Mathematical techniques: A compilation
NASA Technical Reports Server (NTRS)
1975-01-01
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
"Influence Method". Detailed mathematical description
NASA Astrophysics Data System (ADS)
Rios, I. J.; Mayer, R. E.
2015-07-01
A new method for the absolute determination of nuclear particle flux in the absence of known detector efficiency, the "Influence Method", was recently published (I.J. Rios and R.E. Mayer, Nuclear Instruments & Methods in Physics Research A 775 (2015) 99-104). The method defines an estimator for the population and another estimator for the efficiency. In this article we present a detailed mathematical description which yields the conditions for its application, the probability distributions of the estimators and their characteristic parameters. An analysis of the different cases leads to expressions of the estimators and their uncertainties.
Mathematical Description of Dendrimer Structure
NASA Technical Reports Server (NTRS)
Majoros, Istvan J.; Mehta, Chandan B.; Baker, James R., Jr.
2004-01-01
Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.
Mathematical Description of Bacterial Traveling Pulses
Bournaveas, Nikolaos; Buguin, Axel; Silberzan, Pascal; Perthame, Benoît
2010-01-01
The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on Escherichia coli have shown the precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at the macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition, we can capture quantitatively the traveling speed of the pulse as well as its characteristic length. This work opens several experimental and theoretical perspectives since coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance, the particular response of a single cell to chemical cues turns out to have a strong effect on collective motion. Furthermore, the bottom-up scaling allows us to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion. PMID:20808878
FRESHMAN MATHEMATICS COURSE DESCRIPTIONS, TEXAS COLLEGES AND UNIVERSITIES.
ERIC Educational Resources Information Center
Texas Education Agency, Austin.
FOR EACH OF 84 TEXAS COLLEGES AND UNIVERSITIES, THE FOLLOWING INFORMATION IS PRESENTED--(1) ENTRANCE REQUIREMENTS, WITH EMPHASIS ON TESTS AND MATHEMATICS COURSES, (2) GENERAL ORGANIZATION, WITH STATEMENTS OF GRADUATION REQUIREMENTS IN MATHEMATICS FOR BOTH GENERAL STUDENTS AND THOSE WITH MAJORS IN SPECIALIZED FIELDS, (3) A BRIEF DESCRIPTION OF EACH…
Towards a Bernsteinian Language of Description for Mathematics Classroom Discourse
ERIC Educational Resources Information Center
Straehler-Pohl, Hauke; Gellert, Uwe
2013-01-01
This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein's conceptualisation of power in classification, we develop a three-dimensional model that operationalises the…
Connecting Intonation Labels to Mathematical Descriptions of Fundamental Frequency
ERIC Educational Resources Information Center
Grabe, Esther; Kochanski, Greg; Coleman, John
2007-01-01
The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In…
Fuzzy mathematical techniques with applications
Kandel, A.
1986-01-01
This text presents the basic concepts of fuzzy set theory within a context of real-world applications. The book is self-contained and can be used as a starting point for people interested in this fast growing field as well as by researchers looking for new application techniques. The section on applications includes: Manipulation of knowledge in expert systems; relational database structures; pattern clustering; analysis of transient behavior in digital systems; modeling of uncertainty and search trees. Contents: Fuzzy sets; Possibility theory and fuzzy quantification; Fuzzy functions; Fuzzy events and fuzzy statistics; Fuzzy relations; Fuzzy logics; Some applications; Bibliography.
NASA Technical Reports Server (NTRS)
Lennington, R. K.; Rassbach, M. E.
1979-01-01
Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.
A description of seismic amplitude techniques
NASA Astrophysics Data System (ADS)
Shadlow, James
2014-02-01
The acquisition of seismic data is a non-invasive technique used for determining the sub surface geology. Changes in lithology and fluid fill affect the seismic wavelet. Analysing seismic data for direct hydrocarbon indicators (DHIs), such as full stack amplitude anomalies, or amplitude variation with offset (AVO), can help a seismic interpreter relate the geophysical response to real geology and, more importantly, to distinguish the presence of hydrocarbons. Inversion is another commonly used technique that attempts to tie the seismic data back to the geology. Much has been written about these techniques, and attempting to gain an understanding on the theory and application of them by reading through various journals can be quite daunting. The purpose of this paper is to briefly outline DHI analysis, including full stack amplitude anomalies, AVO and inversion and show the relationship between all three. The equations presented have been included for completeness, but the reader can pass over the mathematical detail.
Researchers' Descriptions and the Construction of Mathematical Thinking
ERIC Educational Resources Information Center
Barwell, Richard
2009-01-01
Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing,…
Connecting intonation labels to mathematical descriptions of fundamental frequency.
Grabe, Esther; Kochanski, Greg; Coleman, John
2007-01-01
The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In this paper, we explore the interface between the disciplines, in search of bridges between intonational phonology and speech technology. In a corpus of speech data from seven dialects of English, we hand-labeled over 700 sentences and identified seven nuclear accent types. Then we fitted a third-order polynomial to the fundamental frequency (F0) contour in the region around the accent mark. The polynomial captures the local shape (time-dependence) of F0 in a few numbers, in our case, four coefficients. The coefficients were subjected to statistical analysis. Nineteen of the 21 pairs of accent types differed significantly in one or more coefficients. Our approach bridges the gap between intonational phonology and speech technology. It provides quantitative, empirically testable models of intonation labels that can be implemented in applications. PMID:17974321
McKee, J K; Molnar, S
1988-01-01
The ability to describe dental arch shape is necessary for biomechanical studies of occlusion as well as for anthropological studies of human and primate dental variation. A mathematical method of describing and classifying human dental arch shape was used to assess the nature of individual variability. The method involved the calculation of a series of third-degree polynomials which were fitted to coordinate points along the dental arcade. The slopes of the polynomials, evaluated at these coordinate points, provided a multivariate description of shape, independent of arch size. Graphic representations of arch shape could be constructed from the polynomial equations. These mathematical techniques were used in association with multivariate and univariate statistics to explore the types of variability in dental arch shape among a population of Australian aborigines. The results illustrated the ambiguities of conventional subjective classifications. PMID:3256297
Short description of mathematical support programs for space experiments in the Interkosmos program
NASA Technical Reports Server (NTRS)
Elyasberg, P. Y.
1979-01-01
A synopsis of programs of mathematical support designed at the Institute for Cosmic Research of the USSR Academy of Sciences for cosmic experiments being conducted in the Interkosmos Program is presented. A short description of the appropriate algorithm is given.
Descriptions of Free and Freeware Software in the Mathematics Teaching
NASA Astrophysics Data System (ADS)
Antunes de Macedo, Josue; Neves de Almeida, Samara; Voelzke, Marcos Rincon
2016-05-01
This paper presents the analysis and the cataloging of free and freeware mathematical software available on the internet, a brief explanation of them, and types of licenses for use in teaching and learning. The methodology is based on the qualitative research. Among the different types of software found, it stands out in algebra, the Winmat, that works with linear algebra, matrices and linear systems. In geometry, the GeoGebra, which can be used in the study of functions, plan and spatial geometry, algebra and calculus. For graphing, can quote the Graph and Graphequation. With Graphmatica software, it is possible to build various graphs of mathematical equations on the same screen, representing cartesian equations, inequalities, parametric among other functions. The Winplot allows the user to build graphics in two and three dimensions functions and mathematical equations. Thus, this work aims to present the teachers some free math software able to be used in the classroom.
Kim, David; Farthing, Matthew W; Miller, Cass T; Nylander-French, Leena A
2008-05-30
The objective of this research was to develop a mathematical description of uptake of aromatic and aliphatic hydrocarbons into the stratum corneum of human skin in vivo. A simple description based on Fick's laws of diffusion was used to predict the spatiotemporal variation of naphthalene, 1- and 2-methylnaphthalene, undecane, and dodecane in the stratum corneum of human volunteers. The estimated values of the diffusion coefficients for each chemical were comparable to values predicted using in vitro skin systems and biomonitoring studies. These results demonstrate the value of measuring dermal exposure using the tape-strip technique and the importance of quantifying of dermal uptake. PMID:18423910
Kim, David; Farthing, Matthew W.; Miller, Cass T.; Nylander-French, Leena A.
2008-01-01
The objective of this research was to develop a mathematical description of uptake of aromatic and aliphatic hydrocarbons into the stratum corneum of human skin in vivo. A simple description based on Fick’s Laws of diffusion was used to predict the spatiotemporal variation of naphthalene, 1- and 2-methylnaphthalene, undecane, and dodecane in the stratum corneum of human volunteers. The estimated values of the diffusion coefficients for each chemical were comparable to values predicted using in vitro skin systems and biomonitoring studies. These results demonstrate the value of measuring dermal exposure using the tape-strip technique and the importance of quantifying of dermal uptake. PMID:18423910
Tailoring Modified Moore Method Techniques to Liberal Arts Mathematics Courses
ERIC Educational Resources Information Center
Hitchman, Theron J.; Shaw, Douglas
2015-01-01
Inquiry-based learning (IBL) techniques can be used in mathematics courses for non-majors, such as courses required for liberal arts majors to fulfill graduation requirements. Unique challenges are discussed, followed by adaptations of IBL techniques to overcome those challenges.
Multiscale mapping: Physical concepts and mathematical techniques
Technology Transfer Automated Retrieval System (TEKTRAN)
This is an introductory summary for papers either invited or a part of a symposium at the 18th World Congress of Soil Science, July 2006 in Philadelphia. The symposium, titled "Multiscale Mapping of Soil Properties for Environmental Studies, Agriculture, and Decision Making," focused on techniques u...
Mathematical description of human body constitution and fatness.
Sheikh-Zade, Yu R; Galenko-Yaroshevskii, P A; Cherednik, I L
2014-02-01
Using mathematical modeling of human body, we demonstrated logical drawbacks of body mass index (BMI1 = M/H(2); A. Quetelet, 1832) and proposed more precise body mass index (BMI2 = M/H(3)) as well as body constitution index (BCI = (M/H(3))(1/2)) and fatness index (FI = M/HC(2)), where M, H, and C are body weight, height, and wrist circumference of the individual. PMID:24771443
Description of a tilt wing mathematical model for piloted simulation
NASA Technical Reports Server (NTRS)
Totah, Joseph J.
1991-01-01
A tilt-wing mathematical model that was used in a piloted six-deg-of-freedom flight simulation application is presented. Two types of control systems developed for the model - a conventional programmed-flap wing-tilt control system and a geared-flap wing-tilt control system - are discussed. The objective of this effort was to develop the capability to study tilt-wing aircraft. Experienced tilt-wing pilots subjectively evaluated the model using programmed-flap control to assess the quality of the simulation. The objective was met and the model was then applied to study geared-flap control to investigate the possibility of eliminating the need for auxiliary pitch control devices. This was performed in the moving-base simulation environment, and the vehicle responses with programmed-flap and geared-flap control were compared.
NASA Astrophysics Data System (ADS)
Glazachev, A. V.; Dementyev, Yu. N.; Negodin, K. N.; Umursakova, A. D.
2016-02-01
The article gives the mathematical description of an asynchronous motor with the indirect control of the output mechanical variables of an asynchronous motor in the electric drive. To determine the electromagnetic torque and angular velocity of the asynchronous motor in the electric drive the mathematical description is used in which the values are determined by the readings of the motor and easily measured values by means of known in practice devices. The proposed in the article the mathematical description for the indirect measuring the electromagnetic torque and angular velocity of the asynchronous motor in the electric drive does not contain the integral components that introduce the great error into the value of the controlled electromagnetic torque and angular velocity.
Research on Mathematical Techniques in Psychology. Final Report.
ERIC Educational Resources Information Center
Gulliksen, Harold
Mathematical techniques are developed for studying psychological problems in three fields: (1) psychological scaling, (2) learning and concept formation, and (3) mental measurement. Psychological scaling procedures are demonstrated to be useful in many areas, ranging from sensory discrimination of physical stimuli, such as colors, sounds, etc.,…
a Mathematical Description of the Critical Point in Phase Transitions
NASA Astrophysics Data System (ADS)
Bilge, Ayse Humeyra; Pekcan, Onder
2013-10-01
Let y(x) be a smooth sigmoidal curve, y(n) be its nth derivative and {xm,i} and {xa,i}, i = 1,2,…, be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {xm,i} and {xa,i} are both convergent and they have a common limit xc that we characterize as the critical point of the phase transition. In this study, we examine the logistic growth curve and the Susceptible-Infected-Removed (SIR) epidemic model as typical examples of symmetrical and asymmetrical transition curves. Numerical computations indicate that the critical point of the logistic growth curve that is symmetrical about the point (x0, y0) is always the point (x0, y0) but the critical point of the asymmetrical SIR model depends on the system parameters. We use the description of the sol-gel phase transition of polyacrylamide-sodium alginate (SA) composite (with low SA concentrations) in terms of the SIR epidemic model, to compare the location of the critical point as described above with the "gel point" determined by independent experiments. We show that the critical point tc is located in between the zero of the third derivative ta and the inflection point tm of the transition curve and as the strength of activation (measured by the parameter k/η of the SIR model) increases, the phase transition occurs earlier in time and the critical point, tc, moves toward ta.
ERIC Educational Resources Information Center
Badru, Ademola K.
2015-01-01
This study examined the prediction of academic success of Junior secondary school mathematics students using their cognitive style and problem solving technique. A descriptive survey of correlation type was adopted for this study. A purposive sampling procedure was used to select five Public Junior secondary schools in Ijebu-Ode local government…
ERIC Educational Resources Information Center
Chinelo, Okigbo Ebele; Nwanneka, Okoli Josephine
2016-01-01
This study investigated the techniques used by secondary school Science Technology and Mathematics (STM) teachers in controlling undesirable behaviours in their classrooms. It adopted descriptive survey design in which 178 Anambra State teachers teaching STM subjects in senior secondary were involved in the research. Two sections of questionnaire…
Mathematical analysis techniques for modeling the space network activities
NASA Technical Reports Server (NTRS)
Foster, Lisa M.
1992-01-01
The objective of the present work was to explore and identify mathematical analysis techniques, and in particular, the use of linear programming. This topic was then applied to the Tracking and Data Relay Satellite System (TDRSS) in order to understand the space network better. Finally, a small scale version of the system was modeled, variables were identified, data was gathered, and comparisons were made between actual and theoretical data.
A computerized method for mathematical description of three-dimensional root canal axis.
Dobó-Nagy, C; Keszthelyi, G; Szabó, J; Sulyok, P; Ledeczky, G; Szabó, J
2000-11-01
Knowledge of the three-dimensional (3D) morphology of root canals is important for successful endodontic treatment. The objective of the present study was to determine the 3D root canal axis mathematically. Two views (mesiodistal and buccolingual) of digitized images were taken from extracted natural human teeth. Geometric reconstruction to standardize projection geometry was conducted on images. Because 90-degree turn-around image pairs are Monge images of a given root canal, these Monge images were positioned using photogrammetric methods. Each well-ordered axis pair of a given root canal was put into a common coordinate system resulting in 3D polynomial function of the actual root canal. On the basis of the results gained using 10 samples evaluated with the Friedman statistical test, this description seems to be reproducible. The 3D representation of the root canal may help the clinicians in choosing the optimal instruments and shaping techniques. The root canal axis that is described by the 3D function forms a basis for determination of curvature values and torsion values in each of the axis points. Evaluating these values may also yield a new type of classification. PMID:11469291
A simple mathematical description of an off-grid hybrid solar-wind power generating system
NASA Astrophysics Data System (ADS)
Blasone, M.; Dell'Anno, F.; De Luca, R.; Torre, G.
2013-05-01
We give a detailed description of the energy balance equation for a stand-alone hybrid solar-wind power generating system. The dimensions of the power generator and the energy capacity of a buffer battery (used as an energy storage system) are chosen to suit a known consumer's profile. Future applications of the mathematical model developed and analogies with a similar hydrodynamic problem are discussed.
Physical and Mathematical Description of Nuclear Weapons Identification System (NWIS) Signatures
Mattingly, J.K.; Mihalczo, J.T.; Mullens, J.A.; Valentine, T.E.
1997-09-26
This report describes all time and frequency analysis parameters measured with the new Nuclear Weapons Identification System (NWIS) processor with three input channels: (1) the 252Cf source ionization chamber (2) a detection channel; and (3) a second detection channel for active measurements. An intuitive and physical description of the various functions is given as well as a brief mathematical description and a brief description of how the data are acquired. If the fill five channel capability is used, the number of functions increases in number but not in type. The parameters provided by this new NWIS processor can be divided into two general classes: time analysis signatures including multiplicities and frequency analysis signatures. Data from measurements with an 18.75 kg highly enriched uranium (93.2 wt 0/0, 235U) metai casting for storage are presented to illustrate the various time and frequency analysis parameters.
Innovative techniques for the description of reservoir heterogeneity using tracers
Pope, G.; Sepehrnoori, K.
1991-09-01
The objective of this research is to develop an advanced, innovative technique for the description of reservoir heterogeneity. This proposed method consists of using tracers in single-well backflow tests. The general idea is to make use of fluid drift in the reservoir either due to naturally occurring pressure gradients in the reservoir, or by deliberately imposed pressure gradients using adjacent injection and production wells in the same reservoir. The analytical tool that will be used to design and interpret these tests is a compositional reservoir simulator with special features added and tested specifically for this purpose. 2 refs., 5 figs.
A mathematical description of inhaled particle behavior suitable for analysis of factors affecting deposition in the human upper respiratory tract (nasopharyngeal and oropharyngeal compartments), larynx, and ciliated airways is presented. When upper respiratory tract and larynx f...
Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth
Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip
2014-01-01
Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199
Bayesian Minimum Description Length Techniques for Multiple Changepoint Detection
NASA Astrophysics Data System (ADS)
Anuradha Priyadarshani, Hewa Arachchige
This dissertation develops a minimum description length (MDL) multiple changepoint detection procedure that allows for prior distributions. MDL methods, which are penalized likelihood techniques with penalties based on data description-length information principles, have been successfully applied to many recent multiple changepoint problems. This work shows how to modify the MDL penalty to account for various prior knowledge. Our motivation lies in climatology. Here, a metadata record, which is a file listing times when a recording station physically moved, instrumentation was changed, etc., sometimes exists. While metadata records are notoriously incomplete, they permit the construct a prior distribution that helps detect changepoints. This allows both documented and undocumented changepoints to be analyzed in tandem. The method developed here takes into account 1) metadata, 2) reference series, 3) seasonal means, and 4) autocorrelations. Asymptotically, our estimated multiple changepoint configuration of monthly data is shown to be consistent. The methods are illustrated in the analysis of 114 years of monthly temperatures from Tuscaloosa, Alabama. The multivariate aspect of the methods allow maximum and minimum temperatures to be jointly studied. A method for homogenizing daily temperature series is also developed. While daily temperatures have a complex structure, statistical techniques have been accumulating that can now accommodate all of the salient characteristics of daily temperatures. The goal here is to combine these techniques in a reasonable manner for multiple changepoint identification in daily series; computational speed is key as a century of daily data has over 36,000 data points. Autocorrelation aspects are important since correlation can destroy changepoint techniques and sample correlations of day-to-day temperature anomalies are often as large as 0.7. While homogenized daily temperatures may not be as useful as homogenized monthly or yearly
Description and evaluation of an intraoral cervical plexus anesthetic technique.
Bitner, Daniel P; Uzbelger Feldman, Daniel; Axx, Kevin; Albandar, Jasim M
2015-07-01
Unsuccessful anesthesia of the inferior alveolar nerve (IAN) may be due to supplementary innervations of mandibular molars from other branches, namely the cervical plexus (CP). The purpose of this prospective, randomized, double-blind, controlled trial was to determine the effectiveness of an intraoral cervical plexus anesthetic technique (ICPAT) in mandibular molars with symptomatic irreversible pulpitis (SIR) when the IAN and lingual nerve (LN) blocks failed, and to provide a description of the technique. Forty patients diagnosed with SIR received IAN and LN block anesthesia prior to treatment. After clinical signs of anesthesia, patients were subjected to an electrical pulp test (EPT) at 2-min cycles for 10 min post-injection. The anesthesia was considered unsuccessful if there was a positive EPT response ten minutes following profound lip numbness. The experimental group (n = 20) were administered 2% Lidocaine with 1:100,000 epinephrine using the ICPAT. The control group (n = 20) were administered 0.9% sterile saline using the ICPAT. Success was defined as no response on two consecutive readings from an EPT. In the experimental group, 60% of subjects showed successful anesthesia, whereas none of the subjects in the control group had successful anesthesia. A multiple logistic regression analysis showed that the anesthesia success rate using the ICPAT method was significantly higher (P < 0.05) than in the control group, irrespective of molar tooth type. The ICPAT method may be useful as a supplementary anesthetic technique for mandibular molars with SIR in subjects whom the IAN and LN blocks do not provide adequate anesthesia. PMID:25864872
Computational Technique for Teaching Mathematics (CTTM): Visualizing the Polynomial's Resultant
ERIC Educational Resources Information Center
Alves, Francisco Regis Vieira
2015-01-01
We find several applications of the Dynamic System Geogebra--DSG related predominantly to the basic mathematical concepts at the context of the learning and teaching in Brasil. However, all these works were developed in the basic level of Mathematics. On the other hand, we discuss and explore, with DSG's help, some applications of the polynomial's…
Oral Examination in College Mathematics: An Alternative Assessment Technique
ERIC Educational Resources Information Center
Odafe, Victor U.
2006-01-01
Preparing for an oral examination is an alternative way for students to learn mathematics by working cooperatively in small teams to solve problems. Reformed college mathematics courses are emphasizing the ability to communicate ideas clearly, both orally and in writing. The instructor is able to ask probing questions that are not usually possible…
Description and Application of a Mathematical Method for the Analysis of Harmony
Zuo, Qiting; Jin, Runfang; Ma, Junxia; Cui, Guotao
2015-01-01
Harmony issues are widespread in human society and nature. To analyze these issues, harmony theory has been proposed as the main theoretical approach for the study of interpersonal relationships and relationships between humans and nature. Therefore, it is of great importance to study harmony theory. After briefly introducing the basic concepts of harmony theory, this paper expounds the five elements that are essential for the quantitative description of harmony issues in water resources management: harmony participant, harmony objective, harmony regulation, harmony factor, and harmony action. A basic mathematical equation for the harmony degree, that is, a quantitative expression of harmony issues, is introduced in the paper: HD = ai − bj, where a is the uniform degree, b is the difference degree, i is the harmony coefficient, and j is the disharmony coefficient. This paper also discusses harmony assessment and harmony regulation and introduces some application examples. PMID:26167535
ERIC Educational Resources Information Center
Jansen, Amanda; Spitzer, Sandy M.
2009-01-01
In this study, we examined prospective middle school mathematics teachers' reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers' descriptions of students' thinking and frequency of their…
Online Resources in Mathematics, Teachers' Geneses and Didactical Techniques
ERIC Educational Resources Information Center
Bueno-Ravel, Laetitia; Gueudet, Ghislaine
2009-01-01
The study we present here concerns the consequences of integrating online resources into the teaching of mathematics. We focus on the interaction between teachers and specific online resources they draw on: e-exercise bases. We propose a theoretical approach to study the associated phenomena, combining instrumental and anthropological…
A Non-Mathematical Technique for Teaching Binary Computer Concepts.
ERIC Educational Resources Information Center
Steele, Fred
This document describes an aid invented by the author for teaching binary computer concepts in a data processing course for business students unfamiliar with mathematical concepts. It permits the instructor to simulate the inner, invisible operation of storing data electronically. The standard 8-bit "byte" is represented by a portable…
Descriptive Feedback; Increasing Teacher Awareness, Adapting Research Techniques.
ERIC Educational Resources Information Center
Kepler, Karen B.
This study investigated the ability of middle school teachers to use descriptive feedback from their students in changing their teaching behavior. One homeroom group of twenty-five students was observed in interaction with nine teachers of math, English, social studies, and science over a one-year period to elicit both quantifiable and qualitative…
Explosion-proof fiber optic fire detector: design and mathematical description
NASA Astrophysics Data System (ADS)
Kazakov, V. I.; Moskaletz, O. D.
2014-10-01
The problem of early fire detection in areas classified as potentially explosive is considered in this paper. These include, for example, some types of facilities and plants, which may cause environmental disasters in case of fires. Hard safety requirements impose serious terms for the technical performance the detectors for the protection of such objects from the fire. Detector itself should not cause a fire. The main danger is open conductive parts in the construction of the sensitive elements of detectors, which can lead to the generation of sparks and fire. The using of fiber-optic technology allows creating smoke and heating fire detectors, which only the sensors will be located in the protected area, and all electronic components generate signals and their processing may be removed at considerable distances measured by kilometers. The block diagram of the fire smoke point detector based on fiber-optic technology is considered, the mathematical description of the propagation of optical radiation through the sensing element of the detector is provided, sensitivity is analyzed.
Goddard trajectory determination subsystem: Mathematical specifications
NASA Technical Reports Server (NTRS)
Wagner, W. E. (Editor); Velez, C. E. (Editor)
1972-01-01
The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.
Cross-National Variations in Rural Mathematics Achievement: A Descriptive Overview
ERIC Educational Resources Information Center
Williams, James H.
2005-01-01
Using PISA 2000 data, this article examines cross-national variation in rural mathematics achievement among 15-year-olds in 24 industrialized nations. Rural mathematics scores were significantly lower than scores in urban and medium-size communities in 14 of 24 countries. However, patterns were complex. Most commonly, a linear relationship…
Cross-National Variations in Rural Mathematics Achievement: A Descriptive Overview
ERIC Educational Resources Information Center
Williams, James H.
2005-01-01
Using PISA 2000 data, this article examines cross-national variation in rural mathematics achievement among 15-year olds in 24 industrialized nations. Rural mathematics scores were significantly lower than scores in urban and medium-size communities in 14 of 24 countries. However, patterns were complex. Most commonly, a linear relationship…
Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes
NASA Technical Reports Server (NTRS)
Bittker, D. A.
1993-01-01
A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.
Mathematical description of complex chemical kinetics and application to CFD modeling codes
NASA Technical Reports Server (NTRS)
Bittker, D. A.
1993-01-01
A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.
Mathematical description of the structure of a capillary-porous body
NASA Astrophysics Data System (ADS)
Lyashkevich, I. M.; Volchenok, V. F.; Raptunovich, G. S.
1981-02-01
The properties of a capillary-porous disperse body are described and a mathematical model of its structure is constructed. As the model body, gypsum stone, which hardens under conditions of oriented mass transfer involving the liquid phase, is selected.
NASA Astrophysics Data System (ADS)
Sadrtdinov, A. R.; Safin, R. G.; Gerasimov, M. K.; Petrov, V. I.; Gilfanov, K. K.
2016-04-01
The article presents the scheme of processing of plant biomass in the gasification installation with a plasma heat source to produce synthesis gas suitable for chemical industry. The analyzed physical picture of raw materials' recycling process underlies a mathematical description of the process set out in the form of the basic differential equations with boundary conditions. The received mathematical description allows calculating of the main parameters of equipment for biomass recycling and to determine the optimal modes of its operation.
Mathematical representations of turbulent mixing
NASA Technical Reports Server (NTRS)
Farmer, R. C.; Audeh, B.
1973-01-01
A basic description is given of the mathematical tools and models which are presently used to represent turbulent, free shear layers. Recommendations are included for ways in which current modeling techniques can be improved.
Dimensional Analysis: an Elegant Technique for Facilitating the Teaching of Mathematical Modelling.
ERIC Educational Resources Information Center
Fay, Temple H.; Joubert, Stephan V.
2002-01-01
Dimension analysis is promoted as a technique that promotes better understanding of the role of units and dimensions in mathematical modeling problems. Dimensional analysis is shown to lead to interesting systems of linear equations to solve, and can point the way to more quantitative analysis. Two student problems are discussed. (Author/MM)
ERIC Educational Resources Information Center
Duxbury, Mark
2004-01-01
An enzymatic laboratory experiment based on the analysis of serum is described that is suitable for students of clinical chemistry. The experiment incorporates an introduction to mathematical method-comparison techniques in which three different clinical glucose analysis methods are compared using linear regression and Bland-Altman difference…
A Description and Characterization of Student Activity in an Open, Online, Mathematics Help Forum
ERIC Educational Resources Information Center
van de Sande, Carla
2011-01-01
Free, open, online, calculus forums are websites where students from around the world can post course-related queries that may be viewed and responded to by anonymous others. These sites are an emergent resource for students seeking help and have become a part of many students' mathematical experience. The purpose of this paper is to introduce and…
The mathematical description of the body centre of mass 3D path in human and animal locomotion.
Minetti, Alberto E; Cisotti, Caterina; Mian, Omar S
2011-05-17
Although the 3D trajectory of the body centre of mass during ambulation constitutes the 'locomotor signature' at different gaits and speeds for humans and other legged species, no quantitative method for its description has been proposed in the literature so far. By combining the mathematical discoveries of Jean Baptiste Joseph Fourier (1768-1830, analysis of periodic events) and of Jules Antoine Lissajous (1822-1880, parametric equation for closed loops) we designed a method simultaneously capturing the spatial and dynamical features of that 3D trajectory. The motion analysis of walking and running humans, and the re-processing of previously published data on trotting and galloping horses, as moving on a treadmill, allowed to obtain closed loops for the body centre of mass showing general and individual locomotor characteristics. The mechanical dynamics due to the different energy exchange, the asymmetry along each 3D axis, and the sagittal and lateral energy recovery, among other parameters, were evaluated for each gait according to the present methodology. The proposed mathematical description of the 3D trajectory of the body centre of mass could be used to better understand the physiology and biomechanics of normal locomotion, from monopods to octopods, and to evaluate individual deviations with respect to average values as resulting from gait pathologies and the restoration of a normal pattern after pharmacological, physiotherapeutic and surgical treatments. PMID:21463861
TPS as an Effective Technique to Enhance the Students' Achievement on Writing Descriptive Text
ERIC Educational Resources Information Center
Sumarsih, M. Pd.; Sanjaya, Dedi
2013-01-01
Students' achievement in writing descriptive text is very low, in this study Think Pair Share (TPS) is applied to solve the problem. Action research is conducted for the result. Additionally, qualitative and quantitative techniques are applied in this research. The subject of this research is grade VIII in Junior High School in Indonesia. From…
ERIC Educational Resources Information Center
Zainuddin
2015-01-01
This study was aimed at finding out the effectiveness of applying Cooperative Integrated Reading and Composition (CIRC) Technique on Students' Reading Descriptive Text Achievement. In other words, the objective of this study was to find out if there was a significant effect of applying Cooperative Integrated Reading and Composition (CIRC)…
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Singhal, A. K.; Tam, L. T.
1984-01-01
The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.
Garcia Sestafe, J V; García Paez, J M; Carrera San Martín, A; Jorge-Herrero, E; Navidad, R; Candela, I; Castillo-Olivares, J L
1994-06-01
A material subjected to traction stress increases in length; if we maintain the elongation constant, the stress varies over a period of time. This phenomenon has been referred to as relaxation. The purpose of this study was to define a mathematical law that relates the variation in stress to time when elongation remains constant in bovine pericardium. The mathematical function obtained after assaying 34 samples to the point of relaxation, subjected to initial stresses ranging from 0.17-10.07 MPa, responds to the following equation: y = -0.0252 + 0.953 alpha - (0.0165 + 0.015 alpha)lnt, where y is the stress withstood at an instant in time, t, after initial stress alpha. A normogram, validated by assays of up to 6,340 min duration (4.40 days), is presented for graphic calculation, permitting the computation of the loss of stress due to relaxation of this biomaterial, with initial stresses ranging from 1-10 MPa. PMID:8071387
Lopez-Benitez, Ruben Rusch, Oliver Heverhagen, Johannes Levent, Kara Hanno, Hoppe Geiser, Christa Kettenbach, Joachim
2013-10-15
We describe a new, useful embolization technique applied to occlude narrow vessel branches ({<=}1.5 mm (0.06 Double-Prime ) in diameter) by deployment of one hydrocoil, through a microcatheter, in a way similar to the way in which one might navigate through the vascular lumen with a guidewire.
Petin, Vladislav G; Kim, Jin Kyu; Kritsky, Roman O; Komarova, Ludmila N
2008-06-01
The potential ability of various physical or chemical agents to enhance their effect when they are applied simultaneously with each other is well-known. The purpose of this study was to adjust a simple mathematical model to describe, optimize and predict a synergistic interaction between fluoride and xylitol on acid production by mutans streptococci. The model suggests that the synergism is caused by the additional effective damage arising from an interaction of sublesions induced by each agent. These sublesions are considered to be ineffective when each agent is used individually. The predictions of the model were verified by comparison with experimental data published by other researchers. It was shown that the model describes the experimental data, predicts the greatest value of the synergistic effect and the condition under which it can be achieved. The synergistic effect appeared to decline with any deviation from the optimal value of the ratio of effective damages produced by each agent alone. PMID:18367232
Mathematical description and measurement of refractive parameters of freeform spectacle lenses.
Yu, Jing; Qiu, Zhongjun; Fang, Fengzhou
2014-08-01
Refractive parameters are the main design and evaluation parameters of freeform spectacle lenses. In this paper, the mathematical model of refractive parameters is established, and the refractive power distribution on the whole surface is drawn with a radial basis function. The measurement methods are analyzed, and typical freeform spectacle lenses are measured with a freeform verifier. The refractive power distribution on the whole surface, the cylinder view, and the refractive power curve along the progressive corridor are drawn up. There are no evident image changes on the whole surface. The refractive power smoothly varies along the progressive corridor. In comparing the results with the analysis, measurement results are in agreement with the calculation. PMID:25090322
[Mathematical description of the three-dimensional axis of the root canal of human teeth].
Dobó, Nagy Csaba; Keszthelyi, Gusztáv; Sulyok, Péter; Ledeczky, Gábor; Szabó, József
2002-08-01
The objective of the present study was to describe root canal axes of natural human teeth mathematically. Two views (clinical and proximal) radiographs were taken from extracted human teeth. Geometry defines the 90-degree turn-around image pairs as Monge images. These Monge images of the root canals were positioned using photogrammetric methods. Each well-ordered axis pair of a given root canal was put into a common coordinate system resulting in three-dimensional polynomial function of the actual root canal. Testing differences between determined and repeatedly determined axes of ten samples by statistical analysis did not show any significant differences. Evaluation of data gained on a large number of samples may also yield a new type of classification. PMID:12236090
ERIC Educational Resources Information Center
Ringer, Catharina W.
2013-01-01
In today's mathematics education, there is an increasing emphasis on students' understanding of the mathematics set forth in standards documents such as the "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics, 2000) and, most recently, the "Common Core State Standards for Mathematics"…
SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY
2016-01-01
In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.
Research on target recognition techniques of radar networking based on fuzzy mathematics
NASA Astrophysics Data System (ADS)
Guan, Chengbin; Wang, Guohong; Guan, Chengzhun; Pan, Jinshan
2007-11-01
Nowadays there are more and more targets, so it is more difficult for radar networking to track the important targets. To reduce the pressure on radar networking and the waste of ammunition, it is very necessary for radar networking to recognize the targets. Two target recognition approaches of radar networking based on fuzzy mathematics are proposed in this paper, which are multi-level fuzzy synthetical evaluation technique and lattice approaching degree technique. By analyzing the principles, the application techniques are given, the merits and shortcomings are also analyzed, and applying environments are advised. Another emphasis is the compare between the multiple mono-level fuzzy synthetical evaluation and the multi-level fuzzy synthetical evaluation, an instance is carried out to illuminate the problem, then the results are analyzed in theory, the conclusions are gotten which can be instructions for application in engineering.
ERIC Educational Resources Information Center
Fowler, Crystal Nicole
2013-01-01
This qualitative descriptive case study explored the perceptions of parents and teachers of the academic achievement gap in mathematics between African-American middle school males and their White counterparts. Ten parents, both African-American and White, with students attending middle school in the Cherokee County School District and 5 teachers…
A 3-year program was conducted to examine the ecology of Cladophora glomerata and to develop a mathematical model useful in evaluating various management strategies for the control of this nuisance alga. This manuscript provides a detailed description of the field program and stu...
NASA Technical Reports Server (NTRS)
Bekey, G. A.
1971-01-01
Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.
ERIC Educational Resources Information Center
McLoughlin, M. Padraig M. M.
2008-01-01
The author of this paper submits the thesis that learning requires doing; only through inquiry is learning achieved, and hence this paper proposes a programme of use of a modified Moore method in a Probability and Mathematical Statistics (PAMS) course sequence to teach students PAMS. Furthermore, the author of this paper opines that set theory…
Roberge, P.R.
1994-12-31
Electrochemical impedance spectroscopy (EIS) has been proven to be a rapid and accurate technique for measuring corrosion rates in the most difficult situations and for yielding precious information concerning the occurrence of localized corrosion. But routine monitoring with EIS requires that certain assumptions be made and the data be processed automatically. To achieve these goals, a method was developed which consists in finding the geometric center of an arc formed by three successive data points on a complex impedance diagram. The three point analysis technique was further developed by permuting the data points involved in the projection of centers in order to obtain a population of projected centers. This last improvement permitted automation of the data analysis while providing some necessary statistical information concerning the adherence of the results with the resistive-capacitive (RC) behavior which is assumed for the evaluation of the parameters related to the general and localized corrosion rates. This paper illustrates the efficiency of EIS in a field situation with results obtained during the evaluation of organic corrosion inhibitors against sour media and reviews the mathematical principles of the projection/permutation (ProPer) technique for routine analysis of EIS data points.
Recommended procedures and techniques for the petrographic description of bituminous coals
Chao, E.C.T.; Minkin, J.A.; Thompson, C.L.
1982-01-01
bed. The use of bulk-specific-gravity determinations is alo recommended for identification and characterization of the distinctive lithologic units. The availability of an AIAS also enhances the capability to acquire textural information. Ranges of size of maceral and mineral grains can be quickly and precisely determined by use of an AIAS. We assume that shape characteristics of coal particles can also be readily evaluated by automated image analysis, although this evaluation has not yet been attempted in our laboratory. Definitive data on the particulate mineral content of coal constitute another important segment of petrographic description. Characterization of mineral content may be accomplished by optical identification, electron microprobe analysis, X-ray diffraction, and scanning and transmission electron microscopy. Individual mineral grains in place in polished blocks or polished this sections, or separated from the coal matrix by sink-float methods are studied by analytical techniques appropriate to the conditions of sampling. Finally, whenever possible, identification of the probable genus or plant species from which a given coal component is derived will add valuable information and meaning to the petrographic description. ?? 1982.
ERIC Educational Resources Information Center
Kritzer, Karen L.
2009-01-01
This study examined young deaf children's early informal/formal mathematical knowledge as measured by the Test of Early Mathematics Ability (TEMA-3). Findings from this study suggest that prior to the onset of formal schooling, young deaf children might already demonstrate evidence of academic delays. Of these 28 participants (4-6 years of age),…
MacLean, Adam L; Harrington, Heather A; Stumpf, Michael P H; Byrne, Helen M
2016-01-01
The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine. PMID:26677193
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
NASA Astrophysics Data System (ADS)
de Vicente, S.; Galiano, G.; Velasco, J.; Aróstegui, J. M.
Two-phase systems where a dense phase of small particles is fluidized with a gas flow appear in many industrial applications, among which the fluidized bed combustors are probably the most important. A homogenization technique allows us to formulate the mathematical model in form of the compressible Navier-Stokes system type with some particularities: 1) the volumetric fraction of the dense phase (analogous to the density in the Navier-Stokes equations) may vanish, 2) the constitutive viscosity law may depend in a nonlinear form on this density, 3) the source term is nonlinear and coupled with state equations involving drag forces and hydrodynamic pressure, and 4) the state equation for the collision pressure of dense phase blows up for finite values of the density. We develop a rigorous theory for a special kind of solutions we call stationary clouds. Such solutions exist only under restrictions on the geometry of combustor and on the boundary conditions that usually meet in engineering applications. In return, these solutions have a stationary one-dimensional structure very simple and, from them, it is possible to reconstruct much of the dynamics of the whole system, responding to most of the practical issues of interest. Finally, we study the linear stability for the trivial solutions corresponding to uniform fluidized states injecting plane wave perturbations in our equations. Depending on the parameters of the equations of state describing the collisions between solid particles, hydrodynamic pressure, and the values of blowing boundary condition, we can draw detailed abacus separating stable regions of unstable regions where bubbles appear. Then, we use the dispersion relations of this multidimensional linearized model, combined with the stationary phase theorem, to approach the profiles and the evolution of the bubbles appearing in unstable regimes, and verify that the obtained results adjust to the observations.
Pope, G.A.; Sepehrnoori, K.; Delshad, M.; Ferreira, L.; Gupta, A.; Maroongroge, V.
1994-11-01
This is the final report of a three year research project on the use of tracers for reservoir characterization. The objective of this research was to develop advanced, innovative techniques for the description of reservoir characteristics using both single-well backflow and interwell tracer tests. (1) The authors implemented and validated tracer modeling features in a compositional simulator (UTCOMP). (2) They developed and applied a new single well tracer test for estimating reservoir heterogeneity. (3) They developed and applied a new single well tracer test for estimating reservoir wettability in-situ. (4) They developed a new, simple and efficient method to analyze two well tracer tests based upon type curve matching and illustrated its use with actual field tracer data. (5) They developed a new method for deriving an integrated reservoir description based upon combinatorial optimization schemes. (6) They developed a new, interwell tracer test for reservoir heterogeneity called vertical tracer profiling (VTP) and demonstrated its advantages over conventional interwell tracer testing. (7) They developed a simple and easy analytical method to estimate swept pore volume from interwell tracer data and showed both the theoretical basis for this method and its practical utility. (8) They made numerous enhancements to our compositional reservoir simulator such as including the full permeability tensor, adding faster solvers, improving its speed and robustness and making it easier to use (better I/0) for tracer simulation problems. (9) They applied the enhanced version of UTCOMP to the analysis of interwell tracer data using perfluorocarbons at Elks Hill Naval Petroleum Reserve. All of these accomplishments taken together have significantly improved the state of reservoir tracer technology and have demonstrated that it is a far more powerful and useful tool for quantitative reservoir characterization than previously realized or practiced by the industry.
Venugopal, R.
1992-01-01
Advanced mathematical tools have been developed for calculating corrections that are applied to neutron scattering data in order to account for the finite size of the scattering samples. The multiple scattering events (due to finite size) that occur in a neutron scattering experiment typically comprise 8 to 10% of the total measured scattering events. A Monte Carlo program was developed to simulate the disk geometry arrangement used in the Lowell neutron scattering experiments. A modern random number generator which passes all known randomness tests was implemented in the Monte Carlo program. A direction-biasing method was applied in order to improve the statistical results of the Monte Carlo simulation. The ratio of the probability of n + 1 scatterings to n scatterings was investigated for the disk geometry. The Monte Carlo calculation was also used to simulate the time-of-flight spectra and energy spectra. Corrections for multiple scattering were calculated for two sets of data; one at 128 keV and the other at 200 keV. The Monte Carlo results provided significant improvement over previous results. A parallel study was carried out to determine the feasibility of calculating the corrections analytically. Analytical techniques involving eigenfunction expansion, sparse matrix method and the Rayliegh-Ritz variational method were found to be inadequate to solve the problem.
Accuracy and Techniques in the Preparation of Mathematics Worksheets for Tactile Learners
ERIC Educational Resources Information Center
Rosenblum, L. Penny; Herzberg, Tina
2011-01-01
Data were gathered from 166 participants regarding their qualifications for and training in preparing mathematics materials for tactile learners. The participants shared information about the courses and workshops they had attended, the books and resources they used, the amount of time they spent preparing mathematics materials, and information…
ERIC Educational Resources Information Center
Tsatsaroni, Anna; Lerman, Stephen; Xu, Guo-Rong
This paper presents aspects of a study that aims to describe and make sense of changes over time in the intellectual field of mathematics education research. Drawing on the work of B. Bernstein, especially his essay on intellectual fields and knowledge structures, the paper seeks to raise questions about the fields standing in the wider field of…
Mathematical Methods in Counterterrorism: Tools and Techniques for a New Challenge
NASA Astrophysics Data System (ADS)
Hicks, David L.; Memon, Nasrullah; Farley, Jonathan D.; Rosenørn, Torben
Throughout the years mathematics has served as the most basic and fundamental tool employed by scientists and researchers to study and describe a wide variety of fields and phenomena. One of the most important practical application areas of mathematics has been for national defense and security purposes. For example, during the Second World War, the mathematical principles underlying game theory and cryptography played a very important role in military planning. Since that time, it has become clear that mathematics has an important role to play in securing victory in any global conflict, including the struggle faced by national security and law enforcement officials in the fight against those engaged in terrorism and other illicit activities.
NASA Astrophysics Data System (ADS)
Ribeiro, Vitor B.; Silva, Flávio A.; Oliveira, Julio C. R. F.; Franz, Lucas V.; Schneider, Eduardo O.; Moretti, Cleber; Ranzini, Stenio M.
2013-01-01
Today and next generation optical coherent systems rely more and more in DSP algorithms to improve capacity, spectral efficiency and fiber impairments mitigation. The amount of signal processing is remarkable, and because of that ASICs are preferable in order to comply with cost, power consumption and size, required in OIF 100G optical module standards. One important step in the ASIC development process is the validation of the DSP algorithms mathematical models in a high level language that consider HW characteristics and constrains. In this work we present, compare and evaluate in experimental data the mathematical model developed in Matlab and the SystemC model developed in C++. The DSP algorithms functionalities implemented were orthonormalization, CD equalizer, clock recovery, dynamic equalizer, frequency offset and phase estimation. The SystemC model considers clock signals, reset/enable structures, parallelization, finite fixed-point operations and structures that are closer to the ASIC HW implementation; due to these restrictions the performance is not as good as the mathematical modeling. The DSP algorithms models are evaluated in two 112 Gbit/s DP-QPSK experimental scenarios. In the first scenario the models are evaluated in back-to-back with ASE noise loading; in the second scenario the models are compared in a 226km optical fiber recirculation loop, with 80x112 Gbit/s DP-QPSK channels (8.96 Tbit/s). In the back-to-back experiment the OSNR penalty from the mathematical model to the SystemC model is only 1,0dB and in the recirculation loop the maximum reach is 2,600 km and 2,200 km for the Matlab and SystemC models respectively.
Gray, W.G.
2001-01-25
This project has contributed to the improved understanding and precise physical description of multiphase subsurface flow by combining theoretical derivation of equations, lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and simplification of field-scale equations to assess the advantages and disadvantages of the complete theory.
NASA Technical Reports Server (NTRS)
Fortenbaugh, R. L.
1980-01-01
A mathematical model of a high performance airplane capable of vertical attitude takeoff and landing (VATOL) was developed. An off line digital simulation program incorporating this model was developed to provide trim conditions and dynamic check runs for the piloted simulation studies and support dynamic analyses of proposed VATOL configuration and flight control concepts. Development details for the various simulation component models and the application of the off line simulation program, Vertical Attitude Take-Off and Landing Simulation (VATLAS), to develop a baseline control system for the Vought SF-121 VATOL airplane concept are described.
Kritzer, Karen L
2009-01-01
This study examined young deaf children's early informal/formal mathematical knowledge as measured by the Test of Early Mathematics Ability (TEMA-3). Findings from this study suggest that prior to the onset of formal schooling, young deaf children might already demonstrate evidence of academic delays. Of these 28 participants (4-6 years of age), for whom data were analyzed, none received a score on the TEMA-3, indicating above-"average" ability according to normative ranking. More than half of participants received scores substantially below average with 11 participants receiving scores a year or more behind normative age-equivalent scores. Upon more focused analysis, specific areas of difficulty were found to include word/story problems, skip counting (i.e., counting by twos, threes, etc.), number comparisons, the reading/writing of two to three digit numbers, and addition/subtraction number facts. A qualitative analysis of the answers participants gave and the behaviors they demonstrated while answering the test items was conducted and revealed possible explanations for why specific test items may have been challenging. Implications of findings for parents, early interventionists, and teachers of young deaf children are discussed. PMID:19596725
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
Educational assessment of mathematics skills and abilities.
Bryant, B R; Rivera, D P
1997-01-01
Mathematics assessments play a valuable role in identifying students' strengths and weaknesses and in developing and monitoring instructional practice. Over the last century, mathematics assessment has been refined as math content has changed as a result of curriculum reform. Today, researchers and practitioners use various assessment techniques to (a) identify students who have mathematics learning disabilities (LD), (b) target individual strengths and weaknesses across mathematics areas, (c) document the effects of mathematics instruction in a remedial or special program, (d) identify strategies that students employ during math activities, (e) conduct research about the characteristics of students with math LD, and (f) examine the technical characteristics of mathematics tests. This article provides an historical overview of the development of mathematics assessment and a description of specific strategies for conducting math evaluations. PMID:9009875
Grimes, Kevin L; Inoue, Haruhiro
2016-05-01
Historically, the most robust outcomes in treatment of achalasia were seen with surgical myotomy. Per oral endoscopic myotomy (POEM) introduced an endoscopic method for creating a surgical myotomy. Thousands of cases of POEM have been performed; however, there is no standard technique, and the rates of clinical success and adverse events vary widely among centers. This article presents a detailed description of the POEM technique, including the rationale and potential pitfalls of the main variations, in the context of the international literature. PMID:27112254
Günther, T; Büttner, C; Käsbohrer, A; Filter, M
2015-01-01
Mathematical models on properties and behavior of harmful organisms in the food chain are an increas- ingly relevant approach of the agriculture and food industry. As a consequence, there are many efforts to develop biological models in science, economics and risk assessment nowadays. However, there is a lack of international harmonized standards on model annotation and model formats, which would be neces- sary to set up efficient tools supporting broad model application and information exchange. There are some established standards in the field of systems biology, but there is currently no corresponding provi- sion in the area of plant protection. This work therefore aimed at the development of an annotation scheme using domain-specific metadata. The proposed scheme has been validated in a prototype implementation of a web-database model repository. This prototypic community resource currently contains models on aflatoxin secreting fungal Aspergillus flavus in maize, as these models have a high relevance to food safety and economic impact. Specifically, models describing biological processes of the fungus (growth, Aflatoxin secreting), as well as dose-response- and carry over models were included. Furthermore, phenological models for maize were integrated as well. The developed annotation scheme is based on the well-established data exchange format SBML, which is broadly applied in the field of systems biology. The identified example models were annotated according to the developed scheme and entered into a Web-table (Google Sheets), which was transferred to a web based demonstrator available at https://sites.google.com/site/test782726372685/. By implementation of a software demonstrator it became clear that the proposed annotation scheme can be applied to models on plant pathogens and that broad adoption within the domain could promote communication and application of mathematical models. PMID:27141756
NASA Technical Reports Server (NTRS)
Seinfeld, J. H. (Principal Investigator)
1982-01-01
The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three dimensional concentration fields from atmospheric diffusion models. General conditions are derived for the "reconstructability' of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data is developed.
NASA Technical Reports Server (NTRS)
Seinfeld, J. H. (Principal Investigator)
1982-01-01
The problem of the assimilation of remote sensing data into mathematical models of atmospheric pollutant species was investigated. The data assimilation problem is posed in terms of the matching of spatially integrated species burden measurements to the predicted three-dimensional concentration fields from atmospheric diffusion models. General conditions were derived for the reconstructability of atmospheric concentration distributions from data typical of remote sensing applications, and a computational algorithm (filter) for the processing of remote sensing data was developed.
Bagnasco, Annamaria; Galaverna, Lucia; Aleo, Giuseppe; Grugnetti, Anna Maria; Rosa, Francesca; Sasso, Loredana
2016-01-01
In the literature we found many studies that confirmed our concerns about nursing students' poor maths skills that directly impact on their ability to correctly calculate drug dosages with very serious consequences for patient safety. The aim of our study was to explore where students had most difficulty and identify appropriate educational interventions to bridge their mathematical knowledge gaps. This was a quali-quantitative descriptive study that included a sample of 726 undergraduate nursing students. We identified exactly where students had most difficulty and identified appropriate educational interventions to bridge their mathematical knowledge gaps. We found that the undergraduate nursing students mainly had difficulty with basic maths principles. Specific learning interventions are needed to improve their basic maths skills and their dosage calculation skills. For this purpose, we identified safeMedicate and eDose (Authentic World Ltd.), only that they are only available in English. In the near future we hope to set up a partnership to work together on the Italian version of these tools. PMID:26347449
Kamat, Nagesh
2008-11-01
Perineal urethrostomy stenosis can be a difficult problem to treat, especially in patients with balanitis xerotica obliterans. We have devised a technique of using the buccal mucosa, with the idea of forming a composite stoma comprising skin and buccal mucosa. We describe the technique and short-term results in 4 patients. PMID:18789512
NASA Technical Reports Server (NTRS)
Wong, K. W.
1974-01-01
In lunar phototriangulation, there is a complete lack of accurate ground control points. The accuracy analysis of the results of lunar phototriangulation must, therefore, be completely dependent on statistical procedure. It was the objective of this investigation to examine the validity of the commonly used statistical procedures, and to develop both mathematical techniques and computer softwares for evaluating (1) the accuracy of lunar phototriangulation; (2) the contribution of the different types of photo support data on the accuracy of lunar phototriangulation; (3) accuracy of absolute orientation as a function of the accuracy and distribution of both the ground and model points; and (4) the relative slope accuracy between any triangulated pass points.
Noorbhai, M Habib; Noakes, Timothy D
2016-10-01
One of the first principles of cricket batsmanship that is coached from a young age is to play with a straight bat. Limited studies to date have examined whether top international batsmen use this traditionally described technique. Accordingly, we performed a descriptive, observational study of the backlift technique adopted by 65 of the most successful batsmen of all time, based on their career averages, strike rate and runs scored. The batsmen were divided into two groups depending on whether they played the game before or after 1954. Surprisingly, more than 70% of these successful batsmen did not adopt the traditionally taught technique. Instead, they adopted a more looped action in which the initial movement of the bat was in the direction of the slips, and in extreme cases it was either towards the gully/point region or to have the face of the bat directed towards the off-side. This suggests that traditionally taught batting coaching techniques may hinder, rather than enhance future cricketing performance. Since the vast majority of cricketers are not coached in this technique, this finding probably indicates that this looped technique is likely a contributing factor to effective batsmanship. PMID:26956380
NASA Astrophysics Data System (ADS)
Artese, G.; Fiaschi, S.; Di Martire, D.; Tessitore, S.; Fabris, M.; Achilli, V.; Ahmed, A.; Borgstrom, S.; Calcaterra, D.; Ramondini, M.; Artese, S.; Floris, M.; Menin, A.; Monego, M.; Siniscalchi, V.
2016-06-01
The Emilia Romagna Region (N-E Italy) and in particular the Adriatic Sea coastline of Ravenna, is affected by a noticeable subsidence that started in the 1950s, when the exploitation of on and off-shore methane reservoirs began, along with the pumping of groundwater for industrial uses. In such area the current subsidence rate, even if lower than in the past, reaches the -2 cm/y. Over the years, local Authorities have monitored this phenomenon with different techniques: spirit levelling, GPS surveys and, more recently, Differential Interferometric Synthetic Aperture Radar (DInSAR) techniques, confirming the critical situation of land subsidence risk. In this work, we present the comparison between the results obtained with DInSAR and GPS techniques applied to the study of the land subsidence in the Ravenna territory. With regard to the DInSAR, the Small Baseline Subset (SBAS) and the Coherent Pixel Technique (CPT) techniques have been used. Different SAR datasets have been exploited: ERS-1/2, ENVISAT, TerraSAR-X and Sentinel-1. Some GPS campaigns have been also carried out in a subsidence prone area. 3D vertices have been selected very close to existing persistent scatterers in order to link the GPS measurement results to the SAR ones. GPS data were processed into the International reference system and the comparisons between the coordinates, for the first 6 months of the monitoring, provided results with the same trend of the DInSAR data, even if inside the precision of the method.
CAD/CAM silicone simulator for teaching cheiloplasty: description of the technique.
Zheng, Y; Lu, B; Zhang, J; Wu, G
2015-02-01
Techniques of virtual simulation have been used to teach junior surgeons how to do a cheiloplasty, but still do not meet the trainees' demands. We describe a CAD/CAM silicone simulator, which we made using several maxillofacial prosthetic techniques. An optical scanning system was used to collect the data about the cleft lip. Reverse engineering software was then used to build the virtual model, and this was processed in wax by machine. The definitive simulator was made with prosthetic silicone and extrinsic colourants. The surgical trainees practised the basic skills of cheiloplasty on the simulator, and proved its worth. PMID:25476261
DESCRIPTION OF THE PROCESS MODEL PROJECTION TECHNIQUE (PROMPT). VERSION 3.0
The report describes the model logic and data sources for Version 3.0 of the Process Model Projection Technique (PROMPT), one of four stationary source emission and control cost forecasting models developed for the National Acid Precipitation Assessment Program (NAPAP). PROMPT pr...
Smith, Zachary A.; Armin, Sean; Raphael, Dan; Khoo, Larry T.
2011-01-01
Background: We describe a new posterior dynamic stabilizing system that can be used to augment the mechanics of the degenerating lumbar segment. The mechanism of this system differs from other previously described surgical techniques that have been designed to augment lumbar biomechanics. The implant and technique we describe is an extension-limiting one, and it is designed to support and cushion the facet complex. Furthermore, it is inserted through an entirely percutaneous technique. The purpose of this technical note is to demonstrate a novel posterior surgical approach for the treatment of lumbar degenerative. Methods: This report describes a novel, percutaneously placed, posterior dynamic stabilization system as an alternative option to treat lumbar degenerative disk disease with and without lumbar spinal stenosis. The system does not require a midline soft-tissue dissection, nor subperiosteal dissection, and is a truly minimally invasive means for posterior augmentation of the functional facet complex. This system can be implanted as a stand-alone procedure or in conjunction with decompression procedures. Results: One-year clinical results in nine individual patients, all treated for degenerative disease of the lower lumbar spine, are presented. Conclusions: This novel technique allows for percutaneous posterior dynamic stabilization of the lumbar facet complex. The use of this procedure may allow a less invasive alternative to traditional approaches to the lumbar spine as well as an alternative to other newly developed posterior dynamic stabilization systems. PMID:22145084
Schach von Wittenau, A.E.; Cox, L.J.; Bergstrom, P.H., Jr.; Chandler, W.P.; Hartmann-Siantar, C.L.; Hornstein, S.M.
1997-10-31
We outline the techniques used within PEREGRINE, a 3D Monte Carlo code calculation system, to model the photon output from medical accelerators. We discuss the methods used to reduce the phase-space data to a form that is accurately and efficiently sampled.
Hernández-Velarde, R; Muñoz, O; Garduño-Rodríguez, G; Gonzáles-Arroyo, S; Gutiérrez, G
1979-01-01
In the serum of patients with typhoid fever counterimmunoelectrophoretic techniques were used for the detection of antibodies to Salmonella "O" antigen. Lipopolysacharides (LPS) obtained with phenol and water from Salmonella typhi (antigens 0, 9 and 12) were used. Positive results were obtained in those patients with typhoid fever (20). The lower and higher titration levels were 1:8 and 1:32 respectively; the geometric mean was 1:16. The variation coefficient during the intra assay tests was 0.19, and remained stable throughout the inter-assay tests. Reproducibility, as well as a rapid technique, make this test a valuable tool for the serologic diagnosis of typhoid fever. PMID:420534
Jeong, Chang Wook; Oh, Jong Jin; Jeong, Seong Jin; Hong, Sung Kyu; Byun, Seok-Soo; Choe, Gheeyoung; Lee, Sang Eun
2012-07-01
The aim of the present study was to assess the impact of a novel posterior reconstruction technique during robot-assisted laparoscopic prostatectomy on continence recovery. A total of 116 consecutive patients who received the novel posterior reconstruction (case group) were retrospectively compared with a cohort of 126 patients who did not receive posterior reconstruction (control group). The primary end-point was the duration of continence recovery (no pad use) after robot-assisted laparoscopic prostatectomy. The posterior reconstruction was obtained by opposing the median dorsal fibrous raphe to the posterior counterpart of the detrusor apron, rather than the Denonvilliers' fascia. The case group showed higher continence rates at all points of evaluation, which were 2 weeks (30.1% vs 19.8%), 1 month (58.4% vs 45.7%), 3 months (82.7% vs 70.5%) and 6 months postoperatively (95.3% vs 86.4%) (P = 0.007). Application of the novel posterior reconstruction technique, age and length of membranous urethra were significant variables for the complete recovery of continence on multivariable analysis. This study shows that the application of this novel PR technique significantly improves the recovery of continence in patients undergoing robot-assisted laparoscopic prostatectomy. PMID:22404556
Harris, Mark; Bishop, Timothy; Bernard, Jason
2015-01-01
Introduction: A small proportion of simple elbow dislocations are grossly unstable and joint congruence is not maintained after reduction. In this rare situation operative treatment is indicated. We describe a new intra articular reconstruction that utilises a slip of triceps tendon to provide immediate stability to the elbow. Methods: We assessed 20 cadaveric elbows, measuring the length of triceps tendon available and required to complete the reconstruction. We then sequentially sectioned the ligamentous stabilisers of an elbow before performing the new technique. We measured the displacement and angulation possible at the elbow before and after the reconstruction. Results: All 20 elbows had sufficient triceps tendon length to complete the new technique. Prior to the reconstruction greater than 30 mm of joint distraction and 90 degrees varus or valgus angulation was possible. Following the reconstruction it was not possible to re-dislocate the elbow. Only 2 mm of joint distraction and 10 degrees of varus or valgus angulation were possible with the triceps graft fixed in position. Discussion: This novel technique elegantly avoids many of the problems associated with current methods. We have demonstrated that it is technically feasible and easy to perform with minimal equipment requirements or costs. PMID:27163079
Deng, Jie; Larson, Andrew C.
2010-01-01
Objectives To test the feasibility of combining inner-volume imaging (IVI) techniques with conventional multishot periodically rotated overlapping parallel lines with enhanced reconstruction (PROPELLER) techniques for targeted-PROPELLER magnetic resonance imaging. Materials and Methods Perpendicular section-selective gradients for spatially selective excitation and refocusing RF pulses were applied to limit the refocused field-of-view (FOV) along the phase-encoding direction for each rectangular blade image. We performed comparison studies in phantoms and normal volunteers by using targeted-PROPELLER methods for a wide range of imaging applications that commonly use turbo-spin-echo (TSE) approaches (brain, abdominal, vessel wall, cardiac). Results In these initial studies, we demonstrated the feasibility of using targeted-PROPELLER approaches to limit the imaging FOV thereby reducing the number of blades or permitting increased spatial resolution without commensurate increases in scan time. Both phantom and in vivo motion studies demonstrated the potential for more robust regional self-navigated motion correction compared with conventional full FOV PROPELLER methods. Conclusion We demonstrated that the reduced FOV targeted-PROPELLER technique offers the potential for reducing imaging time, increasing spatial resolution, and targeting specific areas for robust regional motion correction. PMID:19465860
Mathematical model of strip specimens for application of pulse-heating technique
NASA Astrophysics Data System (ADS)
Xiao, Peng; Wang, Qingwei; Dai, Jingmin
2008-10-01
The dynamic measurement of selected thermophysical properties of electrically conducting solids in the temperature range of 1100 K to the melting point was conducted using strip specimens, for simultaneous measurement of the normal spectral emissivity by using integrating sphere reflectometry. The method is based on rapid resistive self-heating of the specimen from room temperature to any desired high temperature in less than several seconds by the passage of an electical current pulse through it to measure the pertinent quantities, as current, voltage, and randiance temperature, with sub-millisecond resolution. The estimation of heat capacity and hemispherical total emissivity is based on various computational methods derived by assuming that the temperature was uniform in the central part of the specimen. The validity of this approach was verified when specimens with large cross sections and when the temperature on the specimen surface was measured. A numerical model was established with the temperature variations across the specimen was taken into consideration. The mathematical model established can be used in the simulation experiments to access the magnitude of specific phenomena due to the temperature gradient inside the specimen, in relation to the specimen geometry and to the specific thermophysical properties of different materials.
ERIC Educational Resources Information Center
Idowu, Olumuyiwa Ayodeji
2013-01-01
Over the past 2 years, almost 45% of the students attending a local suburban high school failed Algebra 2. The purpose of this study was to compare the impact of a cooperative instructional technique (student teams-achievement divisions [STAD]) to traditional instructional methods on performance in high school algebra. Motivational and cognitive…
A Description of the Revised ATHEANA (A Technique for Human Event Analysis)
FORESTER,JOHN A.; BLEY,DENNIS C.; COOPER,SUSANE; KOLACZKOWSKI,ALAN M.; THOMPSON,CATHERINE; RAMEY-SMITH,ANN; WREATHALL,JOHN
2000-07-18
This paper describes the most recent version of a human reliability analysis (HRA) method called ``A Technique for Human Event Analysis'' (ATHEANA). The new version is documented in NUREG-1624, Rev. 1 [1] and reflects improvements to the method based on comments received from a peer review that was held in 1998 (see [2] for a detailed discussion of the peer review comments) and on the results of an initial trial application of the method conducted at a nuclear power plant in 1997 (see Appendix A in [3]). A summary of the more important recommendations resulting from the peer review and trial application is provided and critical and unique aspects of the revised method are discussed.
Gelbwachs, Jerry A; Farley, Robert W
2004-05-10
Knowledge of cloud-base heights is important for climate studies, weather, and military operations. Conventional lidar methods monitor cloud depths by direct transmission of the beam through the cloud and sensing the backscattered returns. These techniques are limited by severe optical scattering by cloud particles to thickness <0.5 km. We have conceived of a novel lidar method measurement for thick-cloud-base altimetry from above that is not restricted by cloud scattering. The new method, known as GLITTER (an acronym for glimpses of the lidar images through the empty regions), relies on cloud porosity and diffuse reflection from land features to sense cloud bottoms. An aircraft GLITTER lidar measured cloud bases at 3.7- and 4.5-km altitudes. These initial results represent a proof-of-principle demonstration of the new lidar method. PMID:15143824
Boix, Macarena; Cantó, Begoña
2013-04-01
Accurate image segmentation is used in medical diagnosis since this technique is a noninvasive pre-processing step for biomedical treatment. In this work we present an efficient segmentation method for medical image analysis. In particular, with this method blood cells can be segmented. For that, we combine the wavelet transform with morphological operations. Moreover, the wavelet thresholding technique is used to eliminate the noise and prepare the image for suitable segmentation. In wavelet denoising we determine the best wavelet that shows a segmentation with the largest area in the cell. We study different wavelet families and we conclude that the wavelet db1 is the best and it can serve for posterior works on blood pathologies. The proposed method generates goods results when it is applied on several images. Finally, the proposed algorithm made in MatLab environment is verified for a selected blood cells. PMID:23458301
NASA Astrophysics Data System (ADS)
Davies, Nicholas M.; Lettington, Alan H.; Hilton, Moira
1997-05-01
Fourier transform IR (FTIR) spectroscopy has become a powerful analytical tool for the detection and measurement of atmospheric pollutant gases. This work describes the application of concentration analysis techniques to data recorded with a versatile FTIR spectroscopy system, developed at the University of Reading PHysics Department. Spectra were recorded at three separate sites, each possessing a distinct source of atmospheric pollution gases. The two sites monitored in the active mode were a traffic congested town center at rush hour and a dairy farm cow shed. The site monitored passively contained three 5 m high methane burners. The analysis techniques have been designed to provide rapid and accurate analysis of the spectrometer data, without the need for high computing power, thus making analysis possible in the field using a laptop PC. In an attempt to enhance the resolution of the spectral data, and therefore resolve overlapping spectral lines, a super- resolution algorithm has been tested on part of the recorded data. The results of applying the algorithm has been tested on part of the recorded data. The results of applying the algorithm, predominantly an image processing technique, are shown and improvements to the algorithm are discussed. Results from the urban and agricultural sites show that CO, CH4, and NH3 can be measured to a ppm level with a maximum uncertainly of 8 percent.
Widgren, Stefan; Frössling, Jenny
2010-11-01
Understanding the intensity and spatial patterns of animal transfers is of prime importance as geographical moves play an important part in the spread and potential control of contagious animal diseases of veterinary importance. For the purpose of visualizing all registered between-herd animal movements in Sweden between 1 July 2005 and 31 December 2008 by map animation, a grid network technique based on the Bresenham line algorithm was developed. Potential spatio-temporal clustering of animals registered as sold or purchased based on location and month of trade was also detected and tested using a spatial scan statistic. Calculations were based on data from 31,375 holdings and 3,487,426 head of cattle. In total, 988,167 between-herd movements of individual bovines were displayed in a sequence of maps covering three and a half years by 2-week intervals. The maps showed that several cattle movements, both short- and long-distance, take place in Sweden each week of the year. However, most animals (75%) were only registered at one single holding during the study period and 23% were sold to a different holding once. Spatial scan statistics based on data from the year 2008 indicated uneven distributions of purchased or sold animals in space and time. During each autumn, there was an increase in cattle movements and October and November showed significantly more cases of sold or purchased animals (relative risk ~1.7, p = 0.001). Based on the results, we conclude that cattle trade is constantly active at a considerable level. This, in combination with possibly insufficient biosecurity routines applied on many farms, constitutes a risk that contagious diseases are spread in the population. The grid network maps were generated through the use of open-source tools and software in order to decrease software costs and facilitate sharing of programme code. In addition, the technique was based on scripts that allow for the inclusion of iterative processes and that comprise all
NASA Astrophysics Data System (ADS)
Majewski, Steven R.; Ostheimer, James C.; Kunkel, William E.; Patterson, Richard J.
2000-11-01
We have begun a survey of the structure of the Milky Way halo, as well as the halos of other Local Group galaxies, as traced by their constituent giant stars. These giant stars are identified via large-area, CCD photometric campaigns. Here we present the basis for our photometric search method, which relies on the gravity sensitivity of the Mg I triplet+MgH features near 5150 Å in F-K stars, and which is sensed by the flux in the intermediate-band DDO51 filter. Our technique is a simplified variant of the combined Washington/DDO51 four-filter technique described by Geisler, which we modify for the specific purpose of efficiently identifying distant giant stars for follow-up spectroscopic study: We show here that for most stars the Washington T1-T2 color is correlated monotonically with the Washington M-T2 color with relatively low scatter; for the purposes of our survey, this correlation obviates the need to image in the T1 filter, as originally proposed by Geisler. To calibrate our (M-T2, M-DDO51) diagram as a means to discriminate field giant stars from nearby dwarfs, we utilize new photometry of the main sequences of the open clusters NGC 3680 and NGC 2477 and the red giant branches of the clusters NGC 3680, Melotte 66, and ω Centauri, supplemented with data on field stars, globular clusters and open clusters by Doug Geisler and collaborators. By combining the data on stars from different clusters, and by taking advantage of the wide abundance spread within ω Centauri, we verify the primary dependence of the M-DDO51 color on luminosity and demonstrate the secondary sensitivity to metallicity among giant stars. Our empirical results are found to be generally consistent with those from analysis of synthetic spectra by Paltoglou & Bell. Finally, we provide conversion formulae from the (M, M-T2) system to the (V, V-I) system, corresponding reddening laws, as well as empirical red giant branch curves from ω Centauri stars for use in deriving photometric
Jens, Sjoerd Marquering, Henk A.; Koelemay, Mark J. W.; Reekers, Jim A.
2015-02-15
ObjectiveTo study the feasibility of 2D perfusion imaging in critical limb ischemia (CLI).Methods/ResultsPerfusion angiography is a new technology which was tested in 18 patients with CLI of the foot. A standardized protocol was used with a catheter placed at the mid-part of the popliteal artery, and a total of 9 cc of non-ionic iodinated contrast material was injected at a rate of 3 cc/sec. The technology is based on early cardiology research where iodinated contrast agents were used for imaging of cardiac perfusion. During the first pass of the contrast, there is a significant diffusion of the contrast agents into the interstitial space, particularly for non-ionic and low-molecular-weight compounds.DiscussionThe original angiography data can be used to make a time–density curve, which represents the actual perfusion of the foot in time. Angiographic perfusion imaging is a post-processing modality for which no extra contrast or radiation is needed. With this technique, it is possible to get more information about the perfusion status and microcirculation of the foot. This is a step toward functional imaging in CLI patients.
Rural Mathematics Educator, 2002.
ERIC Educational Resources Information Center
Rural Mathematics Educator, 2002
2002-01-01
This document contains the two issues of "Rural Mathematics Educator" published in 2002. This newsletter of the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM) includes articles on rural mathematics education, as well as information and descriptions of professional development opportunities for…
Combined FPPE-PTR Calorimetry Involving TWRC Technique. Theory and Mathematical Simulations
NASA Astrophysics Data System (ADS)
Dadarlat, Dorin; Pop, Mircea Nicolae; Streza, Mihaela; Longuemart, Stephane; Depriester, Michael; Hadj Sahraoui, Abdelhak; Simon, Viorica
2010-12-01
Photopyroelectric calorimetry in the front detection configuration (FPPE) was combined with photothermal radiometry (PTR), in order to investigate dynamic thermal parameters of different layers of a detection cell. The layout of the detection cell consists of three layers: directly irradiated pyroelectric sensor, liquid layer, and solid backing material; and the scanning parameter is the thickness of the liquid layer (thermal-wave resonator cavity method). The theory developed for the two techniques indicates that both FPPE and PTR signals can lead, in the thermally thin regime for the sensor and liquid layer, to the direct measurement of the thermal diffusivity or effusivity of the sensor and/or liquid layer, or the thermal effusivity of the backing material. The two methods offer complementary results and/or reciprocally support each other.
NASA Technical Reports Server (NTRS)
Gassaway, J. D.; Mahmood, Q.; Trotter, J. D.
1978-01-01
A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.
Fluoroscopy-Guided Sacroiliac Joint Injection: Description of a Modified Technique.
Kasliwal, Prasad Jaychand; Kasliwal, Sapana
2016-02-01
Sacroiliac joint (SIJ) pathology is a common etiologic cause for 10 - 27% of cases of mechanical low back pain (LBP) below the L5 level. In the absence of definite clinical or radiologic diagnostic criteria, controlled blocks of the SIJ have become the choice assessment method for making the diagnosis of SIJ pain. The SI joint is most often characterized as a large, auricular-shaped, diarthrodial synovial joint. In reality, its synovial characteristic is limited only to the distal third and anterior third. In SIJ interventions, the lateral view has been underutilized. In our technique, we used the lateral view to create a three-dimensional view of the SIJ to aid in gauging the accurateness of the contrast spread and to obtain a precise block. After obtaining appropriate fluoroscopic images, a curved tip spinal needle was directed into the inferior aspect of the SIJ using a posterior approach. As the needle contacts firm tissues on the posterior aspect of the joint, position of the needle tip is checked using lateral fluoroscopy. In the lateral view, the needle tip position is manipulated to keep it in the anterior third of the SIJ and contrast is injected. Our criteria for accurate SIJ block, in posteroanterior (PA) view, is the injection of the contrast medium should outline the joint space and the contrast medium should be seen to travel cephalad along the joint line. In the lateral view, the contrast medium most densely outlines the parameter of the joint. We have utilized this method with good effect in approximately 30 cases over one year. Out of 30 cases, needle position and contrast spread was satisfactory in 28 and 27 cases, respectively. So satisfactory needle placement and contrast spread was in 93% and 87% cases. Pain relief of 80% or more after intra-articular injection of local anesthetic was seen in 50% (15 of 30) patients; pain relief of 50 - 79% was witnessed in 30% (9 of 30) patients. Thus, pain decreased 50% or more in 80% (24 of 30) of the joints
Mathematical morphology for shape description
NASA Astrophysics Data System (ADS)
Schmitt, M.
2002-03-01
We first examine the measurements one can perform on the space of compact and convex sets. A famous theorem, due to Hadwiger (1957), shows that any measurement with nice properties, namely additivity, is a linear combination of Minkowski functionals. Then, some useful formulae, linking measurements in different dimensions of space are derived.In the second step, we make use of the morphological operations transforming sets into sets. These sets are then measured using the previous measurements. The most famous attempt yields the concept of granulomerties and their extensions.In the last part, we examine a way to build morphological random sets which are compatible with morphological operators like erosions or openings and apply it to the most famous example in morphology, the Boolean model, describing objects located at random.
Technology Transfer Automated Retrieval System (TEKTRAN)
Pest control managers can benefit from using mathematical approaches, particularly models, when implementing area-wide pest control programs that include sterile insect technique (SIT), especially when these are used to calculate required rates of sterile releases to result in suppression or eradica...
ERIC Educational Resources Information Center
Livne, Nava L.; Milgram, Roberta M.
2000-01-01
A questionnaire of out-of-school activities was developed to assess mathematical creative ability at four levels using a three-stage circular technique. Israeli high school students (n=139) reported whether they had performed the activities. Resulting data provided evidence of the construct validity of a 12-item scale for assessing creative…
NASA Technical Reports Server (NTRS)
Buckey, J. C.; Beattie, J. M.; Gaffney, F. A.; Nixon, J. V.; Blomqvist, C. G.
1984-01-01
Accurate, reproducible, and non-invasive means for ventricular volume determination are needed for evaluating cardiovascular function zero-gravity. Current echocardiographic methods, particularly for the right ventricle, suffer from a large standard error. A new mathematical approach, recently described by Watanabe et al., was tested on 1 normal formalin-fixed human hearts suspended in a mineral oil bath. Volumes are estimated from multiple two-dimensional echocardiographic views recorded from a single point at sequential angles. The product of sectional cavity area and center of mass for each view summed over the range of angles (using a trapezoidal rule) gives volume. Multiple (8-14) short axis right ventricle and left ventricle views at 5.0 deg intervals were videotaped. The images were digitized by two independent observers (leading-edge to leading-edge technique) and analyzed using a graphics tablet and microcomputer. Actual volumes were determined by filling the chambers with water. These data were compared to the mean of the two echo measurements.
What Counts as Mathematical Discourse?
ERIC Educational Resources Information Center
Moschkovich, Judit
2003-01-01
In this paper I use situated and socio-cultural perspective (Gee, 1996 & 1999) to examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. Using this example, I discuss how the distinction between everyday and mathematical discourse can help or hinder us in hearing the mathematical content in…
ERIC Educational Resources Information Center
Locklear, Tonja Motley
2012-01-01
The Sources of Middle School Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) was adapted for use in this study investigating the impact that gender, race, sexual orientation, hometown location (rural, suburban, or urban), high school GPA, college GPA and letter grade of a mathematics course in the previous semester had on the four…
ERIC Educational Resources Information Center
Idil, Feriha Hande; Narli, Serkan; Aksoy, Esra
2016-01-01
The aim of this study is to examine middle school students' attitude towards mathematics in the context of their mathematic learning preferences using data mining which is data analysis methodology that has been successfully used in different areas including educational domains. "How do I actually learn?" questionnaire and attitude scale…
ERIC Educational Resources Information Center
Afzal, Muhammad Tanveer; Gondal, Bashir; Fatima, Nuzhat
2014-01-01
The major objective of the study was to elicit the effect of three instructional methods for teaching of mathematics on low, average and high achiever elementary school students. Three methods: traditional instructional method, computer assisted instruction (CAI) and teacher facilitated mathematics learning software were employed for the teaching…
Changing Mathematics Education in Mozambique.
ERIC Educational Resources Information Center
Gerdes, Paulus
1981-01-01
A brief description and analysis of mathematics education in different phases of the history of Mozambique are provided. Particular attention is given to teacher training and the first National Seminar on the Teaching of Mathematics. (MP)
Mathematical and statistical analysis
NASA Technical Reports Server (NTRS)
Houston, A. Glen
1988-01-01
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
PETERSON, CLARENCE E.
THIS IS THE FIRST OF A SERIES DESIGNED TO PROVIDE AID TO STATES IN ORGANIZING AND OPERATING PROGRAMS UNDER TITLE VIII OF THE NATIONAL DEFENSE EDUCATION ACT, PUBLIC LAW 85-864. IT FURNISHES--(1) GENERAL INFORMATION ABOUT A TECHNOLOGY OR BROAD FIELD OF WORK, (2) COMPOSITE JOB DESCRIPTIONS OF REPRESENTATIVE OCCUPATIONS IN THAT FIELD OF WORK, (3) A…
Acquisition of teleological descriptions
NASA Astrophysics Data System (ADS)
Franke, David W.
1992-03-01
Teleology descriptions capture the purpose of an entity, mechanism, or activity with which they are associated. These descriptions can be used in explanation, diagnosis, and design reuse. We describe a technique for acquiring teleological descriptions expressed in the teleology language TeD. Acquisition occurs during design by observing design modifications and design verification. We demonstrate the acquisition technique in an electronic circuit design.
Krill, Michael; Peck, Evan
2014-12-01
An anterior cruciate ligament ganglion cyst is an infrequent but potentially clinically significant cause of knee pain. Although the cyst may be removed surgically, percutaneous ultrasound-guided anterior cruciate ligament ganglion cyst aspiration and injection is feasible. To our knowledge, we present the first reported case description of the utilization of ultrasound guidance to perform this procedure with a successful clinical outcome. PMID:25088315
NASA Technical Reports Server (NTRS)
Dieudonne, J. E.
1978-01-01
A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.
Redundancy management of electrohydraulic servoactuators by mathematical model referencing
NASA Technical Reports Server (NTRS)
Campbell, R. A.
1971-01-01
A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.
NASA Technical Reports Server (NTRS)
Zolotukhin, V. G.; Kolosov, B. I.; Usikov, D. A.; Borisenko, V. I.; Mosin, S. T.; Gorokhov, V. N.
1980-01-01
A description of a batch of programs for the YeS-1040 computer combined into an automated system for processing photo (and video) images of the Earth's surface, taken from spacecraft, is presented. Individual programs with the detailed discussion of the algorithmic and programmatic facilities needed by the user are presented. The basic principles for assembling the system, and the control programs are included. The exchange format within whose framework the cataloging of any programs recommended for the system of processing will be activated in the future is displayed.
ERIC Educational Resources Information Center
Kliman, Gilbert
The Cornerstone Project is an application of child psychoanalytic techniques in synergy with therapeutic nursery education. The Cornerstone School and the method associated with it provide treatment for children ages three to six years within a nursery classroom group setting. A therapist works six or more hours per week in the classroom, during…
I Learn Mathematics from My Students--Multiculturalism in Action.
ERIC Educational Resources Information Center
Henderson, David W.
1996-01-01
Gives examples of new mathematics theorems and proofs shown to the author by his students. Reflects on the notion of proof and discusses issues of multiculturalism in mathematics and descriptions of mathematics. (MKR)
2015-01-01
The traditional method of recording ionic currents in neurons has been with voltage-clamp steps. Other waveforms such as action potentials (APs) can be used. The AP clamp method reveals contributions of ionic currents that underlie excitability during an AP (Bean BP. Nat Rev Neurosci 8: 451–465, 2007). A novel usage of the method is described in this report. An experimental recording of an AP from the literature is digitized and applied computationally to models of ionic currents. These results are compared with experimental AP-clamp recordings for model verification or, if need be, alterations to the model. The method is applied to the tetrodotoxin-sensitive sodium ion current, INa, and the calcium ion current, ICa, from suprachiasmatic nucleus (SCN) neurons (Jackson AC, Yao GL, Bean BP. J Neurosci 24: 7985–7998, 2004). The latter group reported voltage-step and AP-clamp results for both components. A model of INa is constructed from their voltage-step results. The AP clamp computational methodology applied to that model compares favorably with experiment, other than a modest discrepancy close to the peak of the AP that has not yet been resolved. A model of ICa was constructed from both voltage-step and AP-clamp results of this component. The model employs the Goldman-Hodgkin-Katz equation for the current-voltage relation rather than the traditional linear dependence of this aspect of the model on the Ca2+ driving force. The long-term goal of this work is a mathematical model of the SCN AP. The method is general. It can be applied to any excitable cell. PMID:26041831
Gray, W.G.; Tompson, A.; Soll, W.E.
1998-06-01
'Improved capabilities for modeling multiphase flow in the subsurface requires that several aspects of the system which impact the flow and transport processes be more properly accounted for. A distinguishing feature of multiphase flow in comparison to single phase flow is the existence of interfaces between fluids. At the microscopic (pore) scale, these interfaces are known to influence system behavior by supporting non-zero stresses such that the pressures in adjacent phases are not equal. In problems of interphase transport at the macroscopic (core) scale, knowledge of the total amount of interfacial area in the system provides a clue to the effectiveness of the communication between phases. Although interfacial processes are central to multiphase flow physics, their treatment in traditional porous-media theories has been implicit rather than explicit; and no attempts have been made to systematically account for the evolution of the interfacial area in dynamic systems or to include the dependence of constitutive functions, such as capillary pressure, on the interfacial area. This project implements a three-pronged approach to assessing the importance of various features of multiphase flow to its description. The research contributes to the improved understanding and precise physical description of multiphase subsurface flow by combining: (1) theoretical derivation of equations, (2) lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and (3) solution of the field-scale equations using a discrete numerical method to assess the advantages and disadvantages of the complete theory. This approach includes both fundamental scientific inquiry and a path for inclusion of the scientific results obtained in a technical tool that will improve assessment capabilities for multiphase flow situations that have arisen due to the introduction of organic materials in the natural environment. This report summarizes work after 1.5 years of a 3
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Vargas-Schaffer, Grisell; Nowakowsky, Michal; Eghtesadi, Marzieh; Cogan, Jennifer
2015-09-15
Chronic chest pain is a challenge, and serratus anterior muscle pain syndrome (SAMPS) is often overlooked. We have developed an ultrasound-guided technique for infiltrating local anesthetics and steroids in patients with SAMPS. In 8 patients, the duration of chronic pain was approximately 19 months. Three months after treatment, all patients had experienced a significant reduction in pain. Infiltration for SAMPS confirms the diagnosis and provides adequate pain relief. PMID:26361386
NASA Astrophysics Data System (ADS)
Balac, Stéphane; Fernandez, Arnaud
2014-10-01
In optics the nonlinear Schrödinger equation (NLSE) which modelizes light-wave propagation in an optical fibre is the most widely solved by the Symmetric Split-Step method. The practical efficiency of the Symmetric Split-Step method is highly dependent on the computational grid points distribution along the fiber and therefore an efficient adaptive step-size control strategy is mandatory. A lot of adaptive step-size methods designed to be used in conjunction with the Symmetric Split-Step method for solving the various forms taken by the NLSE can be found in the literature dedicated to optics. These methods can be gathered together into two groups. Broadly speaking, a first group of methods is based on the observation along the propagation length of the behavior of a given optical quantity (e.g. the photons number) and the step-size at each computational step is set so as to guarantee that the known properties of the quantity are preserved. Most of the time these approaches are derived under specific assumptions and the step-size selection criterion depends on the fiber parameters. The second group of methods makes use of some mathematical concepts to estimate the local error at each computational grid point and the step-size is set so as to maintain it lower than a prescribed tolerance. This approach should be preferred due to its generality of use but suffers from a lack of understanding in the mathematical concepts of numerical analysis it involves. The aim of this paper is to present an analysis of local error estimate and adaptive step-size control techniques for solving the NSLE by the Symmetric Split-Step method with all the unavoidable mathematical rigor required for a comprehensive understanding of the topic.
Kleynen, Melanie; Braun, Susy M.; Bleijlevens, Michel H.; Lexis, Monique A.; Rasquin, Sascha M.; Halfens, Jos; Wilson, Mark R.; Beurskens, Anna J.; Masters, Rich S. W.
2014-01-01
Background Motor learning is central to domains such as sports and rehabilitation; however, often terminologies are insufficiently uniform to allow effective sharing of experience or translation of knowledge. A study using a Delphi technique was conducted to ascertain level of agreement between experts from different motor learning domains (i.e., therapists, coaches, researchers) with respect to definitions and descriptions of a fundamental conceptual distinction within motor learning, namely implicit and explicit motor learning. Methods A Delphi technique was embedded in multiple rounds of a survey designed to collect and aggregate informed opinions of 49 international respondents with expertise related to motor learning. The survey was administered via an online survey program and accompanied by feedback after each round. Consensus was considered to be reached if ≥70% of the experts agreed on a topic. Results Consensus was reached with respect to definitions of implicit and explicit motor learning, and seven common primary intervention strategies were identified in the context of implicit and explicit motor learning. Consensus was not reached with respect to whether the strategies promote implicit or explicit forms of learning. Discussion The definitions and descriptions agreed upon may aid translation and transfer of knowledge between domains in the field of motor learning. Empirical and clinical research is required to confirm the accuracy of the definitions and to explore the feasibility of the strategies that were identified in research, everyday practice and education. PMID:24968228
The Dilemma of Descriptive Geometry
ERIC Educational Resources Information Center
Boleslavski, Moshe
1977-01-01
Proposes that engineering students undergo a preparatory summer school training program in fundamentals of engineering drawing, descriptive geometry, and mathematics prior to being admitted to regular engineering studies. (SL)
Pope, G.A.; Sepehrnoori, K.
1992-12-31
This second annual report on innovative uses of tracers for reservoir characterization contains four sections each describing a novel use of oilfield tracers. The first section describes and illustrates the use of a new single-well tracer test to estimate wettability. This test consists of the injection of brine containing tracers followed by oil containing tracers, a shut-in period to allow some of the tracers to react, and then production of the tracers. The inclusion of the oil injection slug with tracers is unique to this test, and this is what makes the test work. We adapted our chemical simulator, UTCHEM, to enable us to study this tracer method and made an extensive simulation study to evaluate the effects of wettability based upon characteristic curves for relative permeability and capillary pressure for differing wetting states typical of oil reservoirs. The second section of this report describes a new method for analyzing interwell tracer data based upon a type-curve approach. Theoretical frequency response functions were used to build type curves of ``transfer function`` and ``phase spectrum`` that have dimensionless heterogeneity index as a parameter to characterize a stochastic permeability field. We illustrate this method by analyzing field tracer data. The third section of this report describes a new theory for interpreting interwell tracer data in terms of channeling and dispersive behavior for reservoirs. Once again, a stochastic approach to reservoir description is taken. The fourth section of this report describes our simulation of perfluorocarbon gas tracers. This new tracer technology developed at Brookhaven National Laboratory is being tested at the Elk Hills Naval Petroleum Reserve No. 1 in California. We report preliminary simulations made of these tracers in one of the oil reservoirs under evaluation with these tracers in this field. Our compostional simulator (UTCOMP) was used for this simulation study.
ERIC Educational Resources Information Center
Vazquez, Lorna Thomas
2008-01-01
This article describes the A, E, I, O, U technique, designed to help teachers ensure that teaching and learning are not mutually exclusive in the classroom. Most teachers would agree that motivating average teenagers to communicate how they got an answer or justify their problem-solving strategies can be as difficult as teaching a dog to whistle.…
ERIC Educational Resources Information Center
Alter, Krystyn P.; Molloy, John L.; Niemeyer, Emily D.
2005-01-01
A laboratory experiment reinforces the concept of acid-base equilibria while introducing a common application of spectrophotometry and can easily be completed within a standard four-hour laboratory period. It provides students with an opportunity to use advanced data analysis techniques like data smoothing and spectral deconvolution to…
NASA Technical Reports Server (NTRS)
Edwards, S. F.; Kantsios, A. G.; Voros, J. P.; Stewart, W. F.
1975-01-01
The development of a radiometric technique for determining the spectral and total normal emittance of materials heated to temperatures of 800, 1100, and 1300 K by direct comparison with National Bureau of Standards (NBS) reference specimens is discussed. Emittances are measured over the spectral range of 1 to 15 microns and are statistically compared with NBS reference specimens. Results are included for NBS reference specimens, Rene 41, alundum, zirconia, AISI type 321 stainless steel, nickel 201, and a space-shuttle reusable surface insulation.
Chabot, David Leonard; Polimenakos, Anastasios C.
2011-01-01
Abstract: Since the introduction of the Norwood procedure for surgical palliation of hypoplastic left heart syndrome in 1983, refinements have been made to the original procedure to improve patient outcomes while still accomplishing the original goals of the procedure. One of these refinements has been the introduction of regional selective perfusion to limit the duration of circulatory arrest times and optimize the regional flow distribution. In this paper we describe our technique for performing selective cerebral and lower body perfusion during the Norwood procedure. PMID:22416608
Aguiar Leonardi, Adriano Barros de; Severino, Nilson Roberto; Junior, Aires Duarte
2015-01-01
To assess the presence of tibial bone tunnel enlargement after surgery to reconstruct the anterior cruciate ligament using quadruple flexor tendon grafts, and to propose a new technique for its measurement. Methods: The study involved 25 patients aged 18-43 years over a six-month period. The assessment was based on radiographs taken immediately postoperatively and in the third and sixth months of evolution after operations to reconstruct the anterior cruciate ligament using grafts from the tendons of the semitendinosus and gracilis muscles, fixed in the femur with a transverse metal screw and in the tibia with an interference screw. The radiographs were evaluated in terms of the relative value between the diameter of the tunnel and the bone, both at 2 cm below the medial tibial condyle. Results: There were significant increases in tunnel diameters: 20.56% for radiographs in anteroposterior view and 26.48% in lateral view. Enlargement was present in 48% of anteroposterior and lateral radiographs, but was present in both views in only 16% of the cases. Conclusions: Bone tunnel enlargement is a phenomenon found in the first months after surgery to reconstruct the anterior cruciate ligament. The measurement technique proposed in this study was sufficient to detect it. PMID:27027030
Koudoumnakis, Emmanouel; Vlastos, Ioannis M; Parpounas, Kostas; Houlakis, Michael
2012-03-01
Two-flap palatoplasty is commonly used to treat cleft palate defects, but only a few reports on outcomes have been published in the literature. We conducted a retrospective analysis of 257 cases of cleft palate treated with two-flap palatoplasty at a single center in Greece over a 13-year period. Our outcomes data included surgical complication rates, the results of speech assessments, midface development, and other parameters. We found a low rate of short- and long-term complications that required revision surgery, such as symptomatic fistula (5.4%) and velopharyngeal insufficiency (5.3%). Speech outcomes in relation to intelligibility, hypernasality, and nasal emissions were satisfactory in 70 to 86% of patients. Dental arch relationships, as estimated by the 5-Year-Olds Index, were judged to be either good or excellent in 62% of those evaluated. A considerable proportion of patients (45%) who had otitis media with effusion experienced a spontaneous resolution without the use of tympanostomy tubes 2 to 8 months after their operation. We conclude that two-flap palatoplasty is an effective procedure that warrants further attention. We describe the surgical technique in detail. Our technique includes a modified intravelar veloplasty that incorporates near-total muscle retropositioning. PMID:22430346
Experimenting with Mathematical Biology
ERIC Educational Resources Information Center
Sanft, Rebecca; Walter, Anne
2016-01-01
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
ERIC Educational Resources Information Center
Hallenberg, Harvey
1995-01-01
Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…
Cokkinos, D; Antypa, E; Stefanidis, K; Tserotas, P; Kostaras, V; Parlamenti, A; Tavernaraki, K; Piperopoulos, P N
2012-02-01
Patients with blunt abdominal trauma are initially imaged with ultrasound (US) for the evaluation of free abdominal fluid. However, lacerations of solid organs can be overlooked. Although computed tomography (CT) is the gold standard technique for abdominal trauma imaging, overutilization, ionizing radiation, need to transport the patient and potential artifacts are well known disadvantages. Contrast-enhanced US (CEUS) can be used as an imaging tool between the two methods. It can easily and reliably reveal solid abdominal organ injuries in patients with low-energy localized trauma and decrease the number of CT scans performed. It can be rapidly performed at the patient's bedside with no need for transportation. There are only very few contraindications and anaphylactoid reactions are extremely rare. Altogether, CEUS has proved to be very helpful for the initial imaging of traumatic lesions of the liver, kidney and spleen, as well as for patient follow-up. PMID:22274907
Computation and graphics in mathematical research
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
NASA Astrophysics Data System (ADS)
Fraga, Ignacio; Cea, Luis; Puertas, Jerónimo; Salsón, Santiago; Petazzi, Alberto
2016-04-01
In this paper we present a new methodology to compute rainfall fields including the quantification of predictions uncertainties using raingauge network data. The proposed methodology comprises two steps. Firstly, the ordinary krigging technique is used to determine the estimated rainfall depth in every point of the study area. Then multiple equi-probable errors fields, which comprise both interpolation and measuring uncertainties, are added to the krigged field resulting in multiple rainfall predictions. To compute these error fields first the standard deviation of the krigging estimation is determined following the cross-validation based procedure described in Delrieu et al. (2014). Then, the standard deviation field is sampled using non-conditioned Gaussian random fields. The proposed methodology was applied to study 7 rain events in a 60x60 km area of the west coast of Galicia, in the Northwest of Spain. Due to its location at the junction between tropical and polar regions, the study area suffers from frequent intense rainfalls characterized by a great variability in terms of both space and time. Rainfall data from the tipping bucket raingauge network operated by MeteoGalicia were used to estimate the rainfall fields using the proposed methodology. The obtained predictions were then validated using rainfall data from 3 additional rain gauges installed within the CAPRI project (Probabilistic flood prediction with high resolution hydrologic models from radar rainfall estimates, funded by the Spanish Ministry of Economy and Competitiveness. Reference CGL2013-46245-R.). Results show that both the mean hyetographs and the peak intensities are correctly predicted. The computed hyetographs present a good fit to the experimental data and most of the measured values fall within the 95% confidence intervals. Also, most of the experimental values outside the confidence bounds correspond to time periods of low rainfall depths, where the inaccuracy of the measuring devices
Mathematical epidemiology is not an oxymoron
2009-01-01
A brief description of the importance of communicable diseases in history and the development of mathematical modelling of disease transmission is given. This includes reasons for mathematical modelling, the history of mathematical modelling from the foundations laid in the late nineteenth century to the present, some of the accomplishments of mathematical modelling, and some challenges for the future. Our purpose is to demonstrate the importance of mathematical modelling for the understanding and management of infectious disease transmission. PMID:19922686
2012-01-01
Background Wire closure still remains the preferred technique despite reasonable disadvantages. Associated complications, such as infection and sternal instability, cause time- and cost-consuming therapies. We present a new tool for sternal closure with its first clinical experience and results. Methods The sternal ZipFixTM System is based on the cable-tie principle. It primarily consists of biocompatible Poly-Ether-Ether-Ketone implants and is predominantly used peristernally through the intercostal space. The system provides a large implant-to-bone contact for better force distribution and for avoiding bone cut through. Results 50 patients were closed with the ZipFixTM system. No sternal instability was observed at 30 days. Two patients developed a mediastinitis that necessitated the removal of the device; however, the ZipFixTM were intact and the sternum remained stable. Conclusions In our initial evaluation, the short-term results have shown that the sternal ZipFixTM can be used safely and effectively. It is fast, easy to use and serves as a potential alternative for traditional wire closure. PMID:22731778
NASA Astrophysics Data System (ADS)
Crisan, Emil Gabriel
Certification requirements, optimization and minimum project costs, design of flight control laws and the implementation of flight simulators are among the principal applications of system identification in the aeronautical industry. This document examines the practical application of parameter estimation techniques to the problem of estimating helicopter stability and control derivatives from flight test data provided by Bell Helicopter Textron Canada. The purpose of this work is twofold: a time-domain application of the Output Error method using the Gauss-Newton algorithm and a frequency-domain identification method to obtain the aerodynamic and control derivatives of a helicopter. The adopted model for this study is a fully coupled, 6 degree of freedom (DoF) state space model. The technique used for rotorcraft identification in time-domain was the Maximum Likelihood Estimation method, embodied in a modified version of NASA's Maximum Likelihood Estimator program (MMLE3) obtained from the National Research Council (NRC). The frequency-domain system identification procedure is incorporated in a comprehensive package of user-oriented programs referred to as CIFERRTM. The coupled, 6 DoF model does not include the high frequency main rotor modes (flapping, lead-lag, twisting), yet it is capable of modeling rotorcraft dynamics fairly accurately as resulted from the model verification. The identification results demonstrate that MMLE3 is a powerful and effective tool for extracting reliable helicopter models from flight test data. The results obtained in frequency-domain approach demonstrated that CIFERRTM could achieve good results even on limited data.
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
The Mathematics of Global Change
ERIC Educational Resources Information Center
Kreith, Kurt
2011-01-01
This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…
Fostering Creativity Through Mathematics.
ERIC Educational Resources Information Center
Lichtenberg, Betty K., Ed.; Troutman, Andria P., Ed.
The 26 activities described in this volume deal with a wide variety of mathematical ideas. Most of the activities are appropriate for grades 6-9; many could be used with older or younger groups as well. All activities are described in detail; some descriptions include sample worksheets, and several provide suggestions for followup activities. The…
Assessment Mathematics Teacher's Competencies
ERIC Educational Resources Information Center
Alnoor, A. G.; Yuanxiang, Guo; Abudhuim, F. S.
2007-01-01
This paper aimed to identifying the professional efficiencies for the intermediate schools mathematics teachers and tries to know at what level the math teachers experience those competencies. The researcher used a descriptive research approach, the study data collected from specialist educators and teacher's experts and previous studies to…
Experimental Mathematics and Computational Statistics
Bailey, David H.; Borwein, Jonathan M.
2009-04-30
The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.
NASA Technical Reports Server (NTRS)
Johannsen, G.; Rouse, W. B.
1978-01-01
A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued.
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
CARE 3 phase 2 report - mathematical description
NASA Technical Reports Server (NTRS)
Stiffler, J. J.; Bryant, L. A.
1982-01-01
CARE III (Computer-Aided Reliability Estimation, version three) a computer program designed to help estimate the reliability of complex, redundant systems is described. Although the program can model a wide variety of redundant structures, it was developed specifically for fault tolerant avionics systems. CARE III generalizes the class of system structures that can be modeled and greatly expands the coverage model to take into account such effects as intermittent and transient faults, latent faults, and error propagation.
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…
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…
New Trends in Mathematics Teaching, Volume 2.
ERIC Educational Resources Information Center
United Nations Educational, Scientific, and Cultural Organization, Paris (France).
This volume consists of 29 papers and articles from leading mathematics-teaching journals in many countries. Discussed is new content and curricula and unusual approaches and techniques in the teaching of mathematics at the elementary and secondary levels. Some topics discussed are theories of mathematics instruction, new mathematical experiences…
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Matalas, N.C.
1991-01-01
What constitutes a comprehensive description of drought, a description forming a basis for answering why a drought occurred is outlined. The description entails two aspects that are "naturally" coupled, named physical and economic, and treats the set of hydrologic measures of droughts in terms of their multivariate distribution, rather than in terms of a collection of the marginal distributions. ?? 1991 Springer-Verlag.
Self-Efficacy Beliefs of Prospective Primary Mathematics Teachers about Mathematical Literacy
ERIC Educational Resources Information Center
Yavuz, Gunes; Gunhan, Berna Canturk; Ersoy, Esen; Narli, Serkan
2013-01-01
The aim of this study was to examine the self-efficacy beliefs about mathematical literacy among teachers of primary school mathematics and the relationship between the self-efficacy beliefs and attitudes towards mathematics. To that end, a descriptive research study was conducted with 550 prospective teachers studying primary school mathematics…
Mathematical model of a flexible space shuttle vehicle
NASA Technical Reports Server (NTRS)
Harvey, C. A.
1972-01-01
The development of a mathematical model of the lateral motion of a flexible space shuttle vehicle during ascent is described. The model was developed to perform control system synthesis using stochastic constrained optimization techniques. The goals of the control system synthesis are to demonstrate the applicability of the techniques and to discover any problems peculiar to the flexible nature of a shuttle vehicle. The equations of motion are derived. A brief description of the generation of numerical data is given. Explicit definitions and numerical values of trajectory data and coefficients appearing in the equations of motion are included.
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Siskiyou County Superintendent of Schools, Yreka, CA.
The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
Hardware description languages
NASA Technical Reports Server (NTRS)
Tucker, Jerry H.
1994-01-01
Hardware description languages are special purpose programming languages. They are primarily used to specify the behavior of digital systems and are rapidly replacing traditional digital system design techniques. This is because they allow the designer to concentrate on how the system should operate rather than on implementation details. Hardware description languages allow a digital system to be described with a wide range of abstraction, and they support top down design techniques. A key feature of any hardware description language environment is its ability to simulate the modeled system. The two most important hardware description languages are Verilog and VHDL. Verilog has been the dominant language for the design of application specific integrated circuits (ASIC's). However, VHDL is rapidly gaining in popularity.
Factors Influencing Competency in Mathematics Among Entering Elementary Education Majors.
ERIC Educational Resources Information Center
Caraway, Sue Dennis
Relationships among attitude toward mathematics, mathematics background, and junior college transfer versus non-transfer status upon competency in elementary mathematics were investigated using multiple linear regression techniques. Instruments for collecting data included a mathematics placement test, the "Mathematics Attitude Scale" by Aiken,…
Applications of Secondary School Mathematics.
ERIC Educational Resources Information Center
Kastner, Bernice
This text is based on the idea that teachers of mathematics at any level will find it advantageous to be able to point to interesting, useful, and diverse applications of the mathematics they teach. The first chapter describes several graphing techniques used for displaying data and finding meaningful relationships as a result. Subsequent chapters…
Storytelling + Origami = Storigami Mathematics
ERIC Educational Resources Information Center
Mastin, Marla
2007-01-01
This article presents a way to engage students in mathematics learning by using the innovative instructional method of storigami. The author shares reactions from teachers who have used her storigami techniques in their classes and provides an example of storigami using the Norwegian fable "The Dog and the Mountain." (Contains 6 figures.)
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.
ERIC Educational Resources Information Center
Johnson, Jerry
1997-01-01
Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)
ERIC Educational Resources Information Center
Gardner, Martin
1978-01-01
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
Teaching Mathematics to Civil Engineers
ERIC Educational Resources Information Center
Sharp, J. J.; Moore, E.
1977-01-01
This paper outlines a technique for teaching a rigorous course in calculus and differential equations which stresses applicability of the mathematics to problems in civil engineering. The method involves integration of subject matter and team teaching. (SD)
Computer-Game-Based Tutoring of Mathematics
ERIC Educational Resources Information Center
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
Mathematics Teachers' Criteria of Dimension
ERIC Educational Resources Information Center
Ural, Alattin
2014-01-01
The aim of the study is to determine mathematics teachers' decisions about dimensions of the geometric figures, criteria of dimension and consistency of decision-criteria. The research is a qualitative research and the model applied in the study is descriptive method on the basis of general scanning model. 15 mathematics teachers attended the…
On the Role of Mathematics in Physics
ERIC Educational Resources Information Center
Quale, Andreas
2011-01-01
I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a…
Teaching Mathematics with Computers 9-12.
ERIC Educational Resources Information Center
New York State Education Dept., Albany.
This publication is designed to show how computers can be used effectively in secondary school mathematics curricula. Section I provides a description of the various types of software that could be incorporated into the secondary school mathematics curriculum. Procedures for evaluating the software and using it in a classroom or laboratory…
Secondary School Mathematics Curriculum Improvement Study.
ERIC Educational Resources Information Center
Secondary School Mathematics Curriculum Improvement Study, New York, NY.
This bulletin contains: (1) a summary and conclusions of a study of mathematics curricula in Europe and Japan, and (2) a description of beginning efforts to evaluate the Secondary School Mathematics Curriculum Improvement Study (SSMCIS) project. Some of the conclusions of the European and Japanese study are: (1) the study of Euclidean synthetic…
Analysis of Physiological Systems via Mathematical Models.
ERIC Educational Resources Information Center
Hazelrig, Jane B.
1983-01-01
Discusses steps to be executed when studying physiological systems with theoretical mathematical models. Steps considered include: (1) definition of goals; (2) model formulation; (3) mathematical description; (4) qualitative evaluation; (5) parameter estimation; (6) model fitting; (7) evaluation; and (8) design of new experiments based on the…
The First Mathematics Olympiads in Mozambique.
ERIC Educational Resources Information Center
Gerdes, Paulus
1984-01-01
Explains why mathematics olympiads were introduced in Mozambique. A description and analysis of results (scores, type of problems, social background, and composition by sex of participants and winners) and short biographies of winners are given to offer insight into the social aspects of the development of their mathematical talent. (Author/JN)
Shi, Runhua; McLarty, Jerry W
2009-10-01
In this article, we introduced basic concepts of statistics, type of distributions, and descriptive statistics. A few examples were also provided. The basic concepts presented herein are only a fraction of the concepts related to descriptive statistics. Also, there are many commonly used distributions not presented herein, such as Poisson distributions for rare events and exponential distributions, F distributions, and logistic distributions. More information can be found in many statistics books and publications. PMID:19891281
Malkevitch, J. ); McCarthy, D. )
1990-01-01
The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
ERIC Educational Resources Information Center
Whitman, David L.; Terry, Ronald E.
1985-01-01
Demonstrating petroleum engineering concepts in undergraduate laboratories often requires expensive and time-consuming experiments. To eliminate these problems, a graphical simulation technique was developed for junior-level laboratories which illustrate vapor-liquid equilibrium and the use of mathematical modeling. A description of this…
ERIC Educational Resources Information Center
ROSEN, ELLEN F.; STOLUROW, LAWRENCE M.
MANIPULATION OF FRAMES WITHIN PROGRAMED MATHEMATICS TEXTS IN ORDER TO STUDY FOUR VARIABLES YIELDED, IN A PREVIOUSLY REPORTED PAPER, CORRELATIONAL DATA (FOR RELATIVELY SMALL TREATMENT GROUPS) THAT ARE PRESENTED HERE. FIRST, THE ORDER OF PRESENTATION OF PROGRAMED MATERIAL (BEFORE, AFTER, AND WITHOUT CONVENTIONAL INSTRUCTION) HAD NO EFFECT ON…
ERIC Educational Resources Information Center
Britton, Edward; Raizen, Senta; Kaser, Joyce; Porter, Andrew
When entering this new millennium, educators and researchers need to know much more about how to address the increasingly acute diversity and equity issues in educating children in mathematics and science. This headline was the conclusion of the over 200 distinguished panelists, chairs, discussants, featured speakers, and participants who…
Elementary Statistics I--Mathematics 274 Course Syllabus, Fall 2001.
ERIC Educational Resources Information Center
Clark, Deborah L.
This document features the syllabus for a course in Elementary Statistics/Mathematics at Southern University in Baton Rouge, LA. The course textbook, a course description, readings, goals, and course requirements are presented. Basic descriptive analysis and mathematical concepts commonly used in statistics are emphasized in the course. Topics…
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
ERIC Educational Resources Information Center
Lapointe, Archie E.; And Others
In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…
ERIC Educational Resources Information Center
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
A HALF CENTURY OF TEACHING SCIENCE AND MATHEMATICS.
ERIC Educational Resources Information Center
ISENBARGER, KATHARINE U.; AND OTHERS
MAJOR DEVELOPMENTS IN SCIENCE AND MATHEMATICS EDUCATION DURING THE PERIOD 1900-50 ARE REVIEWED. AN EARLY CHAPTER IS DEVOTED TO A DETAILED DESCRIPTION OF THE FORMATION AND SUBSEQUENT DEVELOPMENT OF THE CENTRAL ASSOCIATION OF SCHOOL SCIENCE AND MATHEMATICS TEACHERS AND THE JOURNAL, "SCHOOL SCIENCE AND MATHEMATICS." OTHER SECTIONS INCLUDE (1)…
Development of the Database "Mathematical Web-resources"
NASA Astrophysics Data System (ADS)
Barakhnin, V. B.
The development and creation technology of the mathematical web-resources portal is offered. Basic components of this portal are the mathematical Internet-resources catalogue and the mathematical sciences ontology. The description of resources is carried according to the international standards (DC and GILS) by means of structural metadata.
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
Mathematical Formulation of Multilayer Networks
NASA Astrophysics Data System (ADS)
De Domenico, Manlio; Solé-Ribalta, Albert; Cozzo, Emanuele; Kivelä, Mikko; Moreno, Yamir; Porter, Mason A.; Gómez, Sergio; Arenas, Alex
2013-10-01
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.
Fernández-Colino, A; Bermudez, J M; Arias, F J; Quinteros, D; Gonzo, E
2016-04-01
Transversality between mathematical modeling, pharmacology, and materials science is essential in order to achieve controlled-release systems with advanced properties. In this regard, the area of biomaterials provides a platform for the development of depots that are able to achieve controlled release of a drug, whereas pharmacology strives to find new therapeutic molecules and mathematical models have a connecting function, providing a rational understanding by modeling the parameters that influence the release observed. Herein we present a mechanism which, based on reasonable assumptions, explains the experimental data obtained very well. In addition, we have developed a simple and accurate “lumped” kinetics model to correctly fit the experimentally observed drug-release behavior. This lumped model allows us to have simple analytic solutions for the mass and rate of drug release as a function of time without limitations of time or mass of drug released, which represents an important step-forward in the area of in vitro drug delivery when compared to the current state of the art in mathematical modeling. As an example, we applied the mechanism and model to the release data for acetazolamide from a recombinant polymer. Both materials were selected because of a need to develop a suitable ophthalmic formulation for the treatment of glaucoma. The in vitro release model proposed herein provides a valuable predictive tool for ensuring product performance and batch-to-batch reproducibility, thus paving the way for the development of further pharmaceutical devices. PMID:26838852
NASA Astrophysics Data System (ADS)
Weidner, Anja; Biermann, Horst
2015-08-01
The class of low-carbon, high-alloy CrMnNi steels exhibits outstanding mechanical properties with respect to high strength and ductility due to either transformation-induced plasticity (TRIP) or twinning-induced plasticity (TWIP) effect depending on chemical composition and deformation temperature. However, the ongoing deformation mechanisms like the formation of stacking faults, martensitic phase transformation or deformation-induced twinning are overlapping and the kinetics of the microstructure evolution are quite complex. Therefore, in addition to macroscopic deformation tests and microstructural investigations by scanning electron microscopy, a combination of several in situ characterization techniques with either high lateral and/or temporal resolution as well as providing integral volume information were chosen in order to give a thoroughly and comprehensive description of the deformation behavior of CrMnNi TRIP/TWIP steels. In addition, the complementary in situ techniques like in situ nanoindentation, micro-digital image correlation, and acoustic emission measurements provide excellent possibility for description of materials behavior on a multiscale level from the submicrometer scale up to the macroscopic range. The results obtained by the complementary techniques can support the future modeling of the deformation behavior of TRIP/TWIP steels dependent on chemical composition, temperature, grain size and grain orientation.
Poenitz, W.P.
1980-01-01
The evaluation of several energy-dependent neutron cross sections which are of importance for practical applications is considered. The evaluation process is defined as the procedure which is used to derive the best knowledge of these cross sections based on the available direct experimental data information, and, using theoretical models, on the auxiliary data base. The experimental data base represents a multiple overdetermination of the unknown cross sections with various correlations between the measured values. Obtaining the least-squares estimator is considered as the standard mathematical procedure to derive a consistent set of evaluated cross section values. Various approximations made in order to avoid the monstrous system of normal equations are considered and the feasibility of the exact solution is demonstrated. The variance-covariance of the result, its reliability and the improvements obtained in iterative steps are discussed. Finally, the inclusion of auxiliary, supplementary information is considered. 45 references.
Ritchie, L.T.; Alpert, D.J.; Burke, R.P.; Johnson, J.D.; Ostmeyer, R.M.; Aldrich, D.C.; Blond, R.M.
1984-03-01
The CRAC2 computer code is a revised version of CRAC (Calculation of Reactor Accident Consequences) which was developed for the Reactor Safety Study. This document provides an overview of the CRAC2 code and a description of each of the models used. Significant improvements incorporated into CRAC2 include an improved weather sequence sampling technique, a new evacuation model, and new output capabilities. In addition, refinements have been made to the atmospheric transport and deposition model. Details of the modeling differences between CRAC2 and CRAC are emphasized in the model descriptions.
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
Mathematical String Sculptures: A Case Study in Computationally-Enhanced Mathematical Crafts
ERIC Educational Resources Information Center
Eisenberg, Michael
2007-01-01
Mathematical string sculptures constitute an extremely beautiful realm of mathematical crafts. This snapshot begins with a description of a marvelous (and no longer manufactured) toy called Space Spider, which provided a framework with which children could experiment with string sculptures. Using a computer-controlled laser cutter to create frames…
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…
Symmetry in Mathematics and Art: An Exploration of an Art Venue for Mathematics Learning
ERIC Educational Resources Information Center
Stylianou, Despina A.; Grzegorczyk, Ivona
2005-01-01
Symmetry is an aspect of mathematics that is strongly linked to art and design. We chose to explore this connection in the context of a liberal arts mathematics course. Here we present a brief description of this course, including an outline of the curriculum and specific features of the course. We subsequently present the results of a study we…
SKYMAP system description: Star catalog data base generation and utilization
NASA Technical Reports Server (NTRS)
Gottlieb, D. M.
1979-01-01
The specifications, design, software description, and use of the SKYMAP star catalog system are detailed. The SKYMAP system was developed to provide an accurate and complete catalog of all stars with blue or visual magnitudes brighter than 9.0 for use by attitude determination programs. Because of the large number of stars which are brighter than 9.0 magnitude, efficient techniques of manipulating and accessing the data were required. These techniques of staged distillation of data from a Master Catalog to a Core Catalog, and direct access of overlapping zone catalogs, form the basis of the SKYMAP system. The collection and tranformation of data required to produce the Master Catalog data base is described. The data flow through the main programs and levels of star catalogs is detailed. The mathematical and logical techniques for each program and the format of all catalogs are documented.
NASA Astrophysics Data System (ADS)
Baader, Franz
Description Logics (DLs) are a well-investigated family of logic-based knowledge representation formalisms, which can be used to represent the conceptual knowledge of an application domain in a structured and formally well-understood way. They are employed in various application domains, such as natural language processing, configuration, and databases, but their most notable success so far is the adoption of the DL-based language OWL as standard ontology language for the semantic web.
On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process
Flegg, Jennifer A.; Menon, Shakti N.; Maini, Philip K.; McElwain, D. L. Sean
2015-01-01
Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration. PMID:26483695
ERIC Educational Resources Information Center
Charconnet, Marie-George
This study describes various patterns of peer tutoring and is based on the use of cultural traditions and endogenous methods, on techniques and equipment acquired from other cultures, on problems presented by the adoption of educational technologies, and on methods needing little sophisticated equipment. A dozen peer tutoring systems are…
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.
Mathematical Modeling of Diverse Phenomena
NASA Technical Reports Server (NTRS)
Howard, J. C.
1979-01-01
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
NASA Technical Reports Server (NTRS)
Peuquet, Donna J.
1987-01-01
A new approach to building geographic data models that is based on the fundamental characteristics of the data is presented. An overall theoretical framework for representing geographic data is proposed. An example of utilizing this framework in a Geographic Information System (GIS) context by combining artificial intelligence techniques with recent developments in spatial data processing techniques is given. Elements of data representation discussed include hierarchical structure, separation of locational and conceptual views, and the ability to store knowledge at variable levels of completeness and precision.
ERIC Educational Resources Information Center
Barrera-Osorio, Felipe; Garcia-Moreno, Vicente; Patrinos, Harry Anthony; Porta, Emilio
2011-01-01
The Oaxaca-Blinder technique was originally used in labor economics to decompose earnings gaps and to estimate the level of discrimination. It has been applied since in other social issues, including education, where it can be used to assess how much of a gap is due to differences in characteristics (explained variation) and how much is due to…
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…
Edwards, A W F
2011-03-01
Ernst Mayr called the first part of the evolutionary synthesis the 'Fisherian synthesis' on account of the dominant role played by R.A. Fisher in forging a mathematical theory of natural selection together with J.B.S. Haldane and Sewall Wright in the decade 1922-1932. It is here argued that Fisher's contribution relied on a close reading of Darwin's work to a much greater extent than did the contributions of Haldane and Wright, that it was synthetic in contrast to their analytic approach and that it was greatly influenced by his friendship with the Darwin family, particularly with Charles's son Leonard. PMID:21423339
Rochereau, P; Bernardé, A
2012-01-01
This retrospective study documents deep gluteal tenodesis (DGT) used to stabilize coxo- femoral luxation (CFL) in dogs and cats, and to report reluxation rate and clinical outcome after DGT. Medical records (1995-2008) of 65 dogs and cats with traumatic CFL treated by capsulorrhaphy and DGT were reviewed. Animals with radiographic evidence of pre-existing hip dysplasia or articular fractures had been excluded. Reluxation rate and outcome were assessed by clinical examination, performed two and ten weeks postoperatively. Surgical treatment was performed between one and 20 days after the initiating event. No perioperative complications occurred. All hip joints were correctly reduced and stabilized immediately after DGT completion. Except for five patients, placement of the screw was considered correct. In two of these patients, the screws were too long and were protruding into the pelvic canal. In two dogs, the screws were not tightened adequately, and in one dog the screw was too short. Twenty-six dogs and eight cats were re-examined between eight and 13 weeks postoperatively. Re- luxation did not occur in any of them. Outcomes were good in two cases and excellent in 32 cases; all but two had a normal range-of-motion of the reconstructed hip, and were free of lameness and did not show any signs of pain. Traumatic CFL can be stabilized safely and effectively by DGT in dogs and cats. This technique should be considered among other capsular reinforcement techniques in the presence of an intact deep gluteal muscle. PMID:22028015
NASA Astrophysics Data System (ADS)
McDermott, C. I.; Wenqing, W.; Kolditz, O.
2009-04-01
Exploiting and geo-engineering of fractured rocks in the context of reservoir storage and utilisation is important to applications such as hydrogeology, petroleum geology, geothermal energy, nuclear waste storage and CO2-sequestration. Understanding fluid, mass and energy transport in the three dimensional fracture network is critical to the evaluation planned operating efficiency. Hydraulic, thermal, mechanical and chemical coupled processes under the typical reservoir conditions operate at different scales. Depending on whether the process is continuum dominated (e.g. transfer of stress in the rock body) or discontinuity dominated (e.g. hydraulic transport processes) different methods of numerically investigating and quantifying the system can be applied. A geomechanical facies approach provides the basis for large scale numerical analysis of the coupled processes and prediction of system response. It also provides the basis for a three dimensional holistic understanding of the reservoir systems and the appropriate investigation techniques which could be used to evaluate the capacities of the reservoirs to be investigated as well as appropriate development techniques. Concentrating on the numerical modelling there is often a difficult balance between the numerical stability criteria of the different equation systems which need to be solved to describe the interaction of the dominant processes. The introduction of analytical solutions where possible, functional dependencies and multiple meshes provides on the framework of the geo-mechanical facies concept provides an efficient and stable method for the prediction of the effect of the in situ coupling.
Mathematical modelling in MHD technology
Scheindlin, A.E.; Medin, S.A. )
1990-01-01
The technological scheme and the general parameters of the commercial scale pilot MHD power plant are described. The characteristics of the flow train components and the electrical equipment are discussed. The basic ideas of the mathematical modelling of the processes and the devices operation in MHD systems are considered. The application of different description levels in computer simulation is analyzed and the examples of typical solutions are presented.
NASA Technical Reports Server (NTRS)
Dunn, M. G.; George, W. K.; Rae, W. J.; Woodward, S. H.; Moller, J. C.
1986-01-01
An analytical technique for obtaining the time-resolved heat flux of a turbine blade is applied to the case of a TFE 731-2 hp full-stage rotating turbine. In order to obtain the heat flux values from the thin film gage temperature histories, a finite difference procedure is used to solve the heat equation with variable thermal properties. After setting out the data acquisition and analysis procedures, their application is illustrated for three midspan locations on the blade and operation at the design flow function. Results demonstrate that the magnitude of the heat flux fluctuation due to vane-balde interaction is large by comparison to the time-averaged heat flux at all investigated locations; FFT of a portion of the heat flux record illustrates that the dominant frequencies occur at the wake-cutting frequency and its harmonics.
Hühn, Jonas; Fedeli, Chiara; Zhang, Qian; Masood, Atif; Del Pino, Pablo; Khashab, Niveen M; Papini, Emanuele; Parak, Wolfgang J
2016-06-01
Protein adsorption to nanoparticles is described as a chemical reaction in which proteins attach to binding sites on the nanoparticle surface. This process is defined by a dissociation coefficient, which tells how many proteins are adsorbed per nanoparticle in dependence of the protein concentration. Different techniques to experimentally determine dissociation coefficients of protein adsorption to nanoparticles are reviewed. Results of more than 130 experiments in which dissociation coefficients have been determined are compared. Data show that different methods, nanoparticle systems, and proteins can lead to significantly different dissociation coefficients. However, we observed a clear tendency of smaller dissociation coefficients upon less negative towards more positive zeta potentials of the nanoparticles. The zeta potential thus is a key parameter influencing protein adsorption to the surface of nanoparticles. Our analysis highlights the importance of the characterization of the parameters governing protein-nanoparticle interaction for quantitative evaluation and objective literature comparison. PMID:26748245
Mathematical modeling of ligaments and tendons.
Woo, S L; Johnson, G A; Smith, B A
1993-11-01
Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model. PMID:8302027
Mathematical modelling of animate and intentional motion.
Rittscher, Jens; Blake, Andrew; Hoogs, Anthony; Stein, Gees
2003-01-01
Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whether a particular human action should be captured in a single complex model or whether it is more promising to make extensive use of semantic knowledge and a collection of low-level models that encode certain motion primitives. Scene context plays a crucial role if we intend to give a higher-level interpretation rather than a low-level physical description of the observed motion. A semantic knowledge base is used to establish the scene context. This approach consists of three main components: visual analysis, the mapping from vision to language and the search of the semantic database. A small number of robust visual detectors is used to generate a higher-level description of the scene. The approach together with a number of results is presented in the third part of this article. PMID:12689374
Applied mathematical problems in modern electromagnetics
NASA Astrophysics Data System (ADS)
Kriegsman, Gregory
1994-05-01
We have primarily investigated two classes of electromagnetic problems. The first contains the quantitative description of microwave heating of dispersive and conductive materials. Such problems arise, for example, when biological tissue are exposed, accidentally or purposefully, to microwave radiation. Other instances occur in ceramic processing, such as sintering and microwave assisted chemical vapor infiltration and other industrial drying processes, such as the curing of paints and concrete. The second class characterizes the scattering of microwaves by complex targets which possess two or more disparate length and/or time scales. Spatially complex scatterers arise in a variety of applications, such as large gratings and slowly changing guiding structures. The former are useful in developing microstrip energy couplers while the later can be used to model anatomical subsystems (e.g., the open guiding structure composed of two legs and the adjoining lower torso). Temporally complex targets occur in applications involving dispersive media whose relaxation times differ by orders of magnitude from thermal and/or electromagnetic time scales. For both cases the mathematical description of the problems gives rise to complicated ill-conditioned boundary value problems, whose accurate solutions require a blend of both asymptotic techniques, such as multiscale methods and matched asymptotic expansions, and numerical methods incorporating radiation boundary conditions, such as finite differences and finite elements.
The composite sequential clustering technique for analysis of multispectral scanner data
NASA Technical Reports Server (NTRS)
Su, M. Y.
1972-01-01
The clustering technique consists of two parts: (1) a sequential statistical clustering which is essentially a sequential variance analysis, and (2) a generalized K-means clustering. In this composite clustering technique, the output of (1) is a set of initial clusters which are input to (2) for further improvement by an iterative scheme. This unsupervised composite technique was employed for automatic classification of two sets of remote multispectral earth resource observations. The classification accuracy by the unsupervised technique is found to be comparable to that by traditional supervised maximum likelihood classification techniques. The mathematical algorithms for the composite sequential clustering program and a detailed computer program description with job setup are given.
Examining Classroom Interactions & Mathematical Discourses
ERIC Educational Resources Information Center
Grant, Melva R.
2009-01-01
This investigation examined interactions in three classrooms to determine how they influenced Discourses related to mathematics learning and teaching. Mathematics education literature suggests that effective mathematics instruction includes mathematical Discourses. However, effective mathematical Discourses within mathematics classrooms vary…
Mind Mapping as a Tool in Mathematics Education.
ERIC Educational Resources Information Center
Brinkmann, Astrid
2003-01-01
Presents the technique of mind mapping and points out its special fitting as a pedagogical tool for mathematics education. Discusses possible applications of mind mapping in mathematics education together with their advantages and limitations. (Author/NB)
Mertziotis, Nikos; Kozyrakis, Diomidis; Bogris, Elias
2013-11-01
Our objective is to describe a novel ligamentolysis approach using a subcoronal incision technique and to determine its safety and efficacy. During the last 7 years, 82 consecutive patients had penile augmentation surgery. Ligamentolysis, through a lower abdominal incision (V-Y plasty) in the first 35 males, was performed (Group A), followed by circumcision ligamentolysis in the next 47 males (Group B). The operation time, complications, and the preoperative and postoperative values of penile length and girth along with the self-esteem and relations questionnaire score as well as satisfaction score was calculated before and after the surgery, and a comparison was conducted between the groups. The mean age at presentation was 32 years (range: 18-56 years). Seventy-nine patients suffered from penile dysmorphophobia, and three patients had micropenises (length <7.5 cm). The mean surgical times were 150.7 and 125.2 min for Groups A and B, respectively (P=0.005). Postoperatively, four Group A patients and three Group B patients (11% versus 6%, respectively) experienced penile retraction (P=0.453). Hypertrophic scars were observed in 18 men (51%) in the former [corrected] group. In the circumcision group, no major wound complications were recorded. The length and girth improvements between the groups were similar. In terms of satisfaction and SEAR improvement, the resulting difference for both variables favored the circumcision group (P=0.007 and <0.001, respectively). With strict selection criteria, the circumcision ligamentolysis procedure compared to the V-Y plasty demonstrated improved results in terms of safety, operation time, retraction rate and cosmetic appearance without any compromise in the gained penile size. PMID:23792340
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Integrating Literature in Mathematics: A Teaching Technique for Mathematics Teachers
ERIC Educational Resources Information Center
Ruiz, Elsa C.; Thornton, Jenifer Salter; Cuero, Kimberley K.
2010-01-01
The integration of content areas is not a new concept (Moyer, 2000). Integration is promoted by many teacher educators because of its benefits for learners of all ages and backgrounds (Burns, 2005; Douville, Pugalee, & Wallace, 2003; Pica, 2002). Literacy in general, but reading in particular, is important across the content areas. Mathematics…
NASA Astrophysics Data System (ADS)
Ford, David; Huntsman, Steven
2006-06-01
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. Whereas conventionally, the systems investigated require this form of data reduction in order to facilitate prediction, a different problem also occurs, in the context of communication networks, markets, etc. Such “empirically accessible” systems typically overwhelm observers with the sort of information that in the case of (say) a gas is effectively unobtainable. What is required for such complex interacting systems is not prediction (this may be impossible when humans besides the observer are responsible for the interactions) but rather, description as a route to understanding. Still, the need for a thermodynamical data reduction scheme remains. In this paper, we show how an empirical temperature can be computed for finite, empirically accessible systems, and further outline how this construction allows the age-old science of thermodynamics to be fruitfully applied to them.
Mathematical models in medicine: Diseases and epidemics
Witten, M.
1987-01-01
This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling.
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.
NASA Astrophysics Data System (ADS)
Kasturirangan, Rajesh
2014-07-01
Mathematics is a human pursuit. Whether the truths of mathematics lie outside the human mind or emerge out of it, the actual practice of mathematics is conducted by human beings. In other words, human mathematics is the only kind of mathematics that we can pursue and human mathematics has to be built on top of cognitive capacities that are possessed by all human beings. Another way of stating the same claim is that mathematics is experienced by human beings using their cognitive capacities. This paper argues that exploring the experience of mathematics is a useful way to make headway on the foundations of mathematics. Focusing on the experience of mathematics is an empirical approach to the study of mathematics that sidesteps some of the thorniest debates from an earlier era about Platonism and Formalism in the foundations of mathematics.
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Mathematical Language and Advanced Mathematics Learning
ERIC Educational Resources Information Center
Ferrari, Pier Luigi
2004-01-01
This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Mathematics for Life: Sustainable Mathematics Education
ERIC Educational Resources Information Center
Renert, Moshe
2011-01-01
Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…
Mathematical Story: A Metaphor for Mathematics Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
The Mathematics of Starry Nights
ERIC Educational Resources Information Center
Barman, Farshad
2008-01-01
The mathematics for finding and plotting the locations of stars and constellations are available in many books on astronomy, but the steps involve mystifying and fragmented equations, calculations, and terminology. This paper will introduce an entirely new unified and cohesive technique that is easy to understand by mathematicians, and simple…
Mathematical Modeling of Chemical Stoichiometry
ERIC Educational Resources Information Center
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
Computation and graphics in mathematical research. Progress report, June 1, 1991--May 31, 1992
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
Katsnelson, Boris A; Panov, Vladimir G; Minigaliyeva, Ilzira A; Varaksin, Anatoly N; Privalova, Larisa I; Slyshkina, Tatyana V; Grebenkina, Svetlana V
2015-08-01
For characterizing the three-factorial toxicity, we proposed a new health risk-oriented approach, the gist of which is a classification of effects depending on whether a binary combined toxicity's type remains virtually the same or appears to be either more or less adverse when modeled against the background of a third toxic. To explore possibilities of this approach, we used results of an experiment in which rats had been injected ip 3 times a week (up to 20 injections) with a water solution of either one of the toxics (Mn, Ni or Cr-VI salts) in a dose equivalent to 0.05 LD50, or any two of them, or all the three in the same doses, the controls receiving injections of the same volume of distilled water (4mL per rat). Judging by more than 30 indices for the organism's status, all exposures caused subchronic intoxication of mild to moderate strength. For each two-factorial exposure, we found by mathematical modeling based on the isobolograms that the binary combined subchronic toxicity either was of additive type or departed from it (predominantly toward subadditivity) depending on the effect assessed, dose, and effect level. For the three-factorial combination, different classes of effects were observed rather consistently: class A - those regarding which the third toxic's addition made the binary toxicity type more unfavorable for the organism, class B - those regarding which the result was opposite, and class C - those regarding which the type of binary combined toxicity on the background of a third toxic virtually remained the same as in its absence. We found a complicated reciprocal influence of combined metals on their retention in kidneys, liver, spleen and brain which might presumably be one of the possible mechanisms of combined toxicity, but the lack of an explicit correspondence between the above influence and the influence on toxicity effects suggests that this mechanism is not always the most important one. The relevance of the proposed classification
The reasonable effectiveness of mathematics in the natural sciences
NASA Astrophysics Data System (ADS)
Harvey, Alex
2011-12-01
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.
The College Entrance Examination Board and Mathematics Education.
ERIC Educational Resources Information Center
Jones, Chancey O.; Valentine, John A.
1984-01-01
To help explain the relationship between board activities and mathematics education today, the creation and evolution of the College Board are described. The development of the Advanced Placement computer science course description and examination are noted particularly. (MNS)
Values taught, values learned, attitude and performance in mathematics
NASA Astrophysics Data System (ADS)
Limbaco, K. S. A.
2015-03-01
The purpose of the study was to identify, describe and find the relationship among values taught, values learned, attitude and performance in mathematics. The researcher used descriptive-correlational method of research to gather information and to describe the nature of situation. The following instruments were used in this study: Math Attitude Inventory, Inventory of Values Taught and Learned which were content validated by experts in the field of Mathematics, Values and Education. Generally, most of the values were taught by the teachers. All of the values were learned by the students. The following got the highest mean ratings for values taught: moral strength, sharing, charity, valuing life, love of God, truth and honesty, reason, alternativism and articulation. The following got highest mean ratings for values learned: patience/tolerance, sharing, charity, valuing life, faith, love of God, truth and honesty, analogical thinking, confidence and individual liberty. Majority of the respondents have moderately positive attitude towards mathematics. Positive statements in the Mathematics Attitude Inventory are "Generally true" while negative statements are "Neutral." In conclusion, values were taught by mathematics teacher, thus, learned by the students. Therefore, mathematics is very much related to life. Values can be learned and strengthened through mathematics; there is a significant relationship between values taught by the teachers and values learned by the students and attitude towards mathematics and performance in mathematics; values taught does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance in mathematics even if the mathematics teacher did not teach values; values learned does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance
PREFACE: Physics-Based Mathematical Models for Nanotechnology
NASA Astrophysics Data System (ADS)
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
In November 2007, some of the world's best nanoscientists and nanoengineers met at the Banff Centre, where the Banff International Research Station hosted a workshop on recent developments in the mathematical study of the physics of nanomaterials and nanostructures. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located in a scenic part of Alberta, Canada and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). We would like to thank the BIRS and its sponsors for the given opportunity and the BIRS staff for their excellent support during the workshop. Nanotechnology is the study and application of phenomena at or below the dimensions of 100 nm and has received a lot of public attention following popular accounts such as in the bestselling book by Michael Crichton, Prey. It is an area where fundamental questions of applied mathematics and mathematical physics, design of computational methodologies, physical insight, engineering and experimental techniques are meeting together in a quest for an adequate description of nanomaterials and nanostructures for applications in optoelectronics, medicine, energy-saving, bio- and other key technologies which will profoundly influence our life in the 21st century and beyond. There are already hundreds of applications in daily life such as in cosmetics and the hard drives in MP3 players (the 2007 Nobel prize in physics was recently awarded for the science that allowed the miniaturization of the drives), delivering drugs, high-definition DVD players and
Multidimensional wave field signal theory: Mathematical foundations
NASA Astrophysics Data System (ADS)
Baddour, Natalie
2011-06-01
Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green's functions in different coordinate systems.
Transforming Primary Mathematics
ERIC Educational Resources Information Center
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
Mathematical Epistemologies at Work.
ERIC Educational Resources Information Center
Noss, Richard
2002-01-01
Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…
NASA Astrophysics Data System (ADS)
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…
Mathematics Lessons without ...
ERIC Educational Resources Information Center
Cross, Kath; Hibbs, John
2006-01-01
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
Student Teachers' Views about Assessment and Evaluation Methods in Mathematics
ERIC Educational Resources Information Center
Dogan, Mustafa
2011-01-01
This study aimed to find out assessment and evaluation approaches in a Mathematics Teacher Training Department based on the views and experiences of student teachers. The study used a descriptive survey method, with the research sample consisting of 150 third- and fourth-year Primary Mathematics student teachers. Data were collected using a…
Success of Online Mathematics Courses at the Community College Level
ERIC Educational Resources Information Center
Lee, Lisa S.
2011-01-01
Low success rates in online mathematics courses at the community college level have raised concerns. The purpose of this study was to investigate the factors that contribute to student success in online mathematics courses at community colleges. The non-experimental quantitative design began with descriptive statistics to explore the quantitative…
Mathematics Education and the Objectivist Programme in HPS
ERIC Educational Resources Information Center
Glas, Eduard
2013-01-01
Using history of mathematics for studying concepts, methods, problems and other internal features of the discipline may give rise to a certain tension between descriptive adequacy and educational demands. Other than historians, educators are concerned with mathematics as a "normatively defined" discipline. Teaching cannot but be based on a…
Motivational Classroom Climate for Learning Mathematics: A Reversal Theory Perspective
ERIC Educational Resources Information Center
Lewis, Gareth
2015-01-01
In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…
The Necessary Teaching Competences for Mathematics Teachers in Middle Schools
ERIC Educational Resources Information Center
Alnoor, A. G.; xiang, G. Y.
2007-01-01
The professional competences of middle school mathematics teachers has been identified, also the significance extent of such competences for chinese and yemenies mathematics teachers has been studied. The researcher used descriptive research approach. The study data collected from Specialist educators and teachers experts to determine the…
NLSMA Reports, No. 33, Intercorrelations of Mathematical and Psychological Variables.
ERIC Educational Resources Information Center
Wilson, James W., Ed.; Begle, Edward G., Ed.
This is one of a series of reports on the National Longitudinal Study of Mathematical Abilities (NLSMA). It is a listing of correlation coefficients where each mathematical scale has been paired with each psychological scale. (See NLSMA Reports Nos. 4-6 for a description of these scales.) Besides each correlation matrix, a rotated factor matrix is…
[Cambridge Conference on School Mathematics Feasibility Studies 9-13.
ERIC Educational Resources Information Center
Cambridge Conference on School Mathematics, Newton, MA.
These materials are a part of a series of studies sponsored by the Cambridge Conference on School Mathematics which reflects the ideas of CCSM regarding the goals and objectives for school mathematics K-12. Feasibility Studies 9-13 contain a wide range of topics. The following are the titles and brief descriptions of these studies. Number…
Three essays in mathematical finance
NASA Astrophysics Data System (ADS)
Wang, Ruming
This dissertation uses mathematical techniques to solve three problems in mathematical finance. The first two problems are on model-independent pricing and hedging of financial derivatives. We use asymptotic expansions to express derivative prices and implied volatilities. Then just by using the first few terms in the expansions, we get simple and accurate formulas, which can also help us find connections between different products. The last problem is on optimal trading strategies in a limit order book. Under a very general setup, we solve explicitly for a dynamic decision problem involving choosing between limit order and market order.
Chinese Calendar and Mathematical Astronomy
NASA Astrophysics Data System (ADS)
Sun, Xiaochun
The Chinese calendar (li 历) was a system of mathematical astronomy that included mathematical techniques for the computation of celestial movements. It was the basis for producing astronomical ephemerides and annual almanacs. Calendar making started early in China. Since the Great Inception calendar reform in 104 BC, China has produced about 100 calendars (astronomical systems). The focus of calendar making was the prediction of solar, lunar, and planetary motions. As astronomy developed, new observational discoveries were incorporated into the calendar to make the system more precise. The history of astronomy in ancient China was largely a history of calendar making.
Mathematical and Statistical Software Index. Final Report.
ERIC Educational Resources Information Center
Black, Doris E., Comp.
Brief descriptions are provided of general-purpose mathematical and statistical software, including 27 "stand-alone" programs, three subroutine systems, and two nationally recognized statistical packages, which are available in the Air Force Human Resources Laboratory (AFHRL) software library. This index was created to enable researchers to…
Teaching Mathematics from a Chemist's Viewpoint.
ERIC Educational Resources Information Center
DeLorenzo, Ronald A.
This paper describes a chemistry professor's approach to teaching mathematics in the college classroom. Based on the assumption that the four main goals of the educational process in general are to teach students to communicate clearly, study regularly, master basic math skills, and think logically, a description is provided of the manner in which…
Qualitative Graphing: A Construction in Mathematics.
ERIC Educational Resources Information Center
Narode, Ronald
This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…
Classroom Instruction and Students' Attitudes Towards Mathematics
ERIC Educational Resources Information Center
Tessema, Taddesse G.
2010-01-01
This quantitative study examined the association between classroom instruction and students' attitudes towards mathematics at the secondary level. Data were collected through a Likert-type survey of Hope High School students and then analyzed for statistical significance by utilizing descriptive statistics, tests of significance, and correlation…
Rival approaches to mathematical modelling in immunology
NASA Astrophysics Data System (ADS)
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
Structural damage identification using mathematical optimization techniques
NASA Technical Reports Server (NTRS)
Shen, Mo-How Herman
1991-01-01
An identification procedure is proposed to identify damage characteristics (location and size of the damage) from dynamic measurements. This procedure was based on minimization of the mean-square measure of difference between measurement data (natural frequencies and mode shapes) and the corresponding predictions obtained from the computational model. The procedure is tested for simulated damage in the form of stiffness changes in a simple fixed free spring mass system and symmetric cracks in a simply supported Bernoulli Euler beam. It is shown that when all the mode information is used in the identification procedure it is possible to uniquely determine the damage properties. Without knowing the complete set of modal information, a restricted region in the initial data space has been found for realistic and convergent solution from the identification process.
Provocative Mathematics Questions: Drawing Attention to a Lack of Attention
ERIC Educational Resources Information Center
Klymchuk, Sergiy
2015-01-01
The article investigates the role of attention in the reflective thinking of school mathematics teachers. It analyses teachers' ability to pay attention to detail and "use" their mathematical knowledge. The vast majority of teachers can be expected to have an excellent knowledge of mathematical techniques. The question examined here is…
Automated reasoning and enumerative search, with applications to mathematics
Zhang, Jian; Wos, L.
1991-12-31
More and more mathematical problems are being solved with the aid of computers. In this paper, we examine the applications of reasoning and search programs to mathematics. It is also shown that the combination of these two techniques can solve mathematical problems more effectively.
Automated reasoning and enumerative search, with applications to mathematics
Zhang, Jian ); Wos, L. )
1991-01-01
More and more mathematical problems are being solved with the aid of computers. In this paper, we examine the applications of reasoning and search programs to mathematics. It is also shown that the combination of these two techniques can solve mathematical problems more effectively.
A mathematical simulation model of a 1985-era tilt-rotor passenger aircraft
NASA Technical Reports Server (NTRS)
Mcveigh, M. A.; Widdison, C. A.
1976-01-01
A mathematical model for use in real-time piloted simulation of a 1985-era tilt rotor passenger aircraft is presented. The model comprises the basic six degrees-of-freedom equations of motion, and a large angle of attack representation of the airframe and rotor aerodynamics, together with equations and functions used to model turbine engine performance, aircraft control system and stability augmentation system. A complete derivation of the primary equations is given together with a description of the modeling techniques used. Data for the model is included in an appendix.
Mathematical Modelling: A New Approach to Teaching Applied Mathematics.
ERIC Educational Resources Information Center
Burghes, D. N.; Borrie, M. S.
1979-01-01
Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)
The NIST Digital Library of Mathematical Functions
NASA Astrophysics Data System (ADS)
Clark, Charles W.
1998-05-01
Not updated since its 1964 publication, the Handbook of Mathematical Functions (Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables), ed. M. Abramowitz and I. A. Stegun, National Bureau of Standards Applied Mathematics Series v. 55 (U. S. Government Printing Office, Washington DC, 1964) presents the state of applied mathematics 40 years ago, in a form suited for computation in an age of numerical tables and mechanical calculators. Yet it remains a workhorse reference of AMO physics and of other scientific fields, having been cited in archival literature over 26,000 times since 1974 (at a still-increasing rate). To incorporate subsequent advances in basic mathematical knowledge, in computational power and technique, and in dissemination of information, the National Institute of Standards and Technology has begun a project to provide a modern source of evaluated mathematical reference data: the NIST Digital Library of Mathematical Functions. The Digital Library is designed to serve the needs of users of applied mathematics via the World Wide Web. We shall demonstrate the operation of a prototype, and hope to elicit expressed needs of the AMO community.
Mathematical modelling of flow distribution in the human cardiovascular system
NASA Technical Reports Server (NTRS)
Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.
1992-01-01
The paper presents a detailed model of the entire human cardiovascular system which aims to study the changes in flow distribution caused by external stimuli, changes in internal parameters, or other factors. The arterial-venous network is represented by 325 interconnected elastic segments. The mathematical description of each segment is based on equations of hydrodynamics and those of stress/strain relationships in elastic materials. Appropriate input functions provide for the pumping of blood by the heart through the system. The analysis employs the finite-element technique which can accommodate any prescribed boundary conditions. Values of model parameters are from available data on physical and rheological properties of blood and blood vessels. As a representative example, simulation results on changes in flow distribution with changes in the elastic properties of blood vessels are discussed. They indicate that the errors in the calculated overall flow rates are not significant even in the extreme case of arteries and veins behaving as rigid tubes.
ERIC Educational Resources Information Center
Silver, Edward A.; Lane, Suzanne
Recent reports on mathematics education reform have focused the attention of educational practitioners and policymakers on new goals for mathematics education and new descriptions of mathematical proficiency. QUASAR is a national project (Quantitative Understanding: Amplifying Student Achievement and Reasoning) designed to improve the mathematics…
Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics
ERIC Educational Resources Information Center
Große, Cornelia S.
2014-01-01
Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2015-01-01
The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…
ERIC Educational Resources Information Center
Salani, End
2013-01-01
Lesson starts are transitional events which may cause management problems for teachers. This study sought junior secondary school mathematics teachers' beliefs about calculator use in mathematics instruction in Botswana and was descriptive in nature adopting a survey design. The sample of seventeen (17) mathematics teachers from four (4) junior…
Mathematics Coursework Regulates Growth in Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; Wilkins, Jesse L. M.
2007-01-01
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…
Preparatory Mathematics Programs in Departments of Mathematics.
ERIC Educational Resources Information Center
Lindberg, Karl
This paper reports on a survey of remedial mathematics programs offered at the college level. The paper is divided into five sections. Section I describes the sampling procedures used in the study. In Section II, the occurrence of remedial mathematics programs in the various types of institutions and some general characteristics of these programs…
Negotiation of Mathematical Meaning and Learning Mathematics.
ERIC Educational Resources Information Center
Voigt, Jorg
1994-01-01
Presents a case study of a first-grade class and their teacher who were observed as they ascribed mathematical meanings of numbers and of numerical operations to empirical phenomena. Differences in ascriptions led to negotiation of meanings. Discusses some indirect relations between social interaction and mathematics learning. (Contains 60…
Mathematics. [SITE 2001 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics" (Kathy R. Autrey and Leigh…
Making Mathematics Culturally Relevant.
ERIC Educational Resources Information Center
Moyer, Patricia
2001-01-01
Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…
ERIC Educational Resources Information Center
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
ERIC Educational Resources Information Center
Clary, Joseph R.; Nery, Karen P.
This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…
ERIC Educational Resources Information Center
Martin, Tami S.; Speer, William R.
2009-01-01
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Abraham, Ralph
2015-12-01
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination. PMID:26278644
ERIC Educational Resources Information Center
Pratt, Dave
2012-01-01
Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…
Applying Mathematical Processes (AMP)
ERIC Educational Resources Information Center
Kathotia, Vinay
2011-01-01
This article provides insights into the "Applying Mathematical Processes" resources, developed by the Nuffield Foundation. It features Nuffield AMP activities--and related ones from Bowland Maths--that were designed to support the teaching and assessment of key processes in mathematics--representing a situation mathematically, analysing,…
Mathematical Epistemologies at Work.
ERIC Educational Resources Information Center
Noss, Richard
In this paper, I draw together a corpus of findings derived from two sources: studies of students using computers to learn mathematics, and research into the use of mathematics in professional practice. Using this as a basis, I map some elements of a theoretical framework for understanding the nature of mathematical knowledge in use, and how it is…
Revisiting Mathematics Manipulative Materials
ERIC Educational Resources Information Center
Swan, Paul; Marshall, Linda
2010-01-01
It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative…
Mathematics in Masons' Workplace
ERIC Educational Resources Information Center
Moreira, Darlinda; Pardal, Eugénia
2012-01-01
This paper presents masons' professional practices, which are related to mathematics. It aims to contribute to the area of adult mathematics education and to enlarge knowledge about how mathematics is used at the workplace. Methodologically it was followed an ethnographic approach. The key informants of the study were four masons aged between 40…
ERIC Educational Resources Information Center
Ortiz-Franco, Luis
An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…
Mathenger Hunt: Mathematics Matters.
ERIC Educational Resources Information Center
Falba, Christy J.; Weiss, Maria J.
1991-01-01
Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)
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…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
ERIC Educational Resources Information Center
Darlington, Ellie
2014-01-01
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Applied Vocational Mathematics.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
Developed for use in teaching a two-semester, one-unit course, this course guide is intended to aid the high school instructor in teaching mathematical problem-solving and computational skills to vocational education students. The state-adopted textbook for general mathematics III, "Applied General Mathematics" serves as the major resource…
A "Mathematics Background Check"
ERIC Educational Resources Information Center
Hubisz, John
2009-01-01
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…
ERIC Educational Resources Information Center
Nisbet, Steven
1991-01-01
The relationship between mathematics and music has been investigated for thousands of years. Presented are the mathematical features of music through a study of melody, harmony, and rhythm, and the musical features of mathematics through a study of pattern, ratio, modular arithmetic, Pythagorean triples, and number sequences. (MDH)
The Creative Mathematics Teacher.
ERIC Educational Resources Information Center
Ediger, Marlow
The creative mathematics teacher who has love and enthusiasm for mathematics as a curriculum area should be in great demand in all schools. This paper discusses the characteristics of creative mathematics teachers, including those who guide students to engage in divergent thinking; have learners do much creative writing; and integrate creative…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
Sayed, Fayez
2015-01-01
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
ERIC Educational Resources Information Center
Posey, Johnsie Jo, Ed.; And Others
This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…
ERIC Educational Resources Information Center
Gallian, Joseph A., Ed.
2010-01-01
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Mathematical Friends and Relations
ERIC Educational Resources Information Center
Tomalin, Jo
2012-01-01
The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…
Dense Granular Avalanches: Mathematical Description and Experimental Validation
NASA Astrophysics Data System (ADS)
Tai, Y.-C.; Hutter, K.; Gray, J. M. N. T.
Snow avalanches, landslides, rock falls and debris flows are extremely dangerous and destructive natural phenomena. The frequency of occurrence and amplitudes of these disastrous events appear to have increased in recent years perhaps due to recent climate warming. The events endanger the personal property and infra-structure in mountainous regions. For example, from the winters 1940/41 to 1987/88 more than 7000 snow avalanches occurred in Switzerland with damaged property leading to a total of 1269 deaths. In February 1999, 36 people were buried by a single avalanche in Galtür, Austria. In August 1996, a very large debris flow in middle Taiwan resulted in 51 deaths, 22 lost and an approximate property damage of more than 19 billion NT dollars (ca. 600 million US dollars) [18]. In Europe, a suddenly released debris flow in North Italy in August 1998 buried 5 German tourists on the Superhighway "Brenner-Autobahn". The topic has gained so much significance that in 1990 the United Nations declared the International Decade for Natural Disasters Reduction (IDNDR); Germany has its own Deutsches IDNDR-Komitee für Katastrophenvorbeugung e.V. Special conferences are devoted to the theme, e.g., the CALAR conference on Avalanches, Landslides, Rock Falls and Debris Flows (Vienna, January 2000), INTERPRAEVENT, annual conferences on the protection of habitants from floods, debris flows and avalanches, special conferences on debris flow hazard mi tigation and those exclusively on Avalanches.
ERIC Educational Resources Information Center
Barwell, Richard
2013-01-01
Climate change is one of the most pressing issues of the 21st Century. Mathematics is involved at every level of understanding climate change, including the description, prediction and communication of climate change. As a highly complex issue, climate change is an example of "post-normal" science -- it is urgent, complex and involves a…
Qualitative and quantitative descriptions of glenohumeral motion.
Hill, A M; Bull, A M J; Wallace, A L; Johnson, G R
2008-02-01
Joint modelling plays an important role in qualitative and quantitative descriptions of both normal and abnormal joints, as well as predicting outcomes of alterations to joints in orthopaedic practice and research. Contemporary efforts in modelling have focussed upon the major articulations of the lower limb. Well-constrained arthrokinematics can form the basis of manageable kinetic and dynamic mathematical predictions. In order to contain computation of shoulder complex modelling, glenohumeral joint representations in both limited and complete shoulder girdle models have undergone a generic simplification. As such, glenohumeral joint models are often based upon kinematic descriptions of inadequate degrees of freedom (DOF) for clinical purposes and applications. Qualitative descriptions of glenohumeral motion range from the parody of a hinge joint to the complex realism of a spatial joint. In developing a model, a clear idea of intention is required in order to achieve a required application. Clinical applicability of a model requires both descriptive and predictive output potentials, and as such, a high level of validation is required. Without sufficient appreciation of the clinical intention of the arthrokinematic foundation to a model, error is all too easily introduced. Mathematical description of joint motion serves to quantify all relevant clinical parameters. Commonly, both the Euler angle and helical (screw) axis methods have been applied to the glenohumeral joint, although concordance between these methods and classical anatomical appreciation of joint motion is limited, resulting in miscommunication between clinician and engineer. Compounding these inconsistencies in motion quantification is gimbal lock and sequence dependency. PMID:17509885
Some Mathematics of Information Storage and Retrieval.
ERIC Educational Resources Information Center
Sammon, John W., Jr.
This report explains the following mathematical techniques which may be used for relating search requests to documents contained in a library: (1) Boolean Algebraic Retrieval, (2) Linear Statistical Retrieval, (3) Statistical Association Techniques for expanding a query and/or for expanding the set of retrieval documents, (4) Vector Space…
Salt Block II: description and results
Hohlfelder, J.J.
1980-06-01
A description of and results from the Salt Block II experiment, which involved the heating of and measurement of water transport within a large sample of rock salt, are presented. These results include the measurement of water released into a heated borehole in the sample as well as measured temperatures within the salt. Measured temperatures are compared with the results of a mathematical model of the experiment.
Scaffolding students' opportunities to learn mathematics through social interactions
NASA Astrophysics Data System (ADS)
Bell, Clare V.; Pape, Stephen J.
2012-12-01
In this study, we take a sociocultural perspective on teaching and learning to examine how teachers in an urban Algebra 1 classroom constructed opportunities to learn. Drawing on analyses of discourse practices, including videotaped classroom lessons as well as other classroom artifacts and telephone interviews, we describe ways that two teachers and their students interacted to develop mathematical understanding. Through descriptive narrative, we highlight practices that positioned students as competent mathematical thinkers and provided evidence of students' mathematical agency. This study suggests that critical awareness of discourse practices in conjunction with teacher mediation of other affordances for learning within the classroom environment might engage students in mathematical practices such as problem solving, explaining mathematical ideas, arguing for or against specific solutions to problems, and justifying mathematical thinking.
Mathematical methods for protein science
Hart, W.; Istrail, S.; Atkins, J.
1997-12-31
Understanding the structure and function of proteins is a fundamental endeavor in molecular biology. Currently, over 100,000 protein sequences have been determined by experimental methods. The three dimensional structure of the protein determines its function, but there are currently less than 4,000 structures known to atomic resolution. Accordingly, techniques to predict protein structure from sequence have an important role in aiding the understanding of the Genome and the effects of mutations in genetic disease. The authors describe current efforts at Sandia to better understand the structure of proteins through rigorous mathematical analyses of simple lattice models. The efforts have focused on two aspects of protein science: mathematical structure prediction, and inverse protein folding.
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
ERIC Educational Resources Information Center
House, Peggy A.
1994-01-01
Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)
Philosophy and mathematics: interactions.
Rashed, Roshdi
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so. PMID:25029825
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Jett, Christopher C.
2014-01-01
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Mathematics for Teaching: A Form of Applied Mathematics
ERIC Educational Resources Information Center
Stylianides, Gabriel J.; Stylianides, Andreas J.
2010-01-01
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics
ERIC Educational Resources Information Center
Wang, Youjun
2009-01-01
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…
Students' perceptions of the relevance of mathematics in engineering
NASA Astrophysics Data System (ADS)
Flegg, Jennifer; Mallet, Dann; Lupton, Mandy
2012-09-01
In this article, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society [M. Kirschenman and B. Brenner, Education for Civil Engineering: A Profession of Practice, Leader. Manag. Eng. 10 (2010), p. 54]. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of engineering mathematics curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour and the effectiveness of problem-solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.
The emerging and emergent present: a view on the indeterminate nature of mathematics lessons
NASA Astrophysics Data System (ADS)
Roth, Wolff-Michael; Maheux, Jean-François
2014-06-01
The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of emergence. After providing an exemplifying description and analysis of an episode from a second-grade mathematics classroom studying three-dimensional geometry, we discuss implications for theoretical and classroom praxis in mathematics education, especially for the curriculum planning and the preparation, training, and enhancement of teachers of mathematics.
Mathematics in narratives of Geodetic expeditions.
Terrall, Mary
2006-12-01
In eighteenth-century France, geodesy (the measure of the earth's shape) became an arena where mathematics and narrative intersected productively. Mathematics played a crucial role not only in the measurements and analysis necessary to geodesy but also in the narrative accounts that presented the results of elaborate and expensive expeditions to the reading public. When they returned to France to write these accounts after their travels, mathematician-observers developed a variety of ways to display numbers and mathematical arguments and techniques. The numbers, equations, and diagrams they produced could not be separated from the story of their acquisition. Reading these accounts for the interplay of these two aspects--the mathematical and the narrative--shows how travelers articulated the intellectual and physical difficulties of their work to enhance the value of their results for specialist and lay readers alike. PMID:17367005
NASA Astrophysics Data System (ADS)
Haba, H.; Motomura, S.; Kamino, S.; Enomoto, S.
In radioactive tracer technique, radioactive nuclides are used to follow the behavior of elements or chemical species in chemical and other processes. This is realized by means of radioactivity measurement. In 1913, Hevesy and Paneth succeeded in determining the extremely low solubility of lead salts by using naturally occurring 210Pb as a radioactive tracer. As various radioactive nuclides became artificially available, this technique has been widely employed in studies of chemical equilibrium and reactions as well as in chemical analysis. It is also an essential technique in biochemical, biological, medical, geological, and environmental studies. Medical diagnosis and industrial process control are the fields of its most important practical application. In this chapter, fundamental ideas concerning radioactive tracers will be described followed by their application with typical examples. Detailed description on their application to life sciences and medicine is given in Vol. 4.
Remedial Mathematics for Quantum Chemistry
ERIC Educational Resources Information Center
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
2008-01-01
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…
The Relativity of Mathematics.
ERIC Educational Resources Information Center
Kleiner, Israel; Avital, Shmuel
1984-01-01
The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)
The Applied Mathematics Laboratory.
ERIC Educational Resources Information Center
Siegel, Martha J.
This report describes the Applied Mathematics Laboratory (AML) operated by the Department of Mathematics at Towson State University, Maryland. AML is actually a course offered to selected undergraduates who are given the opportunity to apply their skills in investigating industrial and governmental problems. By agreement with sponsoring…
ERIC Educational Resources Information Center
Heck, Andre; Van Gastel, Leendert
2006-01-01
Lowering the dropout rate of incoming mathematics and science students, and enhancing the provision of mathematics support for freshmen are two important aims of the University of Amsterdam. The approach recently adopted to support first year students is to set up a diagnostic pretest and posttest and use these tests to identify students being at…
Designing Assessment for Mathematics
ERIC Educational Resources Information Center
Depka, Eileen
2007-01-01
Teaching mathematics in today's world requires practices and procedures integrated with performance tasks that actively involve students. In this second edition of Designing Rubrics for Mathematics, Eileen Depka clarifies the purpose of rubrics in math instruction and illustrates the relationship between assessment, rubrics, and the National…
Modularizing Remedial Mathematics
ERIC Educational Resources Information Center
Wong, Aaron
2013-01-01
As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…
Quality Teaching in Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2012-01-01
The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…
Mathematics. [SITE 2002 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
ERIC Educational Resources Information Center
Dodd, Jennifer
2010-01-01
In this article, the author reports on the findings of her research on what her Year 10 students consider to be "mathematical." The class contains thirteen students who will all sit the higher tier IGCSE next year. The author found out that the students considered things she told them to have a higher mathematical status than work they did…
Mathematics: The Universal Language?
ERIC Educational Resources Information Center
Hoffert, Sharon B.
2009-01-01
Mathematics is considered the universal language, but students who speak languages other than English have difficulty doing mathematics in English. For instance, because of a lack of familiarity with the problem's context, many have trouble understanding exactly what operations to perform. In the United States, approximately one in seven students…
Elementary Mathematics Leaders
ERIC Educational Resources Information Center
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
2013-01-01
Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
ERIC Educational Resources Information Center
Corle, Clyde G.
This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…
Solving Common Mathematical Problems
NASA Technical Reports Server (NTRS)
Luz, Paul L.
2005-01-01
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
Mathematical Graphic Organizers
ERIC Educational Resources Information Center
Zollman, Alan
2009-01-01
As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…
Learning Mathematics while Black
ERIC Educational Resources Information Center
Martin, Danny Bernard
2012-01-01
While research by scholars has contributed greatly to an emerging knowledge base on Black children and mathematics, there continues to be a dire need for insightful research that de-centers longstanding accounts that have contributed to the construction of Black children as mathematically illiterate and as less than ideal learners relative to…
ERIC Educational Resources Information Center
Goldsmith, Lynn T.
2000-01-01
Parents can help ensure that their children are well-equipped with the necessary mathematical skills and understanding for the future by: having high expectations for their children's learning; helping their children see mathematical connections and applications in the world; being curious about their children's thinking; and being enthusiastic…
ERIC Educational Resources Information Center
Stallings, L. Lynn
2007-01-01
This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…
[Collected Papers on Mathematics.
ERIC Educational Resources Information Center
Connell, Michael L., Ed.
This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student Learning and…
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.
ERIC Educational Resources Information Center
Fennema, Elizabeth, Ed.; Leder, Gilah C., Ed.
This book reports on various studies that have increased our understanding of why females and males learn different kinds and amounts of mathematics. In particular, this book explicates the Autonomous Learning Behavior model, proposed by Fennema and Peterson, which is a possible explanation of the development of gender differences in mathematics.…
Business Mathematics Curriculum.
ERIC Educational Resources Information Center
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
Strengthen Your Mathematical Muscles
ERIC Educational Resources Information Center
Wohlhuter, Kay A.; Breyfogle, M. Lynn; McDuffie, Amy Roth
2010-01-01
Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…
ERIC Educational Resources Information Center
Sharp, John
2012-01-01
This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…
Genders, Mathematics, and Feminisms.
ERIC Educational Resources Information Center
Damarin, Suzanne
Historical studies reveal that mathematics has been claimed as a private domain by men, while studies of the popular press document that women and girls are considered incompetent in that field. The study of gender and mathematics as viewed through feminism can create a new reading which exposes hidden assumptions, unwarranted conclusions, and…
NASA Astrophysics Data System (ADS)
Rohrlich, Fritz
2011-12-01
Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
Mathematics Projects Handbook.
ERIC Educational Resources Information Center
Hess, Adrien L.
This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entrance in fairs and competitions. The use of projects to…
Developing Mathematical Proficiency
ERIC Educational Resources Information Center
Groves, Susie
2012-01-01
It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as "relational" rather than "instrumental" understanding. More recently, Kilpatrick, Swafford and Findell (2001)…
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The first of three volumes of a mathematics training course for Navy personnel, this document covers a wide range of basic mathematics. The text begins with number systems, signed numbers, fractions, decimals, and percentages and continues into algebra with exponents, polynomials, and linear equations. Early chapters were designed to give insight…
Issues in Teaching Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2013-01-01
In this article, the author states that there are selected issues in mathematics instruction that educators should be well aware of when planning lessons and units of study. These issues provide a basis for thought and discussion when assisting pupils to attain more optimally. Purposeful studying of issues guides mathematics teachers in…
Teaching Mathematics Using Steplets
ERIC Educational Resources Information Center
Bringslid, Odd; Norstein, Anne
2008-01-01
This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory…
Dyslexia, Dyspraxia and Mathematics.
ERIC Educational Resources Information Center
Yeo, Dorian
This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…
Mathematical thinking and origami
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2016-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
Mathematics Education in Argentina
ERIC Educational Resources Information Center
Varsavsky, Cristina; Anaya, Marta
2009-01-01
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
ERIC Educational Resources Information Center
Oldfield, Christine
1996-01-01
Describes aspects of learning the language of mathematics including vocabulary and grammar, the origins of the vocabulary, the pronunciation problem, and translation of English phrases and sentences into mathematical language accompanied by conceptual understanding of the process being described. Gives suggestions for teachers in class and…
Developing Mathematically Promising Students.
ERIC Educational Resources Information Center
Sheffield, Linda Jensen, Ed.
This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…
Student Nurses and Mathematics.
ERIC Educational Resources Information Center
Hutton, B. Meriel
For the safety of the public, it is essential that nurses are competent at least in the mathematics that enables them to calculate medications accurately. From a survey by G. Hek (1994), it is apparent that mathematics is not universally included in the nursing curricula, nor asked for as a pre-requisite to entry. Changes in the profile of the…
Encouraging Good Mathematical Writing
ERIC Educational Resources Information Center
O'Shea, J.
2006-01-01
This paper is a report on an attempt to teach students in their first and second year of university how to write mathematics. The problems faced by these students are outlined and the system devised to emphasize the importance of communicating mathematics is explained.
ERIC Educational Resources Information Center
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Mathematical models of diabetes progression.
De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels
2008-12-01
Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page. PMID:18780774
Technical Mathematics: Restructure of Technical Mathematics.
ERIC Educational Resources Information Center
Flannery, Carol A.
Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…
Improving accessibility to mathematical formulas: the Wikipedia Math Accessor
NASA Astrophysics Data System (ADS)
Fuentes Sepúlveda, J.; Ferres, L.
2012-09-01
Mathematics accessibility is an important topic for inclusive education. In this paper, we make Wikipedia's repository of mathematical formulas accessible by providing a natural language description of its more than 420,000 formulas using a well-researched sub-language. We also contribute by targeting Spanish speakers, for whom assistive technologies, particularly domain-specific technologies like the one described here, are scarce. Our focus on the semantics of formulas (rather than their visual appearance) allowed us to generate verbalizations with a precision of approximately 80% of understandable descriptions, as shown in an evaluation with sighted users.
Poisson type models and descriptive statistics of computer network information flows
Downing, D.; Fedorov, V.; Dunigan, T.; Batsell, S.
1997-08-01
Many contemporary publications on network traffic gravitate to ideas of self-similarity and long-range dependence. The corresponding elegant and parsimonious mathematical techniques proved to be efficient for the description of a wide class of aggregated processes. Sharing the enthusiasm about the above ideas the authors also believe that whenever it is possible any problem must be considered at the most basic level in an attempt to understand the driving forces of the processes under analysis. Consequently the authors try to show that some behavioral patterns of descriptive statistics which are typical for long-memory processes (a particular case of long-range dependence) can also be explained in the framework of the traditional Poisson process paradigm. Applying the concepts of inhomogeneity, compoundness and double stochasticity they propose a simple and intuitively transparent approach of explaining the expected shape of the observed histograms of counts and the expected behavior of the sample covariance functions. Matching the images of these two descriptive statistics allows them to infer the presence of trends or double stochasticity in analyzed time series. They considered only statistics which are based on counts. A similar approach may be applied to waiting or inter-arrival time sequences and will be discussed in other publications. They hope that combining the reported results with the statistical methods based on aggregated models may lead to computationally affordable on-line techniques of compact and visualized data analysis of network flows.
NASA Astrophysics Data System (ADS)
Foster, Colin
2013-07-01
In a high-stakes assessment culture, it is clearly important that learners of mathematics develop the necessary fluency and confidence to perform well on the specific, narrowly defined techniques that will be tested. However, an overemphasis on the training of piecemeal mathematical skills at the expense of more independent engagement with richer, multifaceted tasks risks devaluing the subject and failing to give learners an authentic and enjoyable experience of being a mathematician. Thus, there is a pressing need for mathematical tasks which embed the practice of essential techniques within a richer, exploratory and investigative context. Such tasks can be justified to school management or to more traditional mathematics teachers as vital practice of important skills; at the same time, they give scope to progressive teachers who wish to work in more exploratory ways. This paper draws on the notion of a musical étude to develop a powerful and versatile approach in which these apparently contradictory aspects of teaching mathematics can be harmoniously combined. I illustrate the tactic in three central areas of the high-school mathematics curriculum: plotting Cartesian coordinates, solving linear equations and performing enlargements. In each case, extensive practice of important procedures takes place alongside more thoughtful and mathematically creative activity.
ERIC Educational Resources Information Center
Dede, Yuksel
2013-01-01
This study reported the specific findings of a larger comparative study concerning Turkish and German mathematics teachers' values. The main focus was on the teaching experience of the mathematics teachers. Interactions related to nationality were also of interest. The research methodology employed in this study was a descriptive study. The…
Mathematical modelling in nuclear medicine
Kuikka, Jyrki T.; Bassingthwaighte, James B.; Henrich, Michael M.; Feinendegen, Ludwig E.
2010-01-01
Modern imaging techniques can provide sequences of images giving signals proportional to the concentrations of tracers (by emission tomography), of X-ray-absorbing contrast materials (fast CT or perhaps NMR contrast), or of native chemical substances (NMR) in tissue regions at identifiable locations in 3D space. Methods for the analysis of the concentration-time curves with mathematical models describing the physiological processes and the appropriate anatomy are now available to give a quantitative portrayal of both structure and function: such is the approach to metabolic or functional imaging. One formulates a model first by defining what it should represent: this is the hypothesis. When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. This is what one would like to test against data. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations. The former are known as distributed models and the latter as lumped compartmental or mixing chamber models. Since both are derived from the same ideas, the parameters are usually the same; their differences are in their ability to represent the hypothesis correctly, quantitatively, and sometimes in their computability. In this essay we review the philosophical and practical aspects of such modelling analysis for translating image sequences into physiological terms. PMID:1936044
Multimedia content description framework
NASA Technical Reports Server (NTRS)
Bergman, Lawrence David (Inventor); Kim, Michelle Yoonk Yung (Inventor); Li, Chung-Sheng (Inventor); Mohan, Rakesh (Inventor); Smith, John Richard (Inventor)
2003-01-01
A framework is provided for describing multimedia content and a system in which a plurality of multimedia storage devices employing the content description methods of the present invention can interoperate. In accordance with one form of the present invention, the content description framework is a description scheme (DS) for describing streams or aggregations of multimedia objects, which may comprise audio, images, video, text, time series, and various other modalities. This description scheme can accommodate an essentially limitless number of descriptors in terms of features, semantics or metadata, and facilitate content-based search, index, and retrieval, among other capabilities, for both streamed or aggregated multimedia objects.
Assessing Students Beliefs about Mathematics.
ERIC Educational Resources Information Center
Spangler, Denise A.
1992-01-01
Presents 11 open-ended questions that can be presented to students and teachers at all educational levels in various formats to assess mathematical beliefs. Questions investigate beliefs toward mathematics, the problem-solving process, mathematicians, and mathematical applications. (MDH)
Creating a Differentiated Mathematics Classroom
ERIC Educational Resources Information Center
Strong, Richard; Thomas, Ed; Perini, Matthew; Silver, Harvey
2004-01-01
Student differences in learning mathematics are categorized under four different mathematical learning styles. The names of books providing examples on how mathematics teachers can differentiate their classroom instructions are mentioned.
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. PMID:25595115
Mathematization in introductory physics
NASA Astrophysics Data System (ADS)
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
The Greatest Mathematical Discovery?
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.
2001-01-01
In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024
Mathematical Models of the Value of Achievement Testing.
ERIC Educational Resources Information Center
Pinsky, Paul D.
The mathematical models of this paper were developed as an outgrowth of working with the Comprehensive Achievement Monitoring project (Project CAM) which was conceived as a model and application of sampling procedures such as those used in industrial quality control techniques to educational measurement. This paper explores mathematical modeling…
People's Mathematics in Working Life: Why Is It Invisible?
ERIC Educational Resources Information Center
Wedege, Tine
2010-01-01
The labour market requirements play a central role in the answer from politicians and educational planners to the question "Why teach mathematics to adults?" Mathematics is interwoven with technology in the workplace - in technique, work organisation and people's competences. Still "No" is the most common answer to the question…
Applied Mathematics via Student-Created Computer Graphics.
ERIC Educational Resources Information Center
Sloyer, Clifford; Smith, Lynn H.
1983-01-01
Describes topics and applications of five lessons dealing with applied mathematics (solving sequential optimization problems, queuing theory, graph theory, glyphs (pictorial techniques for displaying relationships among variables, medical mathematics). Design and evaluation of these materials which employ interactive graphics are also described.…
Integrated Programs for Science and Mathematics: Review of Related Literature
ERIC Educational Resources Information Center
Kurt, Kursat; Pehlivan, Mustafa
2013-01-01
This study presents a review of literature on the integration of science and mathematics, focusing on the dominant trends in the related studies. Majority of the studies conclude that the concept of the integration between science and mathematics is still vogue. On the other hand, there are various methods, techniques and models to achieve this…
Uncovering Student Thinking in Mathematics: 25 Formative Assessment Probes
ERIC Educational Resources Information Center
Rose, Cheryl M.; Minton, Leslie; Arline, Carolyn B.
2006-01-01
Students learn at varying rates, and if a misconception in mathematics develops early, it may be carried from year to year and obstruct a student's progress. To identify fallacies in students' preconceived ideas, "Uncovering Student Thinking in Mathematics" offers educators a powerful diagnostic technique in the form of field-tested assessment…
A New Wave in Applied Mathematics.
ERIC Educational Resources Information Center
Cipra, Barry A.
1990-01-01
Discussed is wavelet theory, which provides ways to rearrange data to reveal features of a physical or mathematical system which might otherwise be hidden. This theory is compared to fourier analysis and the advantages of wavelet theory are stressed. Applications of this technique are suggested. (CW)
Techtalk: Mobile Apps and College Mathematics
ERIC Educational Resources Information Center
Hoang, Theresa V.; Caverly, David C.
2013-01-01
In this column, the authors discuss apps useful in developing mathematical reasoning. They place these into a theoretical framework, suggesting how they could be used in an instructional model such as the Algorithmic Instructional Technique (AIT) developed by Vasquez (2003). This model includes four stages: modeling, practice, transition, and…
Mathematics Is Always Invisible, Professor Dowling
ERIC Educational Resources Information Center
Cable, John
2015-01-01
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…
Exposing the Mathematical Wizard: Approximating Trigonometric Functions
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2011-01-01
For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…
Mathematical Methods for Diffusion MRI Processing
Lenglet, C.; Campbell, J.S.W.; Descoteaux, M.; Haro, G.; Savadjiev, P.; Wassermann, D.; Anwander, A.; Deriche, R.; Pike, G.B.; Sapiro, G.; Siddiqi, K.; Thompson, P.
2009-01-01
In this article, we review recent mathematical models and computational methods for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, cerebral white matter connectivity analysis, and segmentation techniques. We focus on Diffusion Tensor Images (DTI) and Q-Ball Images (QBI). PMID:19063977
The International Mathematical Olympiad Training Session.
ERIC Educational Resources Information Center
Rousseau, Cecil; Patruno, Gregg
1985-01-01
The Mathematical Olympiad Training Session is designed to give United States students a problem-oriented exposure to subject areas (algebra, geometry, number theory, combinatorics, and inequalities) through an intensive three-week course. Techniques used during the session, with three sample problems and their solutions, are presented. (JN)
Physics 3204. Course Description.
ERIC Educational Resources Information Center
Newfoundland and Labrador Dept. of Education.
A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…
Descriptive Metadata: Emerging Standards.
ERIC Educational Resources Information Center
Ahronheim, Judith R.
1998-01-01
Discusses metadata, digital resources, cross-disciplinary activity, and standards. Highlights include Standard Generalized Markup Language (SGML); Extensible Markup Language (XML); Dublin Core; Resource Description Framework (RDF); Text Encoding Initiative (TEI); Encoded Archival Description (EAD); art and cultural-heritage metadata initiatives;…
Math Description Engine Software Development Kit
NASA Technical Reports Server (NTRS)
Shelton, Robert O.; Smith, Stephanie L.; Dexter, Dan E.; Hodgson, Terry R.
2010-01-01
The Math Description Engine Software Development Kit (MDE SDK) can be used by software developers to make computer-rendered graphs more accessible to blind and visually-impaired users. The MDE SDK generates alternative graph descriptions in two forms: textual descriptions and non-verbal sound renderings, or sonification. It also enables display of an animated trace of a graph sonification on a visual graph component, with color and line-thickness options for users having low vision or color-related impairments. A set of accessible graphical user interface widgets is provided for operation by end users and for control of accessible graph displays. Version 1.0 of the MDE SDK generates text descriptions for 2D graphs commonly seen in math and science curriculum (and practice). The mathematically rich text descriptions can also serve as a virtual math and science assistant for blind and sighted users, making graphs more accessible for everyone. The MDE SDK has a simple application programming interface (API) that makes it easy for programmers and Web-site developers to make graphs accessible with just a few lines of code. The source code is written in Java for cross-platform compatibility and to take advantage of Java s built-in support for building accessible software application interfaces. Compiled-library and NASA Open Source versions are available with API documentation and Programmer s Guide at http:/ / prim e.jsc.n asa. gov.
Ferrari, Pier Luigi
2003-07-29
Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful. PMID:12903658
Black African Traditional Mathematics
ERIC Educational Resources Information Center
Zaslavsky, Claudia
1970-01-01
Discusses the traditional number systems and the origin of the number names used by several African peoples living south of the Sahara. Also included are limitations in African mathematical development, and possible topics for research. (RP)
Standards in Mathematics Teaching.
ERIC Educational Resources Information Center
Brookes, Bill
1978-01-01
This article is based on a lecture given at the 1978 Easter Course at Padgate College of Higher Education. The lecture is an analysis of the complexity of mathematics teaching and the setting of teaching standards. (MN)
Mathematics Case Methods Project.
ERIC Educational Resources Information Center
Barnett, Carne S.
1998-01-01
Presents an overview and analysis of the Mathematics Case Methods Project, which uses cases in order to examine and reflect upon teaching. Focuses on a special kind of teacher knowledge, coined pedagogical-content knowledge. (ASK)
Benjamin Banneker's Mathematical Puzzles.
ERIC Educational Resources Information Center
Mahoney, John F.
2003-01-01
Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)
Applications of Secondary School Mathematics: Readings from the "Mathematics Teacher."
ERIC Educational Resources Information Center
Austin, Joe Dan, Ed.
This book provides applications for use in the secondary school mathematics curriculum by selecting related articles appearing in the "Mathematics Teacher" during the last 15 years. The articles are grouped into chapters that reflect the main secondary school mathematics courses and categorized by the highest level of mathematics needed for…
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…
Promoting Critical Mathematics Literacy in Secondary Mathematics Teacher Education
ERIC Educational Resources Information Center
Fish, Michael Charles
2012-01-01
This study examines how critical mathematical literacy teachers conceptualize their practices and how those practices were demonstrated in the classroom. Practices were considered from an ontology of mathematics education, specific to critical mathematical literacy, in which classroom interactions question what it means to do mathematics as an…
Using Mathematics in Science: Working with Your Mathematics Department
ERIC Educational Resources Information Center
Lyon, Steve
2014-01-01
Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…
Handwritten mathematical symbols dataset
Chajri, Yassine; Bouikhalene, Belaid
2016-01-01
Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975
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.
Handwritten mathematical symbols dataset.
Chajri, Yassine; Bouikhalene, Belaid
2016-06-01
Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975
Mathematical foundations of neurocomputing
Amari, S. . Faculty of Engineering)
1990-09-01
Neurocomputing makes use of parallel dynamical interactions of modifiable neuron-like elements. It is important to show, by mathematical treatments, the capabilities and limitations of information processing by various architectures of neural networks. This paper, gives mathematical foundations to neurocomputing. It considers the capabilities of transformations by layered networks, statistical neurodynamics, the dynamical characteristics of associative memory, a general theory of neural learning, and self-organization of neural networks.
Landauer, C.; Bellman, K.L.
1996-12-31
In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.
Mathematical Rigor vs. Conceptual Change: Some Early Results
NASA Astrophysics Data System (ADS)
Alexander, W. R.
2003-05-01
Results from two different pedagogical approaches to teaching introductory astronomy at the college level will be presented. The first of these approaches is a descriptive, conceptually based approach that emphasizes conceptual change. This descriptive class is typically an elective for non-science majors. The other approach is a mathematically rigorous treatment that emphasizes problem solving and is designed to prepare students for further study in astronomy. The mathematically rigorous class is typically taken by science majors. It also fulfills an elective science requirement for these science majors. The Astronomy Diagnostic Test version 2 (ADT 2.0) was used as an assessment instrument since the validity and reliability have been investigated by previous researchers. The ADT 2.0 was administered as both a pre-test and post-test to both groups. Initial results show no significant difference between the two groups in the post-test. However, there is a slightly greater improvement for the descriptive class between the pre and post testing compared to the mathematically rigorous course. There was great care to account for variables. These variables included: selection of text, class format as well as instructor differences. Results indicate that the mathematically rigorous model, doesn't improve conceptual understanding any better than the conceptual change model. Additional results indicate that there is a similar gender bias in favor of males that has been measured by previous investigators. This research has been funded by the College of Science and Mathematics at James Madison University.
Increasing mathematical problem-solving performance through relaxation training
NASA Astrophysics Data System (ADS)
Sharp, Conni; Coltharp, Hazel; Hurford, David; Cole, Amykay
2000-04-01
Two intact classes of 30 undergraduate students enrolled in the same general education mathematics course were each administered the IPSP Mathematics Problem Solving Test and the Mathematics Anxiety Rating Scale at the beginning and end of the semester. Both groups experienced the same syllabus, lectures, course requirements, and assessment techniques; however, one group received relaxation training during an initial class meeting and during the first 5 to 7 minutes of each subsequent class. The group which had received relaxation training had significantly lower mathematics anxiety and significantly higher mathematics performance at the end of the course. The results suggest that relaxation training may be a useful tool for treating anxiety in undergraduate general education mathematics students.
A Course in Multicultural Mathematics
ERIC Educational Resources Information Center
Hall, Rachel W.
2007-01-01
The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…
Discrete Mathematics and Curriculum Reform.
ERIC Educational Resources Information Center
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Assessing Innovative Proposals in Mathematics.
ERIC Educational Resources Information Center
Ediger, Marlow
Mathematics is at the apex in priorities pertaining to state-mandated testing of students. With 49 out of 50 states having mandated the testing of students, all of these have mathematics in the testing format. This paper discusses the modern school mathematics movement, recent approaches in improving the teaching of mathematics, and specific…
ERIC Educational Resources Information Center
Gough, John
2008-01-01
It is potentially arresting when a mathematical implication is offered in a non-mathematical book. This author contends that students are encouraged to develop mathematical thinking when they read mathematical challenges in books. Aspects of books such as time-lines, historical relationships, maps, journeys, cause-and-affect, deductive inference,…
Mathematical Modeling: A Structured Process
ERIC Educational Resources Information Center
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Mathematics Is a Spectator Sport
ERIC Educational Resources Information Center
Foster, Colin; Williams, Helen
2007-01-01
This article presents a conversation between two editors of "Mathematics Teaching Incorporating Micromath." Topics discussed include the 2004 Association of Teachers of Mathematics conference, titled "Mathematics is Not a Spectator Sport," and the thought of engaging in mathematics and what that might mean. One of the editors stresses the need to…
Semantic Processing of Mathematical Gestures
ERIC Educational Resources Information Center
Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.
2009-01-01
Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…
A Mathematics Software Database Update.
ERIC Educational Resources Information Center
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Truth & Beauty: Mathematics in Literature
ERIC Educational Resources Information Center
Cohen, Marion D.
2013-01-01
Today there are many categories of mathematics literature, including fiction and poetry. Mathematics fiction appears in such anthologies as "Fantasia Mathematica" (Fadiman 1958, 1997) and "The Mathematical Magpie" (Fadiman 1962, 1997). In addition, mathematics fiction is featured at http://kasmana.people.cofc.edu/MATHFICT.…
Reaching All Students with Mathematics.
ERIC Educational Resources Information Center
Cuevas, Gilbert, Ed.; Driscoll, Mark, Ed.
The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this book was put together…
ERIC Educational Resources Information Center
Simon, Martin A.; Tzur, Ron
2004-01-01
Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning.…
ERIC Educational Resources Information Center
Wang, Yang; O'Dwyer, Laura
2011-01-01
Using data from the Trends in International Mathematics and Science Study (TIMSS) 2003 and 2007 administrations, this study examines international trends in technology use and explores the international patterns in how teacher-directed, student-use of technology is related to eighth grade mathematics achievement. Descriptive patterns in…
ERIC Educational Resources Information Center
Yenilmez, Kursat; Ersoy, Mehmet
2008-01-01
The purpose of this study was to determine opinions of mathematics teacher candidates towards applying 7E instructional model on computer aided instruction environments. The descriptive case study model was used in this study. The sample of the study consists of 52 mathematics teacher candidates which were selected randomly from Eskisehir…
An Investigation of Pre-Service Mathematics Teachers' Skills in the Development of Activities
ERIC Educational Resources Information Center
Özgen, Kemal; Alkan, Hu¨seyin
2014-01-01
The purpose of this research is to determine pre-service mathematics teachers' skills in the development of activities. The research was carried out using the case study which is descriptive method. For the collection of data, 57 pre-service mathematics teachers' in their final year secondary math teachers' education department…
Hidden Disparities: How Courses and Curricula Shape Opportunities in Mathematics during High School
ERIC Educational Resources Information Center
Schiller, Kathryn S.; Schmidt, William H.; Muller, Chandra; Houang, Richard T.
2010-01-01
Efforts to promote academic achievement by increasing access to courses, especially in mathematics, may mask educational disparities if variations in curriculum are not also monitored. A multi-dimensional description of students' mathematics curricula during high school was obtained from analyses of surveys, transcripts, and textbooks collected…
Mathematical modeling of molecular diffusion through mucus
Cu, Yen; Saltzman, W. Mark
2008-01-01
The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488
The Applied Mathematics for Power Systems (AMPS)
Chertkov, Michael
2012-07-24
Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxes for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.
Characterization of high school mathematics and physics language genres
NASA Astrophysics Data System (ADS)
Wallace, Michelle L.
Research indicates that language factors play a critical role in the learning of school mathematics and science. Symbols and language-forms have been created to represent and discuss mathematical ideas. Understanding language factors, therefore, is critical in improving the teaching and learning of school mathematics and science. The specific goal of this research was to characterize language genres found in secondary school mathematics and physics classrooms. The research presented here was conducted in two secondary school classrooms---one algebra and one physics---taught by the same teacher. The focus was on the discourse between the teacher and her students. In both mathematics and physics, the teacher attended to the meaning of mathematical concepts and processes, but the talk differed. Physics talk focused on developing meaning for the physics concepts through activities and discussion, which were accompanied by mathematical calculations and analyses. Algebra talk, on the other hand, was procedural and narrative in nature. Thus physics talk was more descriptive of individual concepts and situation, and was more explanatory and exploratory than algebra talk. All discourse inevitably reflects one's thinking and beliefs about the content of that discourse. Thus talking algebra and talking physics, as observed in this study, both represented the teacher's beliefs about teaching and learning and the nature of the school curriculum. Even for a teacher with a strong academic background in both mathematics and science, integrating across the curriculum can be hindered by the approved school curriculum and by the reality of the particular classroom context. Providing professional development and implementing one of several available integrated curricula would be needed if more integration were to be implemented. This study presents a literature-based description of the conceptual notion of language genre. It additionally presents a conceptualization of mathematics and
The Force-Frequency Relationship: Insights from Mathematical Modeling
ERIC Educational Resources Information Center
Puglisi, Jose L.; Negroni, Jorge A.; Chen-Izu, Ye; Bers, Donald M.
2013-01-01
The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by…
[Mathematical model of baroreflex regulation of hemodynamics in the dog].
Palets, B L
1983-11-01
A non-linear mathematical model of dog hemodynamics regulation was developed including descriptions of the cardiovascular system, the arterial baroreflex and the Beinbridge reflex. Model calculated arterial and venous pressure, blood flow, and heart rate are in good agreement with experimental data. PMID:6653829
101 Environmental Education Activities. Booklet 3--Mathematics Activities.
ERIC Educational Resources Information Center
Schaljo, Roger, Comp.
Each of the 14 environment-related mathematics activities included in this publication by the Upper Mississippi River ECO-Center includes objectives, materials needed, preparation, and activity description. Occasionally, variations and helpful hints are added. Because the student can gain experience to help him with the practical application of…
Mathematics Education Series (Summary of GEMTEP series--15 Modules).
ERIC Educational Resources Information Center
National Education Association, Washington, DC. Project on Utilization of Inservice Education R & D Outcomes.
The inservice learning module described focuses on teaching mathematical concepts at the elementary grade level. Specifically covered in the module are discovery learning, drill activities, understanding number concepts, and introduction to geometry. Information is provided in this descriptive report on the scope and sequencing of topics and the…
Engaging Students in Mathematical Modeling through Service-Learning
ERIC Educational Resources Information Center
Carducci, Olivia M.
2014-01-01
I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…
Angles and Space: MINNEMAST Coordinated Mathematics - Science Series, Unit 21.
ERIC Educational Resources Information Center
Biersteker, Joseph; And Others
This volume is the twenty-first in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by second-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of three groups of lessons. The purposes and…
A Generalized Instructional System for Elementary Mathematical Logic.
ERIC Educational Resources Information Center
Goldberg, Adele
A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving…
Brain Hemisphericity and Mathematics Achievement of High School Students
ERIC Educational Resources Information Center
Fernandez, Sanny F.
2011-01-01
This study aimed to find out the brain hemisphericity and mathematics achievement of high school students. The respondents of the study were the 168 first year high school students of Colegio de San Jose, during school year 2010-2011 who were chosen through stratified random sampling. The descriptive and interview methods of research were used in…
Mathematics Education Is Not an Enigma--Part 2
ERIC Educational Resources Information Center
Williams, Doug
2012-01-01
Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". Here he continues storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that seeks to…
Mathematics Education Is Not an Enigma--Part 1
ERIC Educational Resources Information Center
Williams, Doug
2012-01-01
Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". This is storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that seeks to change…
Cultural Issues in the Communication of Research on Mathematics Education
ERIC Educational Resources Information Center
Bartolini Bussi, Maria G.; Martignone, Francesca
2013-01-01
It might be trite to observe that every research study is framed within a cultural background. In this paper we argue that the description of the cultural background is important for discussing, evaluating and exploiting internationally the findings of local educational studies. This issue is fundamental in every study in mathematics education…
Science and Mathematics Software Opportunities and Needs. Executive Summary.
ERIC Educational Resources Information Center
Technical Education Research Center, Cambridge, MA.
This study examined the extent to which opportunities created by computer technology addresses the needs in school science and mathematics instruction. Information was gathered by obtaining descriptions of most available software; reviewing published software evaluations, grant-supported software development projects, and a broad selection of…
An Annotated Bibliography of Films and Videotapes for College Mathematics.
ERIC Educational Resources Information Center
Schneider, David I.
This document is intended to facilitate the use of mathematics films and videotapes. All materials listed are readily available from film and videotape companies or from film rental libraries. All descriptions provided are excerpts from distributor's brochures. The materials are generally suitable for college students, and are categorized into the…
Eliciting Students' Beliefs about Who Is Good at Mathematics
ERIC Educational Resources Information Center
Morge, Shelby P.
2007-01-01
This article highlights a series of activities designed to elicit students' mathematics-related beliefs, particularly those related to gender. As a result of the activities, females in upper-level classes rated themselves as having less confidence than males, and viewing a movie clip was sufficient for some students to modify their descriptions of…
Harmony between Turkish Early Childhood and Primary Mathematics Education Standards
ERIC Educational Resources Information Center
Caliskan Dedeoglu, Nuray; Alat, Zeynep
2012-01-01
The aim of this study was to explore the spiral relation and the congruency between mathematics standards listed in the Early Childhood and First Grade curricula in Turkey. A descriptive content analysis was conducted on Early Child Education Curriculum (OOEP) for 36-72 months old children and Math Curriculum for the Grades 1-5 (IMOP), both…
Parts and Pieces: MINNEMAST Coordinated Mathematics - Science Series, Unit 22.
ERIC Educational Resources Information Center
Sohre, Beverly, Ed.
This volume is the twenty-second in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by second-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of seven groups of lessons. The purposes and…
Cross-national Retrospective Studies of Mathematics Olympians.
ERIC Educational Resources Information Center
Campbell, James Reed, Ed.
1996-01-01
The eight chapters of this theme issue use quantitative and qualitative methods to explore the nature and nurture of young participants in the mathematics Olympiad from five countries. Parallel studies are presented of winners from China, Taiwan, and the United States, along with descriptions of programs in Japan and Russia. (SLD)
The Teaching of Developmental Mathematics in Community Colleges.
ERIC Educational Resources Information Center
Medin, Julie
Details of the remedial mathematics programs offered by three community colleges in the Washington D.C. area and a short description of programs offered by eight Maryland community colleges are given. Research and studies of remedial programs at the community college level in other parts of the United States are briefly reviewed. (DT)
Natural Systems: MINNEMAST Coordinated Mathematics - Science Series, Unit 29.
ERIC Educational Resources Information Center
Bakke, Jeannette; And Others
This volume is the last in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by third-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of three groups of lessons. The purposes and procedures for…
A Synthesis of Solar Cycle Prediction Techniques
NASA Technical Reports Server (NTRS)
Hathaway, David H.; Wilson, Robert M.; Reichmann, Edwin J.
1999-01-01
A number of techniques currently in use for predicting solar activity on a solar cycle timescale are tested with historical data. Some techniques, e.g., regression and curve fitting, work well as solar activity approaches maximum and provide a month-by-month description of future activity, while others, e.g., geomagnetic precursors, work well near solar minimum but only provide an estimate of the amplitude of the cycle. A synthesis of different techniques is shown to provide a more accurate and useful forecast of solar cycle activity levels. A combination of two uncorrelated geomagnetic precursor techniques provides a more accurate prediction for the amplitude of a solar activity cycle at a time well before activity minimum. This combined precursor method gives a smoothed sunspot number maximum of 154 plus or minus 21 at the 95% level of confidence for the next cycle maximum. A mathematical function dependent on the time of cycle initiation and the cycle amplitude is used to describe the level of solar activity month by month for the next cycle. As the time of cycle maximum approaches a better estimate of the cycle activity is obtained by including the fit between previous activity levels and this function. This Combined Solar Cycle Activity Forecast gives, as of January 1999, a smoothed sunspot maximum of 146 plus or minus 20 at the 95% level of confidence for the next cycle maximum.
ERIC Educational Resources Information Center
Jaji, Gail
Presents a detailed discussion of the data collected on calculator and computer use in schools in 20 countries. The document includes discussion of: (1) school policy on calculator use; (2) description of populations A (8th grade students) and B (12th grade students) in the United States; (3) uses of calculators in subjects other than mathematics;…
ERIC Educational Resources Information Center
Clarkson, P. C.
Descriptions of Papua New Guinea's national high schools, grade 12 major/minor mathematics courses, and an analysis of the 1980 and 1981 major/minor course examination results are presented. The analysis is intended for use by post year 12 lecturers/instructors planning their courses. Findings indicate that topic scores were far too low for these…
Summer Institute for Mathematics and Science teachers (SIMS). Final report
1994-07-01
The Summer Institute for Mathematics and Science Teachers (SIMS) was to provide training for science and mathematics educators in strategies and techniques to use for educating and motivating historically under-represented populations. The Institute featured 40 hours of training over five days, July 13-17, 1993 plus half-day follow-up training November 13, 1993 and April 30, 1994. The objective of the training was to include sensitization to cultural and gender issues, and to instruct participants in the utilization of a variety of techniques and activities for encouraging historically under-represented groups to take more advanced science and mathematics courses.
The Effect of Mathematics Research on Mathematics Majors' Mathematical Beliefs
ERIC Educational Resources Information Center
Goodson, Joshua E.
2012-01-01
This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics…
Gaber, David; Schlimm, Dirk
2015-01-01
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. PMID:26263425
Using a Computer Algebra System to Facilitate the Learning of Mathematical Induction
ERIC Educational Resources Information Center
McAndrew, Alasdair
2010-01-01
Mathematical induction is one of the major proof techniques taught to mathematics students in the first years of their undergraduate degrees. In addition to its importance to mathematics, induction is also required for computer science and related disciplines. However, even if the concepts of a proof by induction are taught and understood, many…
What Would the Mathematics Curriculum Look Like if Values Were the Focus?
ERIC Educational Resources Information Center
Seah, Wee Tiong; Andersson, Annica; Bishop, Alan; Clarkson, Philip
2016-01-01
The crucial reason for the common dislike, fear, and even hatred of mathematics by students and others is probably not the nature of mathematics itself, but the way the subject is portrayed and taught. We propose that instead of a mathematics curriculum that focuses on concepts and techniques (which is often seen), it might be more productive if…
General Mathematics II. A CoSer Project of the Cortland-Madison BOCES.
ERIC Educational Resources Information Center
DiLucci, Jackie; And Others
This General Mathematics II curriculum reflects the 1980 National Council of Teachers of Mathematics (NCTM) Agenda for Action statement that emphasis in mathematics learning and teaching should be shifted away from isolated computational skills toward problem-solving techniques. The use of calculators and estimation is encouraged. Emphasis both in…
Engaging Future Teachers in Problem-Based Learning with the Park City Mathematics Institute Problems
ERIC Educational Resources Information Center
Pilgrim, Mary E.
2014-01-01
Problem-based learning (PBL) is a pedagogical technique recommended for K-12 mathematics classrooms. However, the mathematics courses in future teachers' degree programs are often lecture based. Students typically learn about problem-based learning in theory, but rarely get to experience it first-hand in their mathematics courses. The premise…
The Autonomy of Technique Revisited
ERIC Educational Resources Information Center
Vanderburg, Willem H.
2004-01-01
Jacques Ellul's claim that technique became an autonomous phenomenon during the middle of the 20th century, and subsequently a system, means that the influence people have on technique is much less decisive than the influence technique has on people. As a sociohistorical description of the relationship between technique and society, it can be…
MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING
ANGENENT, SIGURD; PICHON, ERIC; TANNENBAUM, ALLEN
2013-01-01
In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation. PMID:23645963
Physical and mathematical cochlear models
NASA Astrophysics Data System (ADS)
Lim, Kian-Meng
2000-10-01
The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity
Experimenting with Impacts in a Conceptual Physics or Descriptive Astronomy Laboratory
ERIC Educational Resources Information Center
LoPresto, Michael C.
2016-01-01
What follows is a description of the procedure for and results of a simple experiment on the formation of impact craters designed for the laboratory portions of lower mathematical-level general education science courses such as conceptual physics or descriptive astronomy. The experiment provides necessary experience with data collection and…
Automatic TLI recognition system, general description
Lassahn, G.D.
1997-02-01
This report is a general description of an automatic target recognition system developed at the Idaho National Engineering Laboratory for the Department of Energy. A user`s manual is a separate volume, Automatic TLI Recognition System, User`s Guide, and a programmer`s manual is Automatic TLI Recognition System, Programmer`s Guide. This system was designed as an automatic target recognition system for fast screening of large amounts of multi-sensor image data, based on low-cost parallel processors. This system naturally incorporates image data fusion, and it gives uncertainty estimates. It is relatively low cost, compact, and transportable. The software is easily enhanced to expand the system`s capabilities, and the hardware is easily expandable to increase the system`s speed. In addition to its primary function as a trainable target recognition system, this is also a versatile, general-purpose tool for image manipulation and analysis, which can be either keyboard-driven or script-driven. This report includes descriptions of three variants of the computer hardware, a description of the mathematical basis if the training process, and a description with examples of the system capabilities.
Math in Motion: Origami in the Classroom. A Hands-On Creative Approach to Teaching Mathematics. K-8.
ERIC Educational Resources Information Center
Pearl, Barbara
This perfect bound teacher's guide presents techniques and activities to teach mathematics using origami paper folding. Part 1 includes a history of origami, mathematics and origami, and careers using mathematics. Parts 2 and 3 introduce paper-folding concepts and teaching techniques and include suggestions for low-budget paper resources. Part 4…
Mathematical and computational models of plasma flows
NASA Astrophysics Data System (ADS)
Brushlinsky, K. V.
Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.
Mathematical Modeling of Photochemical Air Pollution.
NASA Astrophysics Data System (ADS)
McRae, Gregory John
Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes
Mathematical Astronomy in India
NASA Astrophysics Data System (ADS)
Plofker, Kim
Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.
Mathematics in modern immunology
Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M.
2016-01-01
Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered. PMID:27051512
Making connections in mathematics.
Engelmann, S; Carnine, D; Steely, D G
1991-05-01
Math textbooks, which usually represent the mathematics curriculum, seem to be linked to the poor math performance of U.S. students. The major shortcomings of math textbooks are described in this article; then an alternative perspective is offered (the sameness analysis), along with research conducted with students with learning disabilities and at-risk students. The article then presents a detailed illustration of the sameness analysis--how to teach the addition-subtraction and multiplication-division relationships and their interrelationships in the context of solving word problems in mathematics. PMID:2045726
Software Template for Instruction in Mathematics
NASA Technical Reports Server (NTRS)
Shelton, Robert O.; Moebes, Travis A.; Beall, Anna
2005-01-01
Intelligent Math Tutor (IMT) is a software system that serves as a template for creating software for teaching mathematics. IMT can be easily connected to artificial-intelligence software and other analysis software through input and output of files. IMT provides an easy-to-use interface for generating courses that include tests that contain both multiple-choice and fill-in-the-blank questions, and enables tracking of test scores. IMT makes it easy to generate software for Web-based courses or to manufacture compact disks containing executable course software. IMT also can function as a Web-based application program, with features that run quickly on the Web, while retaining the intelligence of a high-level language application program with many graphics. IMT can be used to write application programs in text, graphics, and/or sound, so that the programs can be tailored to the needs of most handicapped persons. The course software generated by IMT follows a "back to basics" approach of teaching mathematics by inducing the student to apply creative mathematical techniques in the process of learning. Students are thereby made to discover mathematical fundamentals and thereby come to understand mathematics more deeply than they could through simple memorization.
Mathematical textbook of deformable neuroanatomies.
Miller, M I; Christensen, G E; Amit, Y; Grenander, U
1993-01-01
Mathematical techniques are presented for the transformation of digital anatomical textbooks from the ideal to the individual, allowing for the representation of the variabilities manifest in normal human anatomies. The ideal textbook is constructed on a fixed coordinate system to contain all of the information currently available about the physical properties of neuroanatomies. This information is obtained via sensor probes such as magnetic resonance, as well as computed axial and emission tomography, along with symbolic information such as white- and gray-matter tracts, nuclei, etc. Human variability associated with individuals is accommodated by defining probabilistic transformations on the textbook coordinate system, the transformations forming mathematical translation groups of high dimension. The ideal is applied to the individual patient by finding the transformation which is consistent with physical properties of deformable elastic solids and which brings the coordinate system of the textbook to that of the patient. Registration, segmentation, and fusion all result automatically because the textbook carries symbolic values as well as multisensor features. Images Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 PMID:8265653
Mathematical textbook of deformable neuroanatomies.
Miller, M I; Christensen, G E; Amit, Y; Grenander, U
1993-12-15
Mathematical techniques are presented for the transformation of digital anatomical textbooks from the ideal to the individual, allowing for the representation of the variabilities manifest in normal human anatomies. The ideal textbook is constructed on a fixed coordinate system to contain all of the information currently available about the physical properties of neuroanatomies. This information is obtained via sensor probes such as magnetic resonance, as well as computed axial and emission tomography, along with symbolic information such as white- and gray-matter tracts, nuclei, etc. Human variability associated with individuals is accommodated by defining probabilistic transformations on the textbook coordinate system, the transformations forming mathematical translation groups of high dimension. The ideal is applied to the individual patient by finding the transformation which is consistent with physical properties of deformable elastic solids and which brings the coordinate system of the textbook to that of the patient. Registration, segmentation, and fusion all result automatically because the textbook carries symbolic values as well as multisensor features. PMID:8265653
Generalized simulation technique for turbojet engine system analysis
NASA Technical Reports Server (NTRS)
Seldner, K.; Mihaloew, J. R.; Blaha, R. J.
1972-01-01
A nonlinear analog simulation of a turbojet engine was developed. The purpose of the study was to establish simulation techniques applicable to propulsion system dynamics and controls research. A schematic model was derived from a physical description of a J85-13 turbojet engine. Basic conservation equations were applied to each component along with their individual performance characteristics to derive a mathematical representation. The simulation was mechanized on an analog computer. The simulation was verified in both steady-state and dynamic modes by comparing analytical results with experimental data obtained from tests performed at the Lewis Research Center with a J85-13 engine. In addition, comparison was also made with performance data obtained from the engine manufacturer. The comparisons established the validity of the simulation technique.
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.
Free-Form Region Description with Second-Order Pooling.
Carreira, João; Caseiro, Rui; Batista, Jorge; Sminchisescu, Cristian
2015-06-01
Semantic segmentation and object detection are nowadays dominated by methods operating on regions obtained as a result of a bottom-up grouping process (segmentation) but use feature extractors developed for recognition on fixed-form (e.g. rectangular) patches, with full images as a special case. This is most likely suboptimal. In this paper we focus on feature extraction and description over free-form regions and study the relationship with their fixed-form counterparts. Our main contributions are novel pooling techniques that capture the second-order statistics of local descriptors inside such free-form regions. We introduce second-order generalizations of average and max-pooling that together with appropriate non-linearities, derived from the mathematical structure of their embedding space, lead to state-of-the-art recognition performance in semantic segmentation experiments without any type of local feature coding. In contrast, we show that codebook-based local feature coding is more important when feature extraction is constrained to operate over regions that include both foreground and large portions of the background, as typical in image classification settings, whereas for high-accuracy localization setups, second-order pooling over free-form regions produces results superior to those of the winning systems in the contemporary semantic segmentation challenges, with models that are much faster in both training and testing. PMID:26357341
Mathematical challenges from theoretical/computational chemistry
1995-12-31
The committee believes that this report has relevance and potentially valuable suggestions for a wide range of readers. Target audiences include: graduate departments in the mathematical and chemical sciences; federal and private agencies that fund research in the mathematical and chemical sciences; selected industrial and government research and development laboratories; developers of software and hardware for computational chemistry; and selected individual researchers. Chapter 2 of this report covers some history of computational chemistry for the nonspecialist, while Chapter 3 illustrates the fruits of some past successful cross-fertilization between mathematical scientists and computational/theoretical chemists. In Chapter 4 the committee has assembled a representative, but not exhaustive, survey of research opportunities. Most of these are descriptions of important open problems in computational/theoretical chemistry that could gain much from the efforts of innovative mathematical scientists, written so as to be accessible introductions to the nonspecialist. Chapter 5 is an assessment, necessarily subjective, of cultural differences that must be overcome if collaborative work is to be encouraged between the mathematical and the chemical communities. Finally, the report ends with a brief list of conclusions and recommendations that, if followed, could promote accelerated progress at this interface. Recognizing that bothersome language issues can inhibit prospects for collaborative research at the interface between distinctive disciplines, the committee has attempted throughout to maintain an accessible style, in part by using illustrative boxes, and has included at the end of the report a glossary of technical terms that may be familiar to only a subset of the target audiences listed above.
The Provision, Use, Study Time and Effectiveness of Media: A Mathematical Model
ERIC Educational Resources Information Center
Burt, Gordon; Lloyd, David
2005-01-01
Many institutions regularly conduct surveys of students. In some cases these provide descriptive statistics about students' actual use of course components and the descriptive statistics are discussed using ordinary language. A number of refinements to these surveys are proposed. It is argued that mathematical modeling as used in the discipline of…
The "Emerging" and "Emergent" Present: A View on the Indeterminate Nature of Mathematics Lessons
ERIC Educational Resources Information Center
Roth, Wolff-Michael; Maheux, Jean-François
2014-01-01
The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of "emergence." After providing an exemplifying description and…
Theoretical Explanations in Mathematical Physics
NASA Astrophysics Data System (ADS)
Rivadulla, Andrés
Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.
The Music of Mathematics: Toward a New Problem Typology
NASA Astrophysics Data System (ADS)
Quarfoot, David
Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking
ERIC Educational Resources Information Center
Popelka, Susan R.
2011-01-01
Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…
ERIC Educational Resources Information Center
Whitin, Phyllis; Whitin, David J.
2011-01-01
The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…
New Technologies in Mathematics.
ERIC Educational Resources Information Center
Sarmiento, Jorge
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
Mathematics in Indigenous Contexts
ERIC Educational Resources Information Center
Perry, Bob; Howard Peter
2008-01-01
From 1999-2005, the Mathematics in Indigenous Contexts (MIC) project was implemented by the Board of Studies, New South Wales (NSW), in conjunction with the NSW Department of Education and Training, and academics from two universities. MIC project members worked with schools and communities at two sites: a primary school in an urban community in…
Designing a Mathematics Curriculum
ERIC Educational Resources Information Center
Yee, Lee Peng
2010-01-01
A decade of PMRI saw the changes in the classroom in some of the primary schools in Indonesia. Based on observation, we can say that though the mathematics syllabus in Indonesia did not change, its curriculum has changed under the movement of PMRI. In this article, we put in writing some of the experience gained through the involvement in…
ERIC Educational Resources Information Center
Bogdany, Melvin
The curriculum guide offers a course of training in the fundamentals of mathematics as applied to baking. Problems specifically related to the baking trade are included to maintain a practical orientation. The course is designed to help the student develop proficiency in the basic computation of whole numbers, fractions, decimals, percentage,…
Measurement, Mathematics, and Music.
ERIC Educational Resources Information Center
Blackburn, Katie; White, David
The Greek mathematician, Pythagoras, was among the first to undertake a mathematical study of music. His work, resulted in a scale of notes which can produce beautiful melodies and which is easily reproduced in the elementary classroom. In an age when teachers look for an interdisciplinary connection between various aspects of the curriculum, in a…
ERIC Educational Resources Information Center
Woof, K. R.
1975-01-01
Describes an experimental type of science course which involves theoretical and practical approaches to scientific topics by using mathematics to develop and explain scientific problems and theory. Gives an example of such a course applied to the teaching of physical anthropology. (MLH)
Celebrate Mathematical Curiosity
ERIC Educational Resources Information Center
Redford, Christine
2011-01-01
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
ERIC Educational Resources Information Center
Taschow, Horst G.
Difficulties inherent in the reading of mathematics at secondary and college levels are discussed. Special emphasis is placed on the reading of arithmetic numerals, literal numbers, operational symbols, and expressions of relationships, as well as the reading of technical vocabularies and specialized meanings of general words. While each…
Correlating Mathematics and Science
ERIC Educational Resources Information Center
Mireles, Selena Vasquez
2009-01-01
The change from students learning all subjects together in a one-room schoolhouse to learning in classes separated by subject and grade resulted in distinct disciplines such as social studies, mathematics, science, and English. What was lost was the unified, holistic curriculum that a one-room setting required. Since students move from…
Mathematical Student Motivation
ERIC Educational Resources Information Center
Bacon, Alison
2012-01-01
The research project will be conducted with a target focus group of six students who have been identified as struggling students in 3rd grade mathematics. The research project will study the effect of using different teaching strategies and methods to increase motivation and focus among these students. The research project will be conducted at…
Mathematics: Montessori of Traditional?
ERIC Educational Resources Information Center
Woessner, Ruth
1995-01-01
Compares and contrasts the approaches to mathematics in Montessori schools and traditional schools. Suggests that in a traditional curriculum, math is studied as a separate subject and isolated discipline, in an abstract format, with the entire group of children moving together through the prescribed curriculum. In contrast, the Montessori school…