and boredom) among adolescents. Using strict and lenient mathematics performance cut-off scores, respective groups of adolescents with mathematics difficulties (MD, n = 136), low (LA,…

Mathematics is always invisible, Professor Dowling

NASA Astrophysics Data System (ADS)

Cable, John

2015-09-01

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

Mathematics Anxiety in Young Children: Concurrent and Longitudinal Associations with Mathematical Performance

ERIC Educational Resources Information Center

Vukovic, Rose K.; Kieffer, Michael J.; Bailey, Sean P.; Harari, Rachel R.

2013-01-01

This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of…

The research of statistical properties of colorimetric features of screens with a three-component color formation principle

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The problem of the research is concerned with quantitative analysis of influence of technological variation of the screen color profile parameters on chromaticity coordinates of the displayed image. Some mathematical expressions which approximate the two-dimensional distribution of chromaticity coordinates of an image, which is displayed on the screen with a three-component color formation principle were proposed. Proposed mathematical expressions show the way to development of correction techniques to improve reproducibility of the colorimetric features of displays.

Using online handwriting and audio streams for mathematical expressions recognition: a bimodal approach

NASA Astrophysics Data System (ADS)

Medjkoune, Sofiane; Mouchère, Harold; Petitrenaud, Simon; Viard-Gaudin, Christian

2013-01-01

The work reported in this paper concerns the problem of mathematical expressions recognition. This task is known to be a very hard one. We propose to alleviate the difficulties by taking into account two complementary modalities. The modalities referred to are handwriting and audio ones. To combine the signals coming from both modalities, various fusion methods are explored. Performances evaluated on the HAMEX dataset show a significant improvement compared to a single modality (handwriting) based system.

Study of the stability of a SEIRS model for computer worm propagation

NASA Astrophysics Data System (ADS)

Hernández Guillén, J. D.; Martín del Rey, A.; Hernández Encinas, L.

2017-08-01

Nowadays, malware is the most important threat to information security. In this sense, several mathematical models to simulate malware spreading have appeared. They are compartmental models where the population of devices is classified into different compartments: susceptible, exposed, infectious, recovered, etc. The main goal of this work is to propose an improved SEIRS (Susceptible-Exposed-Infectious-Recovered-Susceptible) mathematical model to simulate computer worm propagation. It is a continuous model whose dynamic is ruled by means of a system of ordinary differential equations. It considers more realistic parameters related to the propagation; in fact, a modified incidence rate has been used. Moreover, the equilibrium points are computed and their local and global stability analyses are studied. From the explicit expression of the basic reproductive number, efficient control measures are also obtained.

Some comparisons between mining-induced and laboratory earthquakes

USGS Publications Warehouse

McGarr, A.

1994-01-01

Although laboratory stick-slip friction experiments have long been regarded as analogs to natural crustal earthquakes, the potential use of laboratory results for understanding the earthquake source mechanism has not been fully exploited because of essential difficulties in relating seismographic data to measurements made in the controlled laboratory environment. Mining-induced earthquakes, however, provide a means of calibrating the seismic data in terms of laboratory results because, in contrast to natural earthquakes, the causative forces as well as the hypocentral conditions are known. A comparison of stick-slip friction events in a large granite sample with mining-induced earthquakes in South Africa and Canada indicates both similarities and differences between the two phenomena. The physics of unstable fault slip appears to be largely the same for both types of events. For example, both laboratory and mining-induced earthquakes have very low seismic efficiencies {Mathematical expression} where ??a is the apparent stress and {Mathematical expression} is the average stress acting on the fault plane to cause slip; nearly all of the energy released by faulting is consumed in overcoming friction. In more detail, the mining-induced earthquakes differ from the laboratory events in the behavior of ?? as a function of seismic moment M0. Whereas for the laboratory events ?????0.06 independent of M0, ?? depends quite strongly on M0 for each set of induced earthquakes, with 0.06 serving, apparently, as an upper bound. It seems most likely that this observed scaling difference is due to variations in slip distribution over the fault plane. In the laboratory, a stick-slip event entails homogeneous slip over a fault of fixed area. For each set of induced earthquakes, the fault area appears to be approximately fixed but the slip is inhomogeneous due presumably to barriers (zones of no slip) distributed over the fault plane; at constant {Mathematical expression}, larger events correspond to larger??a as a consequence of fewer barriers to slip. If the inequality ??a/ {Mathematical expression} ??? 0.06 has general validity, then measurements of ??a=??Ea/M0, where ?? is the modulus of rigidity and Ea is the seismically-radiated energy, can be used to infer the absolute level of deviatoric stress at the hypocenter. ?? 1994 Birkha??user Verlag.

Parental modelling of mathematical affect: self-efficacy and emotional arousal

NASA Astrophysics Data System (ADS)

Bartley, Sarah R.; Ingram, Naomi

2017-12-01

This study explored the relationship between parents' mathematics self-efficacy and emotional arousal to mathematics and their 12- and 13-year-old children's mathematics self-efficacy and emotional arousal to mathematics. Parental modelling of affective relationships during homework was a focus. Eighty-four parent and child pairings from seven schools in New Zealand were examined using embedded design methodology. No significant correlations were found when the parents' mathematics self-efficacy and emotional arousal to mathematics were compared with the children's mathematics self-efficacy and emotional arousal to mathematics. However, the parents' level of emotional arousal to mathematics was found to have affected their willingness to assist with mathematics homework. For those parents who assisted, a significant positive correlation was found between their mathematics self-efficacy and their children's emotional arousal to mathematics. Parents who did assist were generally reported as being calm, and used techniques associated with positive engagement. Fathers were calmer and more likely to express readiness to assist with mathematics homework than mothers. A further significant positive correlation was found between fathers' emotional arousal to mathematics and children's mathematics self-efficacy. Implications from the study suggest directions for future research.

Teacher and Classroom Characteristics and Their Relations to Mathematics Achievement of the Students in the TIMSS

ERIC Educational Resources Information Center

Akyuz, Gozde; Berberoglu, Giray

2010-01-01

Background: Teacher-related factors such as gender, experience, conceptions related to mathematics, instructional practices have effects with various magnitudes on students' mathematics achievement. Classroom related factors such as class size, class climate and limitations to teaching and their relation to mathematics achievement have also been…

Mathematics and engineering in real life through mathematical competitions

NASA Astrophysics Data System (ADS)

More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Self-concept mediates the relation between achievement and emotions in mathematics.

PubMed

Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M

2017-09-01

Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students. Participants were ninth-grade students (n = 1,014) from eight secondary schools in the Netherlands. Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups. Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model. Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept. © 2017 The British Psychological Society.

A reverse engineering approach to optimize experiments for the construction of biological regulatory networks.

PubMed

Zhang, Xiaomeng; Shao, Bin; Wu, Yangle; Qi, Ouyang

2013-01-01

One of the major objectives in systems biology is to understand the relation between the topological structures and the dynamics of biological regulatory networks. In this context, various mathematical tools have been developed to deduct structures of regulatory networks from microarray expression data. In general, from a single data set, one cannot deduct the whole network structure; additional expression data are usually needed. Thus how to design a microarray expression experiment in order to get the most information is a practical problem in systems biology. Here we propose three methods, namely, maximum distance method, trajectory entropy method, and sampling method, to derive the optimal initial conditions for experiments. The performance of these methods is tested and evaluated in three well-known regulatory networks (budding yeast cell cycle, fission yeast cell cycle, and E. coli. SOS network). Based on the evaluation, we propose an efficient strategy for the design of microarray expression experiments.

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

ERIC Educational Resources Information Center

Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

The Written Expression Abilities of Adolescents with Attention-Deficit/Hyperactivity Disorder

PubMed Central

Molitor, Stephen J.; Langberg, Joshua M.; Evans, Steve W.

2016-01-01

Students with Attention-Deficit/Hyperactivity Disorder (ADHD) often experience deficits in academic achievement. Written expression abilities in this population have not been extensively studied but existing prevalence estimates suggest that rates of comorbid writing underachievement may be substantially higher than rates of comorbid reading and mathematics underachievement. The current study examined written expression abilities in a school-based sample of 326 middle school age students with ADHD. The prevalence of written expression impairment, the associations between written expression and academic outcomes, and specific patterns of written expression were investigated. Students with ADHD in this sample experienced written expression impairment (17.2% – 22.4%) at a similar rate to reading impairment (17.0% – 24.3%) and at a slightly lower rate than mathematics impairment (24.7% – 36.3%). Students’ written expression abilities were significantly associated with school grades and parent ratings of academic functioning, above and beyond the influence of intelligence. Analyses of patterns suggest that students with ADHD exhibit greater deficits in written expression tasks requiring organization and attention to detail, especially in the context of a complex task. PMID:26802631

Estimation and interpretation of genetic effects with epistasis using the NOIA model.

PubMed

Alvarez-Castro, José M; Carlborg, Orjan; Rönnegård, Lars

2012-01-01

We introduce this communication with a brief outline of the historical landmarks in genetic modeling, especially concerning epistasis. Then, we present methods for the use of genetic modeling in QTL analyses. In particular, we summarize the essential expressions of the natural and orthogonal interactions (NOIA) model of genetic effects. Our motivation for reviewing that theory here is twofold. First, this review presents a digest of the expressions for the application of the NOIA model, which are often mixed with intermediate and additional formulae in the original articles. Second, we make the required theory handy for the reader to relate the genetic concepts to the particular mathematical expressions underlying them. We illustrate those relations by providing graphical interpretations and a diagram summarizing the key features for applying genetic modeling with epistasis in comprehensive QTL analyses. Finally, we briefly review some examples of the application of NOIA to real data and the way it improves the interpretability of the results.

Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions

NASA Astrophysics Data System (ADS)

Georgievskii, D. V.

2017-07-01

The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke's law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.

Analytical drafting curves provide exact equations for plotted data

NASA Technical Reports Server (NTRS)

Stewart, R. B.

1967-01-01

Analytical drafting curves provide explicit mathematical expressions for any numerical data that appears in the form of graphical plots. The curves each have a reference coordinate axis system indicated on the curve as well as the mathematical equation from which the curve was generated.

Variables in Elementary Mathematics Education

ERIC Educational Resources Information Center

Brizuela, Bárbara M.

2016-01-01

In this article, I analyze episodes from two third-grade classrooms drawn from a larger classroom teaching experiment to explore how these students began to incorporate nonnumerical symbols in their mathematical expressions when asked to represent indeterminate quantities. The article addresses two research questions: What understandings did these…

A Scale for Measuring Teachers' Mathematics-Related Beliefs: A Validity and Reliability Study

ERIC Educational Resources Information Center

Purnomo,Yoppy Wahyu

2017-01-01

The purpose of this study was to develop and validate a scale of teacher beliefs related to mathematics, namely, beliefs about the nature of mathematics, mathematics teaching, and assessment in mathematics learning. A scale development study was used to achieve it. The draft scale consisted of 54 items in which 16 items related to beliefs about…

PREFACE: NEB 15 - Recent Developments in Gravity

NASA Astrophysics Data System (ADS)

Papakostas, Taxiarchis; Pliakis, Demetrios A.

2013-08-01

In June 20-23 2012 the Technological Institute of Crete in Chania hosted the organization of the conference 'Recent Developments in Gravity, NEB15', arranged biennially by the Greek Society for Relativity and Cosmology (http://www.hsrgc.gr/). The talks ranged over Classical and Quantum Gravity and Cosmology, Holography, Black Hole Theory, Relativistic Astrophysics, Mathematical and Numerical Relativity. These proceedings include contributions from speakers of the conference. T Papakostas and D Pliakis, as members of the local organizing committee, wish to express their gratitude to all the participants of the conference for the warm atmosphere they created.

Development of an algorithm for improving quality and information processing capacity of MathSpeak synthetic speech renderings.

PubMed

Isaacson, M D; Srinivasan, S; Lloyd, L L

2010-01-01

MathSpeak is a set of rules for non speaking of mathematical expressions. These rules have been incorporated into a computerised module that translates printed mathematics into the non-ambiguous MathSpeak form for synthetic speech rendering. Differences between individual utterances produced with the translator module are difficult to discern because of insufficient pausing between utterances; hence, the purpose of this study was to develop an algorithm for improving the synthetic speech rendering of MathSpeak. To improve synthetic speech renderings, an algorithm for inserting pauses was developed based upon recordings of middle and high school math teachers speaking mathematic expressions. Efficacy testing of this algorithm was conducted with college students without disabilities and high school/college students with visual impairments. Parameters measured included reception accuracy, short-term memory retention, MathSpeak processing capacity and various rankings concerning the quality of synthetic speech renderings. All parameters measured showed statistically significant improvements when the algorithm was used. The algorithm improves the quality and information processing capacity of synthetic speech renderings of MathSpeak. This increases the capacity of individuals with print disabilities to perform mathematical activities and to successfully fulfill science, technology, engineering and mathematics academic and career objectives.

A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

NASA Astrophysics Data System (ADS)

Sari, D. S.; Kusnandi, K.; Suhendra, S.

2017-09-01

This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

An Objectivist Critique of Relativism in Mathematics Education

NASA Astrophysics Data System (ADS)

Rowlands, Stuart; Graham, Ted; Berry, John

Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.

An analysis of primary school students’ representational ability in mathematics based on gender perspective

NASA Astrophysics Data System (ADS)

Kowiyah; Mulyawati, I.

2018-01-01

Mathematic representation is one of the basic mathematic skills that allows students to communicate their mathematic ideas through visual realities such as pictures, tables, mathematic expressions and mathematic equities. The present research aims at: 1) analysing students’ mathematic representation ability in solving mathematic problems and 2) examining the difference of students’ mathematic ability based on their gender. A total of sixty primary school students participated in this study comprising of thirty males and thirty females. Data required in this study were collected through mathematic representation tests, interviews and test evaluation rubric. Findings of this study showed that students’ mathematic representation of visual realities (image and tables) was reported higher at 62.3% than at in the form of description (or statement) at 8.6%. From gender perspective, male students performed better than the females at action planning stage. The percentage of males was reported at 68% (the highest), 33% (medium) and 21.3% (the lowest) while the females were at 36% (the highest), 37.7% (medium) and 32.6% (the lowest).

How Are the Mathematical Identities of Low Achieving South African Eleventh Graders Related to Their Ability to Solve Mathematical Tasks?

ERIC Educational Resources Information Center

Cranfield, Corvell

2013-01-01

The construct of mathematical identity has recently been widely used in mathematics education with the intention to understand how students relate to and engage (or disengage) with mathematics. Grootenboer and Zevenbergen (2008) define mathematical identity as the students' knowledge, abilities, skills, beliefs, dispositions, attitudes and…

Insights into Fourier Synthesis and Analysis: Part 2--A Simplified Mathematics.

ERIC Educational Resources Information Center

Moore, Guy S. M.

1988-01-01

Introduced is an analysis of a waveform into its Fourier components. Topics included are simplified analysis of a square waveform, a triangular waveform, half-wave rectified alternating current (AC), and impulses. Provides the mathematical expression and simplified analysis diagram of each waveform. (YP)

Instructional Gaming: Using Technology to Support Early Mathematical Proficiency

ERIC Educational Resources Information Center

Nelson-Walker, Nancy J.; Doabler, Christian T.; Fien, Hank; Gause, Marshall; Baker, Scott K.; Clarke, Ben

2013-01-01

Widespread concern has been expressed about the persistent low mathematics achievement of students in the US, particularly for students from low-income and minority backgrounds and students with disabilities. Instructional gaming technology, when designed and fictionalized well, has the potential to improve the motivation and mathematics…

How to Teach Verbal Problems

ERIC Educational Resources Information Center

Dahmus, Maurice E.

1970-01-01

Presents a technique for teaching the lower ninety percent in mathematics. Concentrates on converting English statements, both expressed and implied, into one or many mathematical statements. Emphasis on translating in a direct, piecemeal, pure, and complete manner (DPPC). This method differs from others in that it is concrete rather than…

Assessment of Student Memo Assignments in Management Science

ERIC Educational Resources Information Center

Williams, Julie Ann Stuart; Stanny, Claudia J.; Reid, Randall C.; Hill, Christopher J.; Rosa, Katie Martin

2015-01-01

Frequently in Management Science courses, instructors focus primarily on teaching students the mathematics of linear programming models. However, the ability to discuss mathematical expressions in business terms is an important professional skill. The authors present an analysis of student abilities to discuss management science concepts through…

Narrative assessment: making mathematics learning visible in early childhood settings

NASA Astrophysics Data System (ADS)

Anthony, Glenda; McLachlan, Claire; Lim Fock Poh, Rachel

2015-09-01

Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories—the preferred form of narrative assessment—currently downplay domain knowledge. In this paper, we draw on data from 13 teacher interviews and samples of 18 children's learning stories to examine how mathematics is made visible within learning stories. Despite appreciating that mathematics is embedded in a range of everyday activities within the centres, we found that the nature of a particular activity appeared to influence `how' and `what' the teachers chose to document as mathematics learning. Many of the teachers expressed a preference to document and analyse mathematics learning that occurred within explicit mathematics activities rather than within play that involves mathematics. Our concern is that this restricted documentation of mathematical activity could potentially limit opportunities for mathematics learning both in the centre and home settings.

Public Views on the Gendering of Mathematics and Related Careers: International Comparisons

ERIC Educational Resources Information Center

Forgasz, Helen; Leder, Gilah; Tan, Hazel

2014-01-01

Mathematics continues to be an enabling discipline for Science, Technology, Engineering, and Mathematics (STEM)-based university studies and related careers. Explanatory models for females' underrepresentation in higher level mathematics and STEM-based courses comprise learner-related and environmental variables--including societal beliefs. Using…

Quantum mechanics problems in observer's mathematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khots, Boris; Khots, Dmitriy; iMath Consulting LLC, Omaha, Nebraska

2012-11-06

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, andmore » {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.« less

New mathematical definition and calculation of axial rotation of anatomical joints.

PubMed

Miyazaki, S; Ishida, A

1991-08-01

In the field of joint kinematics, clinical terms such as internal-external, or medical-lateral, rotations are commonly used to express the rotation of a body segment about its own long axis. However, these terms are not defined in a strict mathematical sense. In this paper, a new mathematical definition of axial rotation is proposed and methods to calculate it from the measured Euler angles are given. The definition and methods to calculate it from the measured Euler angles are given. The definition is based on the integration of the component of the angular velocity vector projected onto the long axis of the body segment. First, the absolute axial rotation of a body segment with respect to the stationary coordinate system is defined. This definition is then generalized to give the relative axial rotation of one body segment with respect to the other body segment where the two segments are moving in the three-dimensional space. The well-known Codman's paradox is cited as an example to make clear the difference between the definition so far proposed by other researchers and the new one.

The Influence of Symbols and Equations on Understanding Mathematical Equivalence

ERIC Educational Resources Information Center

Powell, Sarah R.

2015-01-01

Students with mathematics difficulty demonstrate lower mathematics performance than typical-performing peers. One contributing factor to lower mathematics performance may be misunderstanding of mathematics symbols. In several studies related to the equal sign (=), students who received explicit instruction on the relational definition (i.e.,…

Historical mathematics in the French eighteenth century.

PubMed

Richards, Joan L

2006-12-01

At least since the seventeenth century, the strange combination of epistemological certainty and ontological power that characterizes mathematics has made it a major focus of philosophical, social, and cultural negotiation. In the eighteenth century, all of these factors were at play as mathematical thinkers struggled to assimilate and extend the analysis they had inherited from the seventeenth century. A combination of educational convictions and historical assumptions supported a humanistic mathematics essentially defined by its flexibility and breadth. This mathematics was an expression of l'esprit humain, which was unfolding in a progressive historical narrative. The French Revolution dramatically altered the historical and educational landscapes that had supported this eighteenth-century approach, and within thirty years Augustin Louis Cauchy had radically reconceptualized and restructured mathematics to be rigorous rather than narrative.

Investigations in Mathematics Education, Vol. 10, No. 1.

ERIC Educational Resources Information Center

Osborne, Alan R., Ed.

Eighteen research reports related to mathematics education are abstracted and analyzed. Studies include elementary, secondary, and college mathematics education areas. A majority of the studies relate to instruction and learning. Research related to mathematics education which was reported in RESOURCES IN EDUCATION and CURRENT INDEX TO JOURNALS IN…

The processing of facial identity and expression is interactive, but dependent on task and experience

PubMed Central

Yankouskaya, Alla; Humphreys, Glyn W.; Rotshtein, Pia

2014-01-01

Facial identity and emotional expression are two important sources of information for daily social interaction. However the link between these two aspects of face processing has been the focus of an unresolved debate for the past three decades. Three views have been advocated: (1) separate and parallel processing of identity and emotional expression signals derived from faces; (2) asymmetric processing with the computation of emotion in faces depending on facial identity coding but not vice versa; and (3) integrated processing of facial identity and emotion. We present studies with healthy participants that primarily apply methods from mathematical psychology, formally testing the relations between the processing of facial identity and emotion. Specifically, we focused on the “Garner” paradigm, the composite face effect and the divided attention tasks. We further ask whether the architecture of face-related processes is fixed or flexible and whether (and how) it can be shaped by experience. We conclude that formal methods of testing the relations between processes show that the processing of facial identity and expressions interact, and hence are not fully independent. We further demonstrate that the architecture of the relations depends on experience; where experience leads to higher degree of inter-dependence in the processing of identity and expressions. We propose that this change occurs as integrative processes are more efficient than parallel. Finally, we argue that the dynamic aspects of face processing need to be incorporated into theories in this field. PMID:25452722

Relation between Approximate Number System Acuity and Mathematical Achievement: The Influence of Fluency

PubMed Central

Wang, Li; Sun, Yuhua; Zhou, Xinlin

2016-01-01

Previous studies have observed inconsistent relations between the acuity of the Approximate Number System (ANS) and mathematical achievement. In this paper, we hypothesize that the relation between ANS acuity and mathematical achievement is influenced by fluency; that is, the mathematical achievement test covering a greater expanse of mathematical fluency may better reflect the relation between ANS acuity and mathematics skills. We explored three types of mathematical achievement tests utilized in this study: Subtraction, graded, and semester-final examination. The subtraction test was designed to measure the mathematical fluency. The graded test was more fluency-based than the semester-final examination, but both involved the same mathematical knowledge from the class curriculum. A total of 219 fifth graders from primary schools were asked to perform all three tests, then given a numerosity comparison task, a visual form perception task (figure matching), and a series of other tasks to assess general cognitive processes (mental rotation, non-verbal matrix reasoning, and choice reaction time). The findings were consistent with our expectations. The relation between ANS acuity and mathematical achievement was particularly clearly reflected in the participants’ performance on the visual form perception task, which supports the domain-general explanations for the underlying mechanisms of the relation between ANS acuity and math achievement. PMID:28066291

Undergraduate Mathematics Students' Understanding of the Concept of Function

ERIC Educational Resources Information Center

Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah

2014-01-01

Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…

Confidence and Competence with Mathematical Procedures

ERIC Educational Resources Information Center

Foster, Colin

2016-01-01

Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupils. This study examined how school mathematics pupils (N?=?345) in five different secondary schools…

The Root of the Problem

ERIC Educational Resources Information Center

Grosser-Clarkson, Dana L.

2015-01-01

The Common Core State Standards for Mathematics expect students to build on their knowledge of the number system, expressions and equations, and functions throughout school mathematics. For example, students learn that they can add something to both sides of an equation and that doing so will not affect the equivalency; however, squaring both…

Ethical Concerns: Negotiating Truth and Trust

ERIC Educational Resources Information Center

McGarvey, Lynn M.; Sterenberg, Gladys

2009-01-01

Few studies in mathematics education explicitly address ethical issues arising from student interactions. The ethical concerns held by students are expressed in their words, actions, and interactions. The purpose of this article is to explore the ethical nature of copying as it arises in a mathematics classroom. We investigate the basis for…

A note on misunderstandings of Piron's axioms for quantum mechanics

NASA Astrophysics Data System (ADS)

Foulis, D. J.; Randall, C. H.

1984-01-01

Piron's axioms for a realistically interpreted quantum mechanics are analyzed in detail within the context of a formal mathematical structure expressed in the conventional set-theoretic idiom of mathematics. As a result, some of the serious misconceptions that have encouraged recent criticisms of Piron's axioms are exposed.

Physics Teaching: Mathematics as an Epistemological Tool

ERIC Educational Resources Information Center

Kneubil, Fabiana B.; Robilotta, Manoel R.

2015-01-01

We study the interconnection between Physics and Mathematics in concrete instances, departing from the usual expression for the Coulomb electric field, produced by a point-like charge. It is scrutinized by means of six epistemology-intensive questions and radical answers are proposed, intended to widen one's understanding of the subject. Our…

Mathematical model of a smoldering log.

Treesearch

Fernando de Souza Costa; David Sandberg

2004-01-01

A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts...

Developing Students' Mathematical Skills Involving Order of Operations

ERIC Educational Resources Information Center

Ali Rahman, Ernna Sukinnah; Shahrill, Masitah; Abbas, Nor Arifahwati; Tan, Abby

2017-01-01

This small-scale action research study examines the students' ability in using their mathematical skills when performing order of operations in numerical expressions. In this study, the "hierarchy-of-operators triangle" by Ameis (2011) was introduced as an alternative BODMAS approach to help students in gaining a better understanding…

Comparison of mathematically-predicted toxic equivalents (TEQs) and bioassay-derived dioxin-equivalents (TCDD-EQs) in heron embryos

USGS Publications Warehouse

Rattner, B.; Hatfield, J.; Melancon, M.; Custer, T.; Tillitt, D.

1995-01-01

Pipping black-crowned night-heron (Nycticorax nycticorax) embryos were collected from an uncontaminated site (Chincoteague National Wildlife Refuge,VA) and three polluted sites (Cat Island, Green Bay, WI; Bair and West Marin Islands, San Francisco Bay, CA). Hepatic microsomal monooxygenases were induced up to 85-fold relative to the reference site, and was associated with concentrations of total PCBs and 11 PCB congeners that are presumed to concern.to express toxicity through the Ah receptor. TEQs [mathematically predicted; summed product of PCB congener concentrations using 5 different sets of toxic equivalency factors (TEFs)] were compared to TCDD-EQs [derived by bioassay; ethoxyresorufin-O-dealkylase activity of treated H411E rat hepatoma cells]. Although TEQs were up to 15-fold greater than TCDD-EQs, the pattern among sites was consistent and TEQs were highly correlated with TCDD-EQs. TEFs based on single congener mammalian studies yielded TEQs that greatly exceeded values from the H411E bioassay of field sample. TEFs generated from avian egg injection studies yielded TEQs that most closely approximated bioassay-derived TCDD-EQs. Cytochrome P450 parameters were related to TEQs and TCDD-EQs; adjusted r2 often exceeded 0.5 for the relation among mathematically predicted TEQs and cytochrome P450 measurements. These data document the general predictive value of TEQs and TCDD-EQs for P450 induction in field collected samples, but also indicate the need for development of TEFs for the species and biological end point of concern.

Visual short term memory related brain activity predicts mathematical abilities.

PubMed

Boulet-Craig, Aubrée; Robaey, Philippe; Lacourse, Karine; Jerbi, Karim; Oswald, Victor; Krajinovic, Maja; Laverdière, Caroline; Sinnett, Daniel; Jolicoeur, Pierre; Lippé, Sarah

2017-07-01

Previous research suggests visual short-term memory (VSTM) capacity and mathematical abilities are significantly related. Moreover, both processes activate similar brain regions within the parietal cortex, in particular, the intraparietal sulcus; however, it is still unclear whether the neuronal underpinnings of VSTM directly correlate with mathematical operation and reasoning abilities. The main objective was to investigate the association between parieto-occipital brain activity during the retention period of a VSTM task and performance in mathematics. The authors measured mathematical abilities and VSTM capacity as well as brain activity during memory maintenance using magnetoencephalography (MEG) in 19 healthy adult participants. Event-related magnetic fields (ERFs) were computed on the MEG data. Linear regressions were used to estimate the strength of the relation between VSTM related brain activity and mathematical abilities. The amplitude of parieto-occipital cerebral activity during the retention of visual information was related to performance in 2 standardized mathematical tasks: mathematical reasoning and calculation fluency. The findings show that brain activity during retention period of a VSTM task is associated with mathematical abilities. Contributions of VSTM processes to numerical cognition should be considered in cognitive interventions. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

The nonlinear relations of the approximate number system and mathematical language to early mathematics development.

PubMed

Purpura, David J; Logan, Jessica A R

2015-12-01

Both mathematical language and the approximate number system (ANS) have been identified as strong predictors of early mathematics performance. Yet, these relations may be different depending on a child's developmental level. The purpose of this study was to evaluate the relations between these domains across different levels of ability. Participants included 114 children who were assessed in the fall and spring of preschool on a battery of academic and cognitive tasks. Children were 3.12 to 5.26 years old (M = 4.18, SD = .58) and 53.6% were girls. Both mixed-effect and quantile regressions were conducted. The mixed-effect regressions indicated that mathematical language, but not the ANS, nor other cognitive domains, predicted mathematics performance. However, the quantile regression analyses revealed a more nuanced relation among domains. Specifically, it was found that mathematical language and the ANS predicted mathematical performance at different points on the ability continuum. These dual nonlinear relations indicate that different mechanisms may enhance mathematical acquisition dependent on children's developmental abilities. (c) 2015 APA, all rights reserved).

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

An Open-Source Sandbox for Increasing the Accessibility of Functional Programming to the Bioinformatics and Scientific Communities

PubMed Central

Fenwick, Matthew; Sesanker, Colbert; Schiller, Martin R.; Ellis, Heidi JC; Hinman, M. Lee; Vyas, Jay; Gryk, Michael R.

2012-01-01

Scientists are continually faced with the need to express complex mathematical notions in code. The renaissance of functional languages such as LISP and Haskell is often credited to their ability to implement complex data operations and mathematical constructs in an expressive and natural idiom. The slow adoption of functional computing in the scientific community does not, however, reflect the congeniality of these fields. Unfortunately, the learning curve for adoption of functional programming techniques is steeper than that for more traditional languages in the scientific community, such as Python and Java, and this is partially due to the relative sparseness of available learning resources. To fill this gap, we demonstrate and provide applied, scientifically substantial examples of functional programming, We present a multi-language source-code repository for software integration and algorithm development, which generally focuses on the fields of machine learning, data processing, bioinformatics. We encourage scientists who are interested in learning the basics of functional programming to adopt, reuse, and learn from these examples. The source code is available at: https://github.com/CONNJUR/CONNJUR-Sandbox (see also http://www.connjur.org). PMID:25328913

An Open-Source Sandbox for Increasing the Accessibility of Functional Programming to the Bioinformatics and Scientific Communities.

PubMed

Fenwick, Matthew; Sesanker, Colbert; Schiller, Martin R; Ellis, Heidi Jc; Hinman, M Lee; Vyas, Jay; Gryk, Michael R

2012-01-01

Scientists are continually faced with the need to express complex mathematical notions in code. The renaissance of functional languages such as LISP and Haskell is often credited to their ability to implement complex data operations and mathematical constructs in an expressive and natural idiom. The slow adoption of functional computing in the scientific community does not, however, reflect the congeniality of these fields. Unfortunately, the learning curve for adoption of functional programming techniques is steeper than that for more traditional languages in the scientific community, such as Python and Java, and this is partially due to the relative sparseness of available learning resources. To fill this gap, we demonstrate and provide applied, scientifically substantial examples of functional programming, We present a multi-language source-code repository for software integration and algorithm development, which generally focuses on the fields of machine learning, data processing, bioinformatics. We encourage scientists who are interested in learning the basics of functional programming to adopt, reuse, and learn from these examples. The source code is available at: https://github.com/CONNJUR/CONNJUR-Sandbox (see also http://www.connjur.org).

Geomagnetic matching navigation algorithm based on robust estimation

NASA Astrophysics Data System (ADS)

Xie, Weinan; Huang, Liping; Qu, Zhenshen; Wang, Zhenhuan

2017-08-01

The outliers in the geomagnetic survey data seriously affect the precision of the geomagnetic matching navigation and badly disrupt its reliability. A novel algorithm which can eliminate the outliers influence is investigated in this paper. First, the weight function is designed and its principle of the robust estimation is introduced. By combining the relation equation between the matching trajectory and the reference trajectory with the Taylor series expansion for geomagnetic information, a mathematical expression of the longitude, latitude and heading errors is acquired. The robust target function is obtained by the weight function and the mathematical expression. Then the geomagnetic matching problem is converted to the solutions of nonlinear equations. Finally, Newton iteration is applied to implement the novel algorithm. Simulation results show that the matching error of the novel algorithm is decreased to 7.75% compared to the conventional mean square difference (MSD) algorithm, and is decreased to 18.39% to the conventional iterative contour matching algorithm when the outlier is 40nT. Meanwhile, the position error of the novel algorithm is 0.017° while the other two algorithms fail to match when the outlier is 400nT.

The place of words and numbers in psychiatric research.

PubMed

Falissard, Bruno; Révah, Anne; Yang, Suzanne; Fagot-Largeault, Anne

2013-11-18

In recent decades, there has been widespread debate in the human and social sciences regarding the compatibility and the relative merits of quantitative and qualitative approaches in research. In psychiatry, depending on disciplines and traditions, objects of study can be represented either in words or using two types of mathematization. In the latter case, the use of mathematics in psychiatry is most often only local, as opposed to global as in the case of classical mechanics. Relationships between these objects of study can in turn be explored in three different ways: 1/ by a hermeneutic process, 2/ using statistics, the most frequent method in psychiatric research today, 3/ using equations, i.e. using mathematical relationships that are formal and deterministic. The 3 ways of representing entities (with language, locally with mathematics or globally with mathematics) and the 3 ways of expressing the relationships between entities (using hermeneutics, statistics or equations) can be combined in a cross-tabulation, and nearly all nine combinations can be described using examples. A typology of this nature may be useful in assessing which epistemological perspectives are currently dominant in a constantly evolving field such as psychiatry, and which other perspectives still need to be developed. It also contributes to undermining the overly simplistic and counterproductive beliefs that accompany the assumption of a Manichean "quantitative/qualitative" dichotomy. Systematic examination of this set of typologies could be useful in indicating new directions for future research beyond the quantitative/qualitative divide.

The place of words and numbers in psychiatric research

PubMed Central

2013-01-01

In recent decades, there has been widespread debate in the human and social sciences regarding the compatibility and the relative merits of quantitative and qualitative approaches in research. In psychiatry, depending on disciplines and traditions, objects of study can be represented either in words or using two types of mathematization. In the latter case, the use of mathematics in psychiatry is most often only local, as opposed to global as in the case of classical mechanics. Relationships between these objects of study can in turn be explored in three different ways: 1/ by a hermeneutic process, 2/ using statistics, the most frequent method in psychiatric research today, 3/ using equations, i.e. using mathematical relationships that are formal and deterministic. The 3 ways of representing entities (with language, locally with mathematics or globally with mathematics) and the 3 ways of expressing the relationships between entities (using hermeneutics, statistics or equations) can be combined in a cross-tabulation, and nearly all nine combinations can be described using examples. A typology of this nature may be useful in assessing which epistemological perspectives are currently dominant in a constantly evolving field such as psychiatry, and which other perspectives still need to be developed. It also contributes to undermining the overly simplistic and counterproductive beliefs that accompany the assumption of a Manichean “quantitative/qualitative” dichotomy. Systematic examination of this set of typologies could be useful in indicating new directions for future research beyond the quantitative/qualitative divide. PMID:24246064

Assessment of representational competence in kinematics

NASA Astrophysics Data System (ADS)

Klein, P.; Müller, A.; Kuhn, J.

2017-06-01

A two-tier instrument for representational competence in the field of kinematics (KiRC) is presented, designed for a standard (1st year) calculus-based introductory mechanics course. It comprises 11 multiple choice (MC) and 7 multiple true-false (MTF) questions involving multiple representational formats, such as graphs, pictures, and formal (mathematical) expressions (1st tier). Furthermore, students express their answer confidence for selected items, providing additional information (2nd tier). Measurement characteristics of KiRC were assessed in a validation sample (pre- and post-test, N =83 and N =46 , respectively), including usefulness for measuring learning gain. Validity is checked by interviews and by benchmarking KiRC against related measures. Values for item difficulty, discrimination, and consistency are in the desired ranges; in particular, a good reliability was obtained (KR 20 =0.86 ). Confidence intervals were computed and a replication study yielded values within the latter. For practical and research purposes, KiRC as a diagnostic tool goes beyond related extant instruments both for the representational formats (e.g., mathematical expressions) and for the scope of content covered (e.g., choice of coordinate systems). Together with the satisfactory psychometric properties it appears a versatile and reliable tool for assessing students' representational competency in kinematics (and of its potential change). Confidence judgments add further information to the diagnostic potential of the test, in particular for representational misconceptions. Moreover, we present an analytic result for the question—arising from guessing correction or educational considerations—of how the total effect size (Cohen's d ) varies upon combination of two test components with known individual effect sizes, and then discuss the results in the case of KiRC (MC and MTF combination). The introduced method of test combination analysis can be applied to any test comprising two components for the purpose of finding effect size ranges.

A novel individual-cell-based mathematical model based on multicellular tumour spheroids for evaluating doxorubicin-related delivery in avascular regions.

PubMed

Liu, Jiali; Yan, Fangrong; Chen, Hongzhu; Wang, Wenjie; Liu, Wenyue; Hao, Kun; Wang, Guangji; Zhou, Fang; Zhang, Jingwei

2017-09-01

Effective drug delivery in the avascular regions of tumours, which is crucial for the promising antitumour activity of doxorubicin-related therapy, is governed by two inseparable processes: intercellular diffusion and intracellular retention. To accurately evaluate doxorubicin-related delivery in the avascular regions, these two processes should be assessed together. Here we describe a new approach to such an assessment. An individual-cell-based mathematical model based on multicellular tumour spheroids was developed that describes the different intercellular diffusion and intracellular retention kinetics of doxorubicin in each cell layer. The different effects of a P-glycoprotein inhibitor (LY335979) and a hypoxia inhibitor (YC-1) were quantitatively evaluated and compared, in vitro (tumour spheroids) and in vivo (HepG2 tumours in mice). This approach was further tested by evaluating in these models, an experimental doxorubicin derivative, INNO 206, which is in Phase II clinical trials. Inhomogeneous, hypoxia-induced, P-glycoprotein expression compromised active transport of doxorubicin in the central area, that is, far from the vasculature. LY335979 inhibited efflux due to P-glycoprotein but limited levels of doxorubicin outside the inner cells, whereas YC-1 co-administration specifically increased doxorubicin accumulation in the inner cells without affecting the extracellular levels. INNO 206 exhibited a more effective distribution profile than doxorubicin. The individual-cell-based mathematical model accurately evaluated and predicted doxorubicin-related delivery and regulation in the avascular regions of tumours. The described framework provides a mechanistic basis for the proper development of doxorubicin-related drug co-administration profiles and nanoparticle development and could avoid unnecessary clinical trials. © 2017 The British Pharmacological Society.

Plasma Dispersion Function for the Kappa Distribution

NASA Technical Reports Server (NTRS)

Podesta, John J.

2004-01-01

The plasma dispersion function is computed for a homogeneous isotropic plasma in which the particle velocities are distributed according to a Kappa distribution. An ordinary differential equation is derived for the plasma dispersion function and it is shown that the solution can be written in terms of Gauss' hypergeometric function. Using the extensive theory of the hypergeometric function, various mathematical properties of the plasma dispersion function are derived including symmetry relations, series expansions, integral representations, and closed form expressions for integer and half-integer values of K.

Lecture Notes in Artificial Intelligence 689: Methodologies for Intelligent Systems: International Symposium, ISMIS 󈨡 (7th) Held at Trondheim (Norway) April 1993

DTIC Science & Technology

1993-06-18

expresses 171 From our earliest days we learn to perceive time as a result of two im- portant cognitive abilities : the awareness of change in the world...agent. - Learning and cognition are closely related. Between the levels of sensory percep- tion and abstract language there are several levels of...Kaufmann, Los Altos, California, 1988. Previously available as I Report PM-01-87, School of Mathematics , University of Bristol. [13] Y. Shoham

Porous Media and Mixture Models for Hygrothermal Behavior of Phenolic Composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.; Stokes, Eric H.

1999-01-01

Theoretical models are proposed to describe the interaction of water with phenolic polymer. The theoretical models involve the study of the flow of a viscous fluid through a porous media and the thermodynamic theory of mixtures. From the theory, a set of mathematical relations are developed to simulate the effect of water on the thermostructural response of phenolic composites. The expressions are applied to simulate the measured effect of water in a series of experiments conducted on carbon phenolic composites.

Mathematics Self-Efficacy, Ethnic Identity, Gender, and Career Interests Related to Mathematics and Science.

ERIC Educational Resources Information Center

O'Brien, Virginia; Martinez-Pons, Manual; Kopala, Mary

1999-01-01

Surveyed 11th graders to examine the relations among mathematics self-efficacy (SE), gender, ethnic identity, and career interests (CI) in mathematics and science. Researchers also examined socioeconomic status (SES) and academic achievement. Science CI was predicted solely by science-mathematics SE. SE was predicted by academic performance and…

Attitudes toward and approaches to learning first-year university mathematics.

PubMed

Alkhateeb, Haitham M; Hammoudi, Lakhdar

2006-08-01

This study examined the relationship for 180 undergraduate students enrolled in a first-year university calculus course between attitudes toward mathematics and approaches to learning mathematics using the Mathematics Attitude Scale and the Approaches to Learning Mathematics Questionnaire, respectively. Regression analyses indicated that scores for the Mathematics Attitude Scale were negatively related to scores for the Surface Approach and accounted for 10.4% of the variance and scores for the Mathematics Attitude Scale were positively related to scores for the Deep Approach to learning mathematics and accounted for 31.7% of the variance.

Baseline for Climate Change: Modeling Watershed Aquatic Biodiversity Relative to Environmental and Anthropogenic Factors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maurakis, Eugene G

Objectives of the two-year study were to (1) establish baselines for fish and macroinvertebrate community structures in two mid-Atlantic lower Piedmont watersheds (Quantico Creek, a pristine forest watershed; and Cameron Run, an urban watershed, Virginia) that can be used to monitor changes relative to the impacts related to climate change in the future; (2) create mathematical expressions to model fish species richness and diversity, and macroinvertebrate taxa and macroinvertebrate functional feeding group taxa richness and diversity that can serve as a baseline for future comparisons in these and other watersheds in the mid-Atlantic region; and (3) heighten people’s awareness, knowledgemore » and understanding of climate change and impacts on watersheds in a laboratory experience and interactive exhibits, through internship opportunities for undergraduate and graduate students, a week-long teacher workshop, and a website about climate change and watersheds. Mathematical expressions modeled fish and macroinvertebrate richness and diversity accurately well during most of the six thermal seasons where sample sizes were robust. Additionally, hydrologic models provide the basis for estimating flows under varying meteorological conditions and landscape changes. Continuations of long-term studies are requisite for accurately teasing local human influences (e.g. urbanization and watershed alteration) from global anthropogenic impacts (e.g. climate change) on watersheds. Effective and skillful translations (e.g. annual potential exposure of 750,000 people to our inquiry-based laboratory activities and interactive exhibits in Virginia) of results of scientific investigations are valuable ways of communicating information to the general public to enhance their understanding of climate change and its effects in watersheds.« less

Mathematics beliefs and achievement of adolescent students in Japan: results from the TIMSS 1999 assessment.

PubMed

House, J Daniel

2005-12-01

A recent study (1) of undergraduate students in a precalculus course indicated that they expressed slightly positive attitudes toward mathematics. It is important, however, to examine relationships between students' initial attitudes and achievement outcomes. The present purpose was to assess the relationship between self-beliefs and mathematics achievement for a large national sample of students from the TIMSS 1999 international sample (eighth graders) from Japan. Several significant relationships between mathematics beliefs and test scores were noted. In addition, the overall multiple regression equation that assessed the joint significance of the complete set of self-belief variables was significant (F7.65 = 159.48, p < .001) and explained 20.6% of the variance in mathematics achievement test scores.

Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking

NASA Astrophysics Data System (ADS)

Sumarsih; Budiyono; Indriati, D.

2018-04-01

This research aims to understand the students’ weaknesses in mathematical reasoning ability in junior secondary school. A set of multiple choice tests were used to measure this ability involve components mathematical communication, basic skills, connection, and logical thinking. A total of 259 respondents were determined by stratified cluster random sampling. Data were analyzed using one-way Anova test with Fobs = 109.5760 and F = 3.0000. The results show that students’ ability from schools with high National Exam in mathematics category was the best and followed by medium and low category. Mathematical connection is the most difficult component performed by students. In addition, most students also have difficulty in expressing ideas and developing logical arguments.

Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Perimeter of Rectangle

ERIC Educational Resources Information Center

Anwar, Rahmad Bustanul; Yuwono, Ipung; As'ari, Abdur Rahman; Sisworo; Dwi, Rahmawati

2016-01-01

Representation is an important aspect of learners in building a relational understanding of mathematical concepts. But the ability of a mathematical representation of students in building relational understanding is still very limited. The purpose of this research is to description of mathematical representation of students who appear in building…

Hybrid Task Design: Connecting Learning Opportunities Related to Critical Thinking and Statistical Thinking

ERIC Educational Resources Information Center

Kuntze, Sebastian; Aizikovitsh-Udi, Einav; Clarke, David

2017-01-01

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

Stable isotope studies of metasomatic Ca-Fe-Al-Si skarns and associated metamorphic and igneous rocks, Osgood Mountains, Nevada

USGS Publications Warehouse

Taylor, B.E.; O'Neil, J.R.

1977-01-01

Garnet-pyroxene skarns were formed 90 m.y. B.P. in the Osgood Mountains at or near contacts of grandiorite with calcareous rocks of the Cambrian Preble Formation. The metasomatic replacement followed contact metamorphic recrystallization of the Preble. The sources, temperature, and variation in H2O/CO2 ratios of the metasomatic fluid are interpreted from 269 analyses of oxygen, carbon, hydrogen, and sulfur isotopes in whole rocks, minerals and inclusion fluids. Skarns formed in three mineralogical stages. Oxygen isotope data indicate that temperatures during the crystallization of garnet, pyroxene and wollastonite (Stage I) were least 550 ?? C, and that the metasomatic fluid had an {Mathematical expression} ??? 0.035 in the massive skarns, and ??? 0.12 in vein skarns up to 3 cm thick. Pore fluids in isotopic equilibrium with garnet in calc-silicate metamorphic rocks, on the other hand, had {Mathematical expression} ??? 0.15. The metasomatic fluids of Stage I were derived primarily from the crystallizing magma. The isotopic composition of magmatic water was ??18O =+9.0, ??D= -30 to -45. Oxygen isotope temperatures of greater than 620 ?? C were determined for the granodiorite. Isotopic and chemical equilibria between mineral surfaces and the metasomatic fluid were approached simultaneously in parts of the skarn several meters or more apart, while isotopic and chemical disequilibria (i.e. zoning) have been preserved between 20 to 40 ??m-thick zones in grandite garnet. More Fe-, or andradite-rich garnet crystallized in more H2O-rich C-O-H fluids ( {Mathematical expression} ??? 0.01) than present with grossularite-rich garnet ( {Mathematical expression}??? 0.035). Stage II was marked by the replacement of garnet and pyroxene by quartz, amphibole, plagioclase, epidote, magnetite, and calcite. Many of the replacement reactions took place over a relatively narrow range in temperature (480-550 ?? C), as indicated by 18O fractionations between quartz and amphibole. Meteoric water comprised 20 to 50% of the metasomatic fluid during Stage II. Calcite was formed along with pyrite, minor pyrrhotite, and chalcopyrite during Stage III, although the crystallization of pyrite and calcite had begun earlier, during Stages I and II, respectively. Carbon and sulfur isotope compositions of calcite and pyrite indicate a magmatic source for most of the C and S in the metasomatic fluids of Stage III. By the end of Stage III, meteoric water constituted as much as 100% of the metasomatic fluid. Minerals from grandiorite and skarn do not show large depletions in 18O because the oxygen isotope composition of the metasomatic fluid was buffered by the calcareous wall rocks and the grandiorite. Meteoric water in the vicinity of the Osgood Mountains during the Late Crectaceous (??18Ocale. ??? -14.0, ??D = - 107) was slightly enriched in 18O and D relative to present-day meteoric water (??18O = 15.9, ??D = - 117) ?? 1977 Springer-Verlag.

In the Middle of Nowhere: How a Textbook Can Position the Mathematics Learner

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth; Wagner, David

2005-01-01

We outline a framework for investigating how a mathematics textbook positions the mathematics learner. We use tools and concepts from discourse analysis, a field of linguistic scholarship, to illustrate the ways in which a textbook can position people in relation to mathematics and how the text can position the mathematics learner in relation to…

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

NASA Astrophysics Data System (ADS)

E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

2017-02-01

This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Belgian and Turkish Pre-Service Primary School Teachers' Metaphoric Expressions about Mathematics

ERIC Educational Resources Information Center

Kiliç, Çigdem; Yanpar Yelken, Tugba

2013-01-01

Problem Statement: Recent studies in education have focused on how to handle metaphors as research and evaluation tools. Metaphors have many advantages for researchers, educators and learners with the most important being that they can help educators understand pre-service teachers' thinking and belief systems of mathematics. A study of previous…

Increasing Communication in Geometry by Using a Personal Math Concept Chart

ERIC Educational Resources Information Center

Friedman, Rhonda; Kazerouni, Gety; Lax, Stacey; Weisdorf, Elli

2011-01-01

The action research team developed a "Personal Math Concept Chart". This chart required students to describe the mathematical concepts that they were studying in the Geometry strand of Mathematics using their own images and words. In this study, students were encouraged to express their own understanding of geometric concepts in order to…

Host - HIF- 1alpha Pathway And Hypoxia: In Vitro Studies And Mathematical Model

DTIC Science & Technology

2016-08-30

TERMS mathematical model, signaling pathways, hypoxia, immunohistochemistry, ELISA , inhalation chamber 16. SECURITY CLASSIFICATION OF: U 17...B. HIF-1α ELISA Procedure ........................................................................................27 Appendix C. HIF-1α Model...Quantifying Induction of HIF-1α Expression using ELISA .........................................15 Figure 10. Simulation Outputs from HIF-1α Kinetic

Associations of Students' Beliefs with Self-Regulated Problem Solving in College Algebra

ERIC Educational Resources Information Center

Cifarelli, Victor; Goodson-Espy, Tracy; Chae, Jeong-Lim

2010-01-01

This paper reports results from a study of self-regulated problem solving actions of students enrolled in College Algebra (N = 139). The study examined the associations between the expressed mathematical beliefs of students and the students' self-regulated actions in solving mathematics problems. The research questions are: (a) What are some…

Translating a "Relevance Imperative" into Junior Secondary Mathematics and Science Pedagogy

ERIC Educational Resources Information Center

Darby, Linda

2009-01-01

Inquiries into the state of mathematics and science education in Australia express the need to make curriculum and teaching practices more relevant and meaningful to students' lives. This vision requires that teachers understand how relevance can enter the classroom in meaningful, appropriate, and subject-specific ways. In this paper I use…

Mathematics Education in Rural Communities: A Mathematician's View. Working Paper Series.

ERIC Educational Resources Information Center

Mahoney, Carolyn R.

Elizabeth City State University (ECSU) serves the 21 counties of rural northeastern North Carolina. In Fall 2000 ECSU administrators met with educators in area school districts to discuss their professional development needs. This paper reports on those expressed needs relevant to mathematics education and discusses ways to help achieve excellence…

Focus in High School Mathematics: Reasoning and Sense Making in Algebra

ERIC Educational Resources Information Center

Graham, Karen; Cuoco, Albert; Zimmermann, Gwendolyn

2010-01-01

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

Defining Levels on the 1990 Mathematics Composite.

ERIC Educational Resources Information Center

Johnson, Eugene G.

Procedures used to map the achievement levels, expressed as total expected scores on the full set of items presented to a grade, onto the Mathematics Composite of the 1990 National Assessment of Educational Progress (NAEP) are described. The Composite, defined as a weighted average of subdomain scores, provides a global measure of mathematics…

Scoring Points: Goals for Real World Problem Solving

ERIC Educational Resources Information Center

Galbraith, Peter

2012-01-01

This paper is presented in two parts. Through an example the first part takes up the issue of applying mathematics to situations that form part of the life context of students--the priority expressed in three curriculum statements presented. Then, noting the particular point in time--development of a National Curriculum for Mathematics--the second…

Why do early mathematics skills predict later reading? The role of mathematical language.

PubMed

Purpura, David J; Logan, Jessica A R; Hassinger-Das, Brenna; Napoli, Amy R

2017-09-01

A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills-specifically language-for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy development, the reason for this relation is not well understood. The purpose of this study was to identify how and why early mathematics is predictive of early literacy development. Participants included 125 preschool children 3-5 years old (M = 4 years 3 months). Participants were assessed on mathematics, literacy, and cognitive measures in both the fall and spring of their preschool year. Mediation analyses indicated that the relation between early mathematics and literacy skills is mediated by children's mathematical language skills. These findings suggest that, in prior research identifying mathematical performance as a significant predictor of later literacy skills, mathematical performance may have acted only as a proxy measure for more complex language skills such as those assessed on a mathematical language measure. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Natural selection. IV. The Price equation*

PubMed Central

Frank, Steven A.

2012-01-01

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation’s greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection, and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen. PMID:22487312

Natural selection. IV. The Price equation.

PubMed

Frank, S A

2012-06-01

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation's greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen. © 2012 The Authors. Journal of Evolutionary Biology © 2012 European Society For Evolutionary Biology.

The co-development and interrelation of proof and authority: The case of Yana and Ronit

NASA Astrophysics Data System (ADS)

Fried, Michael N.; Amit, Miriam

2008-12-01

Students' mathematical lives are characterized not only by a set of mathematical ideas and the engagement in mathematical thinking, but also by social relations, specifically, relations of authority. Watching student actions and speaking to students, one becomes cognizant of a `web of authority' ever present in mathematics classrooms. In past work, it has been shown how those relations of authority may sometimes interfere with students' reflecting on mathematical ideas. However, "…by shifting the emphasis from domination and obedience to negotiation and consent…" (Amit & Fried, 2005, p.164) it has also been stressed that these relations are fluid and are, in fact, a sine qua non in the process of students' defining their place in a mathematical community. But can these fluid relations be operative also in the formation of specific mathematical ideas? It is my contention that they may at least coincide with students' thinking about one significant mathematical idea, namely, the idea of proof. In this talk, I shall discuss both the general question of authority in the mathematics classroom and its specific connection with students' thinking about proof in the context of work done in two 8th grade classrooms.

On the stochastic dissemination of faults in an admissible network

NASA Technical Reports Server (NTRS)

Kyrala, A.

1987-01-01

The dynamic distribution of faults in a general type network is discussed. The starting point is a uniquely branched network in which each pair of nodes is connected by a single branch. Mathematical expressions for the uniquely branched network transition matrix are derived to show that sufficient stationarity exists to ensure the validity of the use of the Markov Chain model to analyze networks. In addition the conditions for the use of Semi-Markov models are discussed. General mathematical expressions are derived in an examination of branch redundancy techniques commonly used to increase reliability.

Difficulties in initial algebra learning in Indonesia

NASA Astrophysics Data System (ADS)

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-12-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

Early Executive Function and Mathematics Relations: Correlation Does Not Ensure Concordance.

PubMed

Mazzocco, Michèle M M; Chan, Jenny Yun-Chen; Bock, Allison M

2017-01-01

In this chapter, we address one potentially overlooked component of the relation between executive function (EF) skills and early mathematics, a relation for which there is widespread empirical support. Evidence for this relation has, thus far, been largely correlational. Here we emphasize that because positive correlations do not guarantee concordance among all members of a sample or population, a small but meaningful number of children may either fare well in mathematics despite poor EF skills, or may have strong EF skills despite weak mathematics skills. We propose that attention to different profiles of discordance for EF and mathematics may help identify individualized learning needs for students at risk for mathematics difficulties and disabilities. © 2017 Elsevier Inc. All rights reserved.

Exploring Collective Mathematical Creativity in Elementary School

ERIC Educational Resources Information Center

Levenson, Esther

2011-01-01

This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked,…

Dynamic Boolean Mathematics

ERIC Educational Resources Information Center

Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen

2016-01-01

Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Superradiant effects on pulse propagation in resonant media. [atomic excitations/coherent radiation - operators (mathematics)/matrices (mathematics)

NASA Technical Reports Server (NTRS)

Lee, C.

1975-01-01

Adopting the so-called genealogical construction, the eigenstates of collective operators can be expressed corresponding to a specified mode for an N-atom system in terms of those for an (N-1)-atom system. Matrix element of a collective operator of an arbitrary mode is presented which can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME was obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups was then introduced. This gave a simple and systematic way of calculating the RME. Results show explicitly the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes and clears up the chief difficulty encounted in the problem of N two-level atoms, spread over large regions, interacting with a multimode radiation field.

A Solution to the Cosmic Conundrum including Cosmological Constant and Dark Energy Problems

NASA Astrophysics Data System (ADS)

Singh, A.

2009-12-01

A comprehensive solution to the cosmic conundrum is presented that also resolves key paradoxes of quantum mechanics and relativity. A simple mathematical model, the Gravity Nullification model (GNM), is proposed that integrates the missing physics of the spontaneous relativistic conversion of mass to energy into the existing physics theories, specifically a simplified general theory of relativity. Mechanistic mathematical expressions are derived for a relativistic universe expansion, which predict both the observed linear Hubble expansion in the nearby universe and the accelerating expansion exhibited by the supernova observations. The integrated model addresses the key questions haunting physics and Big Bang cosmology. It also provides a fresh perspective on the misconceived birth and evolution of the universe, especially the creation and dissolution of matter. The proposed model eliminates singularities from existing models and the need for the incredible and unverifiable assumptions including the superluminous inflation scenario, multiple universes, multiple dimensions, Anthropic principle, and quantum gravity. GNM predicts the observed features of the universe without any explicit consideration of time as a governing parameter.

Statistical experiments using the multiple regression research for prediction of proper hardness in areas of phosphorus cast-iron brake shoes manufacturing

NASA Astrophysics Data System (ADS)

Kiss, I.; Cioată, V. G.; Ratiu, S. A.; Rackov, M.; Penčić, M.

2018-01-01

Multivariate research is important in areas of cast-iron brake shoes manufacturing, because many variables interact with each other simultaneously. This article focuses on expressing the multiple linear regression model related to the hardness assurance by the chemical composition of the phosphorous cast irons destined to the brake shoes, having in view that the regression coefficients will illustrate the unrelated contributions of each independent variable towards predicting the dependent variable. In order to settle the multiple correlations between the hardness of the cast-iron brake shoes, and their chemical compositions several regression equations has been proposed. Is searched a mathematical solution which can determine the optimum chemical composition for the hardness desirable values. Starting from the above-mentioned affirmations two new statistical experiments are effectuated related to the values of Phosphorus [P], Manganese [Mn] and Silicon [Si]. Therefore, the regression equations, which describe the mathematical dependency between the above-mentioned elements and the hardness, are determined. As result, several correlation charts will be revealed.

Pedagogical Reform and College WOMEN’S Persistence in Mathematics

NASA Astrophysics Data System (ADS)

Strand, Kerry J. Strand; Mayfield, M. Elizabeth

Significant gender differences persist in the election of mathematics courses and math-related majors in college. Recent research suggests that part of the blame lies with conventional pedagogical approaches and that alternative approaches emphasizing practical applications, collaborative problem solving, and group work make mathematics more understandable and appealing to all students, particularly women. Using questionnaires administered to 355 traditional-age female college students, the authors examined the relationship between alternative teaching strategies in high school mathematics classes and two categories of outcome variables: mathematics-related attitudes and mathematics persistence in college. Multivariate analysis showed that experience with this so-called female-friendly pedagogy is positively related to students’ math-related attitudes and that these attitudes predict math persistence in college. However, the authors’ data also indicate that alternative teaching strategies have no discernible direct effect on students’ choices of mathematics courses or mathrelated

Mouse Hair Cycle Expression Dynamics Modeled as Coupled Mesenchymal and Epithelial Oscillators

PubMed Central

Tasseff, Ryan; Bheda-Malge, Anjali; DiColandrea, Teresa; Bascom, Charles C.; Isfort, Robert J.; Gelinas, Richard

2014-01-01

The hair cycle is a dynamic process where follicles repeatedly move through phases of growth, retraction, and relative quiescence. This process is an example of temporal and spatial biological complexity. Understanding of the hair cycle and its regulation would shed light on many other complex systems relevant to biological and medical research. Currently, a systematic characterization of gene expression and summarization within the context of a mathematical model is not yet available. Given the cyclic nature of the hair cycle, we felt it was important to consider a subset of genes with periodic expression. To this end, we combined several mathematical approaches with high-throughput, whole mouse skin, mRNA expression data to characterize aspects of the dynamics and the possible cell populations corresponding to potentially periodic patterns. In particular two gene clusters, demonstrating properties of out-of-phase synchronized expression, were identified. A mean field, phase coupled oscillator model was shown to quantitatively recapitulate the synchronization observed in the data. Furthermore, we found only one configuration of positive-negative coupling to be dynamically stable, which provided insight on general features of the regulation. Subsequent bifurcation analysis was able to identify and describe alternate states based on perturbation of system parameters. A 2-population mixture model and cell type enrichment was used to associate the two gene clusters to features of background mesenchymal populations and rapidly expanding follicular epithelial cells. Distinct timing and localization of expression was also shown by RNA and protein imaging for representative genes. Taken together, the evidence suggests that synchronization between expanding epithelial and background mesenchymal cells may be maintained, in part, by inhibitory regulation, and potential mediators of this regulation were identified. Furthermore, the model suggests that impairing this negative regulation will drive a bifurcation which may represent transition into a pathological state such as hair miniaturization. PMID:25375120

What's an Adult Numeracy Teacher to Teach? Negotiating the Complexity of Adult Numeracy Instruction

ERIC Educational Resources Information Center

Ginsburg, Lynda

2017-01-01

In this Forum article, the author addresses how to assist adults in improving mathematics and numeracy literacy. Ginsburg observes educators who strive to address their learners' educational gaps and needs are finding themselves in an environment of competing priorities and expectations that can be expressed as mathematics numeracy education. What…

Using a Framework for Three Levels of Sense Making in a Mathematics Classroom

ERIC Educational Resources Information Center

Moss, Diana L.; Lamberg, Teruni

2016-01-01

This discussion-based lesson is designed to support Year 6 students in their initial understanding of using letters to represent numbers, expressions, and equations in algebra. The three level framework is designed for: (1) making thinking explicit, (2) exploring each other's solutions, and (3) developing new mathematical insights. In each level…

Preliminary Findings from the First Two Waves of a Panel Study of Developing Career Expectations.

ERIC Educational Resources Information Center

Hotchkiss, Lawrence; Chiteji, Lisa

This report is an exploratory application of a dynamic mathematical model to express a theory of changes in youth's career expectations over time. Main content is divided into two focuses: (1) theoretical interpretations of the differential equations which embody the mathematical model and (2) reporting and discussion of the results of preliminary…

Students' Expression of Affect in an Inner-City SimCalc Classroom

ERIC Educational Resources Information Center

Schorr, Roberta Y.; Goldin, Gerald A.

2008-01-01

This research focuses on some of the affordances provided by SimCalc software, suggesting that its use can have important consequences for students' mathematical affect and motivation. We describe an episode in an inner-city SimCalc environment illustrating our approach to the study of affect in the mathematics classroom. We infer students'…

Interdisciplinary Working Practices: Can Creative Dance Improve Math?

ERIC Educational Resources Information Center

Leandro, Cristina Rebelo; Monteiro, Elisabete; Melo, Filipe

2018-01-01

This study is integrated in the field of Dance in Education, focusing on the instrumentalist aspect of art. We focused on creative dance as a catalyst to learn Mathematics' contents. This interdisciplinary work can enhance the learning, as far as the understanding of Mathematics' concepts is achieved through the body and revealed by expressive and…

How to Present It? On the Rhetoric of an Outstanding Lecturer

ERIC Educational Resources Information Center

Movshovitz-Hadar, Nitsa; Hazzan, Orit

2004-01-01

This paper analyses a lecture by an excellent teaching award winner professor of mathematics, given to high school mathematics teachers. The analysis is based upon two sources: (i) the lecture plan, as expressed in a series of 29 transparencies, prepared by the lecturer in advance; (ii) the actual implementation of the lecture, as transcribed from…

A "Great Way to Get On"? The Early Career Destinations of Science, Technology, Engineering and Mathematics Graduates

ERIC Educational Resources Information Center

Smith, Emma; White, Patrick

2017-01-01

Concerns about a shortage of highly skilled workers in the science, technology, engineering and mathematics (STEM) sector have been expressed frequently since the late 1940s. Although these claims have been challenged as being insufficiently grounded in evidence, they have formed the basis of policies directing considerable resources to STEM…

A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy (II)

ERIC Educational Resources Information Center

Bradford, Russell; Davenport, James H.; Sangwin, Chris

2010-01-01

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

Level of Student's Creative Thinking in Classroom Mathematics

ERIC Educational Resources Information Center

Siswono, Tatag Yuli Eko

2011-01-01

It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…

The Threshold Hypothesis Applied to Spatial Skill and Mathematics

ERIC Educational Resources Information Center

Freer, Daniel

2017-01-01

This cross-sectional study assessed the relation between spatial skills and mathematics in 854 participants across kindergarten, third grade, and sixth grade. Specifically, the study probed for a threshold for spatial skills when performing mathematics, above which spatial scores and mathematics scores would be significantly less related. This…

A Modeling and Experimental Investigation of the Effects of Antigen Density, Binding Affinity, and Antigen Expression Ratio on Bispecific Antibody Binding to Cell Surface Targets*

PubMed Central

Rhoden, John J.; Dyas, Gregory L.

2016-01-01

Despite the increasing number of multivalent antibodies, bispecific antibodies, fusion proteins, and targeted nanoparticles that have been generated and studied, the mechanism of multivalent binding to cell surface targets is not well understood. Here, we describe a conceptual and mathematical model of multivalent antibody binding to cell surface antigens. Our model predicts that properties beyond 1:1 antibody:antigen affinity to target antigens have a strong influence on multivalent binding. Predicted crucial properties include the structure and flexibility of the antibody construct, the target antigen(s) and binding epitope(s), and the density of antigens on the cell surface. For bispecific antibodies, the ratio of the expression levels of the two target antigens is predicted to be critical to target binding, particularly for the lower expressed of the antigens. Using bispecific antibodies of different valencies to cell surface antigens including MET and EGF receptor, we have experimentally validated our modeling approach and its predictions and observed several nonintuitive effects of avidity related to antigen density, target ratio, and antibody affinity. In some biological circumstances, the effect we have predicted and measured varied from the monovalent binding interaction by several orders of magnitude. Moreover, our mathematical framework affords us a mechanistic interpretation of our observations and suggests strategies to achieve the desired antibody-antigen binding goals. These mechanistic insights have implications in antibody engineering and structure/activity relationship determination in a variety of biological contexts. PMID:27022022

Perception determinants in learning mathematics

NASA Astrophysics Data System (ADS)

Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul

2015-05-01

This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.

The Relation Between Inattentive and Hyperactive/Impulsive Behaviors and Early Mathematics Skills.

PubMed

Sims, Darcey M; Purpura, David J; Lonigan, Christopher J

2016-08-01

Despite strong evidence that inattentive and hyperactive/impulsive behaviors are associated with mathematical difficulties in school-age children, little research has been conducted to examine the link between these constructs before the start of formal education. The purpose of this study was to examine how different manifestations of inattentive and hyperactive/impulsive behaviors, as measured by different assessment tools, are related to early mathematics skills in preschoolers. Eighty-two preschool children completed a measure of early mathematics and the Continuous Performance Test (CPT). Teachers rated children's behaviors using the Conners' Teacher Rating Scale-15 Item. Sixty-five of these children completed mathematics assessments 1 year later. Teacher ratings of inattention were uniquely related to concurrent early mathematics skills, whereas CPT errors were uniquely predictive of early mathematics skills 1 year later. Findings have implications for the understanding and assessment of behavior problems that are associated with early mathematics difficulties. © The Author(s) 2012.

Special relativity from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2015-09-01

When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

The written mathematical communication profile of prospective math teacher in mathematical proving

NASA Astrophysics Data System (ADS)

Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

2018-01-01

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

Relations of different types of numerical magnitude representations to each other and to mathematics achievement.

PubMed

Fazio, Lisa K; Bailey, Drew H; Thompson, Clarissa A; Siegler, Robert S

2014-07-01

We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both magnitude comparison and number line estimation tasks. After controlling for non-mathematical cognitive proficiency, both symbolic and non-symbolic numerical magnitude understandings were uniquely related to mathematics achievement, but the relation was much stronger for symbolic numbers. A meta-analysis of 19 published studies indicated that relations between non-symbolic numerical magnitude knowledge and mathematics achievement are present but tend to be weak, especially beyond 6 years of age. Copyright © 2014 Elsevier Inc. All rights reserved.

A Meta-Analysis of Mathematics and Working Memory: Moderating Effects of Working Memory Domain, Type of Mathematics Skill, and Sample Characteristics

ERIC Educational Resources Information Center

Peng, Peng; Namkung, Jessica; Barnes, Marcia; Sun, Congying

2016-01-01

The purpose of this meta-analysis was to determine the relation between mathematics and working memory (WM) and to identify possible moderators of this relation including domains of WM, types of mathematics skills, and sample type. A meta-analysis of 110 studies with 829 effect sizes found a significant medium correlation of mathematics and WM, r…

Mathematical modelling of phenotypic plasticity and conversion to a stem-cell state under hypoxia

NASA Astrophysics Data System (ADS)

Dhawan, Andrew; Madani Tonekaboni, Seyed Ali; Taube, Joseph H.; Hu, Stephen; Sphyris, Nathalie; Mani, Sendurai A.; Kohandel, Mohammad

2016-02-01

Hypoxia, or oxygen deficiency, is known to be associated with breast tumour progression, resistance to conventional therapies and poor clinical prognosis. The epithelial-mesenchymal transition (EMT) is a process that confers invasive and migratory capabilities as well as stem cell properties to carcinoma cells thus promoting metastatic progression. In this work, we examined the impact of hypoxia on EMT-associated cancer stem cell (CSC) properties, by culturing transformed human mammary epithelial cells under normoxic and hypoxic conditions, and applying in silico mathematical modelling to simulate the impact of hypoxia on the acquisition of CSC attributes and the transitions between differentiated and stem-like states. Our results indicate that both the heterogeneity and the plasticity of the transformed cell population are enhanced by exposure to hypoxia, resulting in a shift towards a more stem-like population with increased EMT features. Our findings are further reinforced by gene expression analyses demonstrating the upregulation of EMT-related genes, as well as genes associated with therapy resistance, in hypoxic cells compared to normoxic counterparts. In conclusion, we demonstrate that mathematical modelling can be used to simulate the role of hypoxia as a key contributor to the plasticity and heterogeneity of transformed human mammary epithelial cells.

Essential Mathematics for the Physical Sciences; Volume I: Homogeneous boundary value problems, Fourier methods, and special functions

NASA Astrophysics Data System (ADS)

Borden, Brett; Luscombe, James

2017-10-01

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.

The relation between children’s constructive play activities, spatial ability, and mathematical word problem-solving performance: a mediation analysis in sixth-grade students

PubMed Central

Oostermeijer, Meike; Boonen, Anton J. H.; Jolles, Jelle

2014-01-01

The scientific literature shows that constructive play activities are positively related to children’s spatial ability. Likewise, a close positive relation is found between spatial ability and mathematical word problem-solving performances. The relation between children’s constructive play and their performance on mathematical word problems is, however, not reported yet. The aim of the present study was to investigate whether spatial ability acted as a mediator in the relation between constructive play and mathematical word problem-solving performance in 128 sixth-grade elementary school children. This mediating role of spatial ability was tested by utilizing the current mediation approaches suggested by Preacher and Hayes (2008). Results showed that 38.16% of the variance in mathematical word problem-solving performance is explained by children’s constructive play activities and spatial ability. More specifically, spatial ability acted as a partial mediator, explaining 31.58% of the relation between constructive play and mathematical word problem-solving performance. PMID:25101038

Equivalent model of a dually-fed machine for electric drive control systems

NASA Astrophysics Data System (ADS)

Ostrovlyanchik, I. Yu; Popolzin, I. Yu

2018-05-01

The article shows that the mathematical model of a dually-fed machine is complicated because of the presence of a controlled voltage source in the rotor circuit. As a method of obtaining a mathematical model, the method of a generalized two-phase electric machine is applied and a rotating orthogonal coordinate system is chosen that is associated with the representing vector of a stator current. In the chosen coordinate system in the operator form the differential equations of electric equilibrium for the windings of the generalized machine (the Kirchhoff equation) are written together with the expression for the moment, which determines the electromechanical energy transformation in the machine. Equations are transformed so that they connect the currents of the windings, that determine the moment of the machine, and the voltages on these windings. The structural diagram of the machine is assigned to the written equations. Based on the written equations and accepted assumptions, expressions were obtained for the balancing the EMF of windings, and on the basis of these expressions an equivalent mathematical model of a dually-fed machine is proposed, convenient for use in electric drive control systems.

Project-Based Learning and Design-Focused Projects to Motivate Secondary Mathematics Students

ERIC Educational Resources Information Center

Remijan, Kelly W.

2017-01-01

This article illustrates how mathematics teachers can develop design-focused projects, related to project-based learning, to motivate secondary mathematics students. With first-hand experience as a secondary mathematics teacher, I provide a series of steps related to the engineering design process, which are helpful to teachers in developing…

The Transition from School to University in Mathematics: Which Influence Do School-Related Variables Have?

ERIC Educational Resources Information Center

Rach, Stefanie; Heinze, Aiso

2017-01-01

Particularly in mathematics, the transition from school to university often appears to be a substantial hurdle in the individual learning biography. Differences between the characters of school mathematics and scientific university mathematics as well as different demands related to the learning cultures in both institutions are discussed as…

Mathematics-Related Anxiety and Attitudes: Examining the Impact among Latina Preservice Teachers

ERIC Educational Resources Information Center

Gautreau, Cynthia; Brye, Michelle VanderVeldt; Lunceford, Christina

2016-01-01

The purpose of this study was to investigate mathematics-related anxiety and attitudes among Latina preservice teachers. Three sections from the Inventory of Mathematics Attitudes, Experience, and Self Awareness were administered to preservice teachers enrolled in a curriculum and instruction mathematics course during the 1st semester of a…

Exploring individual differences in children's mathematical skills: a correlational and dimensional approach.

PubMed

Sigmundsson, H; Polman, R C J; Lorås, H

2013-08-01

Individual differences in mathematical skills are typically explained by an innate capability to solve mathematical tasks. At the behavioural level this implies a consistent level of mathematical achievement that can be captured by strong relationships between tasks, as well as by a single statistical dimension that underlies performance on all mathematical tasks. To investigate this general assumption, the present study explored interrelations and dimensions of mathematical skills. For this purpose, 68 ten-year-old children from two schools were tested using nine mathematics tasks from the Basic Knowledge in Mathematics Test. Relatively low-to-moderate correlations between the mathematics tasks indicated most tasks shared less than 25% of their variance. There were four principal components, accounting for 70% of the variance in mathematical skill across tasks and participants. The high specificity in mathematical skills was discussed in relation to the principle of task specificity of learning.

Detailing Relational Interactions in Urban Elementary Mathematics Classrooms

ERIC Educational Resources Information Center

Battey, Dan; Neal, Rebecca A.

2018-01-01

The lack of quality of instruction in urban mathematics classrooms in the United States has received much attention in the scholarly literature. Other classroom mechanisms such as relational interactions, however, have not received much attention of mathematics education researchers. Relational interactions go above and beyond content instruction…

Mathematical background and attitudes toward statistics in a sample of Spanish college students.

PubMed

Carmona, José; Martínez, Rafael J; Sánchez, Manuel

2005-08-01

To examine the relation of mathematical background and initial attitudes toward statistics of Spanish college students in social sciences the Survey of Attitudes Toward Statistics was given to 827 students. Multivariate analyses tested the effects of two indicators of mathematical background (amount of exposure and achievement in previous courses) on the four subscales. Analysis suggested grades in previous courses are more related to initial attitudes toward statistics than the number of mathematics courses taken. Mathematical background was related with students' affective responses to statistics but not with their valuing of statistics. Implications of possible research are discussed.

SEMI-ANALYTIC CALCULATION OF THE TEMPERATURE DISTRIBUTION IN A PERFORATED CIRCLE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kennedy, J.M.; Fowler, J.K.

The flow of heat in a tube-in-shell fuel element is closely related to the two-dimensional heat flow in a circular region perforated by a number of circular holes. Mathematical expressions for the two-dimensional temperature distribution were obtained in terms of sources and sinks of increasing complexity located within the holes and beyond the outer circle. A computer program, TINS, which solves the temperature problem for an array of one or two rings of holes, with or without a center hole, is also described. (auth)

The Elimination of Corrosion . . . is Nanotechnology the Answer to the USAF’s #1 Aging Aircraft Dilemma

DTIC Science & Technology

2009-04-01

mathematically by the expression, G = H – TS, where H is enthalpy, T is absolute temperature, and S is the entropy of the system. 27 Appendix C...given system’s relative stability at a constant pressure and temperature, and is defined by the equation: TSHG  where H is the enthalpy, T is the...thermodynamic properties. AU/ACSC/AVRAM/AY09 37 Table 4 Thermodynamic Values at Standard State (298K)107 Species Name Enthalpy "∆ H o " (kJ

Relationship between academic motivation and mathematics achievement among Indian adolescents in Canada and India.

PubMed

Areepattamannil, Shaljan

2014-01-01

This study examined the relationships between academic motivation-intrinsic motivation, extrinsic motivation, amotivation-and mathematics achievement among 363 Indian adolescents in India and 355 Indian immigrant adolescents in Canada. Results of hierarchical multiple regression analyses showed that intrinsic motivation, extrinsic motivation, and amotivation were not statistically significantly related to mathematics achievement among Indian adolescents in India. In contrast, both intrinsic motivation and extrinsic motivation were statistically significantly related to mathematics achievement among Indian immigrant adolescents in Canada. While intrinsic motivation was a statistically significant positive predictor of mathematics achievement among Indian immigrant adolescents in Canada, extrinsic motivation was a statistically significant negative predictor of mathematics achievement among Indian immigrant adolescents in Canada. Amotivation was not statistically significantly related to mathematics achievement among Indian immigrant adolescents in Canada. Implications of the findings for pedagogy and practice are discussed.

Prospects for School Mathematics. Seventy-Five Years of Progress.

ERIC Educational Resources Information Center

Carl, Iris M., Ed.

This book offers a broad view for a varied audience of what the vision expressed in all three National Council of Teachers of Mathematics' Standards documents will look like when aligned with practice and outlines ways in which desired changes can be realized. Six sections and 21 chapters in the book are: Section I--History: (1) "Paths to the…

Students' Use of CAS Calculators--Effects on the Trustworthiness and Fairness of Mathematics Assessments

ERIC Educational Resources Information Center

Pantzare, Anna Lind

2012-01-01

Calculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When calculators are allowed to be used during assessments but are not available or provided to every student, they may cause bias. The CAS calculators may also have an impact on the trustworthiness of results.…

Does It Help to Use Mathematically Superfluous Brackets When Teaching the Rules for the Order of Operations?

ERIC Educational Resources Information Center

Gunnarsson, Robert; Sönnerhed, Wang Wei; Hernell, Bernt

2016-01-01

The hypothesis that mathematically superfluous brackets can be useful when teaching the rules for the order of operations is challenged. The idea of the hypothesis is that with brackets it is possible to emphasize the order priority of one operation over another. An experiment was conducted where expressions with mixed operations were studied,…

Authentic Research Experience and “Big Data” Analysis in the Classroom: Maize Response to Abiotic Stress

PubMed Central

Makarevitch, Irina; Frechette, Cameo; Wiatros, Natalia

2015-01-01

Integration of inquiry-based approaches into curriculum is transforming the way science is taught and studied in undergraduate classrooms. Incorporating quantitative reasoning and mathematical skills into authentic biology undergraduate research projects has been shown to benefit students in developing various skills necessary for future scientists and to attract students to science, technology, engineering, and mathematics disciplines. While large-scale data analysis became an essential part of modern biological research, students have few opportunities to engage in analysis of large biological data sets. RNA-seq analysis, a tool that allows precise measurement of the level of gene expression for all genes in a genome, revolutionized molecular biology and provides ample opportunities for engaging students in authentic research. We developed, implemented, and assessed a series of authentic research laboratory exercises incorporating a large data RNA-seq analysis into an introductory undergraduate classroom. Our laboratory series is focused on analyzing gene expression changes in response to abiotic stress in maize seedlings; however, it could be easily adapted to the analysis of any other biological system with available RNA-seq data. Objective and subjective assessment of student learning demonstrated gains in understanding important biological concepts and in skills related to the process of science. PMID:26163561

Computing maximum-likelihood estimates for parameters of the National Descriptive Model of Mercury in Fish

USGS Publications Warehouse

Donato, David I.

2012-01-01

This report presents the mathematical expressions and the computational techniques required to compute maximum-likelihood estimates for the parameters of the National Descriptive Model of Mercury in Fish (NDMMF), a statistical model used to predict the concentration of methylmercury in fish tissue. The expressions and techniques reported here were prepared to support the development of custom software capable of computing NDMMF parameter estimates more quickly and using less computer memory than is currently possible with available general-purpose statistical software. Computation of maximum-likelihood estimates for the NDMMF by numerical solution of a system of simultaneous equations through repeated Newton-Raphson iterations is described. This report explains the derivation of the mathematical expressions required for computational parameter estimation in sufficient detail to facilitate future derivations for any revised versions of the NDMMF that may be developed.

Obstacles Related to Structuring for Mathematization Encountered by Students When Solving Physics Problems

ERIC Educational Resources Information Center

Niss, Martin

2017-01-01

This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called "structuring for mathematization," where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four…

Is There a Causal Relation between Mathematical Creativity and Mathematical Problem-Solving Performance?

ERIC Educational Resources Information Center

Tyagi, Tarun Kumar

2016-01-01

The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…

The Relation between Mathematics and Working Memory in Young Children with Fetal Alcohol Spectrum Disorders

ERIC Educational Resources Information Center

Rasmussen, Carmen; Bisanz, Jeffrey

2011-01-01

The goal of this study was to examine the relation between mathematics and working memory in young children with Fetal Alcohol Spectrum Disorders (FASD). Children with FASD and comparison children (4 to 6 years old) completed standardized tests of mathematics and working memory. Children with FASD showed impairments on mathematics (applied…

The Co-Development and Interrelation of Proof and Authority: The Case of Yana and Ronit

ERIC Educational Resources Information Center

Fried, Michael N.; Amit, Miriam

2008-01-01

Students' mathematical lives are characterized not only by a set of mathematical ideas and the engagement in mathematical thinking, but also by social relations, specifically, relations of authority. Watching student actions and speaking to students, one becomes cognizant of a "web of authority" ever present in mathematics classrooms. In…

Assessing Senior Secondary School Students' Mathematical Proficiency as Related to Gender and Performance in Mathematics in Nigeria

ERIC Educational Resources Information Center

Awofala, Adeneye O. A.

2017-01-01

The study investigated mathematical proficiency as related to gender and performance in mathematics among 400 Nigerian senior secondary school students from 10 elitist senior secondary schools in Lagos State using the quantitative research method within the blueprint of descriptive survey design. Data collected were analysed using the descriptive…

Assessing Preservice Teachers' Mathematics Cognitive Failures as Related to Mathematics Anxiety and Performance in Undergraduate Calculus

ERIC Educational Resources Information Center

Awofala, Adeneye O. A.; Odogwu, Helen N.

2017-01-01

The study investigated mathematics cognitive failures as related to mathematics anxiety, gender and performance in calculus among 450 preservice teachers from four public universities in the South West geo-political zone of Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were…

Prospective Mathematics Teachers' Ability to Identify Mistakes Related to Angle Concept of Sixth Grade Students

ERIC Educational Resources Information Center

Arslan, Cigdem; Erbay, Hatice Nur; Guner, Pinar

2017-01-01

In the present study we try to highlight prospective mathematics teachers' ability to identify mistakes of sixth grade students related to angle concept. And also we examined prospective mathematics teachers' knowledge of angle concept. Study was carried out with 30 sixth-grade students and 38 prospective mathematics teachers. Sixth grade students…

The Characteristics of Mathematical Creativity

ERIC Educational Resources Information Center

Sriraman, Bharath

2004-01-01

Mathematical creativity ensures the growth of mathematics as a whole. However, the source of this growth, the creativity of the mathematician, is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics, a qualitative study involving five creative mathematicians was…

Examining Mathematics Anxiety in Elementary Classroom Teachers

ERIC Educational Resources Information Center

McAnallen, Rachel R.

2010-01-01

Test anxiety and mathematics anxiety have been found to relate to mathematics performance in both children and adults. This study investigated mathematics anxiety in elementary teachers and whether those who experience mathematics anxiety also have professional anxiety about teaching mathematics. A researcher-developed instrument called the…

Promoting Preservice Teachers' Mathematics Identity Exploration

ERIC Educational Resources Information Center

Heffernan, Kayla

2016-01-01

Despite the effort of teacher education programs, early childhood, and elementary preservice teachers often fear mathematics, have high mathematics anxiety, hold negative self-perceptions in relation to mathematics, find mathematics irrelevant, and have low mathematics achievement. The aim of this study was to implement and investigate the…

``From Fundamental Motives to Rational Expectation Equilibrium[REE, henceworth] of Indeterminacy''

NASA Astrophysics Data System (ADS)

Maksoed, Ssi, Wh-

For ``Principle of Indeterminacy''from Heisenberg states: ``one of the fundamental cornerstone of quantum mechanics is the Heisenberg uncertainty principle''.whereas canonically conjugate quantities can be determined simultaneously only with a characteristic indeterminacy[M. Arevalo Aguilar, et.al]. Accompanying Alfred North Whitehead conclusion in ``The Aims of Education''that mathematical symbols are artificial before new meanings given, two kinds of fundamental motives: (i) expectation-expectation, (ii) expectation-certainty inherently occurs with determinacy properties of rational expectation equilibrium(REE, henceworth)- Guido Ascari & Tizano Ropele:''Trend inflation, Taylor principle & Indeterminacy'', Kiel Institute, June 2007. Furthers, relative price expression can be compare of their α and (1 - α) configurations in the expression of possible activity. Acknowledgment to Prof[asc]. Dr. Bobby Eka Gunara for ``made a rank through physics'' denotes...

Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities

PubMed Central

Chu, Felicia W.; vanMarle, Kristy; Geary, David C.

2016-01-01

One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement. PMID:27252675

Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities.

PubMed

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2016-01-01

One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement.

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement

PubMed Central

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A.; Sheffield, Tiffany D.; Nelson, Jennifer Mize

2010-01-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child’s social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. PMID:21676089

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement.

PubMed

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A; Sheffield, Tiffany D; Nelson, Jennifer Mize

2011-07-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child 's social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. © 2010 Blackwell Publishing Ltd.

Understanding space weather with new physical, mathematical and philosophical approaches

NASA Astrophysics Data System (ADS)

Mateev, Lachezar; Velinov, Peter; Tassev, Yordan

2016-07-01

The actual problems of solar-terrestrial physics, in particular of space weather are related to the prediction of the space environment state and are solved by means of different analyses and models. The development of these investigations can be considered also from another side. This is the philosophical and mathematical approach towards this physical reality. What does it constitute? We have a set of physical processes which occur in the Sun and interplanetary space. All these processes interact with each other and simultaneously participate in the general process which forms the space weather. Let us now consider the Leibniz's monads (G.W. von Leibniz, 1714, Monadologie, Wien; Id., 1710, Théodicée, Amsterdam) and use some of their properties. There are total 90 theses for monads in the Leibniz's work (1714), f.e. "(1) The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts'. (Theod. 10.); … (56) Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.); (59) … this universal harmony, according to which every substance exactly expresses all others through the relations it has with them. (63) … every Monad is, in its own way, a mirror of the universe, and the universe is ruled according to a perfect order. (Theod. 403.)", etc. Let us introduce in the properties of monads instead of the word "monad" the word "process". We obtain the following statement: Each process reflects all other processes and all other processes reflect this process. This analogy is not formal at all, it reflects accurately the relation between the physical processes and their unity. The category monad which in the Leibniz's Monadology reflects generally the philosophical sense is fully identical with the physical one, in our case. The corresponding mathematical relations are needed for the application of this analogy in the solar-terrestrial physics and space weather. For this purpose in the contemporary categories theory in the algebra a whole field for it exists - the theory of monads (M. Barr, Ch. Wells, 1985, Toposes, Triples and Theories, Springer-Verlag, 278, p. 82). This theory is generated by analogous elements as in the Leibniz's Monadology. As it is known the categories theory and in particular the monad theory (also named triple or triad theory) tends to make axioms in mathematics. This approach would be very useful for such complex systems and processes as these in the solar-terrestrial physics and space weather. Here some methods for algebraic data structures could be introduced. Or some imperative programs can be embedded in a purely functional program for modeling, respectively. All these problems are principally considered in the proposed report.

Mathematics is differentially related to reading comprehension and word decoding: Evidence from a genetically-sensitive design

PubMed Central

Harlaar, Nicole; Kovas, Yulia; Dale, Philip S.; Petrill, Stephen A.; Plomin, Robert

2013-01-01

Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiological level in a population-based cohort of 5162 twin pairs at age 12. Multivariate genetic analyses of latent phenotypic factors of mathematics, word decoding and reading comprehension revealed substantial genetic and shared environmental correlations among all three domains. However, the phenotypic and genetic correlations between mathematics and reading comprehension were significantly greater than between mathematics and word decoding. Independent of mathematics, there was also evidence for genetic and nonshared environmental links between word decoding and reading comprehension. These findings indicate that word decoding and reading comprehension have partly distinct relationships with mathematics in the middle school years. PMID:24319294

Mathematics is differentially related to reading comprehension and word decoding: Evidence from a genetically-sensitive design.

PubMed

Harlaar, Nicole; Kovas, Yulia; Dale, Philip S; Petrill, Stephen A; Plomin, Robert

2012-08-01

Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiological level in a population-based cohort of 5162 twin pairs at age 12. Multivariate genetic analyses of latent phenotypic factors of mathematics, word decoding and reading comprehension revealed substantial genetic and shared environmental correlations among all three domains. However, the phenotypic and genetic correlations between mathematics and reading comprehension were significantly greater than between mathematics and word decoding. Independent of mathematics, there was also evidence for genetic and nonshared environmental links between word decoding and reading comprehension. These findings indicate that word decoding and reading comprehension have partly distinct relationships with mathematics in the middle school years.

Preschool children's mathematical knowledge: The effect of teacher "math talk.".

PubMed

Klibanoff, Raquel S; Levine, Susan C; Huttenlocher, Janellen; Vasilyeva, Marina; Hedges, Larry V

2006-01-01

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year. Copyright 2006 APA, all rights reserved.

Optimization of Operating Parameters for Minimum Mechanical Specific Energy in Drilling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamrick, Todd

2011-01-01

Efficiency in drilling is measured by Mechanical Specific Energy (MSE). MSE is the measure of the amount of energy input required to remove a unit volume of rock, expressed in units of energy input divided by volume removed. It can be expressed mathematically in terms of controllable parameters; Weight on Bit, Torque, Rate of Penetration, and RPM. It is well documented that minimizing MSE by optimizing controllable factors results in maximum Rate of Penetration. Current methods for computing MSE make it possible to minimize MSE in the field only through a trial-and-error process. This work makes it possible to computemore » the optimum drilling parameters that result in minimum MSE. The parameters that have been traditionally used to compute MSE are interdependent. Mathematical relationships between the parameters were established, and the conventional MSE equation was rewritten in terms of a single parameter, Weight on Bit, establishing a form that can be minimized mathematically. Once the optimum Weight on Bit was determined, the interdependent relationship that Weight on Bit has with Torque and Penetration per Revolution was used to determine optimum values for those parameters for a given drilling situation. The improved method was validated through laboratory experimentation and analysis of published data. Two rock types were subjected to four treatments each, and drilled in a controlled laboratory environment. The method was applied in each case, and the optimum parameters for minimum MSE were computed. The method demonstrated an accurate means to determine optimum drilling parameters of Weight on Bit, Torque, and Penetration per Revolution. A unique application of micro-cracking is also presented, which demonstrates that rock failure ahead of the bit is related to axial force more than to rotation speed.« less

On the fine-structure constant in a plasma model of the fluctuating vacuum substratum

NASA Technical Reports Server (NTRS)

Cragin, B. L.

1986-01-01

The existence of an intimate connection between the quivering motion of electrons and positrons (Zitterbewegung), predicted by the Dirac equation, and the zero-point fluctuations of the vacuum is suggested. The nature of the proposed connection is discussed quantitatively, and an approximate self-consistency relation is derived, supplying a purely mathematical expression that relates the dimensionless coupling strengths (fine-structure constants) alpha sub e and alpha sub g of electromagnetism and gravity. These considerations provide a tentative explanation for the heretofore puzzling number 1/alpha sub e of about 137.036 and suggest that attempts to unify gravity with the electroweak and strong interactions will ultimately prove successful.

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Examining Relations between Mathematics Teachers' Instructional Vision and Knowledge and Change in Practice

ERIC Educational Resources Information Center

Munter, Charles; Correnti, Richard

2017-01-01

This article provides a longitudinal examination of how changes in more than 200 middle-grades mathematics teachers' instructional practices related to their (a) mathematical knowledge for teaching (MKT) and (b) instructional vision. Results of this multilevel regression analysis suggest that MKT and instructional vision are related to instruction…

Self-Concept Mediates the Relation between Achievement and Emotions in Mathematics

ERIC Educational Resources Information Center

Van der Beek, Jojanneke P. J.; Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Leseman, Paul P. M.

2017-01-01

Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. Aims: The aims were (1) to investigate the…

Two-point derivative dispersion relations

NASA Astrophysics Data System (ADS)

Ferreira, Erasmo; Sesma, Javier

2013-03-01

A new derivation is given for the representation, under certain conditions, of the integral dispersion relations of scattering theory through local forms. The resulting expressions have been obtained through an independent procedure to construct the real part and consist of new mathematical structures of double infinite summations of derivatives. In this new form the derivatives are calculated at the generic value of the energy E and separately at the reference point E = m that is the lower limit of the integration. This new form may be more interesting in certain circumstances and directly shows the origin of the difficulties in convergence that were present in the old truncated forms called standard-derivative dispersion relations (DDR). For all cases in which the reductions of the double to single sums were obtained in our previous work, leading to explicit demonstration of convergence, these new expressions are seen to be identical to the previous ones. We present, as a glossary, the most simplified explicit results for the DDR's in the cases of imaginary amplitudes of forms (E/m)λ[ln (E/m)]n that cover the cases of practical interest in particle physics phenomenology at high energies. We explicitly study the expressions for the cases with λ negative odd integers, that require identification of cancelation of singularities, and provide the corresponding final results.

Relating Difficulty in School Mathematics to Nature of Mathematics: Perception of High School Students from Kerala

ERIC Educational Resources Information Center

Gafoor, Kunnathodi Abdul; Sarabi, M. K.

2015-01-01

This study relates factors in nature of Mathematics and its teaching learning to student difficulties for diverse mathematics tasks. Descriptive survey was done on a sample of 300 high school students in Kerala with a questionnaire on difficulties in learning. Student perception of difficulty on 26 types of tasks, under five heads that students…

Intentional and automatic numerical processing as predictors of mathematical abilities in primary school children

PubMed Central

Pina, Violeta; Castillo, Alejandro; Cohen Kadosh, Roi; Fuentes, Luis J.

2015-01-01

Previous studies have suggested that numerical processing relates to mathematical performance, but it seems that such relationship is more evident for intentional than for automatic numerical processing. In the present study we assessed the relationship between the two types of numerical processing and specific mathematical abilities in a sample of 109 children in grades 1–6. Participants were tested in an ample range of mathematical tests and also performed both a numerical and a size comparison task. The results showed that numerical processing related to mathematical performance only when inhibitory control was involved in the comparison tasks. Concretely, we found that intentional numerical processing, as indexed by the numerical distance effect in the numerical comparison task, was related to mathematical reasoning skills only when the task-irrelevant dimension (the physical size) was incongruent; whereas automatic numerical processing, indexed by the congruency effect in the size comparison task, was related to mathematical calculation skills only when digits were separated by small distance. The observed double dissociation highlights the relevance of both intentional and automatic numerical processing in mathematical skills, but when inhibitory control is also involved. PMID:25873909

The relationship among mathematics anxiety, beliefs about mathematics, mathematics self-efficacy, and mathematics performance in associate degree nursing students.

PubMed

Walsh, Kathleen A

2008-01-01

This research explored nursing students' mathematics anxiety, beliefs about mathematics, and mathematics self-efficacy in relation to performance on a medication mathematics test. Results revealed that the participants experienced some mathematics anxiety and had positive beliefs about mathematics and mathematics self-efficacy. Qualitative responses indicated that participants worried about the consequences of failing the medication mathematics test and that practice helped reduce this anxiety. In addition, participants acknowledged the importance of correct dosage calculations for nursing practice. Implications for nursing education are discussed.

The Mathematics Education Debates: Preparing Students to Become Professionally Active Mathematics Teachers

ERIC Educational Resources Information Center

Munakata, Mika

2010-01-01

The Mathematics Education Debate is an assignment designed for and implemented in an undergraduate mathematics methods course for prospective secondary school mathematics teachers. For the assignment, students read and analyze current research and policy reports related to mathematics education, prepare and present their positions, offer…

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

PubMed

Lobo, S M; Liu, Z-J; Yu, N C; Humphries, S; Ahmed, M; Cosman, E R; Lenkinski, R E; Goldberg, W; Goldberg, S N

2005-05-01

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

Reconstructing Cell Lineages from Single-Cell Gene Expression Data: A Pilot Study

DTIC Science & Technology

2016-08-30

Reconstructing cell lineages from single- cell gene expression data: a pilot study The goal of this pilot study is to develop novel mathematical...methods, by leveraging tools developed in the bifurcation theory, to infer the underlying cell -state dynamics from single- cell gene expression data. Our...proposed method contains two steps. The first step is to reconstruct the temporal order of the cells from gene expression data, whereas the second

Investigating middle school students’ difficulties in mathematical literacy problems level 1 and 2

NASA Astrophysics Data System (ADS)

Setiawati, S.; Herman, T.; Jupri, A.

2017-11-01

The background of this study is the lack of mathematical literacy skills of students. The proficiency of students’ mathematical literacy skills based on the results of the PISA 2015 study shows that Indonesian students at the proficiency level 1. This fact gave rise to this study which aims to investigate middle school students’ difficulties in mathematical literacy problems level 1 and 2. Qualitative research was used in this study. An individual written test on mathematical literacy problems was administered, followed by interviews. The subjects of the study were 61 students grade VII in Bandung and 26 of them were interviewed afterward. Data analysis revealed that students’ error in performing arithmetic most frequently observed. Other observed difficulties concerned understanding about algebra concept, applying arithmetic operation in algebraic expressions, and interpreting symbols to represent the unknown. In solving mathematical literacy problems, students use their prior knowledge, although sometimes not relevant to the questions. Based on the results, we suggest that mathematics learning in contextual learning and which invites students to participate in the processes of understanding the concepts.

State and trait effects on individual differences in children's mathematical development.

PubMed

Bailey, Drew H; Watts, Tyler W; Littlefield, Andrew K; Geary, David C

2014-11-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. © The Author(s) 2014.

State and Trait Effects on Individual Differences in Children's Mathematical Development

PubMed Central

Bailey, Drew H.; Watts, Tyler W.; Littlefield, Andrew K.; Geary, David C.

2015-01-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. PMID:25231900

The Green-Schwarz mechanism and geometric anomaly relations in 2d (0,2) F-theory vacua

NASA Astrophysics Data System (ADS)

Weigand, Timo; Xu, Fengjun

2018-04-01

We study the structure of gauge and gravitational anomalies in 2d N = (0 , 2) theories obtained by compactification of F-theory on elliptically fibered Calabi-Yau 5-folds. Abelian gauge anomalies, induced at 1-loop in perturbation theory, are cancelled by a generalized Green-Schwarz mechanism operating at the level of chiral scalar fields in the 2d supergravity theory. We derive closed expressions for the gravitational and the non-abelian and abelian gauge anomalies including the Green-Schwarz counterterms. These expressions involve topological invariants of the underlying elliptic fibration and the gauge background thereon. Cancellation of anomalies in the effective theory predicts intricate topological identities which must hold on every elliptically fibered Calabi-Yau 5-fold. We verify these relations in a non-trivial example, but their proof from a purely mathematical perspective remains as an interesting open problem. Some of the identities we find on elliptic 5-folds are related in an intriguing way to previously studied topological identities governing the structure of anomalies in 6d N = (1 , 0) and 4d N = 1 theories obtained from F-theory.

A combinatorial model of malware diffusion via bluetooth connections.

PubMed

Merler, Stefano; Jurman, Giuseppe

2013-01-01

We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression.

A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology.

PubMed

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology.

A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology

PubMed Central

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

2017-01-01

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology. PMID:29267315

Examining the Relationships among Academic Self-Concept, Instrumental Motivation, and TIMSS 2007 Science Scores: A Cross-Cultural Comparison of Five East Asian Countries/Regions and the United States

ERIC Educational Resources Information Center

Yu, Chong Ho

2012-01-01

Many American authors expressed their concern that US competitiveness in science, technology, engineering, and mathematics (STEM) is losing ground. Using the Trends in International Mathematics and Science Study (TIMSS) 2007 data, this study investigated how academic self-concept and instrumental motivation influence science test performance among…

Test Content Specifications for the Survey of Basic Skills; Mathematics, Grades Six and Twelve.

ERIC Educational Resources Information Center

California State Dept. of Education, Sacramento.

Under the California Assembly Bill 665 of 1972, the state assessment program must test all students in grades 1, 2, 3, 6, and 12 in reading skills, and those in grades 6 and 12 to assess their skills in effectiveness of written expression, spelling, and mathematics. The state may develop its own tests, and a matrix sampling approach may be used…

Specialized Silicon Compilers for Language Recognition.

DTIC Science & Technology

1984-07-01

realizations of non-deterministic automata have been reported that solve these problems in diffierent ways. Floyd and Ullman [ 281 have presented a...in Applied Mathematics, pages 19-31. American Mathematical Society, 1967. [ 281 Floyd, R. W. and J. D. Ullman. The Compilation of Regular Expressions...Shannon (editor). Automata Studies, chapter 1, pages 3-41. Princeton University Press, Princeton. N. J., 1956. [44] Kohavi, Zwi . Switching and Finite

Mathematics Evaluation Procedures K-2. For Use by Teachers With Children in Years K-4.

ERIC Educational Resources Information Center

Australian Council for Educational Research, Hawthorn.

This book was written in response to a need expressed by Infant's Mistresses in the North Sydney Region of the New South Wales Department of Education. They felt there was a need to evaluate children's progress in mathematics in order to diagnose the causes of individual failures, and they discovered there was no readily available information on…

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb-Zn Deposit in Dangchang County, Gansu Province

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Jin-zhong, E-mail: viewsino@163.com; Yao, Shu-zhen; Zhang, Zhong-ping

2013-03-15

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb-Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seenmore » as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.« less

Foundations of mathematics and literacy: The role of executive functioning components.

PubMed

Purpura, David J; Schmitt, Sara A; Ganley, Colleen M

2017-01-01

The current study investigated the relations between the three cognitive processes that comprise executive functioning (EF)-response inhibition, working memory, and cognitive flexibility-and individual components of mathematics and literacy skills in preschool children. Participants were 125 preschool children ranging in age from 3.12 to 5.26years (M=4.17years, SD=0.58). Approximately 53.2% were female, and the sample was predominantly Caucasian (69.8%). Results suggest that the components of EF may be differentially related to the specific components of early mathematics and literacy. For mathematics, response inhibition was broadly related to most components. Working memory was related to more advanced mathematics skills that involve comparison or combination of numbers and quantities. Cognitive flexibility was related to more conceptual or abstract mathematics skills. For early literacy, response inhibition and cognitive flexibility were related to print knowledge, and working memory was related only to phonological awareness. None of the EF components was related to vocabulary. These findings provide initial evidence for better understanding the ways in which EF components and academic skills are related and measured. Furthermore, the findings provide a foundation for further study of the components of each domain using a broader and more diverse array of measures. Copyright © 2016 Elsevier Inc. All rights reserved.

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

Effectiveness of the High Dose/Refuge Strategy for Managing Pest Resistance to Bacillus thuringiensis (Bt) Plants Expressing One or Two Toxins

PubMed Central

Gryspeirt, Aiko; Grégoire, Jean-Claude

2012-01-01

To delay resistance development to Bacillus thuringiensis (Bt) plants expressing their own insecticide, the application of the Insect Resistance Management strategy called “High Dose/Refuge Strategy” (HD/R) is recommended by the US Environmental Protection Agency (US EPA). This strategy was developed for Bt plants expressing one toxin. Presently, however, new Bt plants that simultaneously express two toxins are on the market. We used a mathematical model to evaluate the efficiency of the HD/R strategy for both these Bt toxins. As the current two-toxin Bt plants do not express two new Cry toxins but reuse one toxin already in use with a one-toxin plant, we estimated the spread of resistance when the resistance alleles are not rare. This study assesses: (i) whether the two toxins have to be present in high concentration, and (ii) the impact of the relative size of the refuge zone on the evolution of resistance and population density. We concluded that for Bt plants expressing one toxin, a high concentration is an essential condition for resistance management. For the pyramided Bt plants, one toxin could be expressed at a low titer if the two toxins are used for the first time, and a small refuge zone is acceptable. PMID:23162699

Effectiveness of the high dose/refuge strategy for managing pest resistance to Bacillus thuringiensis (Bt) plants expressing one or two toxins.

PubMed

Gryspeirt, Aiko; Grégoire, Jean-Claude

2012-10-01

To delay resistance development to Bacillus thuringiensis (Bt) plants expressing their own insecticide, the application of the Insect Resistance Management strategy called "High Dose/Refuge Strategy" (HD/R) is recommended by the US Environmental Protection Agency (US EPA). This strategy was developed for Bt plants expressing one toxin. Presently, however, new Bt plants that simultaneously express two toxins are on the market. We used a mathematical model to evaluate the efficiency of the HD/R strategy for both these Bt toxins. As the current two-toxin Bt plants do not express two new Cry toxins but reuse one toxin already in use with a one-toxin plant, we estimated the spread of resistance when the resistance alleles are not rare. This study assesses: (i) whether the two toxins have to be present in high concentration, and (ii) the impact of the relative size of the refuge zone on the evolution of resistance and population density. We concluded that for Bt plants expressing one toxin, a high concentration is an essential condition for resistance management. For the pyramided Bt plants, one toxin could be expressed at a low titer if the two toxins are used for the first time, and a small refuge zone is acceptable.

Attitudinal and Motivational Variables Related to Mathematics Achievement in Jordan: Findings from the Third International Mathematics and Science Study (TIMSS)

ERIC Educational Resources Information Center

Hammouri, Hind

2004-01-01

The purpose of the present study was to examine the effects of student-related variables on achievement in mathematics. The sample consisted of 3736 13-year-old Jordanian 8th-graders who participated in the Third International Mathematics and Science Study (TIMSS). The participants completed a student questionnaire and participated in the…

Peirce's Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry

ERIC Educational Resources Information Center

Campos, Daniel G.

2010-01-01

I articulate Charles S. Peirce's philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce's philosophy of mathematical education primarily aims at fostering the development of the…

African American Mathematics Teachers as Agents in Their African American Students' Mathematics Identity Formation

ERIC Educational Resources Information Center

Clark, Lawrence M.; Badertscher, Eden M.; Napp, Carolina

2013-01-01

Background/Context: Recent research in mathematics education has employed sociocultural and historical lenses to better understand how students experience school mathematics and come to see themselves as capable mathematics learners. This work has identified mathematics classrooms as places where power struggles related to students'…

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Elementary Pre-Service Teachers' Mathematics Anxiety and Mathematics Teaching Anxiety

ERIC Educational Resources Information Center

Haciomeroglu, Guney

2014-01-01

The present study examined the structure of elementary pre-service teachers' mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers.…

Teaching Mathematical Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

Adolescents' perceptions of socializers' beliefs, career-related conversations, and motivation in mathematics.

PubMed

Lazarides, Rebecca; Rubach, Charlott; Ittel, Angela

2017-03-01

Research based on the Eccles model of parent socialization demonstrated that parents are an important source of value and ability information for their children. Little is known, however, about the bidirectional effects between students' perceptions of their parents' beliefs and behaviors and the students' own domain-specific values. This study analyzed how students' perceptions of parents' beliefs and behaviors and students' mathematics values and mathematics-related career plans affect each other bidirectionally, and analyzed the role of students' gender as a moderator of these relations. Data from 475 students in 11th and 12th grade (girls: 50.3%; 31 classrooms; 12 schools), who participated in 2 waves of the study, were analyzed. Results of longitudinal structural equation models demonstrated that students' perceptions of their parents' mathematics value beliefs at Time 1 affected the students' own mathematics utility value at Time 2. Bidirectional effects were not shown in the full sample but were identified for boys. The paths within the tested model varied for boys and girls. For example, boys', not girls', mathematics intrinsic value predicted their reported conversations with their fathers about future occupational plans. Boys', not girls', perceived parents' mathematics value predicted the mathematics utility value. Findings are discussed in relation to their implications for parents and teachers, as well as in relation to gendered motivational processes. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Dependence of the firearm-related homicide rate on gun availability: a mathematical analysis.

PubMed

Wodarz, Dominik; Komarova, Natalia L

2013-01-01

In the USA, the relationship between the legal availability of guns and the firearm-related homicide rate has been debated. It has been argued that unrestricted gun availability promotes the occurrence of firearm-induced homicides. It has also been pointed out that gun possession can protect potential victims when attacked. This paper provides a first mathematical analysis of this tradeoff, with the goal to steer the debate towards arguing about assumptions, statistics, and scientific methods. The model is based on a set of clearly defined assumptions, which are supported by available statistical data, and is formulated axiomatically such that results do not depend on arbitrary mathematical expressions. According to this framework, two alternative scenarios can minimize the gun-related homicide rate: a ban of private firearms possession, or a policy allowing the general population to carry guns. Importantly, the model identifies the crucial parameters that determine which policy minimizes the death rate, and thus serves as a guide for the design of future epidemiological studies. The parameters that need to be measured include the fraction of offenders that illegally possess a gun, the degree of protection provided by gun ownership, and the fraction of the population who take up their right to own a gun and carry it when attacked. Limited data available in the literature were used to demonstrate how the model can be parameterized, and this preliminary analysis suggests that a ban of private firearm possession, or possibly a partial reduction in gun availability, might lower the rate of firearm-induced homicides. This, however, should not be seen as a policy recommendation, due to the limited data available to inform and parameterize the model. However, the model clearly defines what needs to be measured, and provides a basis for a scientific discussion about assumptions and data.

Analysis and modelling of septic shock microarray data using Singular Value Decomposition.

PubMed

Allanki, Srinivas; Dixit, Madhulika; Thangaraj, Paul; Sinha, Nandan Kumar

2017-06-01

Being a high throughput technique, enormous amounts of microarray data has been generated and there arises a need for more efficient techniques of analysis, in terms of speed and accuracy. Finding the differentially expressed genes based on just fold change and p-value might not extract all the vital biological signals that occur at a lower gene expression level. Besides this, numerous mathematical models have been generated to predict the clinical outcome from microarray data, while very few, if not none, aim at predicting the vital genes that are important in a disease progression. Such models help a basic researcher narrow down and concentrate on a promising set of genes which leads to the discovery of gene-based therapies. In this article, as a first objective, we have used the lesser known and used Singular Value Decomposition (SVD) technique to build a microarray data analysis tool that works with gene expression patterns and intrinsic structure of the data in an unsupervised manner. We have re-analysed a microarray data over the clinical course of Septic shock from Cazalis et al. (2014) and have shown that our proposed analysis provides additional information compared to the conventional method. As a second objective, we developed a novel mathematical model that predicts a set of vital genes in the disease progression that works by generating samples in the continuum between health and disease, using a simple normal-distribution-based random number generator. We also verify that most of the predicted genes are indeed related to septic shock. Copyright © 2017 Elsevier Inc. All rights reserved.

A Modeling and Experimental Investigation of the Effects of Antigen Density, Binding Affinity, and Antigen Expression Ratio on Bispecific Antibody Binding to Cell Surface Targets.

PubMed

Rhoden, John J; Dyas, Gregory L; Wroblewski, Victor J

2016-05-20

Despite the increasing number of multivalent antibodies, bispecific antibodies, fusion proteins, and targeted nanoparticles that have been generated and studied, the mechanism of multivalent binding to cell surface targets is not well understood. Here, we describe a conceptual and mathematical model of multivalent antibody binding to cell surface antigens. Our model predicts that properties beyond 1:1 antibody:antigen affinity to target antigens have a strong influence on multivalent binding. Predicted crucial properties include the structure and flexibility of the antibody construct, the target antigen(s) and binding epitope(s), and the density of antigens on the cell surface. For bispecific antibodies, the ratio of the expression levels of the two target antigens is predicted to be critical to target binding, particularly for the lower expressed of the antigens. Using bispecific antibodies of different valencies to cell surface antigens including MET and EGF receptor, we have experimentally validated our modeling approach and its predictions and observed several nonintuitive effects of avidity related to antigen density, target ratio, and antibody affinity. In some biological circumstances, the effect we have predicted and measured varied from the monovalent binding interaction by several orders of magnitude. Moreover, our mathematical framework affords us a mechanistic interpretation of our observations and suggests strategies to achieve the desired antibody-antigen binding goals. These mechanistic insights have implications in antibody engineering and structure/activity relationship determination in a variety of biological contexts. © 2016 by The American Society for Biochemistry and Molecular Biology, Inc.

Comparing the Effects of Representational Tools in Collaborative and Individual Inquiry Learning

ERIC Educational Resources Information Center

Kolloffel, Bas; Eysink, Tessa H. S.; de Jong, Ton

2011-01-01

Constructing a representation in which students express their domain understanding can help them improve their knowledge. Many different representational formats can be used to express one's domain understanding (e.g., concept maps, textual summaries, mathematical equations). The format can direct students' attention to specific aspects of the…

A Combinatorial Model of Malware Diffusion via Bluetooth Connections

PubMed Central

Merler, Stefano; Jurman, Giuseppe

2013-01-01

We outline here the mathematical expression of a diffusion model for cellphones malware transmitted through Bluetooth channels. In particular, we provide the deterministic formula underlying the proposed infection model, in its equivalent recursive (simple but computationally heavy) and closed form (more complex but efficiently computable) expression. PMID:23555677

The contribution of executive functions to emergent mathematic skills in preschool children.

PubMed

Espy, Kimberly Andrews; McDiarmid, Melanie M; Cwik, Mary F; Stalets, Melissa Meade; Hamby, Arlena; Senn, Theresa E

2004-01-01

Mathematical ability is related to both activation of the prefrontal cortex in neuroimaging studies of adults and to executive functions in school-age children. The purpose of this study was to determine whether executive functions were related to emergent mathematical proficiency in preschool children. Preschool children (N = 96) were administered an executive function battery that was reduced empirically to working memory (WM), inhibitory control (IC), and shifting abilities by calculating composite scores derived from principal component analysis. Both WM and IC predicted early arithmetic competency, with the observed relations robust after controlling statistically for child age, maternal education, and child vocabulary. Only IC accounted for unique variance in mathematical skills, after the contribution of other executive functions were controlled statistically as well. Specific executive functions are related to emergent mathematical proficiency in this age range. Longitudinal studies using structural equation modeling are necessary to better characterize these ontogenetic relations.

Explicit expressions of quantum mechanical rotation operators for spins 1 to 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kocakoç, Mehpeyker, E-mail: mkocakoc@cu.edu.tr; Tapramaz, Recep, E-mail: recept@omu.edu.tr

2016-03-25

Quantum mechanical rotation operators are the subject of quantum mechanics, mathematics and pulsed magnetic resonance spectroscopies, namely NMR, EPR and ENDOR. They are also necessary for spin based quantum information systems. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schrödinger equation, or by evaluating Wigner-d formula or by evaluating recently established expressions in polynomial forms discussed in the text. In this work, explicit symbolic expressions of x, y andmore » z components of rotation operators for spins 1 to 2 are worked out by evaluating series expansion of exponential operator for each element of operators and utilizing linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. The operators of spins greater than 2 are under study and will be published in a separate paper.« less

Study on the Effect of water Injection Momentum on the Cooling Effect of Rocket Engine Exhaust Plume

NASA Astrophysics Data System (ADS)

Yang, Kan; Qiang, Yanhui; Zhong, Chenghang; Yu, Shaozhen

2017-10-01

For the study of water injection momentum factors impact on flow field of the rocket engine tail flame, the numerical computation model of gas-liquid two phase flow in the coupling of high temperature and high speed gas flow and low temperature liquid water is established. The accuracy and reliability of the numerical model are verified by experiments. Based on the numerical model, the relationship between the flow rate and the cooling effect is analyzed by changing the water injection momentum of the water spray pipes. And the effective mathematical expression is obtained. What’s more, by changing the number of the water spray and using small flow water injection, the cooling effect is analyzed to check the application range of the mathematical expressions. The results show that: the impact and erosion of the gas flow field could be reduced greatly by water injection, and there are two parts in the gas flow field, which are the slow cooling area and the fast cooling area. In the fast cooling area, the influence of the water flow momentum and nozzle quantity on the cooling effect can be expressed by mathematical functions without causing bifurcation flow for the mainstream gas. The conclusion provides a theoretical reference for the engineering application.

Twenty Years Later: High School Students Who Showed Promise in Mathematics.

ERIC Educational Resources Information Center

Turner, Nura D.

1981-01-01

Data from longitudinal studies of high school students who took the Annual High School Mathematics Examination sponsored by the Mathematical Association of America (MAA) indicate that 56 percent of the top achievers pursued careers in mathematics or mathematically related fields. (MP)

Can government be self-organized? A mathematical model of the collective social organization of ancient Teotihuacan, central Mexico.

PubMed

Froese, Tom; Gershenson, Carlos; Manzanilla, Linda R

2014-01-01

Teotihuacan was the first urban civilization of Mesoamerica and one of the largest of the ancient world. Following a tradition in archaeology to equate social complexity with centralized hierarchy, it is widely believed that the city's origin and growth was controlled by a lineage of powerful individuals. However, much data is indicative of a government of co-rulers, and artistic traditions expressed an egalitarian ideology. Yet this alternative keeps being marginalized because the problems of collective action make it difficult to conceive how such a coalition could have functioned in principle. We therefore devised a mathematical model of the city's hypothetical network of representatives as a formal proof of concept that widespread cooperation was realizable in a fully distributed manner. In the model, decisions become self-organized into globally optimal configurations even though local representatives behave and modify their relations in a rational and selfish manner. This self-optimization crucially depends on occasional communal interruptions of normal activity, and it is impeded when sections of the network are too independent. We relate these insights to theories about community-wide rituals at Teotihuacan and the city's eventual disintegration.

Can Government Be Self-Organized? A Mathematical Model of the Collective Social Organization of Ancient Teotihuacan, Central Mexico

PubMed Central

Froese, Tom; Gershenson, Carlos; Manzanilla, Linda R.

2014-01-01

Teotihuacan was the first urban civilization of Mesoamerica and one of the largest of the ancient world. Following a tradition in archaeology to equate social complexity with centralized hierarchy, it is widely believed that the city’s origin and growth was controlled by a lineage of powerful individuals. However, much data is indicative of a government of co-rulers, and artistic traditions expressed an egalitarian ideology. Yet this alternative keeps being marginalized because the problems of collective action make it difficult to conceive how such a coalition could have functioned in principle. We therefore devised a mathematical model of the city’s hypothetical network of representatives as a formal proof of concept that widespread cooperation was realizable in a fully distributed manner. In the model, decisions become self-organized into globally optimal configurations even though local representatives behave and modify their relations in a rational and selfish manner. This self-optimization crucially depends on occasional communal interruptions of normal activity, and it is impeded when sections of the network are too independent. We relate these insights to theories about community-wide rituals at Teotihuacan and the city’s eventual disintegration. PMID:25303308

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

NASA Technical Reports Server (NTRS)

Ristorcelli, J. R.

1995-01-01

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

The expression and comparison of healthy and ptotic upper eyelid contours using a polynomial mathematical function.

PubMed

Mocan, Mehmet C; Ilhan, Hacer; Gurcay, Hasmet; Dikmetas, Ozlem; Karabulut, Erdem; Erdener, Ugur; Irkec, Murat

2014-06-01

To derive a mathematical expression for the healthy upper eyelid (UE) contour and to use this expression to differentiate the normal UE curve from its abnormal configuration in the setting of blepharoptosis. The study was designed as a cross-sectional study. Fifty healthy subjects (26M/24F) and 50 patients with blepharoptosis (28M/22F) with a margin-reflex distance (MRD1) of ≤2.5 mm were recruited. A polynomial interpolation was used to approximate UE curve. The polynomial coefficients were calculated from digital eyelid images of all participants using a set of operator defined points along the UE curve. Coefficients up to the fourth-order polynomial, iris area covered by the UE, iris area covered by the lower eyelid and total iris area covered by both the upper and the lower eyelids were defined using the polynomial function and used in statistical comparisons. The t-test, Mann-Whitney U test and the Spearman's correlation test were used for statistical comparisons. The mathematical expression derived from the data of 50 healthy subjects aged 24.1 ± 2.6 years was defined as y = 22.0915 + (-1.3213)x + 0.0318x(2 )+ (-0.0005x)(3). The fifth and the consecutive coefficients were <0.00001 in all cases and were not included in the polynomial function. None of the first fourth-order coefficients of the equation were found to be significantly different in male versus female subjects. In normal subjects, the percentage of the iris area covered by upper and lower lids was 6.46 ± 5.17% and 0.66% ± 1.62%, respectively. All coefficients and mean iris area covered by the UE were significantly different between healthy and ptotic eyelids. The healthy and abnormal eyelid contour can be defined and differentiated using a polynomial mathematical function.

Girls, Moms, and Math: A Study of the Relationship of Self and Maternal Attitudes towards Mathematics and Girls' Mathematical Success in an Affluent Suburban Community

ERIC Educational Resources Information Center

DeRosa, Ann T.

2011-01-01

This study focused on gender-based mathematics performance. It was a qualitative study of girls and their mothers conducted to identify variables that may to be associated with the success or lack of success of the girls. By examining maternal responses to mathematics-related questions, themes emerged that could be related to information gathered…

Is There a Relationship between Pre-Service Teachers' Mathematical Values and Their Teaching Anxiety in Mathematics?

ERIC Educational Resources Information Center

Yazici, Ersen; Peker, Murat; Ertekin, Erhan; Dilmac, Bulent

2011-01-01

Introduction: The aim of this study is to investigate the relation between the pre-service teachers' mathematical values and teaching anxieties in mathematics. Method: The research was carried out on 359 teacher candidates attending the elementary school mathematics, secondary school mathematics and primary school teaching programs. To this end,…

A Structural Analysis on Korean Young Children's Mathematical Ability and Its Related Children's and Mothers' Variables

ERIC Educational Resources Information Center

Lee, Hye Jung; Kim, Jihyun

2016-01-01

The objective of this study is to examine the structural relationships among variables that predict the mathematical ability of young children, namely young children's mathematical attitude, exposure to private mathematical learning, mothers' view about their children's mathematical learning, and mothers' mathematical attitude. To this end, we…

From Searle's Chinese Room to the Mathematics Classroom: Technical and Cognitive Mathematics

ERIC Educational Resources Information Center

Gavalas, Dimitris

2007-01-01

Employing Searle's views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call "Cognitive Mathematics" and "Technical Mathematics" respectively. The former type relates to concepts and meanings, logic and sense, whilst the…

Mathematical Knowledge for Teaching, Standards-Based Mathematics Teaching Practices, and Student Achievement in the Context of the "Responsive Classroom Approach"

ERIC Educational Resources Information Center

Ottmar, Erin R.; Rimm-Kaufman, Sara E.; Larsen, Ross A.; Berry, Robert Q.

2015-01-01

This study investigates the effectiveness of the Responsive Classroom (RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was…

Achievement of Eighth-Grade Students in Korea on the TIMSS 2011 Assessment: Effects of Confidence in Mathematics and Engagement in Mathematics Lessons

ERIC Educational Resources Information Center

House, J. Daniel; Telese, James A.

2016-01-01

Research studies have identified several factors related to mathematics achievement of students in Korea. Further, results from the Trends in International Mathematics and Science Study (TIMSS) assessments have shown that instructional practices and beliefs about mathematics were significantly associated with mathematics achievement of students in…

Relations between Mathematical Knowledge for Teaching, Mathematics Instructional Quality, and Student Achievement in the Context of the "Responsive Classroom (RC)" Approach

ERIC Educational Resources Information Center

Ottmar, Erin R.; Rimm-Kaufman, Sara E.; Larsen, Ross; Merritt, Eileen G.

2011-01-01

Despite over thirty years of theoretically based research investigating "how" teacher mathematical knowledge and instructional practice relate to student learning, it is still largely unclear how these constructs are related, and policy makers and practitioners are still situated in a context with insufficient data to make decisions. Thus, there…

An Evaluation of an Elementary Mathematics Program at a Medium-Sized Suburban School District in North Carolina

ERIC Educational Resources Information Center

Honeycutt, Robin A.

2013-01-01

Math instruction has undergone a tremendous amount of change since the late 1950s. "New math" of the 1960s, the standards movement, back to the basics in the early 90s, and now the common core standards have all had an impact on how mathematics is taught. This study examined the Math Expressions program, a conceptually based program…

Timescales and bottlenecks in miRNA-dependent gene regulation.

PubMed

Hausser, Jean; Syed, Afzal Pasha; Selevsek, Nathalie; van Nimwegen, Erik; Jaskiewicz, Lukasz; Aebersold, Ruedi; Zavolan, Mihaela

2013-12-03

MiRNAs are post-transcriptional regulators that contribute to the establishment and maintenance of gene expression patterns. Although their biogenesis and decay appear to be under complex control, the implications of miRNA expression dynamics for the processes that they regulate are not well understood. We derived a mathematical model of miRNA-mediated gene regulation, inferred its parameters from experimental data sets, and found that the model describes well time-dependent changes in mRNA, protein and ribosome density levels measured upon miRNA transfection and induction. The inferred parameters indicate that the timescale of miRNA-dependent regulation is slower than initially thought. Delays in miRNA loading into Argonaute proteins and the slow decay of proteins relative to mRNAs can explain the typically small changes in protein levels observed upon miRNA transfection. For miRNAs to regulate protein expression on the timescale of a day, as miRNAs involved in cell-cycle regulation do, accelerated miRNA turnover is necessary.

Literacy in Language and Mathematics: More in Common Than You Think

ERIC Educational Resources Information Center

Thompson, Denisse R.; Rubenstein, Rheta N.

2014-01-01

This paper shares perspectives on literacy in mathematics, particularly highlighting commonalities with literacy in language arts. We discuss levels of language development appropriate for the mathematics classroom, issues related to mathematical definitions, implied meanings in many mathematics concepts, and the importance of justification. We…

Neural correlates of mathematical problem solving.

PubMed

Lin, Chun-Ling; Jung, Melody; Wu, Ying Choon; She, Hsiao-Ching; Jung, Tzyy-Ping

2015-03-01

This study explores electroencephalography (EEG) brain dynamics associated with mathematical problem solving. EEG and solution latencies (SLs) were recorded as 11 neurologically healthy volunteers worked on intellectually challenging math puzzles that involved combining four single-digit numbers through basic arithmetic operators (addition, subtraction, division, multiplication) to create an arithmetic expression equaling 24. Estimates of EEG spectral power were computed in three frequency bands - θ (4-7 Hz), α (8-13 Hz) and β (14-30 Hz) - over a widely distributed montage of scalp electrode sites. The magnitude of power estimates was found to change in a linear fashion with SLs - that is, relative to a base of power spectrum, theta power increased with longer SLs, while alpha and beta power tended to decrease. Further, the topographic distribution of spectral fluctuations was characterized by more pronounced asymmetries along the left-right and anterior-posterior axes for solutions that involved a longer search phase. These findings reveal for the first time the topography and dynamics of EEG spectral activities important for sustained solution search during arithmetical problem solving.

A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155

Systematic misestimation of cell subpopulations by flow cytometry: a mathematical analysis.

PubMed

Petrunkina, A M; Harrison, R A P

2010-04-15

Various sources of variability in flow cytometric determination of cell concentration have previously been investigated with respect to andrologic applications. Although common aspects related to the variation between samples, variation between operators, and accuracy have been extensively studied, specific sources of false-count estimation have found less attention. In particular, a major and well-recognized source of misestimation of cell counts (i.e., contamination of the sample by non-sperm particles) has not to date been characterized in detail. We show here by means of original mathematical research that not only the cell counts but also the percentages of cells expressing different fluorescence patterns are affected by the presence of alien particles often neglected in studies involving flow cytometric characterization. We demonstrate that there is a systematic overestimation in the proportion of unstained (viable) cells detected by flow cytometry in cases where the non-sperm particles are not excluded from analysis by additional identification other than light-scatter characteristics. Moreover, we provide an exact mathematical estimate for the magnitude of this overestimation, and we discuss the consequences for diagnostic applications and studies on sperm physiology, specifically for studies on sperm capacitation and evaluation of cryopreserved semen. Finally, equations are derived for the correction of the flow cytometric values for use in practical applications. Copyright 2010 Elsevier Inc. All rights reserved.

Analytical expressions for noise and crosstalk voltages of the High Energy Silicon Particle Detector

NASA Astrophysics Data System (ADS)

Yadav, I.; Shrimali, H.; Liberali, V.; Andreazza, A.

2018-01-01

The paper presents design and implementation of a silicon particle detector array with the derived closed form equations of signal-to-noise ratio (SNR) and crosstalk voltages. The noise analysis demonstrates the effect of interpixel capacitances (IPC) between center pixel (where particle hits) and its neighbouring pixels, resulting as a capacitive crosstalk. The pixel array has been designed and simulated in a 180 nm BCD technology of STMicroelectronics. The technology uses the supply voltage (VDD) of 1.8 V and the substrate potential of -50 V. The area of unit pixel is 250×50 μm2 with the substrate resistivity of 125 Ωcm and the depletion depth of 30 μm. The mathematical model includes the effects of various types of noise viz. the shot noise, flicker noise, thermal noise and the capacitive crosstalk. This work compares the results of noise and crosstalk analysis from the proposed mathematical model with the circuit simulation results for a given simulation environment. The results show excellent agreement with the circuit simulations and the mathematical model. The average relative error (AVR) generated for the noise spectral densities with respect to the simulations and the model is 12% whereas the comparison gives the errors of 3% and 11.5% for the crosstalk voltages and the SNR results respectively.

Mathematical Caring Relations: A Challenging Case

ERIC Educational Resources Information Center

Hackenberg, Amy

2010-01-01

Developed from Noddings's (2002) care theory, von Glasersfeld's (1995) constructivism, and Ryan and Frederick's (1997) notion of subjective vitality, a mathematical caring relation (MCR) is a quality of interaction between a student and a mathematics teacher that conjoins affective and cognitive realms in the process of aiming for mathematical…

Construction Industry Related Mathematics: Seventh Grade.

ERIC Educational Resources Information Center

Mundell, Scott

The field tested construction industry-related mathematics unit is intended to familiarize seventh grade students with various facets of the construction industry, including the various occupations available and the mathematical abilities and other skills and training necessary to pursue an occupation in the industry. The final set of activities…

"Effective" Mathematics Teaching of African American Adolescents and the Development of a Mathematics Identity

ERIC Educational Resources Information Center

Green, Marcus Allen

2016-01-01

In order to increase mathematics achievement, persistence, and participation in mathematics-related careers and majors for African American adolescents, researchers have discussed the need for students to develop positive mathematical identities (English-Clarke, Slaughter-Defoe, & Martin, 2012; Gutstein, 2003; Larnell, 2013; Martin, 2000,…

Abstraction in Mathematics and Mathematics Learning

ERIC Educational Resources Information Center

Mitchelmore, Michael; White, Paul

2004-01-01

It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as "abstract-apart." On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called "abstract-general" because they embody…

The Mathematical Sciences: A Report.

ERIC Educational Resources Information Center

National Academy of Sciences, Washington, DC.

Presented are position statements for the support of the mathematical sciences and a description of the present state of both research and education in mathematics and related disciplines. The report calls attention to the penetration of mathematics and mathematical modes of thought into many new areas of scholarship and the resultant increase in…

Locating Mathematics within Post-16 Vocational Education in England

ERIC Educational Resources Information Center

Dalby, Diane; Noyes, Andrew

2016-01-01

The political importance of mathematics in post-16 education is clear. Far less clear is how mathematics does and should relate to vocational education. Successive mathematics curricula (e.g. core skills, key skills) have been developed in England with vocational learners in mind. Meanwhile, general mathematics qualifications remain largely…

Why Do Early Mathematics Skills Predict Later Reading? The Role of Mathematical Language

ERIC Educational Resources Information Center

Purpura, David J.; Logan, Jessica A. R.; Hassinger-Das, Brenna; Napoli, Amy R.

2017-01-01

A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills--specifically language--for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy…

Faces of matrix models

NASA Astrophysics Data System (ADS)

Morozov, A.

2012-08-01

Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and nonlinear equations, as τ-functions of integrable hierarchies and as special-geometry prepotentials, as result of the action of W-operators and of various recursions on elementary input data, as gluing of certain elementary building blocks. All this explains the central role of such matrix models in modern mathematical physics: they provide the basic "special functions" to express the answers and relations between them, and they serve as a dream model of what one should try to achieve in any other field.

Space-Time, Phenomenology, and the Picture Theory of Language

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

To estimate Minkowski's introduction of space-time in relativity, the case is made for the view that abstract language and mathematics carries meaning not only by its connections with observation but as pictures of facts. This view is contrasted to the more traditional intuitionism of Hume, Mach, and Husserl. Einstein's attempt at a conceptual reconstruction of space and time as well as Husserl's analysis of the loss of meaning in science through increasing abstraction is analysed. Wittgenstein's picture theory of language is used to explain how meaning is conveyed by abstract expressions, with the Minkowski space as a case.

Simulation of noise involved in synthetic aperture radar

NASA Astrophysics Data System (ADS)

Grandchamp, Myriam; Cavassilas, Jean-Francois

1996-08-01

The synthetic aperture radr (SAR) returns from a linear distribution of scatterers are simulated and processed in order to estimate the reflectivity coefficients of the ground. An original expression of this estimate is given, which establishes the relation between the terms of signal and noise. Both are compared. One application of this formulation consists of detecting a surface ship wake on a complex SAR image. A smoothing is first accomplished on the complex image. The choice of the integration area is determined by the preceding mathematical formulation. Then a differential filter is applied, and results are shown for two parts of the wake.

Longitudinal Associations between Executive Control and Developing Mathematical Competence in Preschool Boys and Girls

PubMed Central

Clark, Caron A.C.; Sheffield, Tiffany D.; Wiebe, Sandra A.; Espy, Kimberly Andrews

2012-01-01

Executive control (EC) is related to mathematics performance in middle childhood. However, little is known regarding how EC and informal numeracy differentially support mathematics skill acquisition in preschoolers. A sample of preschoolers (115 girls, 113 boys), stratified by social risk, completed an EC task battery at 3 years, informal numeracy assessments at 3.75 and 4.5 years, and a broad mathematics assessment during kindergarten. Strong associations were observed between latent EC at 3 and mathematics achievement in kindergarten, which remained robust after accounting for earlier informal numeracy, socio-economic status, language and processing speed. Relations between EC and mathematics achievement were stronger in girls than boys. Findings highlight the unique role of EC in predicting which children may have difficulty transitioning to formal mathematics instruction. PMID:23006040

When Do Girls Prefer Football to Fashion? An Analysis of Female Underachievement in Relation to "Realistic" Mathematics Context.

ERIC Educational Resources Information Center

Boaler, Jo

1994-01-01

Reports on a study of the move away from abstract calculations toward "mathematics in context" among 50 British female secondary school students. Discusses implications of findings in relation to reported female underachievement and disinterest in school mathematics. (CFR)

Preservice Mathematics Teachers' Experiences about Function and Equation Concepts

ERIC Educational Resources Information Center

Dede, Yuksel; Soybas, Danyal

2011-01-01

The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were…

On Relative and Absolute Conviction in Mathematics

ERIC Educational Resources Information Center

Weber, Keith; Mejia-Ramos, Juan Pablo

2015-01-01

Conviction is a central construct in mathematics education research on justification and proof. In this paper, we claim that it is important to distinguish between absolute conviction and relative conviction. We argue that researchers in mathematics education frequently have not done so and this has lead to researchers making unwarranted claims…

Mathematical Thinking: Challenging Prospective Teachers to Do More than "Talk the Talk"

ERIC Educational Resources Information Center

Prendergast, Mark; Johnson, Patrick; Fitzmaurice, Olivia; Liston, Miriam; O'Keeffe, Lisa; O'Meara, Niamh

2014-01-01

This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of…

An Investigation of Elementary Preservice Teachers' Self-Efficacy for Teaching Mathematics

ERIC Educational Resources Information Center

Giles, Rebecca McMahon; Byrd, Kelly O.; Bendolph, Angelia

2016-01-01

Research has consistently shown that teacher efficacy is related to a variety of desirable student outcomes, thus, making teacher efficacy an important factor in high quality mathematics instruction. The purpose of this study was to determine elementary preservice teachers' self-efficacy beliefs related to teaching mathematics. Forty-one…

Origins of the brain networks for advanced mathematics in expert mathematicians

PubMed Central

Amalric, Marie; Dehaene, Stanislas

2016-01-01

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124

Origins of the brain networks for advanced mathematics in expert mathematicians.

PubMed

Amalric, Marie; Dehaene, Stanislas

2016-05-03

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.

Mathematical Modeling of RNA-Based Architectures for Closed Loop Control of Gene Expression.

PubMed

Agrawal, Deepak K; Tang, Xun; Westbrook, Alexandra; Marshall, Ryan; Maxwell, Colin S; Lucks, Julius; Noireaux, Vincent; Beisel, Chase L; Dunlop, Mary J; Franco, Elisa

2018-05-08

Feedback allows biological systems to control gene expression precisely and reliably, even in the presence of uncertainty, by sensing and processing environmental changes. Taking inspiration from natural architectures, synthetic biologists have engineered feedback loops to tune the dynamics and improve the robustness and predictability of gene expression. However, experimental implementations of biomolecular control systems are still far from satisfying performance specifications typically achieved by electrical or mechanical control systems. To address this gap, we present mathematical models of biomolecular controllers that enable reference tracking, disturbance rejection, and tuning of the temporal response of gene expression. These controllers employ RNA transcriptional regulators to achieve closed loop control where feedback is introduced via molecular sequestration. Sensitivity analysis of the models allows us to identify which parameters influence the transient and steady state response of a target gene expression process, as well as which biologically plausible parameter values enable perfect reference tracking. We quantify performance using typical control theory metrics to characterize response properties and provide clear selection guidelines for practical applications. Our results indicate that RNA regulators are well-suited for building robust and precise feedback controllers for gene expression. Additionally, our approach illustrates several quantitative methods useful for assessing the performance of biomolecular feedback control systems.

H∞ robust fault-tolerant controller design for an autonomous underwater vehicle's navigation control system

NASA Astrophysics Data System (ADS)

Cheng, Xiang-Qin; Qu, Jing-Yuan; Yan, Zhe-Ping; Bian, Xin-Qian

2010-03-01

In order to improve the security and reliability for autonomous underwater vehicle (AUV) navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain. Operating conditions and the design method were then analyzed so that the control problem could be expressed as a mathematical optimization problem. This permitted the use of linear matrix inequalities (LMI) to solve for the H∞ controller for the system. When considering different actuator failures, these conditions were then also mathematically expressed, allowing the H∞ robust controller to solve for these events and thus be fault-tolerant. Finally, simulation results showed that the H∞ robust fault-tolerant controller could provide precise AUV navigation control with strong robustness.

Simple, Flexible, Trigonometric Taper Equations

Treesearch

Charles E. Thomas; Bernard R. Parresol

1991-01-01

There have been numerous approaches to modeling stem form in recent decades. The majority have concentrated on the simpler coniferous bole form and have become increasingly complex mathematical expressions. Use of trigonometric equations provides a simple expression of taper that is flexible enough to fit both coniferous and hard-wood bole forms. As an illustration, we...

Creativity in Teaching: What Can Teachers Learn from Artists?

ERIC Educational Resources Information Center

Hall, Christine; Thomson, Pat

2017-01-01

Since the turn of the century, there have been frequent expressions of concern about a perceived lack of creativity in UK schools, in both curriculum content and in teaching. Recently, as the emphasis on mathematics, science and technology has strengthened, serious concerns have also been expressed about the marginalisation of the arts and…

Articulating Syntactic and Numeric Perspectives on Equivalence: The Case of Rational Expressions

ERIC Educational Resources Information Center

Solares, Armando; Kieran, Carolyn

2013-01-01

Our study concerns the conceptual mathematical knowledge that emerges during the resolution of tasks on the equivalence of polynomial and rational algebraic expressions, by using CAS and paper-and-pencil techniques. The theoretical framework we adopt is the Anthropological Theory of Didactics ("Chevallard" 19:221-266, 1999), in…

Genetic Networks and Anticipation of Gene Expression Patterns

NASA Astrophysics Data System (ADS)

Gebert, J.; Lätsch, M.; Pickl, S. W.; Radde, N.; Weber, G.-W.; Wünschiers, R.

2004-08-01

An interesting problem for computational biology is the analysis of time-series expression data. Here, the application of modern methods from dynamical systems, optimization theory, numerical algorithms and the utilization of implicit discrete information lead to a deeper understanding. In [1], we suggested to represent the behavior of time-series gene expression patterns by a system of ordinary differential equations, which we analytically and algorithmically investigated under the parametrical aspect of stability or instability. Our algorithm strongly exploited combinatorial information. In this paper, we deepen, extend and exemplify this study from the viewpoint of underlying mathematical modelling. This modelling consists in evaluating DNA-microarray measurements as the basis of anticipatory prediction, in the choice of a smooth model given by differential equations, in an approach of the right-hand side with parametric matrices, and in a discrete approximation which is a least squares optimization problem. We give a mathematical and biological discussion, and pay attention to the special case of a linear system, where the matrices do not depend on the state of expressions. Here, we present first numerical examples.

Thermostatistical description of gas mixtures from space partitions

NASA Astrophysics Data System (ADS)

Rohrmann, R. D.; Zorec, J.

2006-10-01

The new mathematical framework based on the free energy of pure classical fluids presented by Rohrmann [Physica A 347, 221 (2005)] is extended to multicomponent systems to determine thermodynamic and structural properties of chemically complex fluids. Presently, the theory focuses on D -dimensional mixtures in the low-density limit (packing factor η<0.01 ). The formalism combines the free-energy minimization technique with space partitions that assign an available volume v to each particle. v is related to the closeness of the nearest neighbor and provides a useful tool to evaluate the perturbations experimented by particles in a fluid. The theory shows a close relationship between statistical geometry and statistical mechanics. New, unconventional thermodynamic variables and mathematical identities are derived as a result of the space division. Thermodynamic potentials μil , conjugate variable of the populations Nil of particles class i with the nearest neighbors of class l are defined and their relationships with the usual chemical potentials μi are established. Systems of hard spheres are treated as illustrative examples and their thermodynamics functions are derived analytically. The low-density expressions obtained agree nicely with those of scaled-particle theory and Percus-Yevick approximation. Several pair distribution functions are introduced and evaluated. Analytical expressions are also presented for hard spheres with attractive forces due to Kac-tails and square-well potentials. Finally, we derive general chemical equilibrium conditions.

Falling head ponded infiltration in the nonlinear limit

NASA Astrophysics Data System (ADS)

Triadis, D.

2014-12-01

The Green and Ampt infiltration solution represents only an extreme example of behavior within a larger class of very nonlinear, delta function diffusivity soils. The mathematical analysis of these soils is greatly simplified by the existence of a sharp wetting front below the soil surface. Solutions for more realistic delta function soil models have recently been presented for infiltration under surface saturation without ponding. After general formulation of the problem, solutions for a full suite of delta function soils are derived for ponded surface water depleted by infiltration. Exact expressions for the cumulative infiltration as a function of time, or the drainage time as a function of the initial ponded depth may take implicit or parametric forms, and are supplemented by simple asymptotic expressions valid for small times, and small and large initial ponded depths. As with surface saturation without ponding, the Green-Ampt model overestimates the effect of the soil hydraulic conductivity. At the opposing extreme, a low-conductivity model is identified that also takes a very simple mathematical form and appears to be more accurate than the Green-Ampt model for larger ponded depths. Between these two, the nonlinear limit of Gardner's soil is recommended as a physically valid first approximation. Relative discrepancies between different soil models are observed to reach a maximum for intermediate values of the dimensionless initial ponded depth, and in general are smaller than for surface saturation without ponding.

Understanding ferromagnetic hysteresis: A theoretical approach

NASA Astrophysics Data System (ADS)

Gangopadhyay, Bijan Kumar

2018-05-01

This work presents a theoretical-mathematical model for the ferromagnetic hysteresis. Theoretical understanding on ferromagnetism can be achieved through addressing the self-interaction propensity between the magnetic dipole moments associated with the magnetic domains, in conjunction with the pinning effects of the dipoles with the defects in the domain sites. An expression which relates ferromagnetic magnetization to the effective magnetic field was established in our previous work (AIP Conference Proceedings 1665, 130042 (2015)). Using this relation and solving for the reversible and the irreversible components of the magnetization, we successfully show that the magnetic saturation and the magnetic remanence can be achieved theoretically. This work also estimates the range of the external field that can be used to trace a reversible M-H curve.

Application of symbolic computations to the constitutive modeling of structural materials

NASA Technical Reports Server (NTRS)

Arnold, Steven M.; Tan, H. Q.; Dong, X.

1990-01-01

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia.

PubMed

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (= negative math priming effect ).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task.

Relation Between Mathematical Performance, Math Anxiety, and Affective Priming in Children With and Without Developmental Dyscalculia

PubMed Central

Kucian, Karin; Zuber, Isabelle; Kohn, Juliane; Poltz, Nadine; Wyschkon, Anne; Esser, Günter; von Aster, Michael

2018-01-01

Many children show negative emotions related to mathematics and some even develop mathematics anxiety. The present study focused on the relation between negative emotions and arithmetical performance in children with and without developmental dyscalculia (DD) using an affective priming task. Previous findings suggested that arithmetic performance is influenced if an affective prime precedes the presentation of an arithmetic problem. In children with DD specifically, responses to arithmetic operations are supposed to be facilitated by both negative and mathematics-related primes (=negative math priming effect).We investigated mathematical performance, math anxiety, and the domain-general abilities of 172 primary school children (76 with DD and 96 controls). All participants also underwent an affective priming task which consisted of the decision whether a simple arithmetic operation (addition or subtraction) that was preceded by a prime (positive/negative/neutral or mathematics-related) was true or false. Our findings did not reveal a negative math priming effect in children with DD. Furthermore, when considering accuracy levels, gender, or math anxiety, the negative math priming effect could not be replicated. However, children with DD showed more math anxiety when explicitly assessed by a specific math anxiety interview and showed lower mathematical performance compared to controls. Moreover, math anxiety was equally present in boys and girls, even in the earliest stages of schooling, and interfered negatively with performance. In conclusion, mathematics is often associated with negative emotions that can be manifested in specific math anxiety, particularly in children with DD. Importantly, present findings suggest that in the assessed age group, it is more reliable to judge math anxiety and investigate its effects on mathematical performance explicitly by adequate questionnaires than by an affective math priming task. PMID:29755376

Mathematics Self-Efficacy and Mistake-Handling Learning as Predictors of Mathematics Anxiety

ERIC Educational Resources Information Center

Aksu, Zeki; Ozkaya, Merve; Gedik, Solmaz Damla; Konyalioglu, Alper Cihan

2016-01-01

This study aims to analyze the relationship between secondary school seventh grade students' perception of mathematical self-efficacy, mistake-handling learning awareness, and mathematical anxiety; and to define the power of mistake-handling learning and self-efficacy in predicting mathematical anxiety. In this study, relational model was used and…

The Use of Teachers' Baseline Normative Beliefs to Guide Professional Development in Teaching Mathematics

ERIC Educational Resources Information Center

Lloyd, Mary Elizabeth Riley; Veal, William; Howell, Malia

2016-01-01

This article describes the normative beliefs and the discursive claims related to mathematics and teaching mathematics made by approximately 50 middle-level and secondary mathematics teachers within four high-need local education associations participating in a Mathematics and Science Partnership with a southeastern college's Science and Math for…

Pre-Service Teachers' Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

ERIC Educational Resources Information Center

Boyd, Soleil

2016-01-01

Preschool teachers are expected to engage young children in challenging and supportive mathematics learning. Rich and responsive language experiences in mathematics support children's language acquisition and engagement related to mathematics, however, such engaging experiences may be minimally available to many young children. Professional…

Transfer of Algebraic and Graphical Thinking between Mathematics and Chemistry

ERIC Educational Resources Information Center

Potgieter, Marietjie; Harding, Ansie; Engelbrecht, Johann

2008-01-01

Students in undergraduate chemistry courses find, as a rule, topics with a strong mathematical basis difficult to master. In this study we investigate whether such mathematically related problems are due to deficiencies in their mathematics foundation or due to the complexity introduced by transfer of mathematics to a new scientific domain. In the…

Are Disadvantaged Students Given Equal Opportunities to Learn Mathematics? PISA in Focus. No. 63

ERIC Educational Resources Information Center

OECD Publishing, 2016

2016-01-01

Socio-economically advantaged and disadvantaged students are not equally exposed to mathematics problems and concepts at school. Exposure to mathematics at school has an impact on performance, and disadvantaged students' relative lack of familiarity with mathematics partly explains their lower performance. Widening access to mathematics content…

Increasing Awareness of Practice through Interaction across Communities: The Lived Experiences of a Mathematician and Mathematics Teacher Educator

ERIC Educational Resources Information Center

Bleiler, Sarah K.

2015-01-01

Collaborations between mathematicians and mathematics teacher educators are increasingly being expected, and realized, within the context of mathematics teacher education. Most research related to collaborative efforts between members of the mathematics and mathematics education communities has focused on the products, rather than the process of…

Early Number Skills Gains and Mathematics Achievement: Intervening to Establish Successful Early Mathematics Trajectories

ERIC Educational Resources Information Center

Shanley, Lina; Clarke, Ben; Doabler, Christian T.; Kurtz-Nelson, Evangeline; Fien, Hank

2017-01-01

Early number skills, comprised of both informal and formal skills, are associated with later mathematics achievement. Thus, the development of foundational early number skills is an important aspect of early mathematics instruction. This study explored relations between early number skills gains and mathematics achievement for students at risk for…

Symbolic Drawings Reveal Changes in Preservice Teacher Mathematics Attitudes after a Mathematics Methods Course

ERIC Educational Resources Information Center

Rule, Audrey C.; Harrell, Mary H.

2006-01-01

A new method of analyzing mathematics attitudes through symbolic drawings, situated within the field of Jungian-oriented analytical psychology, was applied to 52 preservice elementary teachers before and after a mathematics methods course. In this triangulation mixed methods design study, pretest images related to past mathematics experiences…

Content Analysis of Jordanian Elementary Textbooks during 1970-2013 as Case Study

ERIC Educational Resources Information Center

Abed, Eman Rasmi; Al-Absi, Mohammad Mustafa

2015-01-01

This study aims to determine types of mathematic disciplines (in term of topics) in Jordanian Elementary textbooks. This study evaluates mathematics text books especially in the period between 1970 and 2013 and identifies types and quantities of mathematics. To examine the relative quantity of mathematics, branches of mathematics, presentation…

Modeling genome-wide dynamic regulatory network in mouse lungs with influenza infection using high-dimensional ordinary differential equations.

PubMed

Wu, Shuang; Liu, Zhi-Ping; Qiu, Xing; Wu, Hulin

2014-01-01

The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.

The study of middle school mathematics and science teachers' practices, perceptions, and attitudes related to mathematics and science integration

NASA Astrophysics Data System (ADS)

Leszczynski, Eliza

The purpose of this qualitative study was to investigate the nature of mathematics and science connections made by sixth and seventh grade mathematics and science teachers in their classrooms. This study also examined the extent to which these connections represented mathematics and science integration and described the teachers' perceptions of and attitudes about mathematics and science integration. The primary data sources included classroom observations and teacher interviews. Findings suggested that teacher practices in making mathematics and science connections in the classroom incorporated many of the characteristics of integrated instruction presented in the literature. Teacher attitudes toward integration were found to be generally positive and supportive of integrated instruction. Mathematics teachers shared a common perception of integration being two separate lessons taught together in one lesson. In contrast, science teachers perceived integration to be a seamless blend of the two disciplines. The researcher related these perceptions and attitudes to the teachers' past experiences with mathematics and science connections and integration, and also to their practices of mathematics and science connections in the study.

Image-based quantification and mathematical modeling of spatial heterogeneity in ESC colonies.

PubMed

Herberg, Maria; Zerjatke, Thomas; de Back, Walter; Glauche, Ingmar; Roeder, Ingo

2015-06-01

Pluripotent embryonic stem cells (ESCs) have the potential to differentiate into cells of all three germ layers. This unique property has been extensively studied on the intracellular, transcriptional level. However, ESCs typically form clusters of cells with distinct size and shape, and establish spatial structures that are vital for the maintenance of pluripotency. Even though it is recognized that the cells' arrangement and local interactions play a role in fate decision processes, the relations between transcriptional and spatial patterns have not yet been studied. We present a systems biology approach which combines live-cell imaging, quantitative image analysis, and multiscale, mathematical modeling of ESC growth. In particular, we develop quantitative measures of the morphology and of the spatial clustering of ESCs with different expression levels and apply them to images of both in vitro and in silico cultures. Using the same measures, we are able to compare model scenarios with different assumptions on cell-cell adhesions and intercellular feedback mechanisms directly with experimental data. Applying our methodology to microscopy images of cultured ESCs, we demonstrate that the emerging colonies are highly variable regarding both morphological and spatial fluorescence patterns. Moreover, we can show that most ESC colonies contain only one cluster of cells with high self-renewing capacity. These cells are preferentially located in the interior of a colony structure. The integrated approach combining image analysis with mathematical modeling allows us to reveal potential transcription factor related cellular and intercellular mechanisms behind the emergence of observed patterns that cannot be derived from images directly. © 2015 International Society for Advancement of Cytometry.

Interference and Polarized Light.

ERIC Educational Resources Information Center

Charas, Seymour

1988-01-01

Discusses a demonstration of interference phenomena using three sheets of polaroid material, a light source, and a light meter. Describes instructional procedures with mathematical expressions and a diagram. (YP)

A brief historical development of classical mathematics before the Renaissance

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2011-07-01

'If you wish to foresee the future of mathematics our proper course is to study the history and present condition of the science.' Henri Poincaré 'It is India that gave us the ingenious method of expressing all numbers by ten symbols, each symbol receiving a value of position, as well as an absolute value. We shall appreciate the grandeur of the achievement when we remember that it escaped the genius of Archimedes and Apollonius.' P.S. Laplace 'The Greeks were the first mathematicians who are still 'real' to us today. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greek first spoke of a language which modern mathematicians can understand.' G.H. Hardy This article deals with a short history of mathematics and mathematical scientists during the ancient and medieval periods. Included are some major developments of the ancient, Indian, Arabic, Egyptian, Greek and medieval mathematics and their significant impact on the Renaissance mathematics. Special attention is given to many results, theorems, generalizations, and new discoveries of arithmetic, algebra, number theory, geometry and astronomy during the above periods. A number of exciting applications of the above areas is discussed in some detail. It also contains a wide variety of important material accessible to college and even high school students and teachers at all levels. Included also is mathematical information that puts the professionals and prospective mathematical scientists at the forefront of current research.

Early Career Elementary Mathematics Teachers' Noticing Related to Language and Language Learners

ERIC Educational Resources Information Center

Turner, Erin Elizabeth; McDuffie, Amy Roth; Sugimoto, Amanda Tori; Stoehr, Kathleen Jablon; Witters, Angela; Aguirre, Julia; Bartell, Tonya; Drake, Corey; Foote, Mary Q.

2016-01-01

There has been limited attention to early career teachers' (ECTs) understandings and practices related to language in teaching and learning mathematics. In this qualitative case study, we drew upon frameworks for teacher noticing to study the language practices of six early career elementary and middle school mathematics teachers. We describe…

Insurance and Mathematics: Developing Democratic Citizenship through Interdisciplinary Approaches to Contemporary Issues

ERIC Educational Resources Information Center

Misco, Thomas; Lee, Lena; Malone, Kevin; Goley, G. Steven; Seabolt, Phaedra

2012-01-01

Insurance is an interesting interdisciplinary topic that can offer generative meaning and relevance for students. By adapting real life examples and authentic simulations, mathematical concepts can be applied to insurance-related social studies issues and content. This article explores ways to teach insurance and related mathematical concepts to…

Are Taiwanese and Singaporean Future Teachers Similar in Their Mathematics-Related Teaching Competencies?

ERIC Educational Resources Information Center

Hsieh, Feng-Jui; Wong, Khoon Yoong; Wang, Ting-Ying

2013-01-01

This study investigates the similarities and differences of mathematics-related teaching competencies between the future secondary school teachers of Taiwan and Singapore by using data from the international Teacher Education and Development Study in Mathematics (TEDS-M), organized by the International Association for the Evaluation of Educational…

Early numerical foundations of young children's mathematical development.

PubMed

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2015-04-01

This study focused on the relative contributions of the acuity of the approximate number system (ANS) and knowledge of quantitative symbols to young children's early mathematical learning. At the beginning of preschool, 191 children (Mage=46 months) were administered tasks that assessed ANS acuity and explicit knowledge of the cardinal values represented by number words, and their mathematics achievement was assessed at the end of the school year. Children's executive functions, intelligence, and preliteracy skills and their parents' educational levels were also assessed and served as covariates. Both the ANS and cardinality tasks were significant predictors of end-of-year mathematics achievement with and without control of the covariates. As simultaneous predictors and with control of the covariates, cardinality remained significantly related to mathematics achievement, but ANS acuity did not. Mediation analyses revealed that the relation between ANS acuity and mathematics achievement was fully mediated by cardinality, suggesting that the ANS may facilitate children's explicit understanding of cardinal value and in this way may indirectly influence early mathematical learning. Copyright © 2015 Elsevier Inc. All rights reserved.

The limits of weak selection and large population size in evolutionary game theory.

PubMed

Sample, Christine; Allen, Benjamin

2017-11-01

Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the [Formula: see text] limit, in which weak selection is applied before the large population limit, and the [Formula: see text] limit, in which the order is reversed. Formal mathematical definitions of the [Formula: see text] and [Formula: see text] limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the [Formula: see text] and [Formula: see text] limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.

An Attempt of Making Program-Generated Animation in a Beginners’ Programming Class

NASA Astrophysics Data System (ADS)

Matsuyama, Chieko; Nakashima, Toyoshiro; Ishii, Naohiro

In general, mathematical subjects are used for programming education in universities. In this case, many students lose the interest in the programming because the students have the preconception that is difficult to program by using the mathematical expressions. Especially beginners of the programming are a tendency to lose the interest. Therefore it is pointed out to use the subjects which do not need mathematical knowledge as much as possible. In this paper the authors have tried to make animation that are generated by programs instead of the mathematical subjects in a beginners’ programming class using C language used in a wide-ranging field. The authors discuss about improvements of the interest of students for programming by the try that is to make animation by programs in a programming class and refer to its effects.

On the mathematical modeling of the Reynolds stress's equations

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

[Mathematical exploration of essence of herbal properties based on "Three-Elements" theory].

PubMed

Jin, Rui; Zhao, Qian; Zhang, Bing

2014-10-01

Herbal property theory of traditional Chinese medicines is the theoretical guidance on authentication of medicinal plants, herborization, preparation of herbal medicines for decoction and clinical application, with important theoretical value and prac- tical significance. Our research team proposed the "three-element" theory for herbal properties for the first time, conducted a study by using combined methods of philology, chemistry, pharmacology and mathematics, and then drew the research conclusion that herbal properties are defined as the chemical compositions-based comprehensive expression with complex and multi-level (positive/negative) biological effects in specific organism state. In this paper, researchers made a systematic mathematical analysis in four aspects--the correlation between herbal properties and chemical component factors, the correlation between herbal properties and organism state fac- tor, the correlation between herbal properties and biological effect factor and the integration study of the three elements, proposed future outlook, and provided reference to mathematical studies and mathematical analysis of herbal properties.

Facilitating mathematics learning for students with upper extremity disabilities using touch-input system.

PubMed

Choi, Kup-Sze; Chan, Tak-Yin

2015-03-01

To investigate the feasibility of using tablet device as user interface for students with upper extremity disabilities to input mathematics efficiently into computer. A touch-input system using tablet device as user interface was proposed to assist these students to write mathematics. User-switchable and context-specific keyboard layouts were designed to streamline the input process. The system could be integrated with conventional computer systems only with minor software setup. A two-week pre-post test study involving five participants was conducted to evaluate the performance of the system and collect user feedback. The mathematics input efficiency of the participants was found to improve during the experiment sessions. In particular, their performance in entering trigonometric expressions by using the touch-input system was significantly better than that by using conventional mathematics editing software with keyboard and mouse. The participants rated the touch-input system positively and were confident that they could operate at ease with more practice. The proposed touch-input system provides a convenient way for the students with hand impairment to write mathematics and has the potential to facilitate their mathematics learning. Implications for Rehabilitation Students with upper extremity disabilities often face barriers to learning mathematics which is largely based on handwriting. Conventional computer user interfaces are inefficient for them to input mathematics into computer. A touch-input system with context-specific and user-switchable keyboard layouts was designed to improve the efficiency of mathematics input. Experimental results and user feedback suggested that the system has the potential to facilitate mathematics learning for the students.

Rainforest Mathematics

ERIC Educational Resources Information Center

Kilpatrick, Jeremy

2014-01-01

This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls

PubMed Central

2016-01-01

Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls’ STEM participation. PMID:27100631

Countries with Higher Levels of Gender Equality Show Larger National Sex Differences in Mathematics Anxiety and Relatively Lower Parental Mathematics Valuation for Girls.

PubMed

Stoet, Gijsbert; Bailey, Drew H; Moore, Alex M; Geary, David C

2016-01-01

Despite international advancements in gender equality across a variety of societal domains, the underrepresentation of girls and women in Science, Technology, Engineering, and Mathematics (STEM) related fields persists. In this study, we explored the possibility that the sex difference in mathematics anxiety contributes to this disparity. More specifically, we tested a number of predictions from the prominent gender stratification model, which is the leading psychological theory of cross-national patterns of sex differences in mathematics anxiety and performance. To this end, we analyzed data from 761,655 15-year old students across 68 nations who participated in the Programme for International Student Assessment (PISA). Most importantly and contra predictions, we showed that economically developed and more gender equal countries have a lower overall level of mathematics anxiety, and yet a larger national sex difference in mathematics anxiety relative to less developed countries. Further, although relatively more mothers work in STEM fields in more developed countries, these parents valued, on average, mathematical competence more in their sons than their daughters. The proportion of mothers working in STEM was unrelated to sex differences in mathematics anxiety or performance. We propose that the gender stratification model fails to account for these national patterns and that an alternative model is needed. In the discussion, we suggest how an interaction between socio-cultural values and sex-specific psychological traits can better explain these patterns. We also discuss implications for policies aiming to increase girls' STEM participation.

Developing My Mathematics Identity

ERIC Educational Resources Information Center

Gonzalez, Lidia

2016-01-01

Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.

Handling Math Expressions in Economics: Recoding Spreadsheet Teaching Tool of Growth Models

ERIC Educational Resources Information Center

Moro-Egido, Ana I.; Pedauga, Luis E.

2017-01-01

In the present paper, we develop a teaching methodology for economic theory. The main contribution of this paper relies on combining the interactive characteristics of spreadsheet programs such as Excel and Unicode plain-text linear format for mathematical expressions. The advantage of Unicode standard rests on its ease for writing and reading…

Modelling the Relationships between Quantities: Meaning in Literal Expressions

ERIC Educational Resources Information Center

Zeljic, Marijana

2015-01-01

Algebra is often considered as difficult and mysterious doctrine due to numerous symbols that represent mathematical notions. Results of the research on students' interpretation of literal expressions show that only a small number of students are ready to accept that a letter can represent a variable. The aim of this research with students of the…

Mathematical literacy in undergraduates: role of gender, emotional intelligence and emotional self-efficacy

NASA Astrophysics Data System (ADS)

Tariq, Vicki N.; Qualter, Pamela; Roberts, Sian; Appleby, Yvon; Barnes, Lynne

2013-12-01

This empirical study explores the roles that Emotional Intelligence (EI) and Emotional Self-Efficacy (ESE) play in undergraduates' mathematical literacy, and the influence of EI and ESE on students' attitudes towards and beliefs about mathematics. A convenience sample of 93 female and 82 male first-year undergraduates completed a test of mathematical literacy, followed by an online survey designed to measure the students' EI, ESE and factors associated with mathematical literacy. Analysis of the data revealed significant gender differences. Males attained a higher mean test score than females and out-performed the females on most of the individual questions and the associated mathematical tasks. Overall, males expressed greater confidence in their mathematical skills, although both males' and females' confidence outweighed their actual mathematical proficiency. Correlation analyses revealed that males and females attaining higher mathematical literacy test scores were more confident and persistent, exhibited lower levels of mathematics anxiety and possessed higher mathematics qualifications. Correlation analyses also revealed that in male students, aspects of ESE were associated with beliefs concerning the learning of mathematics (i.e. that intelligence is malleable and that persistence can facilitate success), but not with confidence or actual performance. Both EI and ESE play a greater role with regard to test performance and attitudes/beliefs regarding mathematics amongst female undergraduates; higher EI and ESE scores were associated with higher test scores, while females exhibiting higher levels of ESE were also more confident and less anxious about mathematics, believed intelligence to be malleable, were more persistent and were learning goal oriented. Moderated regression analyses confirmed mathematics anxiety as a negative predictor of test performance in males and females, but also revealed that in females EI and ESE moderate the effects of anxiety on test performance, with the relationship between anxiety and test performance linked more to emotional management (EI) than to ESE.

Do Inequalities in Parents' Education Play an Important Role in PISA Students' Mathematics Achievement Test Score Disparities?

ERIC Educational Resources Information Center

Martins, Lurdes; Veiga, Paula

2010-01-01

This paper measures and decomposes socioeconomic-related inequality in mathematics achievement in 15 European Union member states. Data is taken from the 2003 wave of the OECD Programme for International Student Assessment (PISA). There is socioeconomic-related inequality in mathematics achievement, favoring the higher socioeconomic groups in each…

The Factors Related to Preschool Children and Their Mothers on Children's Intuitional Mathematics Abilities

ERIC Educational Resources Information Center

Guven, Yildiz

2009-01-01

The aim of this study is to assess the factors that are related to preschool children and their mothers on children's intuitional mathematics abilities. Results of the study showed that there were significant differences in children's intuitional mathematics abilities when children are given the opportunity to think intuitionally and to make…

The Effect of Inhibitory Control on General Mathematics Achievement and Fraction Comparison in Middle School Children

ERIC Educational Resources Information Center

Gómez, David Maximiliano; Jiménez, Abelino; Bobadilla, Roberto; Reyes, Cristián; Dartnell, Pablo

2015-01-01

Individual differences in inhibitory control have been shown to relate to general mathematics achievement, but whether this relation varies for specific areas within mathematics is a question that remains open. Here, we evaluate if inhibitory processes play a specific role in the particular case of fraction comparison, where learners must ignore…

Individualized Math Problems in Decimals. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

THis is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume concern use of decimals and are related to the…

Comparison of the Mathematics Expectations Related to Number and Quantity for Student Learning

ERIC Educational Resources Information Center

Chen, Jung-chih; Chen, Chia-huang

2011-01-01

In the study reported here, the authors examined the LEs (learning expectations) related to Grades 1 to 8 number and quantity in mathematics across several US states and high performing TIMSS (Third International Mathematics and Science Study) Asian countries, including Singapore, Taiwan and Japan. The general strategy used is based on the topic…

RBSDesigner: software for designing synthetic ribosome binding sites that yields a desired level of protein expression.

PubMed

Na, Dokyun; Lee, Doheon

2010-10-15

RBSDesigner predicts the translation efficiency of existing mRNA sequences and designs synthetic ribosome binding sites (RBSs) for a given coding sequence (CDS) to yield a desired level of protein expression. The program implements the mathematical model for translation initiation described in Na et al. (Mathematical modeling of translation initiation for the estimation of its efficiency to computationally design mRNA sequences with a desired expression level in prokaryotes. BMC Syst. Biol., 4, 71). The program additionally incorporates the effect on translation efficiency of the spacer length between a Shine-Dalgarno (SD) sequence and an AUG codon, which is crucial for the incorporation of fMet-tRNA into the ribosome. RBSDesigner provides a graphical user interface (GUI) for the convenient design of synthetic RBSs. RBSDesigner is written in Python and Microsoft Visual Basic 6.0 and is publicly available as precompiled stand-alone software on the web (http://rbs.kaist.ac.kr). dhlee@kaist.ac.kr

Challenging assumptions of notational transparency: the case of vectors in engineering mathematics

NASA Astrophysics Data System (ADS)

Craig, Tracy S.

2017-11-01

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing the components of a vector are discussed in historical and current context. Popular mathematical texts use the two notations as if they are transparent and interchangeable. In this research project, engineering students' proficiency at vector analysis was assessed and the data were analyzed using the Rasch measurement method. Results indicate that the students found items expressed in unit vector notation more difficult than those expressed in parenthesis notation. The expert experience of notation as transparent and unproblematically symbolic of underlying processes independent of notation is shown to contrast with the student experience where the less familiar notation is experienced as harder to work with.

Sex Differences in Mathematics and Reading Achievement Are Inversely Related: Within- and Across-Nation Assessment of 10 Years of PISA Data

PubMed Central

Stoet, Gijsbert; Geary, David C.

2013-01-01

We analyzed one decade of data collected by the Programme for International Student Assessment (PISA), including the mathematics and reading performance of nearly 1.5 million 15 year olds in 75 countries. Across nations, boys scored higher than girls in mathematics, but lower than girls in reading. The sex difference in reading was three times as large as in mathematics. There was considerable variation in the extent of the sex differences between nations. There are countries without a sex difference in mathematics performance, and in some countries girls scored higher than boys. Boys scored lower in reading in all nations in all four PISA assessments (2000, 2003, 2006, 2009). Contrary to several previous studies, we found no evidence that the sex differences were related to nations’ gender equality indicators. Further, paradoxically, sex differences in mathematics were consistently and strongly inversely correlated with sex differences in reading: Countries with a smaller sex difference in mathematics had a larger sex difference in reading and vice versa. We demonstrate that this was not merely a between-nation, but also a within-nation effect. This effect is related to relative changes in these sex differences across the performance continuum: We did not find a sex difference in mathematics among the lowest performing students, but this is where the sex difference in reading was largest. In contrast, the sex difference in mathematics was largest among the higher performing students, and this is where the sex difference in reading was smallest. The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics. Interventions that focus on high-achieving girls in mathematics and on low achieving boys in reading are likely to yield the strongest educational benefits. PMID:23516422

Sex differences in mathematics and reading achievement are inversely related: within- and across-nation assessment of 10 years of PISA data.

PubMed

Stoet, Gijsbert; Geary, David C

2013-01-01

We analyzed one decade of data collected by the Programme for International Student Assessment (PISA), including the mathematics and reading performance of nearly 1.5 million 15 year olds in 75 countries. Across nations, boys scored higher than girls in mathematics, but lower than girls in reading. The sex difference in reading was three times as large as in mathematics. There was considerable variation in the extent of the sex differences between nations. There are countries without a sex difference in mathematics performance, and in some countries girls scored higher than boys. Boys scored lower in reading in all nations in all four PISA assessments (2000, 2003, 2006, 2009). Contrary to several previous studies, we found no evidence that the sex differences were related to nations' gender equality indicators. Further, paradoxically, sex differences in mathematics were consistently and strongly inversely correlated with sex differences in reading: Countries with a smaller sex difference in mathematics had a larger sex difference in reading and vice versa. We demonstrate that this was not merely a between-nation, but also a within-nation effect. This effect is related to relative changes in these sex differences across the performance continuum: We did not find a sex difference in mathematics among the lowest performing students, but this is where the sex difference in reading was largest. In contrast, the sex difference in mathematics was largest among the higher performing students, and this is where the sex difference in reading was smallest. The implication is that if policy makers decide that changes in these sex differences are desired, different approaches will be needed to achieve this for reading and mathematics. Interventions that focus on high-achieving girls in mathematics and on low achieving boys in reading are likely to yield the strongest educational benefits.

Astronomy and Mathematics Education

NASA Astrophysics Data System (ADS)

Ros, Rosa M.

There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.

A finite parallel zone model to interpret and extend Giddings' coupling theory for the eddy-dispersion in porous chromatographic media.

PubMed

Desmet, Gert

2013-11-01

The finite length parallel zone (FPZ)-model is proposed as an alternative model for the axial- or eddy-dispersion caused by the occurrence of local velocity biases or flow heterogeneities in porous media such as those used in liquid chromatography columns. The mathematical plate height expression evolving from the model shows that the A- and C-term band broadening effects that can originate from a given velocity bias should be coupled in an exponentially decaying way instead of harmonically as proposed in Giddings' coupling theory. In the low and high velocity limit both models converge, while a 12% difference can be observed in the (practically most relevant) intermediate range of reduced velocities. Explicit expressions for the A- and C-constants appearing in the exponential decay-based plate height expression have been derived for each of the different possible velocity bias levels (single through-pore and particle level, multi-particle level and trans-column level). These expressions allow to directly relate the band broadening originating from these different levels to the local fundamental transport parameters, hence offering the possibility to include a velocity-dependent and, if, needed retention factor-dependent transversal dispersion coefficient. Having developed the mathematics for the general case wherein a difference in retention equilibrium establishes between the two parallel zones, the effect of any possible local variations in packing density and/or retention capacity on the eddy-dispersion can be explicitly accounted for as well. It is furthermore also shown that, whereas the lumped transport parameter model used in the basic variant of the FPZ-model only provides a first approximation of the true decay constant, the model can be extended by introducing a constant correction factor to correctly account for the continuous transversal dispersion transport in the velocity bias zones. Copyright © 2013 Elsevier B.V. All rights reserved.

Mathematical modeling of gene expression: a guide for the perplexed biologist

PubMed Central

Ay, Ahmet; Arnosti, David N.

2011-01-01

The detailed analysis of transcriptional networks holds a key for understanding central biological processes, and interest in this field has exploded due to new large-scale data acquisition techniques. Mathematical modeling can provide essential insights, but the diversity of modeling approaches can be a daunting prospect to investigators new to this area. For those interested in beginning a transcriptional mathematical modeling project we provide here an overview of major types of models and their applications to transcriptional networks. In this discussion of recent literature on thermodynamic, Boolean and differential equation models we focus on considerations critical for choosing and validating a modeling approach that will be useful for quantitative understanding of biological systems. PMID:21417596

Children’s visuospatial memory predicts mathematics achievement through early adolescence

PubMed Central

Li, Yaoran

2017-01-01

A previous study showed that gains in visuospatial memory from first to fifth grade predicted end-of-fifth grade mathematics but not reading achievement, controlling other factors. In this follow up study, these relations were assessed from sixth to ninth grade, inclusive (n = 145). The results showed that growth in visuospatial memory across the elementary school years was related to growth in mathematics achievement after fifth grade, controlling intelligence, the central executive and phonological memory components of working memory, in-class attentive behavior, parental education, and fifth grade mathematics achievement. As found for fifth grade, this relation was not found for reading achievement after fifth grade. In total, the results suggest that visuospatial memory has a unique influence on ease of learning some types of mathematics and that this influence becomes more important across successive grades. PMID:28192484

Children's visuospatial memory predicts mathematics achievement through early adolescence.

PubMed

Li, Yaoran; Geary, David C

2017-01-01

A previous study showed that gains in visuospatial memory from first to fifth grade predicted end-of-fifth grade mathematics but not reading achievement, controlling other factors. In this follow up study, these relations were assessed from sixth to ninth grade, inclusive (n = 145). The results showed that growth in visuospatial memory across the elementary school years was related to growth in mathematics achievement after fifth grade, controlling intelligence, the central executive and phonological memory components of working memory, in-class attentive behavior, parental education, and fifth grade mathematics achievement. As found for fifth grade, this relation was not found for reading achievement after fifth grade. In total, the results suggest that visuospatial memory has a unique influence on ease of learning some types of mathematics and that this influence becomes more important across successive grades.

The effect of temperature on the average volume of Barkhausen jump on Q235 carbon steel

NASA Astrophysics Data System (ADS)

Guo, Lei; Shu, Di; Yin, Liang; Chen, Juan; Qi, Xin

2016-06-01

On the basis of the average volume of Barkhausen jump (AVBJ) vbar generated by irreversible displacement of magnetic domain wall under the effect of the incentive magnetic field on ferromagnetic materials, the functional relationship between saturation magnetization Ms and temperature T is employed in this paper to deduce the explicit mathematical expression among AVBJ vbar, stress σ, incentive magnetic field H and temperature T. Then the change law between AVBJ vbar and temperature T is researched according to the mathematical expression. Moreover, the tensile and compressive stress experiments are carried out on Q235 carbon steel specimens at different temperature to verify our theories. This paper offers a series of theoretical bases to solve the temperature compensation problem of Barkhausen testing method.

From Anxiety as a Psychological and Biological Phenomenon to Mathematics Anxiety: A Theoretical Approach

ERIC Educational Resources Information Center

Moreno-García, Elena; García-Santillán, Arturo; Molchanova, Violetta S.; Larracilla-Salazar, Némesis

2017-01-01

In the educational field, anxiety towards mathematics has been a recurrent theme that has been intensified with the results of the PISA test of 2012 and 2015. Since students who are anxious about mathematics tend to avoid any area related to mathematics, it leads to a decrease in the number of professionals in mathematics. However, this construct…

Mathematics and the Flight from the Feminine: The Discursive Construction of Gendered Subjectivity in Mathematics Textbooks

ERIC Educational Resources Information Center

Hottinger, Sara

2010-01-01

There is a widespread awareness in the American culture that women do not pursue careers in mathematics-related fields in equal numbers to men. Efforts to address this disparity by reforming mathematics education have met with some success; recent research shows that girls' achievements in mathematics stay on par with those of boys through…

Friend Influence and Susceptibility to Influence: Changes in Mathematical Reasoning as a Function of Relative Peer Acceptance and Interest in Mathematics

ERIC Educational Resources Information Center

DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa

2016-01-01

This study investigated friend influence over mathematics achievement in 202 same-sex friendship dyads (106 girl dyads). Participants were in the third grade (around age 9) at the outset. Each friend completed a questionnaire describing interest in mathematics and a standardized mathematical reasoning assessment. Peer nominations provided a…

Multicultural and Gender Equity Issues in a History of Mathematics Course: Not Only Dead European Males

ERIC Educational Resources Information Center

Flores, Alfinio; Kimpton, Kelly E.

2012-01-01

We address issues related to gender and cultural equity in a history of mathematics course. We first look at the preponderance of male European mathematicians represented in textbooks of mathematics and history or mathematics. Then we discuss ways to highlight the presence of female and non-European mathematicians in the history of mathematics.…

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Influence of Difficulty with Language of Mathematics on Perceived Self-Efficacy in Learning Mathematics among Upper Primary Students of Kerala

ERIC Educational Resources Information Center

Sarabi, M. K.; Gafoor, K. Abdul

2017-01-01

There is increasing realization that mathematics-related self-efficacy expectations are a strong predictor of an array of significant mathematics outcomes. It is also evident that the curricular practice in schools largely neglects development of a student understanding in the unique language of mathematics. Consequently, this study probes how…

Mathematical skills in Prader-Willi Syndrome.

PubMed

Bertella, L; Girelli, L; Grugni, G; Marchi, S; Molinari, E; Semenza, C

2005-02-01

This paper investigates mathematical skills in Prader-Willi Syndrome (PWS), a pathological condition because of congenital alterations of chromosome pair 15. The following questions were addressed: (1) Are mathematical skills in PWS relatively more impaired with respect to other cognitive functions (as has been repeatedly but anecdotally reported)?; and (2) What is the nature of the mathematical impairment? The first study employed the Wechsler Adult Intelligence Scale (WAIS) and an extensive battery of cognitive tasks for which norms are known. Both batteries include a mathematical section. The second study used a theoretically motivated series of mathematical tasks specifically designed to individually assess the different cognitive components underlying mathematical skills. Mathematical skills were found to be the most impaired cognitive abilities together with short-term memory capacity. No specific mathematical domain was seen to be unaffected in PWS participants. The clearest deficits observed concern 'syntactic' processes in number transcoding, multiplication, number facts retrieval and calculation procedures. Failure of mathematical skills is the most distinctive feature in the cognitive profile of PWS. However, to determine whether this is indeed a specific pattern of performance related to PWS, results must be compared with those obtained with patients manifesting other genetic disorders.

Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.

ERIC Educational Resources Information Center

Nunokawa, Kazuhiko

1996-01-01

The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)

Derivation of some formulae in combinatrics by heuristic methods

NASA Astrophysics Data System (ADS)

Kobayashi, Yukio

2015-04-01

Heuristic methods are more effective for students inlearning permutations and combinations in mathematics than passive learning such as rote memorization of formulae. Two examples, n! and 2n - 1Cn, of finding new combinatorial formulae are discussed from a pedagogical standpoint. First, the factorial of n can be expressed as ∑n - 1k = 0k . k!, which can be found by a heuristic method. This expression is comparable to representations of powers of r using geometrical series. Second, the number of possible combinations with repetition of n drawings from n elements is denoted 2n - 1Cn, which can be calculated from ∑n - 1k = 0nCk + 1n - 1Ck. The relation ∑n - 1k = 0nCk + 1n - 1Ck = 2n - 1Cn can be found by a heuristic method through a corresponding problem on mapping.

Teachers' Beliefs and Teaching Mathematics with Manipulatives

ERIC Educational Resources Information Center

Golafshani, Nahid

2013-01-01

To promote the implementation of manipulatives into mathematics instruction, this research project examined how the instructional practices of four Grade 9 applied mathematics teachers related to their beliefs about the use of manipulatives in teaching mathematics, its effects on students' learning, and enabling and disabling factors. Teacher…

Transitioning to Secondary School: The Case of Mathematics

ERIC Educational Resources Information Center

Carmichael, Colin

2015-01-01

At a time when Australia's international competitiveness is compromised by a shortage of skilled workers in Science, Technology, Engineering and Mathematics (STEM) related careers, reports suggest a decline in Australian secondary school students' performances in international tests of mathematics. This study focuses on the mathematics performance…

Mathematics and General Education. Stirling Seminar Papers No. 2.

ERIC Educational Resources Information Center

Ruthven, Kenneth

1979-01-01

Despite the development of a common mathematics course, and the raising of the school leaving age, Scotland's mathematics curriculum is still designed for specialization. A general education perspective suggests that the curriculum should enable students to relate mathematics to everyday life (f=fiche number). (Author/CP)

Investigations in Mathematics Education, Vol. 10, No. 4.

ERIC Educational Resources Information Center

Osborne, Alan R., Ed.

Eighteen research reports related to mathematics education are abstracted and analyzed. Four of the reports deal with aspects of learning theory, five with topics in mathematics instruction (history of mathematics, exponents, probability, calculus, and calculators), four with teacher characteristics, and one each with testing, student interests,…

Understanding the Chinese Approach to Creative Teaching in Mathematics Classrooms

ERIC Educational Resources Information Center

Niu, Weihua; Zhou, Zheng; Zhou, Xinlin

2017-01-01

Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted,…

Matrix factorization reveals aging-specific co-expression gene modules in the fat and muscle tissues in nonhuman primates

NASA Astrophysics Data System (ADS)

Wang, Yongcui; Zhao, Weiling; Zhou, Xiaobo

2016-10-01

Accurate identification of coherent transcriptional modules (subnetworks) in adipose and muscle tissues is important for revealing the related mechanisms and co-regulated pathways involved in the development of aging-related diseases. Here, we proposed a systematically computational approach, called ICEGM, to Identify the Co-Expression Gene Modules through a novel mathematical framework of Higher-Order Generalized Singular Value Decomposition (HO-GSVD). ICEGM was applied on the adipose, and heart and skeletal muscle tissues in old and young female African green vervet monkeys. The genes associated with the development of inflammation, cardiovascular and skeletal disorder diseases, and cancer were revealed by the ICEGM. Meanwhile, genes in the ICEGM modules were also enriched in the adipocytes, smooth muscle cells, cardiac myocytes, and immune cells. Comprehensive disease annotation and canonical pathway analysis indicated that immune cells, adipocytes, cardiomyocytes, and smooth muscle cells played a synergistic role in cardiac and physical functions in the aged monkeys by regulation of the biological processes associated with metabolism, inflammation, and atherosclerosis. In conclusion, the ICEGM provides an efficiently systematic framework for decoding the co-expression gene modules in multiple tissues. Analysis of genes in the ICEGM module yielded important insights on the cooperative role of multiple tissues in the development of diseases.

Task force on applied mathematics

NASA Technical Reports Server (NTRS)

Prieto, A.

1979-01-01

Tomas Garza relates how the Research Center for Applied Mathematics Systems and Services in Mexico became the Research Institute for Applied Mathematics and Systems and what the type of work performed is.

Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety

PubMed Central

2012-01-01

Background Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Methods Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. Results No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Conclusions Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because there is evidence that MA develops during the primary school years. Furthermore, our study showed no gender difference in mathematics performance, despite girls reporting higher levels of MA. These results might suggest that girls may have had the potential to perform better than boys in mathematics however their performance may have been attenuated by their higher levels of MA. Longitudinal research is needed to investigate the development of MA and its effect on mathematics performance. PMID:22769743

Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety.

PubMed

Devine, Amy; Fawcett, Kayleigh; Szűcs, Dénes; Dowker, Ann

2012-07-09

Mathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys' mathematics performance is more negatively affected by MA than girls' performance is. The aim of the current study was to measure girls' and boys' mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies. Four-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires. No gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys. Our study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on 'online' mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because there is evidence that MA develops during the primary school years. Furthermore, our study showed no gender difference in mathematics performance, despite girls reporting higher levels of MA. These results might suggest that girls may have had the potential to perform better than boys in mathematics however their performance may have been attenuated by their higher levels of MA. Longitudinal research is needed to investigate the development of MA and its effect on mathematics performance.

Biphasic regulation of the transcription factor ABORTED MICROSPORES (AMS) is essential for tapetum and pollen development in Arabidopsis.

PubMed

Ferguson, Alison C; Pearce, Simon; Band, Leah R; Yang, Caiyun; Ferjentsikova, Ivana; King, John; Yuan, Zheng; Zhang, Dabing; Wilson, Zoe A

2017-01-01

Viable pollen is essential for plant reproduction and crop yield. Its production requires coordinated expression at specific stages during anther development, involving early meiosis-associated events and late pollen wall formation. The ABORTED MICROSPORES (AMS) transcription factor is a master regulator of sporopollenin biosynthesis, secretion and pollen wall formation in Arabidopsis. Here we show that it has complex regulation and additional essential roles earlier in pollen formation. An inducible-AMS reporter was created for functional rescue, protein expression pattern analysis, and to distinguish between direct and indirect targets. Mathematical modelling was used to create regulatory networks based on wild-type RNA and protein expression. Dual activity of AMS was defined by biphasic protein expression in anther tapetal cells, with an initial peak around pollen meiosis and then later during pollen wall development. Direct AMS-regulated targets exhibit temporal regulation, indicating that additional factors are associated with their regulation. We demonstrate that AMS biphasic expression is essential for pollen development, and defines distinct functional activities during early and late pollen development. Mathematical modelling suggests that AMS may competitively form a protein complex with other tapetum-expressed transcription factors, and that biphasic regulation is due to repression of upstream regulators and promotion of AMS protein degradation. © 2016 The Authors. New Phytologist © 2016 New Phytologist Trust.

Students attitude towards calculus subject: Bumiputera case-study

NASA Astrophysics Data System (ADS)

Awang, Noorehan; Ilias, Mohd Rijal; Che Hussain, Wan Siti Esah; Mokhtar, Siti Fairus

2013-04-01

Mathematics has always become the most dislike subject among other subjects in school. Study showed that attitudes of students in science subjects such as mathematics were closely related to how they solve problems, accessing ideas and making a right decision. According to another study on mathematics achievement of eighth grade students in Malaysia, mathematics grades among bumiputera students was lower when compared to other races such as Chinese and Indians. The poor performance was due to their attitude and pre-conceived ideas towards the subject. Therefore, this study was designed todetermine the criteria and subcriteria that were considered important in measuring students' attitude toward mathematics among the bumiputeras. Factor analysis was carried out to identify the groups among criterion. Instrument used to measure mathematics attitude was Test of Mathematics Related Attitude (TOMRA) which measured student attitudes in four criteria: normality of mathematics, attitudes towards mathematics inquiry, adoption of mathematics attitude and enjoyment of mathematics lessons. The target population of this study was all computer science and quantitative science students who enrolled Calculus subject in UiTM Kedah. Findings shows that there are two criteria that influenced students attitude toward mathematics namely normality of mathematics with eleven subcriteria and enjoyment of mathematics with eight subcriteria. From the analysis it shows that the total percentage of variation explained is 35.071% with 0.837 Cronbach's alpha reliability test. The findings will help the lecturers, parents and society to consider what action should be taken to install interest and positive attitude of bumiputera students towards mathematics and thus improve their achievement.

A Longitudinal Look at Attitudes and Perceptions Related to the Integration of Mathematics, Science, and Technology Education

ERIC Educational Resources Information Center

Berlin, Donna F.; White, Arthur L.

2012-01-01

The purpose of this study is to provide an in-depth analysis of attitudes and perceptions related to the integration of mathematics, science, and technology education of preservice teachers preparing to teach STEM disciplines. Longitudinal data by individual cohort and across 7 years of the Integrated Mathematics, Science, and Technology (MSAT)…

An Examination of the Role of Technological Tools in Relation to the Cognitive Demand of Mathematical Tasks in Secondary Classrooms

ERIC Educational Resources Information Center

Sherman, Milan

2011-01-01

This study investigates the role of digital cognitive technologies in supporting students' mathematical thinking while engaging with instructional tasks. Specifically, the study sought to better understand how the use of technology is related to the cognitive demand of tasks. Data were collected in four secondary mathematics classrooms via…

Peer Relations and Access to Capital in the Mathematics Classroom: A Bourdieusian Social Network Analysis

ERIC Educational Resources Information Center

Choudry, Sophina; Williams, Julian; Black, Laura

2017-01-01

The aim of this article is to explore the structure of social capital in peer networks and its relation to the unequal access of educational resources within mathematics classrooms. We hypothesise that learners can gain access to mathematics through friendship networks which provide more or less help from peers that might sustain (or curtail)…

Selected Factors Related to the Mathematics Academic Achievement of Eighth Grade English Language Learners

ERIC Educational Resources Information Center

Garza, Anthony

2012-01-01

The purpose of this study was to examine selected factors related to the 8th grade mathematics achievement levels of English Language Learner (ELL) students in selected South Texas middle schools. The dependent variable, ELL mathematics achievement, was measured by the ELL student's raw score on the State of Texas Assessment of Academic Readiness…

Starting a Conversation about Open Data in Mathematics Education Research

ERIC Educational Resources Information Center

Logan, Tracy

2015-01-01

This position paper discusses the role of open access research data within mathematics education, a relatively new initiative across the wider research community. International and national policy documents are explored and examples from both the scientific and social science paradigms of mathematical sciences and mathematics education…

Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

ERIC Educational Resources Information Center

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-01-01

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…

Forces and Issues Related to Curriculum and Instruction, K-6

ERIC Educational Resources Information Center

DeVault, M. Vere; Weaver, J. Fred

1970-01-01

Traces the development of elementary mathematics curriculum and instruction from colonial times to the present. Each section emphasizes four major issues: Why teach mathematics? What mathematics should be taught? How should the mathematics we teach be organized? How should we organize and implement instruction? Also included are several items…

Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis

ERIC Educational Resources Information Center

Hamburg, Maryanna P.

2009-01-01

This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…

Mathematics and Global Survival.

ERIC Educational Resources Information Center

Schwartz, Richard H.

This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…

What Students Say about Their Mathematical Thinking When They Listen

ERIC Educational Resources Information Center

Kosko, Karl W.

2014-01-01

Mathematical listening is an important aspect of mathematical communication. Yet there are relatively few examinations of this phenomenon. Further, existing studies of students' mathematical listening come from observational data, lacking the student perspective. This study examined student replies to an open-response question regarding what…

A New Start for Mathematics Curriculum.

ERIC Educational Resources Information Center

Tucker, Alan

Arguing that a major re-thinking of the mathematics curriculum is needed, this paper urges two-year colleges to take the lead in curriculum revision. Section I suggests that the pre-calculus orientation of high school mathematics may be inappropriate, viewing mathematics related to computers and dependent on computers for computation as more…

Alternate Trajectories: Women Moving into Mathematics Education

ERIC Educational Resources Information Center

Toney, Allison F.

2014-01-01

While only about one-third of each year's doctoral graduates in mathematics are women, about two-thirds of the doctoral graduates in mathematics education are women. This article reports on the results of a qualitative investigation into the nature of the graduate school-related experiences of women in collegiate mathematics education doctoral…

Writing in Mathematics: A Survey of K-12 Teachers' Reported Frequency in the Classroom

ERIC Educational Resources Information Center

Kosko, Karl Wesley

2016-01-01

Although writing in mathematics has been advocated in practitioner journals, policy documents, and various research, surveys of mathematics teachers between 1988 and 2008 in various English-speaking countries have reported relatively infrequent incorporation into mathematics lessons. Further, much of prior survey research has yielded only…

Problem Posing with the Multiplication Table

ERIC Educational Resources Information Center

Dickman, Benjamin

2014-01-01

Mathematical problem posing is an important skill for teachers of mathematics, and relates readily to mathematical creativity. This article gives a bit of background information on mathematical problem posing, lists further references to connect problem posing and creativity, and then provides 20 problems based on the multiplication table to be…

Exploring an Integrative Lens of Identity for a High School Mathematics Teacher

ERIC Educational Resources Information Center

Wilson, Kimi

2016-01-01

Driven largely by societal discourse regarding the underrepresentation of African American males pursuing science, technology, engineering and mathematics (STEM) majors, careers and professions, it becomes salient to understand how African American males experience mathematics in K-12 public schools in relation to their mathematics identity…

Preservice Mathematics Teachers' Perceptions of Drama Based Instruction

ERIC Educational Resources Information Center

Bulut, Neslihan

2016-01-01

The purpose of this study was to determine the perceptions of pre-service mathematics teachers related to drama-based instruction. For this purpose, effects of a drama-based mathematics course on senior class pre-service mathematics teachers' knowledge about drama-based instruction and teacher candidates' competencies for developing and…

Students' and Teachers' Conceptual Metaphors for Mathematical Problem Solving

ERIC Educational Resources Information Center

Yee, Sean P.

2017-01-01

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

Engaging with Issues of Emotionality in Mathematics Teacher Education for Social Justice

ERIC Educational Resources Information Center

Boylan, Mark

2009-01-01

This article focuses on the relationship between social justice, emotionality and mathematics teaching in the context of the education of prospective teachers of mathematics. A relational approach to social justice calls for giving attention to enacting socially just relationships in mathematics classrooms. Emotionality and social justice in…

Information Literacy in Mathematics Undergraduate Education: Where Does It Stand Today?

ERIC Educational Resources Information Center

Bussmann, Jeffra Diane; Bond, Jeffrey D.

2015-01-01

The published literature on information literacy in mathematics is relatively sparse. This article explores the current state of information literacy initiatives in undergraduate mathematics. The authors survey academic librarians (n = 118) who liaise with mathematics departments in order to gain an understanding of their practices and attitudes…

Exploring Relationships between Presage Variables of Florida Preservice Agricultural Education Teachers Related to Teaching Contextualized Mathematics

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2013-01-01

The purpose of this exploratory study was to investigate the relationships between mathematics ability, personal mathematics efficacy, mathematics teaching efficacy, personal teaching efficacy, and background characteristics of preservice agricultural education teachers. Data were collected for two years at the University of Florida. Fourteen…

Teaching Preschoolers to Count: Effective Strategies for Achieving Early Mathematics Milestones

ERIC Educational Resources Information Center

Jacobi-Vessels, Jill L.; Brown, E. Todd; Molfese, Victoria J.; Do, Ahn

2016-01-01

Attention to early childhood mathematics instructional strategies has sharpened due to the relatively poor mathematics performance of U.S. students in comparison to students from other countries and research evidence that early mathematics skills impact later achievement. Early Childhood counting skills form the foundation for subsequent…

Usability of American Sign Language Videos for Presenting Mathematics Assessment Content.

PubMed

Hansen, Eric G; Loew, Ruth C; Laitusis, Cara C; Kushalnagar, Poorna; Pagliaro, Claudia M; Kurz, Christopher

2018-04-12

There is considerable interest in determining whether high-quality American Sign Language videos can be used as an accommodation in tests of mathematics at both K-12 and postsecondary levels; and in learning more about the usability (e.g., comprehensibility) of ASL videos with two different types of signers - avatar (animated figure) and human. The researchers describe the results of administering each of nine pre-college mathematics items in both avatar and human versions to each of 31 Deaf participants with high school and post-high school backgrounds. This study differed from earlier studies by obliging the participants to rely on the ASL videos to answer the items. While participants preferred the human version over the avatar version (apparently due largely to the better expressiveness and fluency of the human), there was no discernible relationship between mathematics performance and signed version.

Mathematical Logic in the Human Brain: Semantics

PubMed Central

Friedrich, Roland M.; Friederici, Angela D.

2013-01-01

As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge. PMID:23301101

Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

NASA Astrophysics Data System (ADS)

Li, Shu-Nan; Cao, Bing-Yang

2017-09-01

The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

Mathematical model and stability analysis of fluttering and autorotation of an articulated plate into a flow

NASA Astrophysics Data System (ADS)

Rostami, Ali Bakhshandeh; Fernandes, Antonio Carlos

2018-03-01

This paper is dedicated to develop a mathematical model that can simulate nonlinear phenomena of a hinged plate which places into the fluid flow (1 DOF). These phenomena are fluttering (oscillation motion), autorotation (continuous rotation) and chaotic motion (combination of fluttering and autorotation). Two mathematical models are developed for 1 DOF problem using two eminent mathematical models which had been proposed for falling plates (3 DOF). The procedures of developing these models are elaborated and then these results are compared to experimental data. The best model in the simulation of the phenomena is chosen for stability and bifurcation analysis. Based on these analyses, this model shows a transcritical bifurcation and as a result, the stability diagram and threshold are presented. Moreover, an analytical expression is given for finding the boundary of bifurcation from the fluttering to the autorotation.

Mathematical logic in the human brain: semantics.

PubMed

Friedrich, Roland M; Friederici, Angela D

2013-01-01

As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge.

Early math matters: kindergarten number competence and later mathematics outcomes.

PubMed

Jordan, Nancy C; Kaplan, David; Ramineni, Chaitanya; Locuniak, Maria N

2009-05-01

Children's number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although low-income children performed more poorly than their middle-income counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children's learning trajectories in elementary school mathematics. Copyright 2009 APA, all rights reserved

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

PubMed Central

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

Early Math Matters: Kindergarten Number Competence and Later Mathematics Outcomes

PubMed Central

Jordan, Nancy C.; Kaplan, David; Ramineni, Chaitanya; Locuniak, Maria N.

2009-01-01

Children’s number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although low-income children performed more poorly than their middle-income counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children’s learning trajectories in elementary school mathematics. PMID:19413436

Local recovery of lithospheric stress tensor from GOCE gravitational tensor

NASA Astrophysics Data System (ADS)

Eshagh, Mehdi

2017-04-01

The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

Mathematical learning disorder in school-age children with attention-deficit hyperactivity disorder.

PubMed

Capano, Lucia; Minden, Debbie; Chen, Shirley X; Schacher, Russell J; Ickowicz, Abel

2008-06-01

To explore the prevalence of mathematics disorder (MD) relative to reading disorders (RD) in school-age children with attention-deficit hyperactivity disorder (ADHD) and examine the effects of age, sex, cooccurring conduct disorder (CD), and ADHD subtype on this comorbidity. Participants were school-age children (n = 476) with confirmed DSM-IV diagnosis of ADHD. The assessment included semistructured parent and teacher interviews and standardized measures of intelligence, academic attainment, and language abilities. Based on the presence or absence of concurrent learning disorders, we compared the emerging 4 groups: ADHD-only, ADHD + MD, ADHD + RD, and ADHD + MD + RD. Overall prevalence of comorbid ADHD + MD was 18.1%. Age, sex, ADHD subtypes, or comorbid CD did not affect the frequency of MD. Children with concurrent ADHD and either MD or RD attained lower IQ, language, and academic scores than those with ADHD alone. Children with ADHD + MD + RD were more seriously impaired and demonstrated distinct deficits in receptive and expressive language. MDs are relatively common in school-age children with ADHD and are frequently associated with RDs. Children with ADHD + MD + RD are more severely impaired. These deficits simply cannot be explained as consequences of ADHD and might have unique biological underpinnings, with implications for diagnostic classification and therapeutic interventions.

Modeling the Growth of Filamentous Fungi at the Particle Scale in Solid-State Fermentation Systems.

PubMed

Sugai-Guérios, Maura Harumi; Balmant, Wellington; Furigo, Agenor; Krieger, Nadia; Mitchell, David Alexander

2015-01-01

Solid-state fermentation (SSF) with filamentous fungi is a promising technique for the production of a range of biotechnological products and has the potential to play an important role in future biorefineries. The performance of such processes is intimately linked with the mycelial mode of growth of these fungi: Not only is the production of extracellular enzymes related to morphological characteristics, but also the mycelium can affect bed properties and, consequently, the efficiency of heat and mass transfer within the bed. A mathematical model that describes the development of the fungal mycelium in SSF systems at the particle scale would be a useful tool for investigating these phenomena, but, as yet, a sufficiently complete model has not been proposed. This review presents the biological and mass transfer phenomena that should be included in such a model and then evaluates how these phenomena have been modeled previously in the SSF and related literature. We conclude that a discrete lattice-based model that uses differential equations to describe the mass balances of the components within the system would be most appropriate and that mathematical expressions for describing the individual phenomena are available in the literature. It remains for these phenomena to be integrated into a complete model describing the development of fungal mycelia in SSF systems.

Texture formation mechanism and constitutive equation for anisotropic thermorheological rare-earth permanent magnets

NASA Astrophysics Data System (ADS)

Zhu, Minggang; Li, Wei

2017-05-01

The study investigates the mechanism and constitutive equations describing oriented texture formation in anisotropic thermorheological rare-earth permanent magnets. The thermorheological process cannot be considered as creep, since the related phenomena are not suitably explained by the diffusion creep model. A mathematical model describing the relationship between the rheological deformation rate and texture orientation was established, and a theoretical expression was obtained for the orientation factor of thermorheological magnets. In addition, nanocrystalline Nd-Fe-B magnets were fabricated, with intrinsic coercivity Hcj=760.1 kA/m, remanence Br=1.469 T, and maximum energy product (BH)max=427.1 kJ/m3.

Solution of non-steady-state substrate concentration in the action of biosensor response at mixed enzyme kinetics

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Jana Ranjani, R.

2018-04-01

In this paper, a mathematical model of an amperometric biosensor at mixed enzyme kinetics and diffusion limitation in the case of substrate inhibition has been developed. The model is based on time dependent reaction diffusion equation containing a non -linear term related to non -Michaelis - Menten kinetics of the enzymatic reaction. Solution for the concentration of the substrate has been derived for all values of parameters using the homotopy perturbation method. All the approximate analytic expressions of substrate concentration are compared with simulation results using Scilab/Matlab program. Finally, we have given a satisfactory agreement between them.

Energy transfer between a nanosystem and its host fluid: A multiscale factorization approach

NASA Astrophysics Data System (ADS)

Sereda, Yuriy V.; Espinosa-Duran, John M.; Ortoleva, Peter J.

2014-02-01

Energy transfer between a macromolecule or supramolecular assembly and a host medium is considered from the perspective of Newton's equations and Lie-Trotter factorization. The development starts by demonstrating that the energy of the molecule evolves slowly relative to the time scale of atomic collisions-vibrations. The energy is envisioned to be a coarse-grained variable that coevolves with the rapidly fluctuating atomistic degrees of freedom. Lie-Trotter factorization is shown to be a natural framework for expressing this coevolution. A mathematical formalism and workflow for efficient multiscale simulation of energy transfer is presented. Lactoferrin and human papilloma virus capsid-like structure are used for validation.

Internationalizing the University Mathematics Curriculum

ERIC Educational Resources Information Center

Appelbaum, Peter; Friedler, Louis M.; Ortiz, Carlos E.; Wolff, Edward F.

2009-01-01

This article offers suggestions for achieving the internationalization of university mathematics-related curricular offerings. It presents learning objectives and related student outcomes, raises general issues related to internationalization, and then discusses how to incorporate the objectives and address these issues within the university…

A multiscale modelling approach to understand atherosclerosis formation: A patient-specific case study in the aortic bifurcation

PubMed Central

Alimohammadi, Mona; Pichardo-Almarza, Cesar; Agu, Obiekezie; Díaz-Zuccarini, Vanessa

2017-01-01

Atherogenesis, the formation of plaques in the wall of blood vessels, starts as a result of lipid accumulation (low-density lipoprotein cholesterol) in the vessel wall. Such accumulation is related to the site of endothelial mechanotransduction, the endothelial response to mechanical stimuli and haemodynamics, which determines biochemical processes regulating the vessel wall permeability. This interaction between biomechanical and biochemical phenomena is complex, spanning different biological scales and is patient-specific, requiring tools able to capture such mathematical and biological complexity in a unified framework. Mathematical models offer an elegant and efficient way of doing this, by taking into account multifactorial and multiscale processes and mechanisms, in order to capture the fundamentals of plaque formation in individual patients. In this study, a mathematical model to understand plaque and calcification locations is presented: this model provides a strong interpretability and physical meaning through a multiscale, complex index or metric (the penetration site of low-density lipoprotein cholesterol, expressed as volumetric flux). Computed tomography scans of the aortic bifurcation and iliac arteries are analysed and compared with the results of the multifactorial model. The results indicate that the model shows potential to predict the majority of the plaque locations, also not predicting regions where plaques are absent. The promising results from this case study provide a proof of concept that can be applied to a larger patient population. PMID:28427316

Mathematical model of biological order state or syndrome in traditional Chinese medicine: based on electromagnetic radiation within the human body.

PubMed

Han, Jinxiang; Huang, Jinzhao

2012-03-01

In this study, based on the resonator model and exciplex model of electromagnetic radiation within the human body, mathematical model of biological order state, also referred to as syndrome in traditional Chinese medicine, was established and expressed as: "Sy = v/ 1n(6I + 1)". This model provides the theoretical foundation for experimental research addressing the order state of living system, especially the quantitative research syndrome in traditional Chinese medicine.

The Forecasting of Future Inventory and the Optimization of Training Requirements within the Airborne Community.

DTIC Science & Technology

1983-12-01

grade levels. Chapter 2 discusses the formulation of the model. It highlights the theoretical and mathematical concepts perti- nant to the model...assignments. This is to insure the professional development of the soldier and is in accordance with the "whole man" concept. 11. IALUI2U Lvels !Wii...objective function can be mathematically expressed as: (aijk (bk ijk This objective function assesses the same penalty to each vacancy of each type of

Application of Vectors to Relative Velocity

ERIC Educational Resources Information Center

Tin-Lam, Toh

2004-01-01

The topic 'relative velocity' has recently been introduced into the Cambridge Ordinary Level Additional Mathematics syllabus under the application of Vectors. In this note, the results of relative velocity and the 'reduction to rest' technique of teaching relative velocity are derived mathematically from vector algebra, in the hope of providing…

Gene Network Construction from Microarray Data Identifies a Key Network Module and Several Candidate Hub Genes in Age-Associated Spatial Learning Impairment

PubMed Central

Uddin, Raihan; Singh, Shiva M.

2017-01-01

As humans age many suffer from a decrease in normal brain functions including spatial learning impairments. This study aimed to better understand the molecular mechanisms in age-associated spatial learning impairment (ASLI). We used a mathematical modeling approach implemented in Weighted Gene Co-expression Network Analysis (WGCNA) to create and compare gene network models of young (learning unimpaired) and aged (predominantly learning impaired) brains from a set of exploratory datasets in rats in the context of ASLI. The major goal was to overcome some of the limitations previously observed in the traditional meta- and pathway analysis using these data, and identify novel ASLI related genes and their networks based on co-expression relationship of genes. This analysis identified a set of network modules in the young, each of which is highly enriched with genes functioning in broad but distinct GO functional categories or biological pathways. Interestingly, the analysis pointed to a single module that was highly enriched with genes functioning in “learning and memory” related functions and pathways. Subsequent differential network analysis of this “learning and memory” module in the aged (predominantly learning impaired) rats compared to the young learning unimpaired rats allowed us to identify a set of novel ASLI candidate hub genes. Some of these genes show significant repeatability in networks generated from independent young and aged validation datasets. These hub genes are highly co-expressed with other genes in the network, which not only show differential expression but also differential co-expression and differential connectivity across age and learning impairment. The known function of these hub genes indicate that they play key roles in critical pathways, including kinase and phosphatase signaling, in functions related to various ion channels, and in maintaining neuronal integrity relating to synaptic plasticity and memory formation. Taken together, they provide a new insight and generate new hypotheses into the molecular mechanisms responsible for age associated learning impairment, including spatial learning. PMID:29066959

Gene Network Construction from Microarray Data Identifies a Key Network Module and Several Candidate Hub Genes in Age-Associated Spatial Learning Impairment.

PubMed

Uddin, Raihan; Singh, Shiva M

2017-01-01

As humans age many suffer from a decrease in normal brain functions including spatial learning impairments. This study aimed to better understand the molecular mechanisms in age-associated spatial learning impairment (ASLI). We used a mathematical modeling approach implemented in Weighted Gene Co-expression Network Analysis (WGCNA) to create and compare gene network models of young (learning unimpaired) and aged (predominantly learning impaired) brains from a set of exploratory datasets in rats in the context of ASLI. The major goal was to overcome some of the limitations previously observed in the traditional meta- and pathway analysis using these data, and identify novel ASLI related genes and their networks based on co-expression relationship of genes. This analysis identified a set of network modules in the young, each of which is highly enriched with genes functioning in broad but distinct GO functional categories or biological pathways. Interestingly, the analysis pointed to a single module that was highly enriched with genes functioning in "learning and memory" related functions and pathways. Subsequent differential network analysis of this "learning and memory" module in the aged (predominantly learning impaired) rats compared to the young learning unimpaired rats allowed us to identify a set of novel ASLI candidate hub genes. Some of these genes show significant repeatability in networks generated from independent young and aged validation datasets. These hub genes are highly co-expressed with other genes in the network, which not only show differential expression but also differential co-expression and differential connectivity across age and learning impairment. The known function of these hub genes indicate that they play key roles in critical pathways, including kinase and phosphatase signaling, in functions related to various ion channels, and in maintaining neuronal integrity relating to synaptic plasticity and memory formation. Taken together, they provide a new insight and generate new hypotheses into the molecular mechanisms responsible for age associated learning impairment, including spatial learning.

Spatial transformation abilities and their relation to later mathematics performance.

PubMed

Frick, Andrea

2018-04-10

Using a longitudinal approach, this study investigated the relational structure of different spatial transformation skills at kindergarten age, and how these spatial skills relate to children's later mathematics performance. Children were tested at three time points, in kindergarten, first grade, and second grade (N = 119). Exploratory factor analyses revealed two subcomponents of spatial transformation skills: one representing egocentric transformations (mental rotation and spatial scaling), and one representing allocentric transformations (e.g., cross-sectioning, perspective taking). Structural equation modeling suggested that egocentric transformation skills showed their strongest relation to the part of the mathematics test tapping arithmetic operations, whereas allocentric transformations were strongly related to Numeric-Logical and Spatial Functions as well as geometry. The present findings point to a tight connection between early mental transformation skills, particularly the ones requiring a high level of spatial flexibility and a strong sense for spatial magnitudes, and children's mathematics performance at the beginning of their school career.

Effects of SKF-83566 and haloperidol on performance on progressive ratio schedules maintained by sucrose and corn oil reinforcement: quantitative analysis using a new model derived from the Mathematical Principles of Reinforcement (MPR).

PubMed

Olarte-Sánchez, C M; Valencia-Torres, L; Cassaday, H J; Bradshaw, C M; Szabadi, E

2013-12-01

Mathematical models can assist the interpretation of the effects of interventions on schedule-controlled behaviour and help to differentiate between processes that may be confounded in traditional performance measures such as response rate and the breakpoint in progressive ratio (PR) schedules. The effects of a D1-like dopamine receptor antagonist, 8-bromo-2,3,4,5-tetrahydro-3-methyl-5-phenyl-1H-3-benzazepin-7-ol hydrobromide (SKF-83566), and a D2-like receptor antagonist, haloperidol, on rats' performance on PR schedules maintained by sucrose and corn oil reinforcers were assessed using a new model derived from Killeen's (Behav Brain Sci 17:105-172, 1994) Mathematical Principles of Reinforcement. Separate groups of rats were trained under a PR schedule using sucrose or corn oil reinforcers. SKF-83566 (0.015 and 0.03 mg kg(-1)) and haloperidol (0.05 and 0.1 mg kg(-1)) were administered intraperitoneally (five administrations of each treatment). Running and overall response rates in successive ratios were analysed using the new model, and estimates of the model's parameters were compared between treatments. Haloperidol reduced a (the parameter expressing incentive value) in the case of both reinforcers, but did not affect the parameters related to response time and post-reinforcement pausing. SKF-83566 reduced a and k (the parameter expressing sensitivity of post-reinforcement pausing to the prior inter-reinforcement interval) in the case of sucrose, but did not affect any of the parameters in the case of corn oil. The results are consistent with the hypothesis that blockade of both D1-like and D2-like receptors reduces the incentive value of sucrose, whereas the incentive value of corn oil is more sensitive to blockade of D2-like than D1-like receptors.

The relative importance of two different mathematical abilities to mathematical achievement.

PubMed

Nunes, Terezinha; Bryant, Peter; Barros, Rossana; Sylva, Kathy

2012-03-01

Two distinct abilities, mathematical reasoning and arithmetic skill, might make separate and specific contributions to mathematical achievement. However, there is little evidence to inform theory and educational practice on this matter. The aims of this study were (1) to assess whether mathematical reasoning and arithmetic make independent contributions to the longitudinal prediction of mathematical achievement over 5 years and (2) to test the specificity of this prediction. Data from Avon Longitudinal Study of Parents and Children (ALSPAC) were available on 2,579 participants for analyses of KS2 achievement and on 1,680 for the analyses of KS3 achievement. Hierarchical regression analyses were used to assess the independence and specificity of the contribution of mathematical reasoning and arithmetic skill to the prediction of achievement in KS2 and KS3 mathematics, science, and English. Age, intelligence, and working memory (WM) were controls in these analyses. Mathematical reasoning and arithmetic did make independent contributions to the prediction of mathematical achievement; mathematical reasoning was by far the stronger predictor of the two. These predictions were specific in so far as these measures were more strongly related to mathematics than to science or English. Intelligence and WM were non-specific predictors; intelligence contributed more to the prediction of science than of maths, and WM predicted maths and English equally well. There is clear justification for making a distinction between mathematical reasoning and arithmetic skills. The implication is that schools must plan explicitly to improve mathematical reasoning as well as arithmetic skills. ©2011 The British Psychological Society.

Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways.

PubMed

Alves, Rui; Vilaprinyo, Ester; Hernádez-Bermejo, Benito; Sorribas, Albert

2008-01-01

There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between these formalisms, discuss the advantages and limitations of each representation, and provide a tentative "road map" for their potential utilization for different problems.

Teachers' Evaluations and Use of Web-Based Curriculum Resources in Relation to the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Webel, Corey; Krupa, Erin E.; McManus, Jason

2015-01-01

This study examines patterns in how a group of fifth- and sixth-grade teachers evaluated and reported using different types of curriculum resources to support their teaching in relation to the mathematical concepts outlined in the Common Core State Standards for Mathematics. In particular, it explores the use of resources that were available to…

A Simple Optical Waveguide Experiment.

ERIC Educational Resources Information Center

Phelps, J.; Sambles, J. R.

1989-01-01

Describes a thin film rectangular dielectric waveguide and its laboratory use. Discusses the theory of uniaxial thin film waveguides with mathematical expressions and the laboratory procedures for a classroom experiment with diagrams. (Author/YP)

Ban Deodorant Ball Mortar.

ERIC Educational Resources Information Center

Carpenter, D. Rae, Jr.; And Others

1988-01-01

Discusses a demonstration of vertical collision of two balls. Shows the theoretical height ratio using mathematical expression and diagrams. Compares it with researchers' experimental results. Expands the two-ball collision to multi-ball system. (YP)

Poynting Theorem, Relativistic Transformation of Total Energy-Momentum and Electromagnetic Energy-Momentum Tensor

NASA Astrophysics Data System (ADS)

Kholmetskii, Alexander; Missevitch, Oleg; Yarman, Tolga

2016-02-01

We address to the Poynting theorem for the bound (velocity-dependent) electromagnetic field, and demonstrate that the standard expressions for the electromagnetic energy flux and related field momentum, in general, come into the contradiction with the relativistic transformation of four-vector of total energy-momentum. We show that this inconsistency stems from the incorrect application of Poynting theorem to a system of discrete point-like charges, when the terms of self-interaction in the product {\\varvec{j}} \\cdot {\\varvec{E}} (where the current density {\\varvec{j}} and bound electric field {\\varvec{E}} are generated by the same source charge) are exogenously omitted. Implementing a transformation of the Poynting theorem to the form, where the terms of self-interaction are eliminated via Maxwell equations and vector calculus in a mathematically rigorous way (Kholmetskii et al., Phys Scr 83:055406, 2011), we obtained a novel expression for field momentum, which is fully compatible with the Lorentz transformation for total energy-momentum. The results obtained are discussed along with the novel expression for the electromagnetic energy-momentum tensor.

Predictive Relation between Early Numerical Competencies and Mathematics Achievement in First Grade Portuguese Children.

PubMed

Marcelino, Lilia; de Sousa, Óscar; Lopes, António

2017-01-01

Early numerical competencies (ENC) (counting, number relations, and basic arithmetic operations) have a central position in the initial learning of mathematics, and their assessment is useful for predicting later mathematics achievement. Using a regression model, this study aims to analyze the correlational and predictive evidence between ENC and mathematics achievement in first grade Portuguese children ( n = 123). The children's ENC were examined at the point of school entry. Three criterion groups (low, moderate, and high ENC) were formed based on the results of the early numerical brief screener and mathematics achievement measured at the end of first grade. The following hypotheses were tested: children who started first grade with low numerical competencies remained low mathematics achievement at the end of first grade; and children who started with high numerical competencies, finished the first grade with high mathematics achievement. The results showed that ENC contributed to a significant amount of explained variance in mathematics achievement at the end of the first grade. Children with low numerical competencies performed lower than children with moderate and high numerical competencies. Findings suggest that ENC are meaningful for predicting first-grade mathematics difficulties.

Predictive Relation between Early Numerical Competencies and Mathematics Achievement in First Grade Portuguese Children

PubMed Central

Marcelino, Lilia; de Sousa, Óscar; Lopes, António

2017-01-01

Early numerical competencies (ENC) (counting, number relations, and basic arithmetic operations) have a central position in the initial learning of mathematics, and their assessment is useful for predicting later mathematics achievement. Using a regression model, this study aims to analyze the correlational and predictive evidence between ENC and mathematics achievement in first grade Portuguese children (n = 123). The children’s ENC were examined at the point of school entry. Three criterion groups (low, moderate, and high ENC) were formed based on the results of the early numerical brief screener and mathematics achievement measured at the end of first grade. The following hypotheses were tested: children who started first grade with low numerical competencies remained low mathematics achievement at the end of first grade; and children who started with high numerical competencies, finished the first grade with high mathematics achievement. The results showed that ENC contributed to a significant amount of explained variance in mathematics achievement at the end of the first grade. Children with low numerical competencies performed lower than children with moderate and high numerical competencies. Findings suggest that ENC are meaningful for predicting first-grade mathematics difficulties. PMID:28713308

Mathematics in Early Childhood: Research-Based Rationale and Practical Strategies

ERIC Educational Resources Information Center

Linder, Sandra M.; Powers-Costello, Beth; Stegelin, Dolores A.

2011-01-01

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for…

Actitud Hacia las Matematicas: Revision Bibliografica (Attitudes Toward Mathematics: Revised Bibliography). Publication No. 39.

ERIC Educational Resources Information Center

Rodriguez Feijoo, Nelida

Investigations about attitudes toward mathematics carried out in the past decade were revised. The instruments used to measure attitudes toward mathematics were analysed as well as the attitudes toward different aspects of mathematics, their relation with other school subjects and their stability through time. Opinions about the influence of…

Influences on Mathematical Preparation of Secondary School Teachers of Mathematics.

ERIC Educational Resources Information Center

Johnson, Carl S.; Byars, Jackson A.

The results of a survey related to the impact of various recommendations on preservice content programs for teachers of mathematics are reported. The content of current programs is compared to the recommendations of the Committee on Undergraduate Programs in Mathematics (CUPM). The acceptance of CUPM and the Cambridge Conference on School…

Final Report of Cambridge Conference on School Mathematics, January 1962 - August 1970.

ERIC Educational Resources Information Center

Cambridge Conference on School Mathematics, Newton, MA.

The Cambridge Conference on School Mathematics (CCSM) was an association of prominent mathematicians who had a concern for mathematics education at school level, from kindergarten through grade twelve. These mathematicians organized three main conferences in three areas of mathematics education, and have carried on activities related to the…

What Is the Problem in Problem-Based Learning in Higher Education Mathematics

ERIC Educational Resources Information Center

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

Working Memory and Language: Skill-Specific or Domain-General Relations to Mathematics?

ERIC Educational Resources Information Center

Purpura, David J.; Ganley, Colleen M.

2014-01-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the…

Gender, Parental Beliefs and Children's Mathematics Performance: Insights from the Longitudinal Study of Australian Children

ERIC Educational Resources Information Center

Carmichael, Colin

2014-01-01

With reports of declining participation in mathematics related careers and low female participation rates, the issue of gender differences in mathematics remains relevant. This study seeks to examine the relationship between: children's sex, parents' beliefs regarding their children's education, and, the children's mathematics performance. Through…

Mathematics Undergraduates' Responses to Semantic Abbreviations, 'Geometric' Images and Multi-Level Abstractions in Group Theory.

ERIC Educational Resources Information Center

Nardi, Elena

2000-01-01

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

Problem Solving in Swedish Mathematics Textbooks for Upper Secondary School

ERIC Educational Resources Information Center

Brehmer, Daniel; Ryve, Andreas; Van Steenbrugge, Hendrik

2016-01-01

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…