The neural architecture of expert calendar calculation: a matter of strategy?

PubMed

Fehr, Thorsten; Wallace, Gregory L; Erhard, Peter; Herrmann, Manfred

2011-08-01

Savants and prodigies are individuals with exceptional skills in particular mental domains. In the present study we used functional magnetic resonance imaging to examine neural correlates of calendar calculation in two individuals, a savant with Asperger's disorder and a self-taught mathematical prodigy. If there is a modular neural organization of exceptional performance in a specific mental domain, calendar calculation should be reflected in a considerable overlap in the recruitment of brain circuits across expert individuals. However, considerable individual differences in activation patterns during calendar calculation were noted. The present results indicate that activation patterns produced by complex mental processing, such as calendar calculation, seem to be influenced strongly by learning history and idiosyncratic strategy usage rather than a modular neural organization. Thus, well-known individual differences in complex cognition play a major role even in experts with exceptional abilities in a particular mental domain and should in particular be considered when examining the neural architecture of complex mental processes and skills.

A Mathematical Motivation for Complex-Valued Convolutional Networks.

PubMed

Tygert, Mark; Bruna, Joan; Chintala, Soumith; LeCun, Yann; Piantino, Serkan; Szlam, Arthur

2016-05-01

A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors, followed by (2) taking the absolute value of every entry of the resulting vectors, followed by (3) local averaging. For processing real-valued random vectors, complex-valued convnets can be viewed as data-driven multiscale windowed power spectra, data-driven multiscale windowed absolute spectra, data-driven multiwavelet absolute values, or (in their most general configuration) data-driven nonlinear multiwavelet packets. Indeed, complex-valued convnets can calculate multiscale windowed spectra when the convnet filters are windowed complex-valued exponentials. Standard real-valued convnets, using rectified linear units (ReLUs), sigmoidal (e.g., logistic or tanh) nonlinearities, or max pooling, for example, do not obviously exhibit the same exact correspondence with data-driven wavelets (whereas for complex-valued convnets, the correspondence is much more than just a vague analogy). Courtesy of the exact correspondence, the remarkably rich and rigorous body of mathematical analysis for wavelets applies directly to (complex-valued) convnets.

Numerical simulation of the structure of the high-latitude ionospheric F region during meridional HF propagation

NASA Astrophysics Data System (ADS)

Andreev, M. Yu.; Mingaleva, G. I.; Mingalev, V. S.

2007-08-01

A previously developed model of the high-latitude ionosphere is used to calculate the distribution of the ionospheric parameters in the polar region. A specific method for specifying input parameters of the mathematical model, using the experimental data obtained by the method of satellite radio tomography, is used in this case. The spatial distributions of the ionospheric parameters characterized by a complex inhomogeneous structure in the high-latitude region, calculated with the help of the mathematical model, are used to simulate the HF propagation along the meridionally oriented radio paths extending from middle to high latitudes. The method for improving the HF communication between a midlatitude transmitter and a polar-cap receiver is proposed.

Energy-technological complex with reactor for torrefaction

NASA Astrophysics Data System (ADS)

Kuzmina, J. S.; Director, L. B.; Zaichenko, V. M.

2016-11-01

To eliminate shortcomings of raw plant materials pelletizing process with thermal treatment (low-temperature pyrolysis or torrefaction) can be applied. This paper presents a mathematical model of energy-technological complex (ETC) for combined production of heat, electricity and solid biofuels torrefied pellets. According to the structure the mathematical model consists of mathematical models of main units of ETC and the relationships between them and equations of energy and material balances. The equations describe exhaust gas straining action through a porous medium formed by pellets. Decomposition rate of biomass was calculated by using the gross-reaction diagram, which is responsible for the disintegration of raw material. A mathematical model has been tested according to bench experiments on one reactor module. From nomographs, designed for a particular configuration of ETC it is possible to determine the basic characteristics of torrefied pellets (rate of weight loss, heating value and heat content) specifying only two parameters (temperature and torrefaction time). It is shown that the addition of reactor for torrefaction to gas piston engine can improve the energy efficiency of power plant.

Does Your Graphing Software Real-ly Work?

ERIC Educational Resources Information Center

Marchand, R. J.; McDevitt, T. J.; Bosse, Michael J.; Nandakumar, N. R.

2007-01-01

Many popular mathematical software products including Maple, Mathematica, Derive, Mathcad, Matlab, and some of the TI calculators produce incorrect graphs because they use complex arithmetic instead of "real" arithmetic. This article expounds on this issue, provides possible remedies for instructors to share with their students, and demonstrates…

Complex Refractive Index of Ammonium Nitrate in the 2-20 micron Spectral Range

NASA Technical Reports Server (NTRS)

Jarzembski, Maurice A.; Norman, Mark L.; Fuller, Kirk A.; Srivastava, Vandana; Cutten, Dean R.

2002-01-01

Using high resolution Fourier Transform Infrared Spectroscopy (FTIR) absorbance/transmittance spectral data for ammonium sulfate (AMS), calcium carbonate (CAC) and ammonium nitrate (AMN), comparisons were made with previously published complex refractive indices data for AMS and CAC to infer experimental parameters to determine the imaginary refractive index for AMN in the infrared wavelength range from 2 to 20 microns. Kramers-Kronig mathematical relations were applied to calculate the real refractive index for the three compositions. Excellent agreement for AMS and CAC with the published values was found, validating the complex refractive indices obtained for AMN. Backscatter calculations using a lognormal size distribution for AMS, AMN, and CAC aerosols were performed to show differences in their backscattered spectra.

Application Of Three-Dimensional Videography To Human Motion Studies: Constraints, Assumptions, And Mathematics

NASA Astrophysics Data System (ADS)

Rab, George T.

1988-02-01

Three-dimensional human motion analysis has been used for complex kinematic description of abnormal gait in children with neuromuscular disease. Multiple skin markers estimate skeletal segment position, and a sorting and smoothing routine provides marker trajectories. The position and orientation of the moving skeleton in space are derived mathematically from the marker positions, and joint motions are calculated from the Eulerian transformation matrix between linked proximal and distal skeletal segments. Reproduceability has been excellent, and the technique has proven to be a useful adjunct to surgical planning.

Workbook, Basic Mathematics and Wastewater Processing Calculations.

ERIC Educational Resources Information Center

New York State Dept. of Environmental Conservation, Albany.

This workbook serves as a self-learning guide to basic mathematics and treatment plant calculations and also as a reference and source book for the mathematics of sewage treatment and processing. In addition to basic mathematics, the workbook discusses processing and process control, laboratory calculations and efficiency calculations necessary in…

On the mathematical modeling of the Reynolds stress's equations

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

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

Bayesian linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

What Einstein Can Teach Us about Education

ERIC Educational Resources Information Center

Hayes, Denis

2007-01-01

People are more likely to associate Einstein with complex scientific theories and mathematical calculations than with education theory. In fact, Einstein's own experiences of schooling and his reflections on the meaning of life and the significance of education are profound and oddly relevant to the situation that pertains in England today. It is…

An Alternative Version of Conditional Probabilities and Bayes' Rule: An Application of Probability Logic

ERIC Educational Resources Information Center

Satake, Eiki; Amato, Philip P.

2008-01-01

This paper presents an alternative version of formulas of conditional probabilities and Bayes' rule that demonstrate how the truth table of elementary mathematical logic applies to the derivations of the conditional probabilities of various complex, compound statements. This new approach is used to calculate the prior and posterior probabilities…

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

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

Plechac, Petr; Vlachos, Dionisios; Katsoulakis, Markos

2013-09-05

The overall objective of this project is to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals. Specific goals include: (i) Development of rigorous spatio-temporal coarse-grained kinetic Monte Carlo (KMC) mathematics and simulation for microscopic processes encountered in biomassmore » transformation. (ii) Development of hybrid multiscale simulation that links stochastic simulation to a deterministic partial differential equation (PDE) model for an entire reactor. (iii) Development of hybrid multiscale simulation that links KMC simulation with quantum density functional theory (DFT) calculations. (iv) Development of parallelization of models of (i)-(iii) to take advantage of Petaflop computing and enable real world applications of complex, multiscale models. In this NCE period, we continued addressing these objectives and completed the proposed work. Main initiatives, key results, and activities are outlined.« less

Symbolic-Graphical Calculators: Teaching Tools for Mathematics.

ERIC Educational Resources Information Center

Dick, Thomas P.

1992-01-01

Explores the role that symbolic-graphical calculators can play in the current calls for reform in the mathematics curriculum. Discusses symbolic calculators and graphing calculators in relation to problem solving, computational skills, and mathematics instruction. (MDH)

Simulation of a manual electric-arc welding in a working gas pipeline. 1. Formulation of the problem

NASA Astrophysics Data System (ADS)

Baikov, V. I.; Gishkelyuk, I. A.; Rus', A. M.; Sidorovich, T. V.; Tonkonogov, B. A.

2010-11-01

Problems of mathematical simulation of the temperature stresses arising in the wall of a pipe of a cross-country gas pipeline in the process of electric-arc welding of defects in it have been considered. Mathematical models of formation of temperatures, deformations, and stresses in a gas pipe subjected to phase transformations have been developed. These models were numerically realized in the form of algorithms representing a part of an application-program package. Results of verification of the computational complex and calculation results obtained with it are presented.

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

Lopez-Ruiz, R.; Nagy, A.; Romera, E.

A two-parameter family of complexity measures C-tilde{sup ({alpha},{beta})} based on the Renyi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the Lopez-Ruiz-Mancini-Calbet complexity, which is recovered for {alpha}=1 and {beta}=2. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, {alpha} or {beta}, goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator, andmore » square well.« less

The Ability of Conceptual Monitoring and the Quality of Working Memory at Children With Calculation Difficulties

ERIC Educational Resources Information Center

Arsic, Sladjana; Eminovic, Fadilj; Stankovic, Ivona

2011-01-01

Calculia is considered to be the ability of performing arithmetic operations, the preconditions for the development of mathematical skills in the complex functioning of psychological functions represented in neuro-anatomical systems, as well in the interaction with the environment. Problems in acquiring arithmetic skills can be described as…

Calculations of resonances parameters for the ((2s2) 1Se, (2s2p) 1,3P0) and ((3s2) 1Se, (3s3p) 1,3P0) doubly excited states of helium-like ions with Z≤10 using a complex rotation method implemented in Scilab

NASA Astrophysics Data System (ADS)

Gning, Youssou; Sow, Malick; Traoré, Alassane; Dieng, Matabara; Diakhate, Babacar; Biaye, Mamadi; Wagué, Ahmadou

2015-01-01

In the present work a special computational program Scilab (Scientific Laboratory) in the complex rotation method has been used to calculate resonance parameters of ((2s2) 1Se, (2s2p) 1,3P0) and ((3s2) 1Se, (3s3p) 1,3P0) states of helium-like ions with Z≤10. The purpose of this study required a mathematical development of the Hamiltonian applied to Hylleraas wave function for intrashell states, leading to analytical expressions which are carried out under Scilab computational program. Results are in compliance with recent theoretical calculations.

An image overall complexity evaluation method based on LSD line detection

NASA Astrophysics Data System (ADS)

Li, Jianan; Duan, Jin; Yang, Xu; Xiao, Bo

2017-04-01

In the artificial world, whether it is the city's traffic roads or engineering buildings contain a lot of linear features. Therefore, the research on the image complexity of linear information has become an important research direction in digital image processing field. This paper, by detecting the straight line information in the image and using the straight line as the parameter index, establishing the quantitative and accurate mathematics relationship. In this paper, we use LSD line detection algorithm which has good straight-line detection effect to detect the straight line, and divide the detected line by the expert consultation strategy. Then we use the neural network to carry on the weight training and get the weight coefficient of the index. The image complexity is calculated by the complexity calculation model. The experimental results show that the proposed method is effective. The number of straight lines in the image, the degree of dispersion, uniformity and so on will affect the complexity of the image.

Optimization of Cooling Water Flow Rate in Nuclear and Thermal Power Plants Based on a Mathematical Model of Cooling Systems{sup 1}

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

Murav’ev, V. P., E-mail: murval1@mail.ru; Kochetkov, A. V.; Glazova, E. G.

A mathematical model and algorithms are proposed for automatic calculation of the optimum flow rate of cooling water in nuclear and thermal power plants with cooling systems of arbitrary complexity. An unlimited number of configuration and design variants are assumed with the possibility of obtaining a result for any computational time interval, from monthly to hourly. The structural solutions corresponding to an optimum cooling water flow rate can be used for subsequent engineering-economic evaluation of the best cooling system variant. The computerized mathematical model and algorithms make it possible to determine the availability and degree of structural changes for themore » cooling system in all stages of the life cycle of a plant.« less

Computer-aided molecular modeling techniques for predicting the stability of drug cyclodextrin inclusion complexes in aqueous solutions

NASA Astrophysics Data System (ADS)

Faucci, Maria Teresa; Melani, Fabrizio; Mura, Paola

2002-06-01

Molecular modeling was used to investigate factors influencing complex formation between cyclodextrins and guest molecules and predict their stability through a theoretical model based on the search for a correlation between experimental stability constants ( Ks) and some theoretical parameters describing complexation (docking energy, host-guest contact surfaces, intermolecular interaction fields) calculated from complex structures at a minimum conformational energy, obtained through stochastic methods based on molecular dynamic simulations. Naproxen, ibuprofen, ketoprofen and ibuproxam were used as model drug molecules. Multiple Regression Analysis allowed identification of the significant factors for the complex stability. A mathematical model ( r=0.897) related log Ks with complex docking energy and lipophilic molecular fields of cyclodextrin and drug.

The Role of Graphing Calculators in Mathematics Reform.

ERIC Educational Resources Information Center

Waits, Bert K.; Demana, Franklin

This essay describes the role of graphing calculators in mathematics reform. Among the topics discussed are the history of graphing calculators in mathematics education, recent technological innovations, and professional development opportunities. The case is made for a balanced approach between calculator use and paper-and-pencil techniques.…

Mathematical Creative Activity and the Graphic Calculator

ERIC Educational Resources Information Center

Duda, Janina

2011-01-01

Teaching mathematics using graphic calculators has been an issue of didactic discussions for years. Finding ways in which graphic calculators can enrich the development process of creative activity in mathematically gifted students between the ages of 16-17 is the focus of this article. Research was conducted using graphic calculators with…

Soils as relative-age dating tools

USGS Publications Warehouse

Markewich, Helaine Walsh; Pavich, Milan J.; Wysocki, Douglas A.

2017-01-01

Soils develop at the earth's surface via multiple processes that act through time. Precluding burial or disturbance, soil genetic horizons form progressively and reflect the balance among formation processes, surface age, and original substrate composition. Soil morphology provides a key link between process and time (soil age), enabling soils to serve as both relative and numerical dating tools for geomorphic studies and landscape evolution. Five major factors define the contemporary state of all soils: climate, organisms, topography, parent material, and time. Soils developed on similar landforms and parent materials within a given landscape comprise what we term a soil/landform/substrate complex. Soils on such complexes that differ in development as a function of time represent a soil chronosequence. In a soil chronosequence, time constitutes the only independent formation factor; the other factors act through time. Time dictates the variations in soil development or properties (field or laboratory measured) on a soil/landform/substrate complex. Using a dataset within the chronosequence model, we can also formulate various soil development indices based upon one or a combination of soil properties, either for individual soil horizons or for an entire profile. When we evaluate soil data or soil indices mathematically, the resulting equation creates a chronofunction. Chronofunctions help quantify processes and mechanisms involved in soil development, and relate them mathematically to time. These rigorous kinds of comparisons among and within soil/landform complexes constitute an important tool for relative-age dating. After determining one or more absolute ages for a soil/landform complex, we can calculate quantitative soil formation, and or landform-development rates. Multiple dates for several complexes allow rate calculations for soil/landform-chronosequence development and soil-chronofunction calibration.

Calculator Use on NAEP: A Look at Fourth- and Eighth-Grade Mathematics Achievement

ERIC Educational Resources Information Center

Walcott, Crystal; Stickles, Paula R.

2012-01-01

This article summarizes research conducted on calculator block items from the 2007 fourth- and eighth-grade National Assessment of Educational Progress Main Mathematics. Calculator items from the assessment were categorized into two categories: problem-solving items and noncomputational mathematics concept items. A calculator has the potential to…

Child-Level Predictors of Responsiveness to Evidence-Based Mathematics Intervention.

PubMed

Powell, Sarah R; Cirino, Paul T; Malone, Amelia S

2017-07-01

We identified child-level predictors of responsiveness to 2 types of mathematics (calculation and word-problem) intervention among 2nd-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We assigned classrooms randomly assigned to calculation intervention, word-problem intervention, or business-as-usual control. Intervention lasted 17 weeks. Path analyses indicated that scores on working memory and language comprehension assessments moderated responsiveness to calculation intervention. No moderators were identified for responsiveness to word-problem intervention. Across both intervention groups and the control group, attentive behavior predicted both outcomes. Initial calculation skill predicted the calculation outcome, and initial language comprehension predicted word-problem outcomes. These results indicate that screening for calculation intervention should include a focus on working memory, language comprehension, attentive behavior, and calculations. Screening for word-problem intervention should focus on attentive behavior and word problems.

Computation of the Genetic Code

NASA Astrophysics Data System (ADS)

Kozlov, Nicolay N.; Kozlova, Olga N.

2018-03-01

One of the problems in the development of mathematical theory of the genetic code (summary is presented in [1], the detailed -to [2]) is the problem of the calculation of the genetic code. Similar problems in the world is unknown and could be delivered only in the 21st century. One approach to solving this problem is devoted to this work. For the first time provides a detailed description of the method of calculation of the genetic code, the idea of which was first published earlier [3]), and the choice of one of the most important sets for the calculation was based on an article [4]. Such a set of amino acid corresponds to a complete set of representations of the plurality of overlapping triple gene belonging to the same DNA strand. A separate issue was the initial point, triggering an iterative search process all codes submitted by the initial data. Mathematical analysis has shown that the said set contains some ambiguities, which have been founded because of our proposed compressed representation of the set. As a result, the developed method of calculation was limited to the two main stages of research, where the first stage only the of the area were used in the calculations. The proposed approach will significantly reduce the amount of computations at each step in this complex discrete structure.

Symbolic-numeric interface: A review

NASA Technical Reports Server (NTRS)

Ng, E. W.

1980-01-01

A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach.

Computing Mass Properties From AutoCAD

NASA Technical Reports Server (NTRS)

Jones, A.

1990-01-01

Mass properties of structures computed from data in drawings. AutoCAD to Mass Properties (ACTOMP) computer program developed to facilitate quick calculations of mass properties of structures containing many simple elements in such complex configurations as trusses or sheet-metal containers. Mathematically modeled in AutoCAD or compatible computer-aided design (CAD) system in minutes by use of three-dimensional elements. Written in Microsoft Quick-Basic (Version 2.0).

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

The relationship between nursing students' mathematics ability and their performance in a drug calculation test.

PubMed

Røykenes, Kari; Larsen, Torill

2010-10-01

Nurses and nursing students need good mathematics skills to do drug calculations correctly. As part of their undergraduate education, Norwegian nursing students must take a drug calculation test, obtaining no errors in the results. In spite of drug calculation tests, many adverse events occur, leading to a focus on drug administration skills both during students' courses and afterwards. Adverse events in drug administration can be related to poor mathematics skills education. The purpose of this study was to investigate the relationship between students' mathematics experiences in school (primary, secondary and high school) and their beliefs about being able to master the drug calculation test. A questionnaire was given to 116 first-year Bachelor of Nursing students. Those students who assessed their mathematics knowledge as poor found the requirement to obtain no errors in the drug calculation test more stressful than students who judged their mathematics knowledge as good. The youngest students were most likely to find the test requirement stressful. Teachers in high school had the most positive influence on mathematics interest, followed by teachers in secondary and primary school. Copyright © 2010 Elsevier Ltd. All rights reserved.

Combinatorics of aliphatic amino acids

NASA Astrophysics Data System (ADS)

Grützmann, Konrad; Böcker, Sebastian; Schuster, Stefan

2011-01-01

This study combines biology and mathematics, showing that a relatively simple question from molecular biology can lead to complicated mathematics. The question is how to calculate the number of theoretically possible aliphatic amino acids as a function of the number of carbon atoms in the side chain. The presented calculation is based on earlier results from theoretical chemistry concerning alkyl compounds. Mathematical properties of this number series are highlighted. We discuss which of the theoretically possible structures really occur in living organisms, such as leucine and isoleucine with a chain length of four. This is done both for a strict definition of aliphatic amino acids only involving carbon and hydrogen atoms in their side chain and for a less strict definition allowing sulphur, nitrogen and oxygen atoms. While the main focus is on proteinogenic amino acids, we also give several examples of non-proteinogenic aliphatic amino acids, playing a role, for instance, in signalling. The results are in agreement with a general phenomenon found in biology: Usually, only a small number of molecules are chosen as building blocks to assemble an inconceivable number of different macromolecules as proteins. Thus, natural biological complexity arises from the multifarious combination of building blocks.

Programmable Calculators: Implications for the Mathematics Curriculum.

ERIC Educational Resources Information Center

Spikell, Mark A., Ed.

This document is a collection of reports presented at a programable calculator symposium held in Seattle, Washington, in April, 1980, as part of the annual meeting of the National Council of Teachers of Mathematics (NCTM). The session was designed to review whether the programable calculator has a place in the school mathematics program, in light…

Medication calculation skills of graduating nursing students in Finland.

PubMed

Grandell-Niemi, H; Hupli, M; Leino-Kilpi, H

2001-01-01

The aim of this study was to describe the basic mathematical proficiency and the medication calculation skills of graduating nursing students in Finland. A further concern was with how students experienced the teaching of medication calculation. We wanted to find out whether these experiences were associated with various background factors and the students' medication calculation skills. In spring 1997 the population of graduating nursing students in Finland numbered around 1280; the figure for the whole year was 2640. A convenience sample of 204 students completed a questionnaire specially developed for this study. The instrument included structured questions, statements and a medication calculation test. The response rate was 88%. Data analysis was based on descriptive statistics. The students found it hard to learn mathematics and medication calculation skills. Those who evaluated their mathematical and medication calculation skills as sufficient successfully solved the problems included in the questionnaire. It was felt that the introductory course on medication calculation was uninteresting and poorly organised. Overall the students' mathematical skills were inadequate. One-fifth of the students failed to pass the medication calculation test. A positive correlation was shown between the student's grade in mathematics (Sixth Form College) and her skills in medication calculation.

Information modeling system for blast furnace control

NASA Astrophysics Data System (ADS)

Spirin, N. A.; Gileva, L. Y.; Lavrov, V. V.

2016-09-01

Modern Iron & Steel Works as a rule are equipped with powerful distributed control systems (DCS) and databases. Implementation of DSC system solves the problem of storage, control, protection, entry, editing and retrieving of information as well as generation of required reporting data. The most advanced and promising approach is to use decision support information technologies based on a complex of mathematical models. The model decision support system for control of blast furnace smelting is designed and operated. The basis of the model system is a complex of mathematical models created using the principle of natural mathematical modeling. This principle provides for construction of mathematical models of two levels. The first level model is a basic state model which makes it possible to assess the vector of system parameters using field data and blast furnace operation results. It is also used to calculate the adjustment (adaptation) coefficients of the predictive block of the system. The second-level model is a predictive model designed to assess the design parameters of the blast furnace process when there are changes in melting conditions relative to its current state. Tasks for which software is developed are described. Characteristics of the main subsystems of the blast furnace process as an object of modeling and control - thermal state of the furnace, blast, gas dynamic and slag conditions of blast furnace smelting - are presented.

Designing Cognitive Complexity in Mathematical Problem-Solving Items

ERIC Educational Resources Information Center

Daniel, Robert C.; Embretson, Susan E.

2010-01-01

Cognitive complexity level is important for measuring both aptitude and achievement in large-scale testing. Tests for standards-based assessment of mathematics, for example, often include cognitive complexity level in the test blueprint. However, little research exists on how mathematics items can be designed to vary in cognitive complexity level.…

A Persistent Feature of Multiple Scattering of Waves in the Time-Domain: A Tutorial

NASA Technical Reports Server (NTRS)

Lock, James A.; Mishchenko, Michael I.

2015-01-01

The equations for frequency-domain multiple scattering are derived for a scalar or electromagnetic plane wave incident on a collection of particles at known positions, and in the time-domain for a plane wave pulse incident on the same collection of particles. The calculation is carried out for five different combinations of wave types and particle types of increasing geometrical complexity. The results are used to illustrate and discuss a number of physical and mathematical characteristics of multiple scattering in the frequency- and time-domains. We argue that frequency-domain multiple scattering is a purely mathematical construct since there is no temporal sequencing information in the frequency-domain equations and since the multi-particle path information can be dispelled by writing the equations in another mathematical form. However, multiple scattering becomes a definite physical phenomenon in the time-domain when the collection of particles is illuminated by an appropriately short localized pulse.

A Multifaceted Mathematical Approach for Complex Systems

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

Alexander, F.; Anitescu, M.; Bell, J.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significantmore » impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.« less

Modelling of the tunnelling effect in granulated metallic nanostructures

NASA Astrophysics Data System (ADS)

Istratov, A. V.; Kucherik, A. O.

2018-01-01

Obtaining thin films of today is unthinkable without use of mathematical modeling, numerical methods and complex programs. In this regard, the practical importance of this calculations is that it can be used to investigate the conductivity of nano-sized granular structures that expands the diagnostic capabilities of thin films, opens up new perspectives in the creation of new devices based on thin-film technology, allow to predict their properties.

How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

ERIC Educational Resources Information Center

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-01-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Design of robotic cells based on relative handling modules with use of SolidWorks system

NASA Astrophysics Data System (ADS)

Gaponenko, E. V.; Anciferov, S. I.

2018-05-01

The article presents a diagramed engineering solution for a robotic cell with six degrees of freedom for machining of complex details, consisting of the base with a tool installation module and a detail machining module made as parallel structure mechanisms. The output links of the detail machining module and the tool installation module can move along X-Y-Z coordinate axes each. A 3D-model of the complex is designed in the SolidWorks system. It will be used further for carrying out engineering calculations and mathematical analysis and obtaining all required documentation.

Developing Teaching Material Software Assisted for Numerical Methods

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

Six to Ten Digits Multiplication Fun Learning Using Puppet Prototype

NASA Astrophysics Data System (ADS)

Islamiah Rosli, D.'oria; Ali, Azita; Peng, Lim Soo; Sujardi, Imam; Usodo, Budi; Adie Perdana, Fengky

2017-01-01

Logic and technical subjects require students to understand basic knowledge in mathematic. For instance, addition, minus, division and multiplication operations need to be mastered by students due to mathematic complexity as the learning mathematic grows higher. Weak foundation in mathematic also contribute to high failure rate in mathematic subjects in schools. In fact, students in primary schools are struggling to learn mathematic because they need to memorize formulas, multiplication or division operations. To date, this study will develop a puppet prototyping for learning mathematic for six to ten digits multiplication. Ten participants involved in the process of developing the prototype in this study. Students involved in the study were those from the intermediate class students whilst teachers were selected based on their vast knowledge and experiences and have more than five years of experience in teaching mathematic. Close participatory analysis will be used in the prototyping process as to fulfil the requirements of the students and teachers whom will use the puppet in learning six to ten digit multiplication in mathematic. Findings showed that, the students had a great time and fun learning experience in learning multiplication and they able to understand the concept of multiplication using puppet. Colour and materials of the puppet also help to attract student attention during learning. Additionally, students able to visualized and able to calculate accurate multiplication value and the puppet help them to recall in multiplying and adding the digits accordingly.

Teachers' Beliefs and Technology: Calculator Use in Mathematics Instruction in Junior Secondary Schools in Botswana

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…

Calculators in the Mathematics Curriculum: Effects and Changes.

ERIC Educational Resources Information Center

Rabe, Rebecca Moore

The purpose of this paper was to determine the effects of calculators in mathematics classes and to assess proposed curriculum revisions related to calculators. Twenty-six calculator studies and other selected sources were reviewed and annotated. Major conclusions of the study include: (1) calculator use has produced significant gains in…

Using Financial Calculators in a Business Mathematics Course.

ERIC Educational Resources Information Center

Heller, William H.; Taylor, Monty B.

2000-01-01

Discusses the authors' experiences with integrating financial calculators into a business mathematics course. Presents a brief overview of the operation of financial calculators, reviews some of the more common models, discusses how to use the equation solver utility on other calculators to emulate a financial calculator, and explores the…

Primordial Particles; Collisions of Inelastic Particles

NASA Astrophysics Data System (ADS)

Sagi, George

2011-03-01

Three-dimensional matter is not defined by Euclidian or Cartesian geometries. Newton's and Einstein's laws are related to the motions of elastic masses. The study of collisions of inelastic particles opens up new vistas in physics. The present article reveals how such particles create clusters composed of various numbers of particles. The Probability of each formation, duplets, triplets, etc. can be calculated. The particles are held together by a binding force, and depending upon the angles of collisions they may also rotate around their center of geometry. Because of these unique properties such inelastic particles are referred to as primordial particles, Pp. When a given density of Pp per cubic space is given, then random collisions create a field. The calculation of the properties of such primordial field is very complex and beyond the present study. However, the angles of collisions are infinite in principle, but the probabilities of various cluster sizes are quantum dependent. Consequently, field calculations will require new complex mathematical methods to be discovered yet.

Mathematics and complex systems.

PubMed

Foote, Richard

2007-10-19

Contemporary researchers strive to understand complex physical phenomena that involve many constituents, may be influenced by numerous forces, and may exhibit unexpected or emergent behavior. Often such "complex systems" are macroscopic manifestations of other systems that exhibit their own complex behavior and obey more elemental laws. This article proposes that areas of mathematics, even ones based on simple axiomatic foundations, have discernible layers, entirely unexpected "macroscopic" outcomes, and both mathematical and physical ramifications profoundly beyond their historical beginnings. In a larger sense, the study of mathematics itself, which is increasingly surpassing the capacity of researchers to verify "by hand," may be the ultimate complex system.

[Three dimensional mathematical model of tooth for finite element analysis].

PubMed

Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka

2010-01-01

The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Measuring modules for the research of compensators of reactive power with voltage stabilization in MATLAB

NASA Astrophysics Data System (ADS)

Vlasayevsky, Stanislav; Klimash, Stepan; Klimash, Vladimir

2017-10-01

A set of mathematical modules was developed for evaluation the energy performance in the research of electrical systems and complexes in the MatLab. In the electrotechnical library SimPowerSystems of the MatLab software, there are no measuring modules of energy coefficients characterizing the quality of electricity and the energy efficiency of electrical apparatus. Modules are designed to calculate energy coefficients characterizing the quality of electricity (current distortion and voltage distortion) and energy efficiency indicators (power factor and efficiency) are presented. There are described the methods and principles of building the modules. The detailed schemes of modules built on the elements of the Simulink Library are presented, in this connection, these modules are compatible with mathematical models of electrical systems and complexes in the MatLab. Also there are presented the results of the testing of the developed modules and the results of their verification on the schemes that have analytical expressions of energy indicators.

Mathematics Anxiety and Mathematics Self-Efficacy in Relation to Medication Calculation Performance in Nurses

ERIC Educational Resources Information Center

Melius, Joyce

2012-01-01

The purpose of this study is to identify and analyze the relationships that exist between mathematics anxiety and nurse self-efficacy for mathematics, and the medication calculation performance of acute care nurses. This research used a quantitative correlational research design and involved a sample of 84 acute care nurses, LVNs and RNs, from a…

Matched field localization based on CS-MUSIC algorithm

NASA Astrophysics Data System (ADS)

Guo, Shuangle; Tang, Ruichun; Peng, Linhui; Ji, Xiaopeng

2016-04-01

The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered. A matched field localization algorithm based on CS-MUSIC (Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning. The signal matrix is calculated through the SVD (Singular Value Decomposition) of the observation matrix. The observation matrix in the sparse mathematical model is replaced by the signal matrix, and a new concise sparse mathematical model is obtained, which means not only the scale of the localization problem but also the noise level is reduced; then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS (Compressive Sensing) method and MUSIC (Multiple Signal Classification) method. The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots, and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large, which will be proved in this paper.

Frequency-dependent FDTD methods using Z transforms

NASA Technical Reports Server (NTRS)

Sullivan, Dennis M.

1992-01-01

While the frequency-dependent finite-difference time-domain, or (FD)2TD, method can correctly calculate EM propagation through media whose dielectric properties are frequency-dependent, more elaborate applications lead to greater (FD)2TD complexity. Z-transform theory is presently used to develop the mathematical bases of the (FD)2TD method, simultaneously obtaining a clearer formulation and allowing researchers to draw on the existing literature of systems analysis and signal-processing.

The presence of mathematics and computer anxiety in nursing students and their effects on medication dosage calculations.

PubMed

Glaister, Karen

2007-05-01

To determine if the presence of mathematical and computer anxiety in nursing students affects learning of dosage calculations. The quasi-experimental study compared learning outcomes at differing levels of mathematical and computer anxiety when integrative and computer based learning approaches were used. Participants involved a cohort of second year nursing students (n=97). Mathematical anxiety exists in 20% (n=19) of the student nurse population, and 14% (n=13) experienced mathematical testing anxiety. Those students more anxious about mathematics and the testing of mathematics benefited from integrative learning to develop conditional knowledge (F(4,66)=2.52 at p<.05). Computer anxiety was present in 12% (n=11) of participants, with those reporting medium and high levels of computer anxiety performing less well than those with low levels (F(1,81)=3.98 at p<.05). Instructional strategies need to account for the presence of mathematical and computer anxiety when planning an educational program to develop competency in dosage calculations.

Mathematical ability of first year undergraduate paramedic students-A before and after study.

PubMed

Eastwood, Kathryn; Boyle, Malcolm; Kim, Visal; Stam, Nathan; Williams, Brett

2015-11-01

An ability to accurately perform drug calculations unassisted is an essential skill for all health professionals, with various occupational-specific stressors exacerbating mathematical deficiencies. The objective of this study was to determine the unaided mathematic ability of first year undergraduate paramedic students before and after mathematical and drug calculation tutorials. Students were administered a questionnaire containing demographic, drug calculation and arithmetic questions during week one of the semester before the tutorials. During the semester students participated in three 2-hour tutorials which included both mathematical and drug calculation questions without assistance of computational devices. At the end of semester was a summative drug calculation examination of which five key questions were compared to similar questions from the first questionnaire. Descriptive statistics describe the demographic data with a paired t-test comparing the questionnaire and exam results. Drug calculation and mathematical ability was markedly improved following the tutorials, mean score of correct answers before 1.74 (SD 1.4) and after 4.14 (SD 0.93), p<0001. When comparing the correct results for the same question type, there were statistically significant differences in four of five different drug calculations: volume of drug drawn up 10 v 57 p<0.0001, infusion rate 29 v 31 p=0.717, drip rate 16 v 54 p<0.0001, volume from a syringe 30 v 59 p<0.0001, and drug dose 42 v 62 p<0.0001. Total errors reduced from 188 to 45. First year undergraduate paramedic students initially demonstrated a poor ability to complete mathematical and drug calculations without the assistance of computational devices. This improved significantly following appropriate education and practice. Further research is required to determine the retention of this ability over time. Copyright © 2015 Elsevier Ltd. All rights reserved.

A decimal carry-free adder

NASA Astrophysics Data System (ADS)

Nikmehr, Hooman; Phillips, Braden; Lim, Cheng-Chew

2005-02-01

Recently, decimal arithmetic has become attractive in the financial and commercial world including banking, tax calculation, currency conversion, insurance and accounting. Although computers are still carrying out decimal calculation using software libraries and binary floating-point numbers, it is likely that in the near future, all processors will be equipped with units performing decimal operations directly on decimal operands. One critical building block for some complex decimal operations is the decimal carry-free adder. This paper discusses the mathematical framework of the addition, introduces a new signed-digit format for representing decimal numbers and presents an efficient architectural implementation. Delay estimation analysis shows that the adder offers improved performance over earlier designs.

Relationship between High School Mathematics Grade and Number of Attempts Required to Pass the Medication Calculation Test in Nurse Education: An Explorative Study

PubMed Central

Alteren, Johanne; Nerdal, Lisbeth

2015-01-01

In Norwegian nurse education, students are required to achieve a perfect score in a medication calculation test before undertaking their first practice period during the second semester. Passing the test is a challenge, and students often require several attempts. Adverse events in medication administration can be related to poor mathematical skills. The purpose of this study was to explore the relationship between high school mathematics grade and the number of attempts required to pass the medication calculation test in nurse education. The study used an exploratory design. The participants were 90 students enrolled in a bachelor’s nursing program. They completed a self-report questionnaire, and statistical analysis was performed. The results provided no basis for the conclusion that a statistical relationship existed between high school mathematics grade and number of attempts required to pass the medication calculation test. Regardless of their grades in mathematics, 43% of the students passed the medication calculation test on the first attempt. All of the students who had achieved grade 5 had passed by the third attempt. High grades in mathematics were not crucial to passing the medication calculation test. Nonetheless, the grade may be important in ensuring a pass within fewer attempts. PMID:27417767

Pre-Service Teachers' Free and Structured Mathematical Problem Posing

ERIC Educational Resources Information Center

Silber, Steven; Cai, Jinfa

2017-01-01

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

Students' and Teachers' Conceptual Metaphors for Mathematical Problem Solving

ERIC Educational Resources Information Center

Yee, Sean P.

2017-01-01

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

Decimals, Denominators, Demons, Calculators, and Connections

ERIC Educational Resources Information Center

Sparrow, Len; Swan, Paul

2005-01-01

The authors provide activities for overcoming some fraction misconceptions using calculators specially designed for learners in primary years. The writers advocate use of the calculator as a way to engage children in thinking about mathematics. By engaging with a calculator as part of mathematics learning, children are learning about and using the…

Does Type Matter: Evaluating the Effectiveness of Four-Function and Graphing Calculators

ERIC Educational Resources Information Center

Bouck, Emily

2010-01-01

Calculators are a controversial, yet widely used tool in mathematics education for all students and especially for students with disabilities. However, little research has explored calculators and students with disabilities. This paper explored the influence of calculator type (four-function and graphing) on the mathematical performance of…

Mathematical modeling for resource and energy saving control of extruders in multi-assortment productions of polymeric films

NASA Astrophysics Data System (ADS)

Polosin, A. N.; Chistyakova, T. B.

2018-05-01

In this article, the authors describe mathematical modeling of polymer processing in extruders of various types used in extrusion and calender productions of film materials. The method consists of the synthesis of a static model for calculating throughput, energy consumption of the extruder, extrudate quality indices, as well as a dynamic model for evaluating polymer residence time in the extruder, on which the quality indices depend. Models are adjusted according to the extruder type (single-screw, reciprocating, twin-screw), its screw and head configuration, extruder’s work temperature conditions, and the processed polymer type. Models enable creating extruder screw configurations and determining extruder controlling action values that provide the extrudate of required quality while satisfying extruder throughput and energy consumption requirements. Model adequacy has been verified using polyolefins’ and polyvinylchloride processing data in different extruders. The program complex, based on mathematical models, has been developed in order to control extruders of various types in order to ensure resource and energy saving in multi-assortment productions of polymeric films. Using the program complex in the control system for the extrusion stage of the polymeric film productions enables improving film quality, reducing spoilage, lessening the time required for production line change-over to other throughput and film type assignment.

Graphing Calculator Mini Course

NASA Technical Reports Server (NTRS)

Karnawat, Sunil R.

1996-01-01

The "Graphing Calculator Mini Course" project provided a mathematically-intensive technologically-based summer enrichment workshop for teachers of American Indian students on the Turtle Mountain Indian Reservation. Eleven such teachers participated in the six-day workshop in summer of 1996 and three Sunday workshops in the academic year. The project aimed to improve science and mathematics education on the reservation by showing teachers effective ways to use high-end graphing calculators as teaching and learning tools in science and mathematics courses at all levels. In particular, the workshop concentrated on applying TI-82's user-friendly features to understand the various mathematical and scientific concepts.

Profiling Student Use of Calculators in the Learning of High School Mathematics

ERIC Educational Resources Information Center

Crowe, Cheryll E.; Ma, Xin

2010-01-01

Using data from the 2005 National Assessment of Educational Progress, students' use of calculators in the learning of high school mathematics was profiled based on their family background, curriculum background, and advanced mathematics coursework. A statistical method new to educational research--classification and regression trees--was applied…

Secondary School Teachers' Conceptions and Their Teaching Practices Using Graphing Calculators

ERIC Educational Resources Information Center

Lee, Jane A.; McDougall, Douglas E.

2010-01-01

This article investigates secondary school teachers' conceptions of mathematics and their teaching practices in the use of graphing calculators in their mathematics classrooms. Case studies on three teacher participants were developed using quantitative and qualitative data that consisted of self-assessments on beliefs in mathematics,…

A computer model for one-dimensional mass and energy transport in and around chemically reacting particles, including complex gas-phase chemistry, multicomponent molecular diffusion, surface evaporation, and heterogeneous reaction

NASA Technical Reports Server (NTRS)

Cho, S. Y.; Yetter, R. A.; Dryer, F. L.

1992-01-01

Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.

Modeling the complex activity of sickle cell and thalassemia specialist nurses in England.

PubMed

Leary, Alison; Anionwu, Elizabeth N

2014-01-01

Specialist advanced practice nursing in hemoglobinopathies has a rich historical and descriptive literature. Subsequent work has shown that the role is valued by patients and families and also by other professionals. However, there is little empirical research on the complexity of activity of these services in terms of interventions offered. In addition, the work of clinical nurse specialists in England has been devalued through a perception of oversimplification. The purpose of this study was to understand the complexity of expert nursing practice in sickle cell and thalassemia. The approach taken to modeling complexity was used from common methods in mathematical modeling and computational mathematics. Knowledge discovery through data was the underpinning framework used in this study using a priori mined data. This allowed categorization of activity and articulation of complexity. In total, 8966 nursing events were captured over 1639 hours from a total of 22.8 whole time equivalents, and several data sources were mined. The work of specialist nurses in this area is complex in terms of the physical and psychosocial care they provide. The nurses also undertook case management activity such as utilizing a very large network of professionals, and others participated in admission avoidance work and education of patients' families and other staff. The work of nurses specializing in hemoglobinopathy care is complex and multidimensional and is likely to contribute to the quality of care in a cost-effective way. An understanding of this complexity can be used as an underpinning to establishing key performance indicators, optimum caseload calculations, and economic evaluation.

Groping and Hoping for a Consensus on Calculator Use.

ERIC Educational Resources Information Center

Mathematics Education Dialogues, 1999

1999-01-01

This issue of Mathematics Education Dialogues focuses on the use of calculators in the mathematics classroom. The eleven articles on this theme include: (1) "Groping and Hoping for a Consensus on Calculator Use" (Zalman Usiskin); (2) "Let's Abolish Pencil-and-Paper Arithmetic" (Anthony Ralston); (3) "Do We Need Calculators?" (Kim Mackey); (4) "How…

Calculator Logic Systems and Mathematical Understandings.

ERIC Educational Resources Information Center

Burrows, Enid R.

This monograph is aimed at helping the reader understand the built-in logic of various calculator operating systems. It is an outgrowth of workshop contacts with in-service and pre-service teachers of mathematics and is in response to their request for a book on the subject of calculator logic systems and calculator algorithms. The mathematical…

Not All Created Equally: Exploring Calculator Use by Students with Mild Intellectual Disability

ERIC Educational Resources Information Center

Yakubova, Gulnoza; Bouck, Emily C.

2014-01-01

Calculators are widely used in mathematics education, yet limited research examines the effects of calculators for students with mild intellectual disability. An alternating treatments design was used to study the effects of calculator types (i.e., scientific and graphing) on the mathematical performance (i.e., computation and word problems) of…

Mathemagical Computing: Order of Operations and New Software.

ERIC Educational Resources Information Center

Ecker, Michael W.

1989-01-01

Describes mathematical problems which occur when using the computer as a calculator. Considers errors in BASIC calculation and the order of mathematical operations. Identifies errors in spreadsheet and calculator programs. Comments on sorting programs and provides a source for Mathemagical Black Holes. (MVL)

An investigation to find strategies to improve student nurses' maths skills.

PubMed

Wright, Kerri

Being able to perform drug calculations accurately is an essential skill for nurses. Many studies, however, have demonstrated that nurses need to improve this area of their practice and in particular their mathematical skills. Several strategies have been implemented to develop the drug calculation skills of nurses, with mixed success. This article reports on a study that was carried out to investigate whether strategies implemented within a second-year pre-registration course were perceived by students to be helpful in improving their mathematical skills for drug calculations. The results demonstrated that students felt their mathematics and confidence improved as a result of these strategies. The students' evaluation of the learning strategy that they found most helpful in learning drug calculation gave a mixed result, indicating that students have differing learning styles and needs. The study also indicates that student nurses were able to integrate the mathematical skills into their nursing practice by having different strategies that allowed them to develop conceptual, mathematical and practical skills concurrently. The study recommends the implementation of integrated strategies to address drug calculation skills in student nurses, although further research is still required.

The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

PubMed

Träff, Ulf

2013-10-01

This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

Medication calculation: the potential role of digital game-based learning in nurse education.

PubMed

Foss, Brynjar; Mordt Ba, Petter; Oftedal, Bjørg F; Løkken, Atle

2013-12-01

Medication dose calculation is one of several medication-related activities that are conducted by nurses daily. However, medication calculation skills appear to be an area of global concern, possibly because of low numeracy skills, test anxiety, low self-confidence, and low self-efficacy among student nurses. Various didactic strategies have been developed for student nurses who still lack basic mathematical competence. However, we suggest that the critical nature of these skills demands the investigation of alternative and/or supplementary didactic approaches to improve medication calculation skills and to reduce failure rates. Digital game-based learning is a possible solution because of the following reasons. First, mathematical drills may improve medication calculation skills. Second, games are known to be useful during nursing education. Finally, mathematical drill games appear to improve the attitudes of students toward mathematics. The aim of this article was to discuss common challenges of medication calculation skills in nurse education, and we highlight the potential role of digital game-based learning in this area.

Production of biofuels and biochemicals: in need of an ORACLE.

PubMed

Miskovic, Ljubisa; Hatzimanikatis, Vassily

2010-08-01

The engineering of cells for the production of fuels and chemicals involves simultaneous optimization of multiple objectives, such as specific productivity, extended substrate range and improved tolerance - all under a great degree of uncertainty. The achievement of these objectives under physiological and process constraints will be impossible without the use of mathematical modeling. However, the limited information and the uncertainty in the available information require new methods for modeling and simulation that will characterize the uncertainty and will quantify, in a statistical sense, the expectations of success of alternative metabolic engineering strategies. We discuss these considerations toward developing a framework for the Optimization and Risk Analysis of Complex Living Entities (ORACLE) - a computational method that integrates available information into a mathematical structure to calculate control coefficients. Copyright 2010 Elsevier Ltd. All rights reserved.

Learning Disabilities

MedlinePlus

... language, do mathematical calculations, coordinate movements, or direct attention. Although learning disabilities occur in very young children, ... language, do mathematical calculations, coordinate movements, or direct attention. Although learning disabilities occur in very young children, ...

DOE Fundamentals Handbook: Mathematics, Volume 1

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

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

DOE Fundamentals Handbook: Mathematics, Volume 2

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

Not Available

1992-06-01

The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclearmore » facility operations.« less

System Statement of Tasks of Calculating and Providing the Reliability of Heating Cogeneration Plants in Power Systems

NASA Astrophysics Data System (ADS)

Biryuk, V. V.; Tsapkova, A. B.; Larin, E. A.; Livshiz, M. Y.; Sheludko, L. P.

2018-01-01

A set of mathematical models for calculating the reliability indexes of structurally complex multifunctional combined installations in heat and power supply systems was developed. Reliability of energy supply is considered as required condition for the creation and operation of heat and power supply systems. The optimal value of the power supply system coefficient F is based on an economic assessment of the consumers’ loss caused by the under-supply of electric power and additional system expences for the creation and operation of an emergency capacity reserve. Rationing of RI of the industrial heat supply is based on the use of concept of technological margin of safety of technological processes. The definition of rationed RI values of heat supply of communal consumers is based on the air temperature level iside the heated premises. The complex allows solving a number of practical tasks for providing reliability of heat supply for consumers. A probabilistic model is developed for calculating the reliability indexes of combined multipurpose heat and power plants in heat-and-power supply systems. The complex of models and calculation programs can be used to solve a wide range of specific tasks of optimization of schemes and parameters of combined heat and power plants and systems, as well as determining the efficiency of various redundance methods to ensure specified reliability of power supply.

Learning to Calculate and Learning Mathematics.

ERIC Educational Resources Information Center

Fearnley-Sander, Desmond

1980-01-01

A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)

Mathematical modelling of metabolic pathways affected by an enzyme deficiency. Energy and redox metabolism of glucose-6-phosphate-dehydrogenase-deficient erythrocytes.

PubMed

Schuster, R; Jacobasch, G; Holzhütter, H G

1989-07-01

The effects of various forms of glucose-6-phosphate dehydrogenase deficiency on erythrocyte metabolism have been studied on the basis of a complex mathematical model which comprises the main pathways of this cell: glycolysis, pentose pathway, reactions of the glutathione and adenine nucleotide metabolism. The calculated flux rates through the oxidative pentose pathway with and without methylene blue are in good accord with experimental results. The degree of deficiency as predicted by the model on the basis of calculated upper oxidative load boundaries, as well as of maximal methylene blue stimulation, correlates with the individual clinical manifestation of the metabolic disease. Therefore, the model allows one to judge the degree of metabolic disorder in the presence of glucose-6-phosphate dehydrogenase enzymopathies if the kinetic properties of the defect enzyme are known. Experimentally accessible parameters for an assessment of the oxidative load capacity of cells in vivo are proposed. It is pointed out that the threshold of tolerance as to energetic load is drastically reduced in the case of severe glucose-6-phosphate dehydrogenase deficiency.

Mathematical Modeling of Cellular Metabolism.

PubMed

Berndt, Nikolaus; Holzhütter, Hermann-Georg

Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.

Estimating the Distance to the Moon--Its Relevance to Mathematics. Core-Plus Mathematics Project.

ERIC Educational Resources Information Center

Stern, David P.

This document features an activity for estimating the distance from the earth to the moon during a solar eclipse based on calculations performed by the ancient Greek astronomer Hipparchus. Historical, mathematical, and scientific details about the calculation are provided. Internet resources for teachers to obtain more information on the subject…

Equity of Student Use of Graphing Calculators for Mathematics Learning and Assessment

ERIC Educational Resources Information Center

Klecker, Beverly M.; Klecker, Richard L.

2015-01-01

This study examined equity through the differences average scale scores on the NAEP 2015 12th-grade mathematics test by parents' socioeconomic status (SES) and students' use of graphing calculators in the classroom and while taking the NAEP 2015 assessment. Data were national public composite mathematics 12-grade 2015 NAEP assessment scores. The…

Association between Brain Hemisphericity, Learning Styles and Confidence in Using Graphics Calculator for Mathematics

ERIC Educational Resources Information Center

Ali, Rosihan M.; Kor, Liew Kee

2007-01-01

This paper presents the preliminary results of a study conducted to investigate the differences in brain hemisphericity and learning styles on students' confidence in using the graphics calculator (GC) to learn mathematics. Data were collected from a sample of 44 undergraduate mathematics students in Malaysia using Brain-Dominance Questionnaire,…

Data inversion algorithm development for the hologen occultation experiment

NASA Technical Reports Server (NTRS)

Gordley, Larry L.; Mlynczak, Martin G.

1986-01-01

The successful retrieval of atmospheric parameters from radiometric measurement requires not only the ability to do ideal radiometric calculations, but also a detailed understanding of instrument characteristics. Therefore a considerable amount of time was spent in instrument characterization in the form of test data analysis and mathematical formulation. Analyses of solar-to-reference interference (electrical cross-talk), detector nonuniformity, instrument balance error, electronic filter time-constants and noise character were conducted. A second area of effort was the development of techniques for the ideal radiometric calculations required for the Halogen Occultation Experiment (HALOE) data reduction. The computer code for these calculations must be extremely complex and fast. A scheme for meeting these requirements was defined and the algorithms needed form implementation are currently under development. A third area of work included consulting on the implementation of the Emissivity Growth Approximation (EGA) method of absorption calculation into a HALOE broadband radiometer channel retrieval algorithm.

Optimization of Collision Detection in Surgical Simulations

NASA Astrophysics Data System (ADS)

Custură-Crăciun, Dan; Cochior, Daniel; Neagu, Corneliu

2014-11-01

Just like flight and spaceship simulators already represent a standard, we expect that soon enough, surgical simulators should become a standard in medical applications. A simulations quality is strongly related to the image quality as well as the degree of realism of the simulation. Increased quality requires increased resolution, increased representation speed but more important, a larger amount of mathematical equations. To make it possible, not only that we need more efficient computers, but especially more calculation process optimizations. A simulator executes one of the most complex sets of calculations each time it detects a contact between the virtual objects, therefore optimization of collision detection is fatal for the work-speed of a simulator and hence in its quality

Exact analytic solutions of Maxwell's equations describing propagating nonparaxial electromagnetic beams.

PubMed

Garay-Avendaño, Roger L; Zamboni-Rached, Michel

2014-07-10

In this paper, we propose a method that is capable of describing in exact and analytic form the propagation of nonparaxial scalar and electromagnetic beams. The main features of the method presented here are its mathematical simplicity and the fast convergence in the cases of highly nonparaxial electromagnetic beams, enabling us to obtain high-precision results without the necessity of lengthy numerical simulations or other more complex analytical calculations. The method can be used in electromagnetism (optics, microwaves) as well as in acoustics.

Air breathing engine/rocket trajectory optimization

NASA Technical Reports Server (NTRS)

Smith, V. K., III

1979-01-01

This research has focused on improving the mathematical models of the air-breathing propulsion systems, which can be mated with the rocket engine model and incorporated in trajectory optimization codes. Improved engine simulations provided accurate representation of the complex cycles proposed for advanced launch vehicles, thereby increasing the confidence in propellant use and payload calculations. The versatile QNEP (Quick Navy Engine Program) was modified to allow treatment of advanced turboaccelerator cycles using hydrogen or hydrocarbon fuels and operating in the vehicle flow field.

Selection theory of free dendritic growth in a potential flow.

PubMed

von Kurnatowski, Martin; Grillenbeck, Thomas; Kassner, Klaus

2013-04-01

The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [Fischaleck, Kassner, Europhys. Lett. 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.

Examining Calculator Use among Students with and without Disabilities Educated with Different Mathematical Curricula

ERIC Educational Resources Information Center

Bouck, Emily C.; Joshi, Gauri S.; Johnson, Linley

2013-01-01

This study assessed if students with and without disabilities used calculators (fourfunction, scientific, or graphing) to solve mathematics assessment problems and whether using calculators improved their performance. Participants were sixth and seventh-grade students educated with either National Science Foundation (NSF)-funded or traditional…

Precalculus Teachers' Perspectives on Using Graphing Calculators: An Example from One Curriculum

ERIC Educational Resources Information Center

Karadeniz, Ilyas; Thompson, Denisse R.

2018-01-01

Graphing calculators are hand-held technological tools currently used in mathematics classrooms. Teachers' perspectives on using graphing calculators are important in terms of exploring what teachers think about using such technology in advanced mathematics courses, particularly precalculus courses. A descriptive intrinsic case study was conducted…

Remedial Instruction to Enhance Mathematical Ability of Dyscalculics

ERIC Educational Resources Information Center

Kumar, S. Praveen; Raja, B. William Dharma

2012-01-01

The ability to do arithmetic calculations is essential to school-based learning and skill development in an information rich society. Arithmetic is a basic academic skill that is needed for learning which includes the skills such as counting, calculating, reasoning etc. that are used for performing mathematical calculations. Unfortunately, many…

Impact of Student Calculator Use on the 2013 NAEP Twelfth-Grade Mathematics Assessment

ERIC Educational Resources Information Center

Klecker, Beverly M.; Klecker, Richard L.

2014-01-01

This descriptive research study examined 2013 NAEP 12th-grade mathematics scores by students' use of graphing calculators in math classes and the kind of calculator students used during NAEP assessment. NAEP Data Explorer analysis included two questions from Student Factors: How often do you use these different kinds of calculators in math class?…

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

ERIC Educational Resources Information Center

Pantzare, Anna Lind

2012-01-01

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

Validation of a personalized dosimetric evaluation tool (Oedipe) for targeted radiotherapy based on the Monte Carlo MCNPX code

NASA Astrophysics Data System (ADS)

Chiavassa, S.; Aubineau-Lanièce, I.; Bitar, A.; Lisbona, A.; Barbet, J.; Franck, D.; Jourdain, J. R.; Bardiès, M.

2006-02-01

Dosimetric studies are necessary for all patients treated with targeted radiotherapy. In order to attain the precision required, we have developed Oedipe, a dosimetric tool based on the MCNPX Monte Carlo code. The anatomy of each patient is considered in the form of a voxel-based geometry created using computed tomography (CT) images or magnetic resonance imaging (MRI). Oedipe enables dosimetry studies to be carried out at the voxel scale. Validation of the results obtained by comparison with existing methods is complex because there are multiple sources of variation: calculation methods (different Monte Carlo codes, point kernel), patient representations (model or specific) and geometry definitions (mathematical or voxel-based). In this paper, we validate Oedipe by taking each of these parameters into account independently. Monte Carlo methodology requires long calculation times, particularly in the case of voxel-based geometries, and this is one of the limits of personalized dosimetric methods. However, our results show that the use of voxel-based geometry as opposed to a mathematically defined geometry decreases the calculation time two-fold, due to an optimization of the MCNPX2.5e code. It is therefore possible to envisage the use of Oedipe for personalized dosimetry in the clinical context of targeted radiotherapy.

REVIEWS OF TOPICAL PROBLEMS: Analytic calculations on digital computers for applications in physics and mathematics

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Tarasov, O. V.; Shirkov, Dmitrii V.

1980-01-01

The present state of analytic calculations on computers is reviewed. Several programming systems which are used for analytic calculations are discussed: SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK, MACSYMA, etc. It is shown that these systems can be used to solve a wide range of problems in physics and mathematics. Some physical applications are discussed in celestial mechanics, the general theory of relativity, quantum field theory, plasma physics, hydrodynamics, atomic and molecular physics, and quantum chemistry. Some mathematical applications which are discussed are evaluating indefinite integrals, solving differential equations, and analyzing mathematical expressions. This review is addressed to physicists and mathematicians working in a wide range of fields.

Matlab Geochemistry: An open source geochemistry solver based on MRST

NASA Astrophysics Data System (ADS)

McNeece, C. J.; Raynaud, X.; Nilsen, H.; Hesse, M. A.

2017-12-01

The study of geological systems often requires the solution of complex geochemical relations. To address this need we present an open source geochemical solver based on the Matlab Reservoir Simulation Toolbox (MRST) developed by SINTEF. The implementation supports non-isothermal multicomponent aqueous complexation, surface complexation, ion exchange, and dissolution/precipitation reactions. The suite of tools available in MRST allows for rapid model development, in particular the incorporation of geochemical calculations into transport simulations of multiple phases, complex domain geometry and geomechanics. Different numerical schemes and additional physics can be easily incorporated into the existing tools through the object-oriented framework employed by MRST. The solver leverages the automatic differentiation tools available in MRST to solve arbitrarily complex geochemical systems with any choice of species or element concentration as input. Four mathematical approaches enable the solver to be quite robust: 1) the choice of chemical elements as the basis components makes all entries in the composition matrix positive thus preserving convexity, 2) a log variable transformation is used which transfers the nonlinearity to the convex composition matrix, 3) a priori bounds on variables are calculated from the structure of the problem, constraining Netwon's path and 4) an initial guess is calculated implicitly by sequentially adding model complexity. As a benchmark we compare the model to experimental and semi-analytic solutions of the coupled salinity-acidity transport system. Together with the reservoir simulation capabilities of MRST the solver offers a promising tool for geochemical simulations in reservoir domains for applications in a diversity of fields from enhanced oil recovery to radionuclide storage.

Final Technical Report: Mathematical Foundations for Uncertainty Quantification in Materials Design

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

Plechac, Petr; Vlachos, Dionisios G.

We developed path-wise information theory-based and goal-oriented sensitivity analysis and parameter identification methods for complex high-dimensional dynamics and in particular of non-equilibrium extended molecular systems. The combination of these novel methodologies provided the first methods in the literature which are capable to handle UQ questions for stochastic complex systems with some or all of the following features: (a) multi-scale stochastic models such as (bio)chemical reaction networks, with a very large number of parameters, (b) spatially distributed systems such as Kinetic Monte Carlo or Langevin Dynamics, (c) non-equilibrium processes typically associated with coupled physico-chemical mechanisms, driven boundary conditions, hybrid micro-macro systems,more » etc. A particular computational challenge arises in simulations of multi-scale reaction networks and molecular systems. Mathematical techniques were applied to in silico prediction of novel materials with emphasis on the effect of microstructure on model uncertainty quantification (UQ). We outline acceleration methods to make calculations of real chemistry feasible followed by two complementary tasks on structure optimization and microstructure-induced UQ.« less

Is Mathematics to Blame? An Investigation into High School Students' Difficulty in Performing Calculations in Chemistry

ERIC Educational Resources Information Center

Scott, Fraser J.

2012-01-01

Mathematical ability is a major contributory factor to the success of a student in any science course. This paper aims to determine the source of the difficulty that students often find when performing calculations in chemistry. Through the design and analysis of a set of chemistry questions and analogous mathematics questions, set in a Standard…

Etiological Distinction of Working Memory Components in Relation to Mathematics

PubMed Central

Lukowski, Sarah L.; Soden, Brooke; Hart, Sara A.; Thompson, Lee A.; Kovas, Yulia; Petrill, Stephen A.

2014-01-01

Working memory has been consistently associated with mathematics achievement, although the etiology of these relations remains poorly understood. The present study examined the genetic and environmental underpinnings of math story problem solving, timed calculation, and untimed calculation alongside working memory components in 12-year-old monozygotic (n = 105) and same-sex dizygotic (n = 143) twin pairs. Results indicated significant phenotypic correlation between each working memory component and all mathematics outcomes (r = 0.18 – 0.33). Additive genetic influences shared between the visuo-spatial sketchpad and mathematics achievement was significant, accounting for roughly 89% of the observed correlation. In addition, genetic covariance was found between the phonological loop and math story problem solving. In contrast, despite there being a significant observed relationship between phonological loop and timed and untimed calculation, there was no significant genetic or environmental covariance between the phonological loop and timed or untimed calculation skills. Further analyses indicated that genetic overlap between the visuo-spatial sketchpad and math story problem solving and math fluency was distinct from general genetic factors, whereas g, phonological loop, and mathematics shared generalist genes. Thus, although each working memory component was related to mathematics, the etiology of their relationships may be distinct. PMID:25477699

Complex optimization for big computational and experimental neutron datasets

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

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Complex optimization for big computational and experimental neutron datasets

DOE PAGES

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard; ...

2016-11-07

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Computer program for calculation of complex chemical equilibrium compositions and applications. Part 1: Analysis

NASA Technical Reports Server (NTRS)

Gordon, Sanford; Mcbride, Bonnie J.

1994-01-01

This report presents the latest in a number of versions of chemical equilibrium and applications programs developed at the NASA Lewis Research Center over more than 40 years. These programs have changed over the years to include additional features and improved calculation techniques and to take advantage of constantly improving computer capabilities. The minimization-of-free-energy approach to chemical equilibrium calculations has been used in all versions of the program since 1967. The two principal purposes of this report are presented in two parts. The first purpose, which is accomplished here in part 1, is to present in detail a number of topics of general interest in complex equilibrium calculations. These topics include mathematical analyses and techniques for obtaining chemical equilibrium; formulas for obtaining thermodynamic and transport mixture properties and thermodynamic derivatives; criteria for inclusion of condensed phases; calculations at a triple point; inclusion of ionized species; and various applications, such as constant-pressure or constant-volume combustion, rocket performance based on either a finite- or infinite-chamber-area model, shock wave calculations, and Chapman-Jouguet detonations. The second purpose of this report, to facilitate the use of the computer code, is accomplished in part 2, entitled 'Users Manual and Program Description'. Various aspects of the computer code are discussed, and a number of examples are given to illustrate its versatility.

Pattern of mathematic representation ability in magnetic electricity problem

NASA Astrophysics Data System (ADS)

Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.

2018-03-01

The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.

Nursing students' confidence in medication calculations predicts math exam performance.

PubMed

Andrew, Sharon; Salamonson, Yenna; Halcomb, Elizabeth J

2009-02-01

The aim of this study was to examine the psychometric properties, including predictive validity, of the newly-developed nursing self-efficacy for mathematics (NSE-Math). The NSE-Math is a 12 item scale that comprises items related to mathematic and arithmetic concepts underpinning medication calculations. The NSE-Math instrument was administered to second year Bachelor of Nursing students enrolled in a nursing practice subject. Students' academic results for a compulsory medication calculation examination for this subject were collected. One-hundred and twelve students (73%) completed both the NSE-Math instrument and the drug calculation assessment task. The NSE-Math demonstrated two factors 'Confidence in application of mathematic concepts to nursing practice' and 'Confidence in arithmetic concepts' with 63.5% of variance explained. Cronbach alpha for the scale was 0.90. The NSE-Math demonstrated predictive validity with the medication calculation examination results (p=0.009). Psychometric testing suggests the NSE-Math is a valid measure of mathematics self-efficacy of second year nursing students.

Instructional Efficiency of the Integration of Graphing Calculators in Teaching and Learning Mathematics

ERIC Educational Resources Information Center

Tajuddin, Nor'ain Mohd; Tarmizi, Rohani Ahmad; Konting, Mohd Majid; Ali, Wan Zah Wan

2009-01-01

This quasi-experimental study with non-equivalent control group post-test only design was conducted to investigate the effects of using graphing calculators in mathematics teaching and learning on Form Four Malaysian secondary school students' performance and their meta-cognitive awareness level. Graphing calculator strategy refers to the use of…

Investment Return Calculations and Senior School Mathematics

ERIC Educational Resources Information Center

Fitzherbert, Richard M.; Pitt, David G. W.

2010-01-01

The methods for calculating returns on investments are taught to undergraduate level business students. In this paper, the authors demonstrate how such calculations are within the scope of senior school students of mathematics. In providing this demonstration the authors hope to give teachers and students alike an illustration of the power and the…

The Place of Calculators in Mathematics Education in Developing Countries

ERIC Educational Resources Information Center

Kissane, Barry; Kemp, Marian

2012-01-01

Technology has become a major force in developing curricula and educational practice in mathematics education internationally. While many technologies are important in affluent developed countries, the hand-held calculator continues to be the technology most likely to be available to students when and where they need it. Modern calculators have…

Using Calculators in Mathematics 11. Teacher Commentary.

ERIC Educational Resources Information Center

Rising, Gerald R.; And Others

This teacher's guide is designed to aid in the incorporation of programable calculators in the school mathematics program for pupils in grade 11. Warnings include the need for care in modifying the curriculum so that students are not punished in the process. The concept of "black boxing," of letting the computer or calculator take charge…

Structure Sense: A Precursor to Competency in Undergraduate Mathematics

ERIC Educational Resources Information Center

Vincent, Jill; Pierce, Robyn; Bardini, Caroline

2017-01-01

In this article the authors analyze the written solutions of some first year undergraduate mathematics students from Victorian universities as they answered tutorial exercise questions relating to complex numbers and differentiation. These students had studied at least Mathematics Methods or its equivalent at secondary school. Complex numbers was…

Preparing Teachers to Lead Mathematics Discussions

ERIC Educational Resources Information Center

Boerst, Timothy A.; Sleep, Laurie; Ball, Deborah Loewenberg; Bass, Hyman

2011-01-01

Background/Context: Discussion is central to mathematics teaching and learning, as well as to mathematics as an academic discipline. Studies have shown that facilitating discussions is complex work that is not easily done or learned. To make such complex aspects of the work of teaching learnable by beginners, recent research has focused on…

Definition and verification of a complex aircraft for aerodynamic calculations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1986-01-01

Techniques are reviewed which are of value in CAD/CAM CFD studies of the geometries of new fighter aircraft. In order to refine the computations of the flows to take advantage of the computing power available from supercomputers, it is often necessary to interpolate the geometry of the mesh selected for the numerical analysis of the aircraft shape. Interpolating the geometry permits a higher level of detail in calculations of the flow past specific regions of a design. A microprocessor-based mathematics engine is described for fast image manipulation and rotation to verify that the interpolated geometry will correspond to the design geometry in order to ensure that the flow calculations will remain valid through the interpolation. Applications of the image manipulation system to verify geometrical representations with wire-frame and shaded-surface images are described.

Adaptive grid generation in a patient-specific cerebral aneurysm

NASA Astrophysics Data System (ADS)

Hodis, Simona; Kallmes, David F.; Dragomir-Daescu, Dan

2013-11-01

Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce computational time for patient-specific hemodynamics simulations, which are used to help assess the likelihood of aneurysm rupture using CFD calculated flow patterns.

Tracing the Construction of Mathematical Activity with an Advanced Graphing Calculator to Understand the Roles of Technology Developers, Teachers and Students

ERIC Educational Resources Information Center

Hillman, Thomas

2014-01-01

This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Research Area 3: Mathematics (3.1 Modeling of Complex Systems)

DTIC Science & Technology

2017-10-31

RESEARCH AREA 3: MATHEMATICS (3.1 Modeling of Complex Systems). Proposal should be directed to Dr. John Lavery The views, opinions and/or findings...so designated by other documentation. 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research ...Title: RESEARCH AREA 3: MATHEMATICS (3.1 Modeling of Complex Systems). Proposal should be directed to Dr. John Lavery Report Term: 0-Other Email

Sources of Individual Differences in Emerging Competence With Numeration Understanding Versus Multidigit Calculation Skill

PubMed Central

Fuchs, Lynn S.; Geary, David C.; Fuchs, Douglas; Compton, Donald L.; Hamlett, Carol L.

2014-01-01

This study investigated contributions of general cognitive abilities and foundational mathematical competencies to numeration understanding (i.e., base-10 structure) versus multidigit calculation skill. Children (n = 394, M = 6.5 years) were assessed on general cognitive abilities and foundational numerical competencies at start of 1st grade; on the same numerical competencies, multidigit calculation skill, and numeration understanding at end of 2nd grade; and on multidigit calculation skill and numeration understanding at end of 3rd grade. Path-analytic mediation analysis revealed that general cognitive predictors exerted more direct and more substantial effects on numeration understanding than on multidigit calculations. Foundational mathematics competencies contributed to both outcomes, but largely via 2nd-grade mathematics achievement, and results suggest a mutually supportive role between numeration understanding and multidigit calculations. PMID:25284885

The Transition to Formal Thinking in Mathematics

ERIC Educational Resources Information Center

Tall, David

2008-01-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

Test Review: Reynolds, C. R., Voress, J. V., Kamphaus, R. W. (2015), "Mathematics Fluency and Calculation Tests (MFaCTs) review." PRO-ED

ERIC Educational Resources Information Center

Marbach, Joshua

2017-01-01

The Mathematics Fluency and Calculation Tests (MFaCTs) are a series of measures designed to assess for arithmetic calculation skills and calculation fluency in children ages 6 through 18. There are five main purposes of the MFaCTs: (1) identifying students who are behind in basic math fact automaticity; (2) evaluating possible delays in arithmetic…

Undergraduate paramedic students cannot do drug calculations.

PubMed

Eastwood, Kathryn; Boyle, Malcolm J; Williams, Brett

2012-01-01

Previous investigation of drug calculation skills of qualified paramedics has highlighted poor mathematical ability with no published studies having been undertaken on undergraduate paramedics. There are three major error classifications. Conceptual errors involve an inability to formulate an equation from information given, arithmetical errors involve an inability to operate a given equation, and finally computation errors are simple errors of addition, subtraction, division and multiplication. The objective of this study was to determine if undergraduate paramedics at a large Australia university could accurately perform common drug calculations and basic mathematical equations normally required in the workplace. A cross-sectional study methodology using a paper-based questionnaire was administered to undergraduate paramedic students to collect demographical data, student attitudes regarding their drug calculation performance, and answers to a series of basic mathematical and drug calculation questions. Ethics approval was granted. The mean score of correct answers was 39.5% with one student scoring 100%, 3.3% of students (n=3) scoring greater than 90%, and 63% (n=58) scoring 50% or less, despite 62% (n=57) of the students stating they 'did not have any drug calculations issues'. On average those who completed a minimum of year 12 Specialist Maths achieved scores over 50%. Conceptual errors made up 48.5%, arithmetical 31.1% and computational 17.4%. This study suggests undergraduate paramedics have deficiencies in performing accurate calculations, with conceptual errors indicating a fundamental lack of mathematical understanding. The results suggest an unacceptable level of mathematical competence to practice safely in the unpredictable prehospital environment.

Teaching Mathematics with Technology. How to Win People and Influence Friends: Calculators in the Primary Grades.

ERIC Educational Resources Information Center

Taylor, Lyn, Ed.; Thompson, Virginia, Comp.

1992-01-01

Postulated here is the notion that the exploration of number patterns with calculators is a valuable mathematical learning activity that should be commenced in the primary grades. Various activities are presented that make use of the constant function key, which is available on many of the inexpensive four-function calculators. (JJK)

Introducing Calculators to Learners Early in Their Schooling: The Effect on Long-Term Arithmetic Proficiency

ERIC Educational Resources Information Center

Mogari, David; Faleye, Sunday

2012-01-01

There are opposing views about calculator use in school mathematics. This paper reports on a study that investigated the arithmetic proficiency of mathematics 1 university students and the effects of calculator usage at school level on their proficiency. The study followed a descriptive survey design involving the use of questionnaire and data…

Hand-Held Calculators in the Classroom: A Review of the Research.

ERIC Educational Resources Information Center

Parkhurst, Scott

This report surveys many of the recent investigations on calculators and their use in mathematics education. The review notes that the widespread availability of hand-held calculators and their affordability has led to their consideration as a viable tool to aid in mathematics instruction. The studies reviewed suggest that many questions are still…

What is the Role of Mathematics Education in the Computer Age?

ERIC Educational Resources Information Center

Popp, Jerome A.

1986-01-01

Proposes that the role of mathematics education be re-examined in terms of an increased emphasis on mathematical knowledge rather than attainment of calculational speed. Offers perspectives on the reform movement in mathematics education and advocates the teaching of the history, logic, and method of mathematical thinking. (ML)

Graphing Calculator Exposure of Mathematics Learning in a Partially Technology Incorporated Environment

ERIC Educational Resources Information Center

Kharuddin, Azrul Fazwan; Ismail, Noor Azina

2017-01-01

Integrating technology in the mathematics curriculum has become a necessary task for curriculum developers as well as mathematics practitioners across the world and time. In general research studies seeking a better understanding of how best to integrate mathematics analysis tools with mathematics subject matter normally observe mathematics…

Child-Level Predictors of Responsiveness to Evidence-Based Mathematics Intervention

ERIC Educational Resources Information Center

Powell, Sarah R.; Cirino, Paul T.; Malone, Amelia S.

2017-01-01

We identified child-level predictors of responsiveness to 2 types of mathematics intervention (calculation and word problem) among second-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We…

Designing and Developing Assessments of Complex Thinking in Mathematics for the Middle Grades

ERIC Educational Resources Information Center

Graf, Edith Aurora; Arieli-Attali, Meirav

2015-01-01

Designing an assessment system for complex thinking in mathematics involves decisions at every stage, from how to represent the target competencies to how to interpret evidence from student performances. Beyond learning to solve particular problems in a particular area, learning mathematics with understanding involves comprehending connections…

Numerical Capacities as Domain-Specific Predictors beyond Early Mathematics Learning: A Longitudinal Study

PubMed Central

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3rd and 4th grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively “start-up” tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school. PMID:24255710

Numerical capacities as domain-specific predictors beyond early mathematics learning: a longitudinal study.

PubMed

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3(rd) and 4(th) grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively "start-up" tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school.

The Applied Mathematics for Power Systems (AMPS)

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

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 toolboxesmore » 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.« less

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

PubMed

Walsh, Kathleen A

2008-01-01

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

A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty.

PubMed

Zhao, Jing-Xin; Su, Xiu-Yun; Xiao, Ruo-Xiu; Zhao, Zhe; Zhang, Li-Hai; Zhang, Li-Cheng; Tang, Pei-Fu

2016-11-01

We established a mathematical method to precisely calculate the radiographic anteversion (RA) and radiographic inclination (RI) angles of the acetabular cup based on anterior-posterior (AP) pelvic radiographs after total hip arthroplasty. Using Mathematica software, a mathematical model for an oblique cone was established to simulate how AP pelvic radiographs are obtained and to address the relationship between the two-dimensional and three-dimensional geometry of the opening circle of the cup. In this model, the vertex was the X-ray beam source, and the generatrix was the ellipse in radiographs projected from the opening circle of the acetabular cup. Using this model, we established a series of mathematical formulas to reveal the differences between the true RA and RI cup angles and the measurements results achieved using traditional methods and AP pelvic radiographs and to precisely calculate the RA and RI cup angles based on post-operative AP pelvic radiographs. Statistical analysis indicated that traditional methods should be used with caution if traditional measurements methods are used to calculate the RA and RI cup angles with AP pelvic radiograph. The entire calculation process could be performed by an orthopedic surgeon with mathematical knowledge of basic matrix and vector equations. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Mathematical Modeling of Dual Layer Shell Type Recuperation System for Biogas Dehumidification

NASA Astrophysics Data System (ADS)

Gendelis, S.; Timuhins, A.; Laizans, A.; Bandeniece, L.

2015-12-01

The main aim of the current paper is to create a mathematical model for dual layer shell type recuperation system, which allows reducing the heat losses from the biomass digester and water amount in the biogas without any additional mechanical or chemical components. The idea of this system is to reduce the temperature of the outflowing gas by creating two-layered counter-flow heat exchanger around the walls of biogas digester, thus increasing a thermal resistance and the gas temperature, resulting in a condensation on a colder surface. Complex mathematical model, including surface condensation, is developed for this type of biogas dehumidifier and the parameter study is carried out for a wide range of parameters. The model is reduced to 1D case to make numerical calculations faster. It is shown that latent heat of condensation is very important for the total heat balance and the condensation rate is highly dependent on insulation between layers and outside temperature. Modelling results allow finding optimal geometrical parameters for the known gas flow and predicting the condensation rate for different system setups and seasons.

Alternative Beam Efficiency Calculations for a Large-aperture Multiple-frequency Microwave Radiometer (LAMMR)

NASA Technical Reports Server (NTRS)

Schmidt, R. F.

1979-01-01

The fundamental definition of beam efficiency, given in terms of a far field radiation pattern, was used to develop alternative definitions which improve accuracy, reduce the amount of calculation required, and isolate the separate factors composing beam efficiency. Well-known definitions of aperture efficiency were introduced successively to simplify the denominator of the fundamental definition. The superposition of complex vector spillover and backscattered fields was examined, and beam efficiency analysis in terms of power patterns was carried out. An extension from single to dual reflector geometries was included. It is noted that the alternative definitions are advantageous in the mathematical simulation of a radiometer system, and are not intended for the measurements discipline where fields have merged and therefore lost their identity.

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Impact of a Required Pharmaceutical Calculations Course on Mathematics Ability and Knowledge Retention

PubMed Central

Buring, Shauna M.; Papas, Elizabeth

2013-01-01

Objective. To assess doctor of pharmacy (PharmD) students’ mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. Methods. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Results. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. Conclusions. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students’ overall ability to perform fundamental and application-based calculations. PMID:23966727

Impact of a required pharmaceutical calculations course on mathematics ability and knowledge retention.

PubMed

Hegener, Michael A; Buring, Shauna M; Papas, Elizabeth

2013-08-12

To assess doctor of pharmacy (PharmD) students' mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students' overall ability to perform fundamental and application-based calculations.

Spectral simplicity of apparent complexity. II. Exact complexities and complexity spectra

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-03-01

The meromorphic functional calculus developed in Part I overcomes the nondiagonalizability of linear operators that arises often in the temporal evolution of complex systems and is generic to the metadynamics of predicting their behavior. Using the resulting spectral decomposition, we derive closed-form expressions for correlation functions, finite-length Shannon entropy-rate approximates, asymptotic entropy rate, excess entropy, transient information, transient and asymptotic state uncertainties, and synchronization information of stochastic processes generated by finite-state hidden Markov models. This introduces analytical tractability to investigating information processing in discrete-event stochastic processes, symbolic dynamics, and chaotic dynamical systems. Comparisons reveal mathematical similarities between complexity measures originally thought to capture distinct informational and computational properties. We also introduce a new kind of spectral analysis via coronal spectrograms and the frequency-dependent spectra of past-future mutual information. We analyze a number of examples to illustrate the methods, emphasizing processes with multivariate dependencies beyond pairwise correlation. This includes spectral decomposition calculations for one representative example in full detail.

Transposing reform pedagogy into new contexts: complex instruction in remote Australia

NASA Astrophysics Data System (ADS)

Sullivan, Peter; Jorgensen, Robyn; Boaler, Jo; Lerman, Steve

2013-03-01

This article draws on the outcomes of a 4-year project where complex instruction was used as the basis for a reform in mathematics teaching in remote Aboriginal communities in Australia. The article describes the overall project in terms of the goals and aspirations for learning mathematics among remote Indigenous Australians. Knowing that the approach had been successful in a diverse setting in California, the project team sought to implement and evaluate the possibilities of such reform in a context in which the need for a culturally responsive pedagogy was critical. Elements of complex instruction offered considerable possibilities in aligning with the cultures of the remote communities, but with recognition of the possibility that some elements may not be workable in these contexts. Complex instruction also valued deep knowledge of mathematics rather than a tokenistic, impoverished mathematics. The strategies within complex instruction allowed for mathematical and cultural scaffolding to promote deep learning in mathematics. Such an approach was in line with current reforms in Indigenous education in Australia where there are high expectations of learners in order to break away from the deficit thinking that has permeated much education in remote Australia. The overall intent is to demonstrate what pedagogies are possible within the constraints of the remote context.

Calculating DWI/DWAI Recidivism with Limited Data: Using State Driver License File for Drinking and Driving Research.

ERIC Educational Resources Information Center

Yu, Jiang; Williford, William R.

1991-01-01

Used sample from New York State Driver License File to mathematically extend dimension of file so that data purging procedure exerts minimum influence on calculation of drinking-driving recidivism. Examined impact of dimension of data on recidivism rate and mathematically extended file until impact of data dimension was minimum. Calculated New…

The Mathematical Formatting of Climate Change: Critical Mathematics Education and Post-Normal Science

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…

Mathematics Teachers' Visualization of Complex Number Multiplication and the Roots of Unity in a Dynamic Geometry Environment

ERIC Educational Resources Information Center

Caglayan, Gunhan

2016-01-01

This qualitative research, drawing on the theoretical frameworks by Even (1990, 1993) and Sfard (2007), investigated five high school mathematics teachers' geometric interpretations of complex number multiplication along with the roots of unity. The main finding was that mathematics teachers constructed the modulus, the argument, and the conjugate…

A Complex Formula: Girls and Women in Science, Technology, Engineering and Mathematics in Asia

ERIC Educational Resources Information Center

Salmon, Aliénor

2015-01-01

What factors might be causing the low participation of women Science, Technology, Engineering and Mathematics (STEM) fields? What can be done to attract more girls and women into STEM in Asia and beyond? The report, "A Complex Formula. Girls and Women in Science, Technology, Engineering and Mathematics in Asia", answers three fundamental…

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…

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

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

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

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

Research on air and missile defense task allocation based on extended contract net protocol

NASA Astrophysics Data System (ADS)

Zhang, Yunzhi; Wang, Gang

2017-10-01

Based on the background of air and missile defense distributed element corporative engagement, the interception task allocation problem of multiple weapon units with multiple targets under network condition is analyzed. Firstly, a mathematical model of task allocation is established by combat task decomposition. Secondly, the initialization assignment based on auction contract and the adjustment allocation scheme based on swap contract were introduced to the task allocation. Finally, through the simulation calculation of typical situation, the model can be used to solve the task allocation problem in complex combat environment.

Semi-classical Electrodynamics

NASA Astrophysics Data System (ADS)

Lestone, John

2016-03-01

Quantum electrodynamics is complex and its associated mathematics can appear overwhelming for those not trained in this field. We describe semi-classical approaches that can be used to obtain a more intuitive physical feel for several QED processes including electro-statics, Compton scattering, pair annihilation, the anomalous magnetic moment, and the Lamb shift, that could be taught easily to undergraduate students. Any physicist who brings their laptop to the talk will be able to build spread sheets in less than 10 minutes to calculate g/2 =1.001160 and a Lamb shift of 1057 MHz.

Design, development and validation of software for modelling dietary exposure to food chemicals and nutrients.

PubMed

McNamara, C; Naddy, B; Rohan, D; Sexton, J

2003-10-01

The Monte Carlo computational system for stochastic modelling of dietary exposure to food chemicals and nutrients is presented. This system was developed through a European Commission-funded research project. It is accessible as a Web-based application service. The system allows and supports very significant complexity in the data sets used as the model input, but provides a simple, general purpose, linear kernel for model evaluation. Specific features of the system include the ability to enter (arbitrarily) complex mathematical or probabilistic expressions at each and every input data field, automatic bootstrapping on subjects and on subject food intake diaries, and custom kernels to apply brand information such as market share and loyalty to the calculation of food and chemical intake.

Hidden Figures Tour Kennedy Space Center Visitor Complex

NASA Image and Video Library

2016-12-12

In the IMAX Theater of the Kennedy Space Center Visitor Complex Cast and crew members of the upcoming motion picture "Hidden Figures" participate in a question and answer session. From the left are Ted Melfi, writer and director of “Hidden Figures,” and Octavia Spencer, who portrays Dorothy Vaughan in the film. The movie is based on the book of the same title, by Margot Lee Shetterly. It chronicles the lives of Katherine Johnson, Dorothy Vaughan and Mary Jackson, three African-American women who worked for NASA as human "computers.” Their mathematical calculations were crucial to the success of Project Mercury missions including John Glenn’s orbital flight aboard Friendship 7 in 1962. The film is due in theaters in January 2017.

Undergraduate paramedic students cannot do drug calculations

PubMed Central

Eastwood, Kathryn; Boyle, Malcolm J; Williams, Brett

2012-01-01

BACKGROUND: Previous investigation of drug calculation skills of qualified paramedics has highlighted poor mathematical ability with no published studies having been undertaken on undergraduate paramedics. There are three major error classifications. Conceptual errors involve an inability to formulate an equation from information given, arithmetical errors involve an inability to operate a given equation, and finally computation errors are simple errors of addition, subtraction, division and multiplication. The objective of this study was to determine if undergraduate paramedics at a large Australia university could accurately perform common drug calculations and basic mathematical equations normally required in the workplace. METHODS: A cross-sectional study methodology using a paper-based questionnaire was administered to undergraduate paramedic students to collect demographical data, student attitudes regarding their drug calculation performance, and answers to a series of basic mathematical and drug calculation questions. Ethics approval was granted. RESULTS: The mean score of correct answers was 39.5% with one student scoring 100%, 3.3% of students (n=3) scoring greater than 90%, and 63% (n=58) scoring 50% or less, despite 62% (n=57) of the students stating they ‘did not have any drug calculations issues’. On average those who completed a minimum of year 12 Specialist Maths achieved scores over 50%. Conceptual errors made up 48.5%, arithmetical 31.1% and computational 17.4%. CONCLUSIONS: This study suggests undergraduate paramedics have deficiencies in performing accurate calculations, with conceptual errors indicating a fundamental lack of mathematical understanding. The results suggest an unacceptable level of mathematical competence to practice safely in the unpredictable prehospital environment. PMID:25215067

Relationships between thermal maturity indices calculated using Arrhenius equation and Lopatin method: implications for petroleum exploration

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

Wood, D.A.

1988-02-01

Thermal maturity can be calculated with time-temperature indices (TTI) based on the Arrhenius equation using kinetics applicable to a range of Types II and III kerogens. These TTIs are compared with TTI calculations based on the Lopatin method and are related theoretically (and empirically via vitrinite reflectance) to the petroleum-generation window. The TTIs for both methods are expressed mathematically as integrals of temperature combined with variable linear heating rates for selected temperature intervals. Heating rates control the thermal-maturation trends of buried sediments. Relative to Arrhenius TTIs, Lopatin TTIs tend to underestimate thermal maturity at high heating rates and overestimate itmore » as low heating rates. Complex burial histories applicable to a range of tectonic environments illustrate the different exploration decisions that might be made on the basis of independent results of these two thermal-maturation models. 15 figures, 8 tables.« less

Mathematical modelling of the transport of hydroxypropyl-β-cyclodextrin inclusion complexes of ranitidine hydrochloride and furosemide loaded chitosan nanoparticles across a Caco-2 cell monolayer.

PubMed

Sadighi, Armin; Ostad, S N; Rezayat, S M; Foroutan, M; Faramarzi, M A; Dorkoosh, F A

2012-01-17

Chitosan nanoparticles (CS-NPs) have been used to enhance the permeability of furosemide and ranitidine hydrochloride (ranitidine HCl) which were selected as candidates for two different biopharmaceutical drug classes having low permeability across Caco-2 cell monolayers. Drugs loaded CS-NPs were prepared by ionic gelation of CS and pentasodium tripolyphosphate (TPP) which added to the drugs inclusion complexes with hydroxypropyl-β-cyclodextrin (HP-βCD). The stability constants for furosemide/HP-βCD and ranitidine HCl/HP-βCD were calculated as 335 M(-1) and 410 M(-1), whereas the association efficiencies (AE%) of the drugs/HP-βCD inclusion complexes with CS-NPs were determined to be 23.0 and 19.5%, respectively. Zetasizer and scanning electron microscopy (SEM) were used to characterise drugs/HP-βCD-NPs size and morphology. Transport of both nano and non-nano formulations of drugs/HP-βCD complexes across a Caco-2 cell monolayer was assessed and fitted to mathematical models. Furosemide/HP-βCD-NPs demonstrated transport kinetics best suited for the Higuchi model, whereas other drug formulations demonstrated power law transportation behaviour. Permeability experiments revealed that furosemide/HP-βCD and ranitidine HCl/HP-βCD nano formulations greatly induce the opening of tight junctions and enhance drug transition through Caco-2 monolayers. Copyright © 2011 Elsevier B.V. All rights reserved.

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,…

Communication patterns in a psychotherapy following traumatic brain injury: A quantitative case study based on symbolic dynamics

PubMed Central

2011-01-01

Background The role of psychotherapy in the treatment of traumatic brain injury is receiving increased attention. The evaluation of psychotherapy with these patients has been conducted largely in the absence of quantitative data concerning the therapy itself. Quantitative methods for characterizing the sequence-sensitive structure of patient-therapist communication are now being developed with the objective of improving the effectiveness of psychotherapy following traumatic brain injury. Methods The content of three therapy session transcripts (sessions were separated by four months) obtained from a patient with a history of several motor vehicle accidents who was receiving dialectical behavior therapy was scored and analyzed using methods derived from the mathematical theory of symbolic dynamics. Results The analysis of symbol frequencies was largely uninformative. When repeated triples were examined a marked pattern of change in content was observed over the three sessions. The context free grammar complexity and the Lempel-Ziv complexity were calculated for each therapy session. For both measures, the rate of complexity generation, expressed as bits per minute, increased longitudinally during the course of therapy. The between-session increases in complexity generation rates are consistent with calculations of mutual information. Taken together these results indicate that there was a quantifiable increase in the variability of patient-therapist verbal behavior during the course of therapy. Comparison of complexity values against values obtained from equiprobable random surrogates established the presence of a nonrandom structure in patient-therapist dialog (P = .002). Conclusions While recognizing that only limited conclusions can be based on a case history, it can be noted that these quantitative observations are consistent with qualitative clinical observations of increases in the flexibility of discourse during therapy. These procedures can be of particular value in the examination of therapies following traumatic brain injury because, in some presentations, these therapies are complicated by deficits that result in subtle distortions of language that produce significant post-injury social impairment. Independently of the mathematical analysis applied to the investigation of therapy-generated symbol sequences, our experience suggests that the procedures presented here are of value in training therapists. PMID:21794113

Mathematical Modeling of Multiphase Filtration in Porous Media with a Chemically Active Skeleton

NASA Astrophysics Data System (ADS)

Khramchenkov, M. G.; Khramchenkov, É. M.

2018-01-01

The authors propose a mathematical model of two-phase filtration that occurs under the conditions of dissolution of a porous medium. The model can be used for joint description of complex chemical-hydrogeomechanical processes that are of frequent occurrence in the oil-and-gas producing and nature conservation practice. As an example, consideration is given to the acidizing of the bottom zone of the injection well of an oil reservoir. Enclosing rocks are represented by carbonates. The phases of the process are an aqueous solution of hydrochloric acid and oil. A software product for computational experiments is developed. For the numerical experiments, use is made of the data on the wells of an actual oil field. Good agreement is obtained between the field data and the calculated data. Numerical experiments with different configurations of the permeability of an oil stratum are conducted.

Heuristic for learning common emitter amplification with bipolar transistors

NASA Astrophysics Data System (ADS)

Staffas, Kjell

2017-11-01

Mathematics in engineering education causes many thresholds in the courses because of the demand of abstract conceptualisation. Electronics depend heavily on more or less complex mathematics. Therefore the concepts of analogue electronics are hard to learn since a great deal of students struggle with the calculations and procedures needed. A survey was done focusing on students' struggle to pass a course in analogue electronics by introducing a top-down perspective and the revised taxonomy of Bloom. From a top-down perspective you can create learning environments from any spot in the taxonomy using a step-by-step approach of the verbs understand and apply. Three textbooks with a top-down perspective on analogue electronics are analysed on the concept of amplifying with a transistor circuit. The study claims issues when losing the top-down perspective to present concepts and procedures of the content to be learned.

A study of stiffness, residual strength and fatigue life relationships for composite laminates

NASA Technical Reports Server (NTRS)

Ryder, J. T.; Crossman, F. W.

1983-01-01

Qualitative and quantitative exploration of the relationship between stiffness, strength, fatigue life, residual strength, and damage of unnotched, graphite/epoxy laminates subjected to tension loading. Clarification of the mechanics of the tension loading is intended to explain previous contradictory observations and hypotheses; to develop a simple procedure to anticipate strength, fatigue life, and stiffness changes; and to provide reasons for the study of more complex cases of compression, notches, and spectrum fatigue loading. Mathematical models are developed based upon analysis of the damage states. Mathematical models were based on laminate analysis, free body type modeling or a strain energy release rate. Enough understanding of the tension loaded case is developed to allow development of a proposed, simple procedure for calculating strain to failure, stiffness, strength, data scatter, and shape of the stress-life curve for unnotched laminates subjected to tension load.

Calculation of spontaneous emission from a V-type three-level atom in photonic crystals using fractional calculus

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

Huang, Chih-Hsien; Hsieh, Wen-Feng; Institute of Electro-Optical Science and Engineering, National Cheng Kung University, 1 Dahsueh Rd., Tainan 701, Taiwan

2011-07-15

Fractional time derivative, an abstract mathematical operator of fractional calculus, is used to describe the real optical system of a V-type three-level atom embedded in a photonic crystal. A fractional kinetic equation governing the dynamics of the spontaneous emission from this optical system is obtained as a fractional Langevin equation. Solving this fractional kinetic equation by fractional calculus leads to the analytical solutions expressed in terms of fractional exponential functions. The accuracy of the obtained solutions is verified through reducing the system into the special cases whose results are consistent with the experimental observation. With accurate physical results and avoidingmore » the complex integration for solving this optical system, we propose fractional calculus with fractional time derivative as a better mathematical method to study spontaneous emission dynamics from the optical system with non-Markovian dynamics.« less

A novel medical information management and decision model for uncertain demand optimization.

PubMed

Bi, Ya

2015-01-01

Accurately planning the procurement volume is an effective measure for controlling the medicine inventory cost. Due to uncertain demand it is difficult to make accurate decision on procurement volume. As to the biomedicine sensitive to time and season demand, the uncertain demand fitted by the fuzzy mathematics method is obviously better than general random distribution functions. To establish a novel medical information management and decision model for uncertain demand optimization. A novel optimal management and decision model under uncertain demand has been presented based on fuzzy mathematics and a new comprehensive improved particle swarm algorithm. The optimal management and decision model can effectively reduce the medicine inventory cost. The proposed improved particle swarm optimization is a simple and effective algorithm to improve the Fuzzy interference and hence effectively reduce the calculation complexity of the optimal management and decision model. Therefore the new model can be used for accurate decision on procurement volume under uncertain demand.

Some aspects of mathematical and chemical modeling of complex chemical processes

NASA Technical Reports Server (NTRS)

Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

1983-01-01

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

Integrating the Design Mathematical Trail in Mathematics Curriculum for the Sixth Grade Student

ERIC Educational Resources Information Center

Tsao, Yea-Ling

2010-01-01

The article focused on the teaching materials of the sixth grade mathematics field and selected four units with the topics of "measurement and actual calculation" of figures and space to design the mathematical trail teaching activities with the characteristics of the school and expect to provide mathematical trail teaching activities for the…

Construction of Mathematical Knowledge Using Graphic Calculators (CAS) in the Mathematics Classroom

ERIC Educational Resources Information Center

Hitt, Fernando

2011-01-01

Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics…

Applying a Conceptual Mini Game for Supporting Simple Mathematical Calculation Skills: Students' Perceptions and Considerations

ERIC Educational Resources Information Center

Panagiotakopoulos, Chris T.

2011-01-01

Mathematics is an area of study that particularly lacks student enthusiasm. Nevertheless, with the help of educational games, any phobias concerning mathematics can be considerably decreased and mathematics can become more appealing. In this study, an educational game addressing mathematics was designed, developed and evaluated by a sample of 33…

Not mathematics Education, not Mathematics education but Mathematics Education

ERIC Educational Resources Information Center

Galbraith, P. L.

1977-01-01

Weaknesses in the initial preparation of school mathematics teachers are proposed. Emphasis is on the underdevelopment of global understanding in lieu of the manipulation of symbols or the performing of complex algorithms. (MN)

Spontaneous knotting of an agitated string.

PubMed

Raymer, Dorian M; Smith, Douglas E

2007-10-16

It is well known that a jostled string tends to become knotted; yet the factors governing the "spontaneous" formation of various knots are unclear. We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyze the knots. Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100%. This behavior differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100% with long, flexible strings. We analyzed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string. Remarkably, almost all were identified as prime knots: 120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed. The relative probability of forming a knot decreased exponentially with minimum crossing number and Möbius energy, mathematical measures of knot complexity. Based on the observation that long, stiff strings tend to form a coiled structure when confined, we propose a simple model to describe the knot formation based on random "braid moves" of the string end. Our model can qualitatively account for the observed distribution of knots and dependence on agitation time and string length.

Strategic development in exact calculation: group and individual differences in four achievement subtypes.

PubMed

Wylie, Judith; Jordan, Julie-Ann; Mulhern, Gerry

2012-09-01

This longitudinal study sought to identify developmental changes in strategy use between 5 and 7 years of age when solving exact calculation problems. Four mathematics and reading achievement subtypes were examined at four time points. Five strategies were considered: finger counting, verbal counting, delayed retrieval, automatic retrieval, and derived fact retrieval. Results provided unique insights into children's strategic development in exact calculation at this early stage. Group analysis revealed relationships between mathematical and/or reading difficulties and strategy choice, shift, and adaptiveness. Use of derived fact retrieval by 7 years of age distinguished children with mathematical difficulties from other achievement subtypes. Analysis of individual differences revealed marked heterogeneity within all subtypes, suggesting (inter alia) no marked qualitative distinction between our two mathematical difficulty subtypes. Copyright © 2012 Elsevier Inc. All rights reserved.

Elaine Hale | NREL

Science.gov Websites

Analysis Center. Areas of Expertise Mathematical modeling, simulation, and optimization of complex Industrial and Applied Mathematics Mathematical Optimization Society Featured Publications Stoll, Brady

Mathematical model of polyethylene pipe bending stress state

NASA Astrophysics Data System (ADS)

Serebrennikov, Anatoly; Serebrennikov, Daniil

2018-03-01

Introduction of new machines and new technologies of polyethylene pipeline installation is usually based on the polyethylene pipe flexibility. It is necessary that existing bending stresses do not lead to an irreversible polyethylene pipe deformation and to violation of its strength characteristics. Derivation of the mathematical model which allows calculating analytically the bending stress level of polyethylene pipes with consideration of nonlinear characteristics is presented below. All analytical calculations made with the mathematical model are experimentally proved and confirmed.

Investigations in Mathematics Education, Vol. 10, No. 4.

ERIC Educational Resources Information Center

Osborne, Alan R., Ed.

Eighteen research reports related to mathematics education are abstracted and analyzed. Four of the reports deal with aspects of learning theory, five with topics in mathematics instruction (history of mathematics, exponents, probability, calculus, and calculators), four with teacher characteristics, and one each with testing, student interests,…

Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners.

PubMed

Mutaf Yıldız, Belde; Sasanguie, Delphine; De Smedt, Bert; Reynvoet, Bert

2018-01-01

Home numeracy has been shown to play an important role in children's mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners' home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners ( M age = 5.43 years, SD = 0.29, range: 4.88-6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved more explicit teaching efforts (i.e., identifying numerals, counting) and children's enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved more implicit teaching attempts , such as "playing games" and "using numbers in daily life," were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities.

Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners

PubMed Central

Mutaf Yıldız, Belde; Sasanguie, Delphine; De Smedt, Bert; Reynvoet, Bert

2018-01-01

Home numeracy has been shown to play an important role in children’s mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners’ home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners (Mage = 5.43 years, SD = 0.29, range: 4.88–6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved more explicit teaching efforts (i.e., identifying numerals, counting) and children’s enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved more implicit teaching attempts, such as “playing games” and “using numbers in daily life,” were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities. PMID:29623055

Symmetrical group theory for mathematical complexity reduction of digital holograms

NASA Astrophysics Data System (ADS)

Perez-Ramirez, A.; Guerrero-Juk, J.; Sanchez-Lara, R.; Perez-Ramirez, M.; Rodriguez-Blanco, M. A.; May-Alarcon, M.

2017-10-01

This work presents the use of mathematical group theory through an algorithm to reduce the multiplicative computational complexity in the process of creating digital holograms. An object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image, where the image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity ( k - 1) × N for the case of sparse matrices and binary images, where k is the number of pixels other than zero and N is the total points in the image.

Dannie Heineman Prize for Mathematical Physics: Applying mathematical techniques to solve important problems in quantum theory

NASA Astrophysics Data System (ADS)

Bender, Carl

2017-01-01

The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.

The Triangle Technique: a new evidence-based educational tool for pediatric medication calculations.

PubMed

Sredl, Darlene

2006-01-01

Many nursing student verbalize an aversion to mathematical concepts and experience math anxiety whenever a mathematical problem is confronted. Since nurses confront mathematical problems on a daily basis, they must learn to feel comfortable with their ability to perform these calculations correctly. The Triangle Technique, a new educational tool available to nurse educators, incorporates evidence-based concepts within a graphic model using visual, auditory, and kinesthetic learning styles to demonstrate pediatric medication calculations of normal therapeutic ranges. The theoretical framework for the technique is presented, as is a pilot study examining the efficacy of the educational tool. Statistically significant results obtained by Pearson's product-moment correlation indicate that students are better able to calculate accurate pediatric therapeutic dosage ranges after participation in the educational intervention of learning the Triangle Technique.

Mathematics in Early Years Education. 3rd Edition

ERIC Educational Resources Information Center

Montague-Smith, Ann; Price, Alison

2012-01-01

This third edition of the best-selling "Mathematics in Nursery Education" provides an accessible introduction to the teaching of mathematics in the early years. Covering all areas of mathematics learning--number and counting, calculation, pattern, shape, measures and data handling--it summarises the research findings and underlying key concepts…

Teaching and Learning Mathematics with Technology. 1997 Yearbook.

ERIC Educational Resources Information Center

Blume, Glendon W., Ed.; Heid, M. Kathleen, Ed.

This yearbook focuses on the role of technology in school mathematics. Chapters are replete with classroom-tested ideas for using technology to teach new mathematical ideas and to teach familiar mathematical ideas better. Chapters included: (1) "Using the Graphing Calculator in the Classroom: Helping Students Solve the "Unsolvable" (Eric Milou,…

The Design of Lessons Using Mathematics Analysis Software to Support Multiple Representations in Secondary School Mathematics

ERIC Educational Resources Information Center

Pierce, Robyn; Stacey, Kaye; Wander, Roger; Ball, Lynda

2011-01-01

Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students' learning requires carefully designed lessons. This paper reports on design…

Time-ordered exponential on the complex plane and Gell-Mann—Low formula as a mathematical theorem

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

Futakuchi, Shinichiro; Usui, Kouta

2016-04-15

The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann—Low formula under certain abstract conditions, in mathematically rigorous manner. We apply the abstract results to quantum electrodynamics with cutoffs.

Calculator-Controlled Robots: Hands-On Mathematics and Science Discovery

ERIC Educational Resources Information Center

Tuchscherer, Tyson

2010-01-01

The Calculator Controlled Robots activities are designed to engage students in hands-on inquiry-based missions. These activities address National science and technology standards, as well as specifically focusing on mathematics content and process standards. There are ten missions and three exploration extensions that provide activities for up to…

Not Just for Computation: Basic Calculators Can Advance the Process Standards

ERIC Educational Resources Information Center

Moss, Laura J.; Grover, Barbara W.

2007-01-01

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

Teaching Mental Computation Strategies in Early Mathematics

ERIC Educational Resources Information Center

Heirdsfield, Ann Margaret

2011-01-01

Mental computation--that is, calculating in the head--is a relatively new topic in mathematics curricula for primary-age children. It is an important skill because it enables children to learn more deeply how numbers work, make decisions about procedures, and create strategies for calculating, thus promoting number sense--a well-developed…

Addressing the United States Navy Need for Software Engineering Education

DTIC Science & Technology

1999-09-01

taught in MA 1996 (5 - 0). Precalculus review, complex numbers and algebra, complex plane, DeMovire’s Theorem, matrix algebra, LU decomposition...This course was designed for the METOC and Combat Systems curricula. PREREQUISITE: Precalculus mathematics. MA1996 MATHEMATICS FOR SCIENTISTS AND...description for MAI995 (5 - 0). This course was designed for the METOC and Combat Systems curricula. PREREQUISITE: Precalculus mathematics. PHYSICS/SYSTEMS

An Investigation of Calculator Use on Employment Tests of Mathematical Ability: Effects on Reliability, Validity, Test Scores, and Speed of Completion

ERIC Educational Resources Information Center

Bing, Mark N.; Stewart, Susan M.; Davison, H. Kristl

2009-01-01

Handheld calculators have been used on the job for more than 30 years, yet the degree to which these devices can affect performance on employment tests of mathematical ability has not been thoroughly examined. This study used a within-subjects research design (N = 167) to investigate the effects of calculator use on test score reliability, test…

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

USGS Publications Warehouse

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

1993-01-01

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

Effecting Affect: Developing a Positive Attitude to Primary Mathematics Learning

ERIC Educational Resources Information Center

Sparrow, Len; Hurst, Chris

2010-01-01

Most adults' attitudes to mathematics come from their experiences of mathematics in school when they were children. Children's mathematical worlds are complex places containing both cognitive and affective elements. One cannot ignore the affective domain if one wishes to understand children's mathematical learning. Teacher education students…

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

ERIC Educational Resources Information Center

Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

2016-01-01

This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

The graphics calculator in mathematics education: A critical review of recent research

NASA Astrophysics Data System (ADS)

Penglase, Marina; Arnold, Stephen

1996-04-01

The graphics calculator, sometimes referred to as the "super calculator," has sparked great interest among mathematics educators. Considered by many to be a tool which has the potential to revolutionise mathematics education, a significant amount of research has been conducted into its effectiveness as a tool for instruction and learning within precalculus and calculus courses, specifically in the study of functions, graphing and modelling. Some results suggest that these devices (a) can facilitate the learning of functions and graphing concepts and the development of spatial visualisation skills; (b) promote mathematical investigation and exploration; and (c) encourage a shift in emphasis from algebraic manipulation and proof to graphical investigation and examination of the relationship between graphical, algebraic and geometric representations. Other studies, however, indicate that there is still a need for manipulative techniques in the learning of function and graphing concepts, that the use of graphics calculators may not facilitate the learning of particular precalculus topics, and that some "de-skilling" may occur, especially among males. It is the contention of this paper, however, that much of the research in this new and important field fails to provide clear guidance or even to inform debate in adequate ways regarding the role of graphics calculators in mathematics teaching and learning. By failing to distinguish the role of the tool from that of the instructional process, many studies reviewed could be more appropriately classified as "program evaluations" rather than as research on the graphics calculator per se. Further, claims regarding the effectiveness of the graphics calculator as a tool for learning frequently fail to recognise that judgments of effectiveness result directly from existing assumptions regarding both assessment practice and student "achievement."

A brief history of the most remarkable numbers e, i and γ in mathematical sciences with applications

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2015-08-01

This paper deals with a brief history of the most remarkable Euler numbers e, i and γ in mathematical sciences. Included are many properties of the constants e, i and γ and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special attention is given to the growth and decay phenomena in many real-world problems including stability and instability of their solutions. Some specific and modern applications of logarithms, complex numbers and complex exponential functions to electrical circuits and mechanical systems are presented with examples. Included are the use of complex numbers and complex functions in the description and analysis of chaos and fractals with the aid of modern computer technology. In addition, the phasor method is described with examples of applications in engineering science. The major focus of this paper is to provide basic information through historical approach to mathematics teaching and learning of the fundamental knowledge and skills required for students and teachers at all levels so that they can understand the concepts of mathematics, and mathematics education in science and technology.

Line integral on engineering mathematics

NASA Astrophysics Data System (ADS)

Wiryanto, L. H.

2018-01-01

Definite integral is a basic material in studying mathematics. At the level of calculus, calculating of definite integral is based on fundamental theorem of calculus, related to anti-derivative, as the inverse operation of derivative. At the higher level such as engineering mathematics, the definite integral is used as one of the calculating tools of line integral. the purpose of this is to identify if there is a question related to line integral, we can use definite integral as one of the calculating experience. The conclusion of this research says that the teaching experience in introducing the relation between both integrals through the engineer way of thinking can motivate and improve students in understanding the material.

Mathematics in the Early Years.

ERIC Educational Resources Information Center

Copley, Juanita V., Ed.

Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…

The TIMSS 1999 Video Study and the Reform of Mathematics Teaching. Invited Commentary.

ERIC Educational Resources Information Center

Cooney, Thomas J.

2003-01-01

The report on the Third International Mathematics and Science Study (TIMSS) Video Study of mathematics teaching demonstrates the complexity of teaching as it provides lessons about conservatism and the role of reform in mathematics teaching. (SLD)

An Examination of the Relationship between Computation, Problem Solving, and Reading

ERIC Educational Resources Information Center

Cormier, Damien C.; Yeo, Seungsoo; Christ, Theodore J.; Offrey, Laura D.; Pratt, Katherine

2016-01-01

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide…

Students' conceptual performance on synthesis physics problems with varying mathematical complexity

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-06-01

A body of research on physics problem solving has focused on single-concept problems. In this study we use "synthesis problems" that involve multiple concepts typically taught in different chapters. We use two types of synthesis problems, sequential and simultaneous synthesis tasks. Sequential problems require a consecutive application of fundamental principles, and simultaneous problems require a concurrent application of pertinent concepts. We explore students' conceptual performance when they solve quantitative synthesis problems with varying mathematical complexity. Conceptual performance refers to the identification, follow-up, and correct application of the pertinent concepts. Mathematical complexity is determined by the type and the number of equations to be manipulated concurrently due to the number of unknowns in each equation. Data were collected from written tasks and individual interviews administered to physics major students (N =179 ) enrolled in a second year mechanics course. The results indicate that mathematical complexity does not impact students' conceptual performance on the sequential tasks. In contrast, for the simultaneous problems, mathematical complexity negatively influences the students' conceptual performance. This difference may be explained by the students' familiarity with and confidence in particular concepts coupled with cognitive load associated with manipulating complex quantitative equations. Another explanation pertains to the type of synthesis problems, either sequential or simultaneous task. The students split the situation presented in the sequential synthesis tasks into segments but treated the situation in the simultaneous synthesis tasks as a single event.

Interesting and Difficult Mathematical Problems: Changing Teachers' Views by Employing Multiple-Solution Tasks

ERIC Educational Resources Information Center

Guberman, Raisa; Leikin, Roza

2013-01-01

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

Learner-Interface Interactions with Mobile-Assisted Learning in Mathematics: Effects on and Relationship with Mathematics Performance

ERIC Educational Resources Information Center

Bringula, Rex P.; Alvarez, John Nikko; Evangelista, Maron Angelo; So, Richard B.

2017-01-01

This study attempted to determine the effects on mathematics performance of learner-interface interaction with mobile-assisted learning in mathematics. It also determined the relationship between these interactions and students' mathematics performance. It revealed that students solved more complex problems as they went through the intervention…

Transfer of Algebraic and Graphical Thinking between Mathematics and Chemistry

ERIC Educational Resources Information Center

Potgieter, Marietjie; Harding, Ansie; Engelbrecht, Johann

2008-01-01

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

Effects of the Application of Graphing Calculator on Students' Probability Achievement

ERIC Educational Resources Information Center

Tan, Choo-Kim

2012-01-01

A Graphing Calculator (GC) is one of the most portable and affordable technology in mathematics education. It quickens the mechanical procedure in solving mathematical problems and creates a highly interactive learning environment, which makes learning a seemingly difficult subject, easy. Since research on the use of GCs for the teaching and…

Fostering Innovation Through Robotics Exploration

DTIC Science & Technology

2015-06-01

16 Jan 09. 13. SUPPLEMENTARY NOTES 14. ABSTRACT This effort enhanced Robotics STEM activities by incorporating Cognitive tutors at key points to...make important mathematical decision or implement critical calculations. Program utilized Cognitive Tutor Authoring tools for designing problem...activities by incorporating cognitive tutors at key points to make important mathematical decision or implement critical calculations. The program

Everything You Always Wanted to Know About the Mathematics of Sex and Family Planning...But Were Afraid to Calculate

ERIC Educational Resources Information Center

Meyer, Rochelle Wilson

1978-01-01

The author uses mathematical models that involve only algebra and a few basic ideas in discrete probability to describe the frequency of conception in large human societies. A number of calculations which can be done by students as exercises are given. (MN)

Basic Mathematics Machine Calculator Course.

ERIC Educational Resources Information Center

Windsor Public Schools, CT.

This series of four text-workbooks was designed for tenth grade mathematics students who have exhibited lack of problem-solving skills. Electric desk calculators are to be used with the text. In the first five chapters of the series, students learn how to use the machine while reviewing basic operations with whole numbers, decimals, fractions, and…

Using Calculators in Mathematics 12. Teacher Commentary.

ERIC Educational Resources Information Center

Rising, Gerald R.; And Others

This teacher's guide is designed to aid in the incorporation of programable calculators in the school mathematics program for pupils in grade 12. Warnings are given, including the need for care in modifying the curriculum so that students are not punished in the process. The concept of "black boxing," of letting the computer or…

Observing Student Working Styles when Using Graphic Calculators to Solve Mathematics Problems

ERIC Educational Resources Information Center

Berry, J.; Graham, E.; Smith, A.

2006-01-01

Some research studies, many of which used quantitative methods, have suggested that graphics calculators can be used to effectively enhance the learning of mathematics. More recently research studies have started to explore students' styles of working as they solve problems with technology. This paper describes the use of a software application…

Can Television Enhance Children's Mathematical Problem Solving?

ERIC Educational Resources Information Center

Fisch, Shalom M.; And Others

1994-01-01

A summative evaluation of "Square One TV," an educational mathematics series produced by the Children's Television Workshop, shows that children who regularly viewed the program showed significant improvement in solving unfamiliar, complex mathematical problems, and viewers showed improvement in their mathematical problem-solving ability…

Professional Noticing: Developing Responsive Mathematics Teaching

ERIC Educational Resources Information Center

Thomas, Jonathan N.; Eisenhardt, Sara; Fisher, Molly H.; Schack, Edna O.; Tassell, Janet; Yoder, Margaret

2014-01-01

Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…

Mathematical models for optimization of the centrifugal stage of a refrigerating compressor

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

Nuzhdin, A.S.

1987-09-01

The authors describe a general approach to the creating of mathematical models of energy and head losses in the flow part of the centrifugal compressor. The mathematical model of the pressure head and efficiency of a two-section stage proposed in this paper is meant for determining its characteristics for the assigned geometric dimensions and for optimizing by variance calculations. Characteristic points on the plot of velocity distribution over the margin of the vanes of the impeller and the diffuser of the centrifugal stage with a combined diffuser are presented. To assess the reliability of the mathematical model the authors comparedmore » some calculated data with the experimental ones.« less

Solving ordinary differential equations by electrical analogy: a multidisciplinary teaching tool

NASA Astrophysics Data System (ADS)

Sanchez Perez, J. F.; Conesa, M.; Alhama, I.

2016-11-01

Ordinary differential equations are the mathematical formulation for a great variety of problems in science and engineering, and frequently, two different problems are equivalent from a mathematical point of view when they are formulated by the same equations. Students acquire the knowledge of how to solve these equations (at least some types of them) using protocols and strict algorithms of mathematical calculation without thinking about the meaning of the equation. The aim of this work is that students learn to design network models or circuits in this way; with simple knowledge of them, students can establish the association of electric circuits and differential equations and their equivalences, from a formal point of view, that allows them to associate knowledge of two disciplines and promote the use of this interdisciplinary approach to address complex problems. Therefore, they learn to use a multidisciplinary tool that allows them to solve these kinds of equations, even students of first course of engineering, whatever the order, grade or type of non-linearity. This methodology has been implemented in numerous final degree projects in engineering and science, e.g., chemical engineering, building engineering, industrial engineering, mechanical engineering, architecture, etc. Applications are presented to illustrate the subject of this manuscript.

Experimental and theoretical research of the interaction between high-strength supercavitation impactors and monolithic barriers in water

NASA Astrophysics Data System (ADS)

Ishchenko, A. N.; Afanas'eva, S. A.; Burkin, V. V.; Diachkovskii, A. S.; Zykova, A. I.; Khabibullin, M. V.; Chupashev, A. V.; Yugov, N. T.

2017-09-01

The article describes experimental and theoretical research of the interaction between supercavitating impactors and underwater aluminum alloy and steel barriers. Strong alloys are used for making impactors. An experimental research technique based on a high-velocity hydro-ballistic complex was developed. Mathematical simulation of the collision the impactor and barrier is based on the continuum mechanics inclusive of the deformation and destruction of interacting bodies. Calculated and experimental data on the ultimate penetration thickness of barriers made of aluminum alloy D16T and steel for the developed supercavitating impactor are obtained.

PREFACE: Counting Complexity: An international workshop on statistical mechanics and combinatorics

NASA Astrophysics Data System (ADS)

de Gier, Jan; Warnaar, Ole

2006-07-01

On 10-15 July 2005 the conference `Counting Complexity: An international workshop on statistical mechanics and combinatorics' was held on Dunk Island, Queensland, Australia in celebration of Tony Guttmann's 60th birthday. Dunk Island provided the perfect setting for engaging in almost all of Tony's life-long passions: swimming, running, food, wine and, of course, plenty of mathematics and physics. The conference was attended by many of Tony's close scientific friends from all over the world, and most talks were presented by his past and present collaborators. This volume contains the proceedings of the meeting and consists of 24 refereed research papers in the fields of statistical mechanics, condensed matter physics and combinatorics. These papers provide an excellent illustration of the breadth and scope of Tony's work. The very first contribution, written by Stu Whittington, contains an overview of the many scientific achievements of Tony over the past 40 years in mathematics and physics. The organizing committee, consisting of Richard Brak, Aleks Owczarek, Jan de Gier, Emma Lockwood, Andrew Rechnitzer and Ole Warnaar, gratefully acknowledges the Australian Mathematical Society (AustMS), the Australian Mathematical Sciences Institute (AMSI), the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), the ARC Complex Open Systems Research Network (COSNet), the Institute of Physics (IOP) and the Department of Mathematics and Statistics of The University of Melbourne for financial support in organizing the conference. Tony, we hope that your future years in mathematics will be numerous. Count yourself lucky! Tony Guttman

La Evolucion del Curriculo de las Matematicas: Un Folleto para los Padres de Familia. (The Changing Mathematics Curriculum: A Booklet for Parents).

ERIC Educational Resources Information Center

California State Dept. of Education, Sacramento.

This booklet, written in Spanish, provides a guide for parents to help their children become successful in school mathematics. The information is divided into four sections: (1) important facts about the mathematics curriculum and mathematics instruction; (2) expectations about participation, calculators, cooperative learning, dialogue, and…

Textbook and Course Materials for 21-127 "Concepts of Mathematics"

ERIC Educational Resources Information Center

Sullivan, Brendan W.

2013-01-01

Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…

The Empathizing-Systemizing Theory, Social Abilities, and Mathematical Achievement in Children

PubMed Central

Escovar, Emily; Rosenberg-Lee, Miriam; Uddin, Lucina Q.; Menon, Vinod

2016-01-01

The Empathizing-Systemizing (E-S) theory describes a profile of traits that have been linked to autism spectrum disorders, and are thought to encompass a continuum that includes typically developing (TD) individuals. Although systemizing is hypothesized to be related to mathematical abilities, empirical support for this relationship is lacking. We examine the link between empathizing and systemizing tendencies and mathematical achievement in 112 TD children (57 girls) to elucidate how socio-cognitive constructs influence early development of mathematical skills. Assessment of mathematical achievement included standardized tests designed to examine calculation skills and conceptual mathematical reasoning. Empathizing and systemizing were assessed using the Combined Empathy Quotient-Child (EQ-C) and Systemizing Quotient-Child (SQ-C). Contrary to our hypothesis, we found that mathematical achievement was not related to systemizing or the discrepancy between systemizing and empathizing. Surprisingly, children with higher empathy demonstrated lower calculation skills. Further analysis using the Social Responsiveness Scale (SRS) revealed that the relationship between EQ-C and mathematical achievement was mediated by social ability rather than autistic behaviors. Finally, social awareness was found to play a differential role in mediating the relationship between EQ-C and mathematical achievement in girls. These results identify empathy, and social skills more generally, as previously unknown predictors of mathematical achievement. PMID:26972835

The Empathizing-Systemizing Theory, Social Abilities, and Mathematical Achievement in Children.

PubMed

Escovar, Emily; Rosenberg-Lee, Miriam; Uddin, Lucina Q; Menon, Vinod

2016-03-14

The Empathizing-Systemizing (E-S) theory describes a profile of traits that have been linked to autism spectrum disorders, and are thought to encompass a continuum that includes typically developing (TD) individuals. Although systemizing is hypothesized to be related to mathematical abilities, empirical support for this relationship is lacking. We examine the link between empathizing and systemizing tendencies and mathematical achievement in 112 TD children (57 girls) to elucidate how socio-cognitive constructs influence early development of mathematical skills. Assessment of mathematical achievement included standardized tests designed to examine calculation skills and conceptual mathematical reasoning. Empathizing and systemizing were assessed using the Combined Empathy Quotient-Child (EQ-C) and Systemizing Quotient-Child (SQ-C). Contrary to our hypothesis, we found that mathematical achievement was not related to systemizing or the discrepancy between systemizing and empathizing. Surprisingly, children with higher empathy demonstrated lower calculation skills. Further analysis using the Social Responsiveness Scale (SRS) revealed that the relationship between EQ-C and mathematical achievement was mediated by social ability rather than autistic behaviors. Finally, social awareness was found to play a differential role in mediating the relationship between EQ-C and mathematical achievement in girls. These results identify empathy, and social skills more generally, as previously unknown predictors of mathematical achievement.

Posing Complex Problems Requiring Multiplicative Thinking Prompts Students to Use Sophisticated Strategies and Build Mathematical Connections

ERIC Educational Resources Information Center

Downton, Ann; Sullivan, Peter

2017-01-01

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated…

Reliability analysis in interdependent smart grid systems

NASA Astrophysics Data System (ADS)

Peng, Hao; Kan, Zhe; Zhao, Dandan; Han, Jianmin; Lu, Jianfeng; Hu, Zhaolong

2018-06-01

Complex network theory is a useful way to study many real complex systems. In this paper, a reliability analysis model based on complex network theory is introduced in interdependent smart grid systems. In this paper, we focus on understanding the structure of smart grid systems and studying the underlying network model, their interactions, and relationships and how cascading failures occur in the interdependent smart grid systems. We propose a practical model for interdependent smart grid systems using complex theory. Besides, based on percolation theory, we also study the effect of cascading failures effect and reveal detailed mathematical analysis of failure propagation in such systems. We analyze the reliability of our proposed model caused by random attacks or failures by calculating the size of giant functioning components in interdependent smart grid systems. Our simulation results also show that there exists a threshold for the proportion of faulty nodes, beyond which the smart grid systems collapse. Also we determine the critical values for different system parameters. In this way, the reliability analysis model based on complex network theory can be effectively utilized for anti-attack and protection purposes in interdependent smart grid systems.

The Unit of Analysis in Mathematics Education: Bridging the Political-Technical Divide?

ERIC Educational Resources Information Center

Ernest, Paul

2016-01-01

Mathematics education is a complex, multi-disciplinary field of study which treats a wide range of diverse but interrelated areas. These include the nature of mathematics, the learning of mathematics, its teaching, and the social context surrounding both the discipline and applications of mathematics itself, as well as its teaching and learning.…

Introduction to a special section on ecohydrology of semiarid environments: Confronting mathematical models with ecosystem complexity

NASA Astrophysics Data System (ADS)

Svoray, Tal; Assouline, Shmuel; Katul, Gabriel

2015-11-01

Current literature provides large number of publications about ecohydrological processes and their effect on the biota in drylands. Given the limited laboratory and field experiments in such systems, many of these publications are based on mathematical models of varying complexity. The underlying implicit assumption is that the data set used to evaluate these models covers the parameter space of conditions that characterize drylands and that the models represent the actual processes with acceptable certainty. However, a question raised is to what extent these mathematical models are valid when confronted with observed ecosystem complexity? This Introduction reviews the 16 papers that comprise the Special Section on Eco-hydrology of Semiarid Environments: Confronting Mathematical Models with Ecosystem Complexity. The subjects studied in these papers include rainfall regime, infiltration and preferential flow, evaporation and evapotranspiration, annual net primary production, dispersal and invasion, and vegetation greening. The findings in the papers published in this Special Section show that innovative mathematical modeling approaches can represent actual field measurements. Hence, there are strong grounds for suggesting that mathematical models can contribute to greater understanding of ecosystem complexity through characterization of space-time dynamics of biomass and water storage as well as their multiscale interactions. However, the generality of the models and their low-dimensional representation of many processes may also be a "curse" that results in failures when particulars of an ecosystem are required. It is envisaged that the search for a unifying "general" model, while seductive, may remain elusive in the foreseeable future. It is for this reason that improving the merger between experiments and models of various degrees of complexity continues to shape the future research agenda.

Exploring Human Growth: Using a Calculator to Integrate Mathematics and Science.

ERIC Educational Resources Information Center

Wandersee, James H.

1992-01-01

Presents integrated activities for mathematics and biology appropriate for various levels from grades five through eight. Explores interesting aspects of human fingernails and hair growth and their mathematical relationship to time. Provides suggestions to integrate the activities with technology. (MDH)

Learning Results from the Viewpoint of Equity: Boys, Girls and Mathematics.

ERIC Educational Resources Information Center

Pehkonen, Erkki

1997-01-01

Explores why girls successful in mathematics choose advanced courses in upper secondary school less than did boys. Analyzes the results of tests and a student questionnaire (N=739) in Finland. Findings indicate that in the case of word problems and calculation without calculators, boys are significantly better than girls. Reports that the boys…

Investigating a Link between Pre-Calculus Students' Uses of Graphing Calculators and Their Understanding of Mathematical Symbols

ERIC Educational Resources Information Center

Kenney, Rachael H.

2014-01-01

This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

Load influence on gear noise. [mathematical model for determining acoustic pressure level as function of load

NASA Technical Reports Server (NTRS)

Merticaru, V.

1974-01-01

An original mathematical model is proposed to derive equations for calculation of gear noise. These equations permit the acoustic pressure level to be determined as a function of load. Application of this method to three parallel gears is reported. The logical calculation scheme is given, as well as the results obtained.

Error Patterns with Fraction Calculations at Fourth Grade as a Function of Students' Mathematics Achievement Status

ERIC Educational Resources Information Center

Schumacher, Robin F.; Malone, Amelia S.

2017-01-01

The goal of this study was to describe fraction-calculation errors among fourth-grade students and to determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low-, average-, or high-achieving). We…

The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

PubMed Central

Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

2016-01-01

The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

Dose conversion coefficients based on the Chinese mathematical phantom and MCNP code for external photon irradiation.

PubMed

Qiu, Rui; Li, Junli; Zhang, Zhan; Liu, Liye; Bi, Lei; Ren, Li

2009-02-01

A set of conversion coefficients from kerma free-in-air to the organ-absorbed dose are presented for external monoenergetic photon beams from 10 keV to 10 MeV based on the Chinese mathematical phantom, a whole-body mathematical phantom model. The model was developed based on the methods of the Oak Ridge National Laboratory mathematical phantom series and data from the Chinese Reference Man and the Reference Asian Man. This work is carried out to obtain the conversion coefficients based on this model, which represents the characteristics of the Chinese population, as the anatomical parameters of the Chinese are different from those of Caucasians. Monte Carlo simulation with MCNP code is carried out to calculate the organ dose conversion coefficients. Before the calculation, the effects from the physics model and tally type are investigated, considering both the calculation efficiency and precision. In the calculation irradiation conditions include anterior-posterior, posterior-anterior, right lateral, left lateral, rotational and isotropic geometries. Conversion coefficients from this study are compared with those recommended in the Publication 74 of International Commission on Radiological Protection (ICRP74) since both the sets of data are calculated with mathematical phantoms. Overall, consistency between the two sets of data is observed and the difference for more than 60% of the data is below 10%. However, significant deviations are also found, mainly for the superficial organs (up to 65.9%) and bone surface (up to 66%). The big difference of the dose conversion coefficients for the superficial organs at high photon energy could be ascribed to kerma approximation for the data in ICRP74. Both anatomical variations between races and the calculation method contribute to the difference of the data for bone surface.

Bilingual Teaching Research and Practice of Complex Function Theory

ERIC Educational Resources Information Center

Ma, Lixin

2011-01-01

Mathematics bilingual teaching is assisted in Chinese with English teaching, and gradually enables students to independently use English to learn, study, reflect and exchange Mathematics. In order to better carry out mathematics teaching, department of mathematics in Dezhou University forms discussion groups and launches bilingual teaching…

Practical modeling approaches for geological storage of carbon dioxide.

PubMed

Celia, Michael A; Nordbotten, Jan M

2009-01-01

The relentless increase of anthropogenic carbon dioxide emissions and the associated concerns about climate change have motivated new ideas about carbon-constrained energy production. One technological approach to control carbon dioxide emissions is carbon capture and storage, or CCS. The underlying idea of CCS is to capture the carbon before it emitted to the atmosphere and store it somewhere other than the atmosphere. Currently, the most attractive option for large-scale storage is in deep geological formations, including deep saline aquifers. Many physical and chemical processes can affect the fate of the injected CO2, with the overall mathematical description of the complete system becoming very complex. Our approach to the problem has been to reduce complexity as much as possible, so that we can focus on the few truly important questions about the injected CO2, most of which involve leakage out of the injection formation. Toward this end, we have established a set of simplifying assumptions that allow us to derive simplified models, which can be solved numerically or, for the most simplified cases, analytically. These simplified models allow calculation of solutions to large-scale injection and leakage problems in ways that traditional multicomponent multiphase simulators cannot. Such simplified models provide important tools for system analysis, screening calculations, and overall risk-assessment calculations. We believe this is a practical and important approach to model geological storage of carbon dioxide. It also serves as an example of how complex systems can be simplified while retaining the essential physics of the problem.

Math Anxiety and Math Ability in Early Primary School Years.

PubMed

Krinzinger, Helga; Kaufmann, Liane; Willmes, Klaus

2009-06-01

Mathematical learning disabilities (MLDs) are often associated with math anxiety, yet until now, very little is known about the causal relations between calculation ability and math anxiety during early primary school years. The main aim of this study was to longitudinally investigate the relationship between calculation ability, self-reported evaluation of mathematics, and math anxiety in 140 primary school children between the end of first grade and the middle of third grade. Structural equation modeling revealed a strong influence of calculation ability and math anxiety on the evaluation of mathematics but no effect of math anxiety on calculation ability or vice versa-contrasting with the frequent clinical reports of math anxiety even in very young MLD children. To summarize, our study is a first step toward a better understanding of the link between math anxiety and math performance in early primary school years performance during typical and atypical courses of development.

Math Anxiety and Math Ability in Early Primary School Years

PubMed Central

Krinzinger, Helga; Kaufmann, Liane; Willmes, Klaus

2010-01-01

Mathematical learning disabilities (MLDs) are often associated with math anxiety, yet until now, very little is known about the causal relations between calculation ability and math anxiety during early primary school years. The main aim of this study was to longitudinally investigate the relationship between calculation ability, self-reported evaluation of mathematics, and math anxiety in 140 primary school children between the end of first grade and the middle of third grade. Structural equation modeling revealed a strong influence of calculation ability and math anxiety on the evaluation of mathematics but no effect of math anxiety on calculation ability or vice versa—contrasting with the frequent clinical reports of math anxiety even in very young MLD children. To summarize, our study is a first step toward a better understanding of the link between math anxiety and math performance in early primary school years performance during typical and atypical courses of development. PMID:20401159

Thinking the Unthinkable: The Story of Complex Numbers (with a Moral).

ERIC Educational Resources Information Center

Kleiner, Israel

1988-01-01

The evolution of complex numbers is described, followed by discussion of some lessons that can be learned from this story, as with other stories from the history of mathematics. Suggestions for teachers about incorporating history into mathematics instruction are included. (MNS)

On The Computational Capabilities of Physical Systems. Part 2; Relationship With Conventional Computer Science

NASA Technical Reports Server (NTRS)

Wolpert, David H.; Koga, Dennis (Technical Monitor)

2000-01-01

In the first of this pair of papers, it was proven that there cannot be a physical computer to which one can properly pose any and all computational tasks concerning the physical universe. It was then further proven that no physical computer C can correctly carry out all computational tasks that can be posed to C. As a particular example, this result means that no physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly "processing information faster than the universe does". These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - "physical computation" - is needed to address the issues considered in these papers, which concern real physical computers. While this novel definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. This second paper of the pair presents a preliminary exploration of some of this mathematical structure. Analogues of Chomskian results concerning universal Turing Machines and the Halting theorem are derived, as are results concerning the (im)possibility of certain kinds of error-correcting codes. In addition, an analogue of algorithmic information complexity, "prediction complexity", is elaborated. A task-independent bound is derived on how much the prediction complexity of a computational task can differ for two different reference universal physical computers used to solve that task, a bound similar to the "encoding" bound governing how much the algorithm information complexity of a Turing machine calculation can differ for two reference universal Turing machines. Finally, it is proven that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity), in that there is one and only version of it that can be applicable throughout our universe.

Envisioning migration: Mathematics in both experimental analysis and modeling of cell behavior

PubMed Central

Zhang, Elizabeth R.; Wu, Lani F.; Altschuler, Steven J.

2013-01-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution—potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. PMID:23660413

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.

PubMed

Zhang, Elizabeth R; Wu, Lani F; Altschuler, Steven J

2013-10-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. Copyright © 2013 Elsevier Ltd. All rights reserved.

A Case against Computer Symbolic Manipulation in School Mathematics Today.

ERIC Educational Resources Information Center

Waits, Bert K.; Demana, Franklin

1992-01-01

Presented are two reasons discouraging computer symbol manipulation systems use in school mathematics at present: cost for computer laboratories or expensive pocket computers; and impracticality of exact solution representations. Although development with this technology in mathematics education advances, graphing calculators are recommended to…

The Mathematics of the Return from Home Ownership.

ERIC Educational Resources Information Center

Vest, Floyd; Griffith, Reynolds

1991-01-01

A mathematical model or project analysis that calculates the financial return from home ownership is described. This analysis illustrates topics such as compound interest, annuities, amortization schedules, internal rate of return, and other elements of school and college mathematics up through numerical analysis. (KR)

Graphing Calculators as Tools

ERIC Educational Resources Information Center

Browning, Christine A.; Garza-Kling, Gina

2010-01-01

Middle school mathematics classrooms are changing. The curriculum has changed as well. Instead of an annual return to previously encountered topics, many middle school students encounter mathematics of a varying nature, characterized in "Principles and Standards for School Mathematics" (NCTM 2000) as the five Content Standards of Number and…

How Young Students Communicate Their Mathematical Problem Solving in Writing

ERIC Educational Resources Information Center

Teledahl, Anna

2017-01-01

This study investigates young students' writing in connection to mathematical problem solving. Students' written communication has traditionally been used by mathematics teachers in the assessment of students' mathematical knowledge. This study rests on the notion that this writing represents a particular activity which requires a complex set of…

Mathematics, Programming, and STEM

ERIC Educational Resources Information Center

Yeh, Andy; Chandra, Vinesh

2015-01-01

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10- week teaching experiment, mathematical meaning-making was enriched when primary…

Shifting more than the goal posts: developing classroom norms of inquiry-based learning in mathematics

NASA Astrophysics Data System (ADS)

Makar, Katie; Fielding-Wells, Jill

2018-03-01

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, "How do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?" The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers' progressive development of classroom norms of mathematical inquiry and how they facilitate learning.

Mathematical modeling of tomographic scanning of cylindrically shaped test objects

NASA Astrophysics Data System (ADS)

Kapranov, B. I.; Vavilova, G. V.; Volchkova, A. V.; Kuznetsova, I. S.

2018-05-01

The paper formulates mathematical relationships that describe the length of the radiation absorption band in the test object for the first generation tomographic scan scheme. A cylindrically shaped test object containing an arbitrary number of standard circular irregularities is used to perform mathematical modeling. The obtained mathematical relationships are corrected with respect to chemical composition and density of the test object material. The equations are derived to calculate the resulting attenuation radiation from cobalt-60 isotope when passing through the test object. An algorithm to calculate the radiation flux intensity is provided. The presented graphs describe the dependence of the change in the γ-quantum flux intensity on the change in the radiation source position and the scanning angle of the test object.

Launching Complex Tasks

ERIC Educational Resources Information Center

Jackson, Kara J.; Shahan, Emily C.; Gibbons, Lynsey K.; Cobb, Paul A.

2012-01-01

Mathematics lessons can take a variety of formats. In this article, the authors discuss lessons organized around complex mathematical tasks. These lessons usually unfold in three phases. First, the task is introduced to students. Second, students work on solving the task. Third, the teacher "orchestrates" a concluding whole-class discussion in…

Preliminary evaluation of cryogenic two-phase flow imaging using electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Xie, Huangjun; Yu, Liu; Zhou, Rui; Qiu, Limin; Zhang, Xiaobin

2017-09-01

The potential application of the 2-D eight-electrode electrical capacitance tomography (ECT) to the inversion imaging of the liquid nitrogen-vaporous nitrogen (LN2-VN2) flow in the tube is theoretically evaluated. The phase distribution of the computational domain is obtained using the simultaneous iterative reconstruction technique with variable iterative step size. The detailed mathematical derivations for the calculations are presented. The calculated phase distribution for the two detached LN2 column case shows the comparable results with the water-air case, regardless of the much reduced dielectric permittivity of LN2 compared with water. The inversion images of total eight different LN2-VN2 flow patterns are presented and quantitatively evaluated by calculating the relative void fraction error and the correlation coefficient. The results demonstrate that the developed reconstruction technique for ECT has the capacity to reconstruct the phase distribution of the complex LN2-VN2 flow, while the accuracy of the inversion images is significantly influenced by the size of the discrete phase. The influence of the measurement noise on the image quality is also considered in the calculations.

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

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

Le Hardy, D.; Favennec, Y., E-mail: yann.favennec@univ-nantes.fr; Rousseau, B.

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken intomore » account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.« less

Mathematical problems in children with developmental coordination disorder.

PubMed

Pieters, Stefanie; Desoete, Annemie; Van Waelvelde, Hilde; Vanderswalmen, Ruth; Roeyers, Herbert

2012-01-01

Developmental coordination disorder (DCD) is a heterogeneous disorder, which is often co-morbid with learning disabilities. However, mathematical problems have rarely been studied in DCD. The aim of this study was to investigate the mathematical problems in children with various degrees of motor problems. Specifically, this study explored if the development of mathematical skills in children with DCD is delayed or deficient. Children with DCD performed significantly worse for number fact retrieval and procedural calculation in comparison with age-matched control children. Moreover, children with mild DCD differed significantly from children with severe DCD on both number fact retrieval and procedural calculation. In addition, we found a developmental delay of 1 year for number fact retrieval in children with mild DCD and a developmental delay of 2 years in children with severe DCD. No evidence for a mathematical deficit was found. Diagnostic implications are discussed. Copyright © 2012 Elsevier Ltd. All rights reserved.

Error Patterns with Fraction Calculations at Fourth Grade as a Function of Students' Mathematics Achievement Status

ERIC Educational Resources Information Center

Schumacher, Robin F.; Malone, Amelia S.

2017-01-01

The goal of the present study was to describe fraction-calculation errors among 4th-grade students and determine whether error patterns differed as a function of problem type (addition vs. subtraction; like vs. unlike denominators), orientation (horizontal vs. vertical), or mathematics-achievement status (low- vs. average- vs. high-achieving). We…

System for corrosion monitoring in pipeline applying fuzzy logic mathematics

NASA Astrophysics Data System (ADS)

Kuzyakov, O. N.; Kolosova, A. L.; Andreeva, M. A.

2018-05-01

A list of factors influencing corrosion rate on the external side of underground pipeline is determined. Principles of constructing a corrosion monitoring system are described; the system performance algorithm and program are elaborated. A comparative analysis of methods for calculating corrosion rate is undertaken. Fuzzy logic mathematics is applied to reduce calculations while considering a wider range of corrosion factors.

The Mathematics of Motion, Sensors, and the Introduction of Function to Eight Graders in Brazil.

ERIC Educational Resources Information Center

Borba, Marcelo C.; Scheffer, Nilce Fatima

This paper describes how 8th grade students are using CBR, a motion detector linked to a graphing calculator, as a way of generating mathematical ideas regarding the motions concepts that surround their action. Students were previously introduced to the calculators in the classroom and teaching experiments were then carried out afterwards with a…

Aberrant Functional Activation in School Age Children At-Risk for Mathematical Disability: A Functional Imaging Study of Simple Arithmetic Skill

ERIC Educational Resources Information Center

Davis, Nicole; Cannistraci, Christopher J.; Rogers, Baxter P.; Gatenby, J. Christopher; Fuchs, Lynn S.; Anderson, Adam W.; Gore, John C.

2009-01-01

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same…

Investigating Zimbabwean Mathematics Teachers' Dispositions on the "O" Level Calculator Syllabus 4028

ERIC Educational Resources Information Center

Nyaumwe, Lovemore

2006-01-01

The questionnaire responses of 38 secondary school mathematics teachers provided initial data for this study. About 26.3% (n = 10) of this number was sampled for classroom observation and in-depth interviews in order to assess the consistency of the dispositions. Only 15.8% of the schools in the study adopted the calculator version of the…

A Correlational Study between Teachers' Use of Calculators and Student Achievement

ERIC Educational Resources Information Center

Jacobs-Miller, Reba

2013-01-01

There is a lack of achievement among 7th grade mathematics students in the United States and a lack of technology use in the 7 th grade classroom. The purpose of this correlational study was to determine the relationship between teachers' use of calculators in Grade 7 mathematics instruction, the independent variable, and student achievement…

Commercially Available Digital Game Technology in the Classroom: Improving Automaticity in Mental-Maths in Primary-Aged Students

ERIC Educational Resources Information Center

O'Rourke, John; Main, Susan; Hill, Susan M.

2017-01-01

In this paper we report on a study of the implementation of handheld game consoles (HGCs) in 10 Year four/five classrooms to develop student automaticity of mathematical calculations. The automaticity of mathematical calculations was compared for those students using the HGC and those being taught using traditional teaching methods. Over a school…

Mutual Calculations in Creating Accounting Models: A Demonstration of the Power of Matrix Mathematics in Accounting Education

ERIC Educational Resources Information Center

Vysotskaya, Anna; Kolvakh, Oleg; Stoner, Greg

2016-01-01

The aim of this paper is to describe the innovative teaching approach used in the Southern Federal University, Russia, to teach accounting via a form of matrix mathematics. It thereby contributes to disseminating the technique of teaching to solve accounting cases using mutual calculations to a worldwide audience. The approach taken in this course…

Surface-Height Determination of Crevassed Glaciers-Mathematical Principles of an Autoadaptive Density-Dimension Algorithm and Validation Using ICESat-2 Simulator (SIMPL) Data

NASA Technical Reports Server (NTRS)

Herzfeld, Ute C.; Trantow, Thomas M.; Harding, David; Dabney, Philip W.

2017-01-01

Glacial acceleration is a main source of uncertainty in sea-level-change assessment. Measurement of ice-surface heights with a spatial and temporal resolution that not only allows elevation-change calculation, but also captures ice-surface morphology and its changes is required to aid in investigations of the geophysical processes associated with glacial acceleration.The Advanced Topographic Laser Altimeter System aboard NASAs future ICESat-2 Mission (launch 2017) will implement multibeam micropulse photon-counting lidar altimetry aimed at measuring ice-surface heights at 0.7-m along-track spacing. The instrument is designed to resolve spatial and temporal variability of rapidly changing glaciers and ice sheets and the Arctic sea ice. The new technology requires the development of a new mathematical algorithm for the retrieval of height information.We introduce the density-dimension algorithm (DDA) that utilizes the radial basis function to calculate a weighted density as a form of data aggregation in the photon cloud and considers density an additional dimension as an aid in auto-adaptive threshold determination. The auto-adaptive capability of the algorithm is necessary to separate returns from noise and signal photons under changing environmental conditions. The algorithm is evaluated using data collected with an ICESat-2 simulator instrument, the Slope Imaging Multi-polarization Photon-counting Lidar, over the heavily crevassed Giesecke Braer in Northwestern Greenland in summer 2015. Results demonstrate that ICESat-2 may be expected to provide ice-surface height measurements over crevassed glaciers and other complex ice surfaces. The DDA is generally applicable for the analysis of airborne and spaceborne micropulse photon-counting lidar data over complex and simple surfaces.

Coalescent: an open-source and scalable framework for exact calculations in coalescent theory

PubMed Central

2012-01-01

Background Currently, there is no open-source, cross-platform and scalable framework for coalescent analysis in population genetics. There is no scalable GUI based user application either. Such a framework and application would not only drive the creation of more complex and realistic models but also make them truly accessible. Results As a first attempt, we built a framework and user application for the domain of exact calculations in coalescent analysis. The framework provides an API with the concepts of model, data, statistic, phylogeny, gene tree and recursion. Infinite-alleles and infinite-sites models are considered. It defines pluggable computations such as counting and listing all the ancestral configurations and genealogies and computing the exact probability of data. It can visualize a gene tree, trace and visualize the internals of the recursion algorithm for further improvement and attach dynamically a number of output processors. The user application defines jobs in a plug-in like manner so that they can be activated, deactivated, installed or uninstalled on demand. Multiple jobs can be run and their inputs edited. Job inputs are persisted across restarts and running jobs can be cancelled where applicable. Conclusions Coalescent theory plays an increasingly important role in analysing molecular population genetic data. Models involved are mathematically difficult and computationally challenging. An open-source, scalable framework that lets users immediately take advantage of the progress made by others will enable exploration of yet more difficult and realistic models. As models become more complex and mathematically less tractable, the need for an integrated computational approach is obvious. Object oriented designs, though has upfront costs, are practical now and can provide such an integrated approach. PMID:23033878

Model of coordination melting of crystals and anisotropy of physical and chemical properties of the surface

NASA Astrophysics Data System (ADS)

Bokarev, Valery P.; Krasnikov, Gennady Ya

2018-02-01

Based on the evaluation of the properties of crystals, such as surface energy and its anisotropy, the surface melting temperature, the anisotropy of the work function of the electron, and the anisotropy of adsorption, were shown the advantages of the model of coordination melting (MCM) in calculating the surface properties of crystals. The model of coordination melting makes it possible to calculate with an acceptable accuracy the specific surface energy of the crystals, the anisotropy of the surface energy, the habit of the natural crystals, the temperature of surface melting of the crystal, the anisotropy of the electron work function and the anisotropy of the adhesive properties of single-crystal surfaces. The advantage of our model is the simplicity of evaluating the surface properties of the crystal based on the data given in the reference literature. In this case, there is no need for a complex mathematical tool, which is used in calculations using quantum chemistry or modeling by molecular dynamics.

Mathematical modeling of physiological systems: an essential tool for discovery.

PubMed

Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

21st Century Mathematics

ERIC Educational Resources Information Center

Seeley, Cathy

2004-01-01

This article addresses some important issues in mathematics instruction at the middle and secondary levels, including the structuring of a district's mathematics program; the choice of textbooks and use of calculators in the classroom; the need for more rigorous lesson planning practices; and the dangers of teaching to standardized tests rather…

Mathematics Learning Development: The Role of Long-Term Retrieval

ERIC Educational Resources Information Center

Calderón-Tena, Carlos O.; Caterino, Linda C.

2016-01-01

This study assessed the relation between long-term memory retrieval and mathematics calculation and mathematics problem solving achievement among elementary, middle, and high school students in nationally representative sample of US students, when controlling for fluid and crystallized intelligence, short-term memory, and processing speed. As…

A Mathematical Mystery Tour: Higher-Thinking Math Tasks.

ERIC Educational Resources Information Center

Wahl, Mark

This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…

Calculating Puddle Size

ERIC Educational Resources Information Center

Burton, Megan; Mims, Patricia

2012-01-01

Learning through meaningful problem solving is integral in any successful mathematics program (Carpenter et al. 1999). The National Council of Teachers of Mathematics (NCTM) promotes the use of problem solving as a means to deepen understanding of all content areas within mathematics (NCTM 2000). This article describes a first-grade lesson that…

A Conceptual Approach to Absolute Value Equations and Inequalities

ERIC Educational Resources Information Center

Ellis, Mark W.; Bryson, Janet L.

2011-01-01

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

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

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

Inconclusive quantum measurements and decisions under uncertainty

NASA Astrophysics Data System (ADS)

Yukalov, Vyacheslav; Sornette, Didier

2016-04-01

We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.

Parametric Transformation Analysis

NASA Technical Reports Server (NTRS)

Gary, G. Allan

2003-01-01

Because twisted coronal features are important proxies for predicting solar eruptive events, and, yet not clearly understood, we present new results to resolve the complex, non-potential magnetic field configurations of active regions. This research uses free-form deformation mathematics to generate the associated coronal magnetic field. We use a parametric representation of the magnetic field lines such that the field lines can be manipulated to match the structure of EUV and SXR coronal loops. The objective is to derive sigmoidal magnetic field solutions which allows the beta greater than 1 regions to be included, aligned and non-aligned electric currents to be calculated, and the Lorentz force to be determined. The advantage of our technique is that the solution is independent of the unknown upper and side boundary conditions, allows non-vanishing magnetic forces, and provides a global magnetic field solution, which contains high- and low-beta regimes and is consistent with all the coronal images of the region. We show that the mathematical description is unique and physical.

Remote sensing observations for monitoring and mathematical simulations of transboundary air pollutants migration from Siberian mass wildfires to Kazakhstan

NASA Astrophysics Data System (ADS)

Kaipov, I. V.

2017-03-01

Anthropogenic and natural factors have increased the power of wildfires in massive Siberian woodlands. As a consequence, the expansion of burned areas and increase in the duration of the forest fire season have led to the release of significant amounts of gases and aerosols. Therefore, it is important to understand the impact of wildland fires on air quality, atmospheric composition, climate and accurately describe the distribution of combustion products in time and space. The most effective research tool is the regional hydrodynamic model of the atmosphere, coupled with the model of pollutants transport and chemical interaction. Taking into account the meteorological parameters and processes of chemical interaction of impurities, complex use of remote sensing techniques for monitoring massive forest fires and mathematical modeling of long-range transport of pollutants in the atmosphere, allow to evaluate spatial and temporal scale of the phenomenon and calculate the quantitative characteristics of pollutants depending on the height and distance of migration.

Addressing the Mathematics-Specific Needs of Beginning Mathematics Teachers

ERIC Educational Resources Information Center

Britton, Edward

2012-01-01

Beginning mathematics teachers at the secondary level (middle and high school grades) have mathematics-specific needs that induction programs should address more substantially. However, a number of issues in how programs can accomplish this are more complex than often framed in discussions occurring in the induction programs and the field of…

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.

Identifying Systems of Interaction in Mathematical Engagement

ERIC Educational Resources Information Center

Brown, Bruce J. L.

2014-01-01

Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed…

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

ERIC Educational Resources Information Center

Dündar, Sefa

2015-01-01

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

Linguistic Challenges in the Mathematical Register for EFL Learners: Linguistic and Multimodal Strategies to Help Learners Tackle Mathematics Word Problems

ERIC Educational Resources Information Center

Chan, Simon

2015-01-01

In learning mathematics through English, one of the major challenges facing English as a Foreign Language (EFL) learners is understanding the language used to present word problems in mathematics texts. Without comprehending such language, learners are not able to carry out the targeted calculations no matter how familiar they are with the…

What Are We Afraid of? Arguments against Teaching Mathematics with Technology in the Professional Publications of Organisations for US Mathematicians

ERIC Educational Resources Information Center

Risser, Hilary Smith

2011-01-01

More than twenty years after the introduction of the first handheld graphing calculator the mathematics community appears to still be struggling with the use of technology in the teaching and learning of mathematics. One major venue for arguments against technology use in the teaching and learning of mathematics is the news magazines of…

Three-dimensional description and mathematical characterization of the parasellar internal carotid artery in human infants

PubMed Central

Meng, Stefan; da F Costa, Luciano; Geyer, Stefan H; Viana, Matheus P; Reiter, Christian; Müller, Gerd B; Weninger, Wolfgang J

2008-01-01

Inside the ‘cavernous sinus’ or ‘parasellar region’ the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery. PMID:18397239

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

ERIC Educational Resources Information Center

Boaler, Jo

1994-01-01

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

Learning to Teach Mathematics with Technology: A Survey of Professional Development Needs, Experiences and Impacts

ERIC Educational Resources Information Center

Bennison, Anne; Goos, Merrilyn

2010-01-01

The potential for digital technologies to enhance students' mathematics learning is widely recognised, and use of computers and graphics calculators is now encouraged or required by secondary school mathematics curriculum documents throughout Australia. However, previous research indicates that effective integration of technology into classroom…

Educational Play: Mathematics. Games and Activities To Stimulate Your Child in Mathematics.

ERIC Educational Resources Information Center

Valentine, Deborah

This book, written for parents, presents short mathematics activities for use with young children. Most chapters contain an overview, educational objectives, needed materials, an estimate of initial time investment, introduction and preparation instructions, and activities. Activities are grouped as follows: kitchen math, calculators, measurement,…

Teaching Children with Down Syndrome in Inclusive Primary Mathematics Classrooms

ERIC Educational Resources Information Center

Faragher, Rhonda; Stratford, Melanie; Clarke, Barbara

2017-01-01

At the turn of this century, expectations for learning mathematics by students with Down syndrome were low. Research and practice continued to indicate considerable difficulty with number and calculation (Bird & Buckley, 2001). Unfortunately, most authors extrapolated difficulty with number to difficulty with mathematics in general, even…

Design principles for cancer therapy guided by changes in complexity of protein-protein interaction networks.

PubMed

Benzekry, Sebastian; Tuszynski, Jack A; Rietman, Edward A; Lakka Klement, Giannoula

2015-05-28

The ever-increasing expanse of online bioinformatics data is enabling new ways to, not only explore the visualization of these data, but also to apply novel mathematical methods to extract meaningful information for clinically relevant analysis of pathways and treatment decisions. One of the methods used for computing topological characteristics of a space at different spatial resolutions is persistent homology. This concept can also be applied to network theory, and more specifically to protein-protein interaction networks, where the number of rings in an individual cancer network represents a measure of complexity. We observed a linear correlation of R = -0.55 between persistent homology and 5-year survival of patients with a variety of cancers. This relationship was used to predict the proteins within a protein-protein interaction network with the most impact on cancer progression. By re-computing the persistent homology after computationally removing an individual node (protein) from the protein-protein interaction network, we were able to evaluate whether such an inhibition would lead to improvement in patient survival. The power of this approach lied in its ability to identify the effects of inhibition of multiple proteins and in the ability to expose whether the effect of a single inhibition may be amplified by inhibition of other proteins. More importantly, we illustrate specific examples of persistent homology calculations, which correctly predict the survival benefit observed effects in clinical trials using inhibitors of the identified molecular target. We propose that computational approaches such as persistent homology may be used in the future for selection of molecular therapies in clinic. The technique uses a mathematical algorithm to evaluate the node (protein) whose inhibition has the highest potential to reduce network complexity. The greater the drop in persistent homology, the greater reduction in network complexity, and thus a larger potential for survival benefit. We hope that the use of advanced mathematics in medicine will provide timely information about the best drug combination for patients, and avoid the expense associated with an unsuccessful clinical trial, where drug(s) did not show a survival benefit.

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

McKemmish, Laura K., E-mail: laura.mckemmish@gmail.com; Research School of Chemistry, Australian National University, Canberra

Algorithms for the efficient calculation of two-electron integrals in the newly developed mixed ramp-Gaussian basis sets are presented, alongside a Fortran90 implementation of these algorithms, RAMPITUP. These new basis sets have significant potential to (1) give some speed-up (estimated at up to 20% for large molecules in fully optimised code) to general-purpose Hartree-Fock (HF) and density functional theory quantum chemistry calculations, replacing all-Gaussian basis sets, and (2) give very large speed-ups for calculations of core-dependent properties, such as electron density at the nucleus, NMR parameters, relativistic corrections, and total energies, replacing the current use of Slater basis functions or verymore » large specialised all-Gaussian basis sets for these purposes. This initial implementation already demonstrates roughly 10% speed-ups in HF/R-31G calculations compared to HF/6-31G calculations for large linear molecules, demonstrating the promise of this methodology, particularly for the second application. As well as the reduction in the total primitive number in R-31G compared to 6-31G, this timing advantage can be attributed to the significant reduction in the number of mathematically complex intermediate integrals after modelling each ramp-Gaussian basis-function-pair as a sum of ramps on a single atomic centre.« less

Colloquium: Fractional calculus view of complexity: A tutorial

NASA Astrophysics Data System (ADS)

West, Bruce J.

2014-10-01

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Effects of Using a Computer Algebra System (CAS) on Junior College Students' Attitudes towards CAS and Achievement in Mathematics

ERIC Educational Resources Information Center

Leng, Ng Wee; Choo, Kwee Tiow; Soon, Lau Hock; Yi-Huak, Koh; Sun, Yap Yew

2005-01-01

This study examines the effects of using Texas Instruments' Voyage 200 calculator (V200), a graphing calculator with a built-in computer algebra system (CAS), on attitudes towards CAS and achievement in mathematics of junior college students (17 year olds). Students' attitudes towards CAS were examined using a 40-item Likert-type instrument…

Developing a Highly Active Blood Anticoagulant—a Heparin Complex with Glutamic Acid—by Simulating Chemical Equilibria Based on pH-Metric Data

NASA Astrophysics Data System (ADS)

Nikolaeva, L. S.; Semenov, A. N.

2018-02-01

The anticoagulant activity of high-molecular-weight heparin is increased by developing a new highly active heparin complex with glutamate using the thermodynamic model of chemical equilibria based on pH-metric data. The anticoagulant activity of the developed complexes is estimated in the pH range of blood plasma according to the drop in the calculated equilibrium Ca2+ concentration associated with the formation of mixed ligand complexes of Ca2+ ions, heparin (Na4hep), and glutamate (H2Glu). A thermodynamic model is calculated by mathematically modelling chemical equilibria in the CaCl2-Na4hep-H2Glu-H2O-NaCl system in the pH range of 2.30 ≤ pH ≤ 10.50 in diluted saline that acts as a background electrolyte (0.154 M NaCl) at 37°C and initial concentrations of the main components of ν × 10-3 M, where n ≤ 4. The thermodynamic model is used to determine the main complex of the monomeric unit of heparin with glutamate (HhepGlu5-) and the most stable mixed ligand complex of Ca2+ with heparin and glutamate (Ca2hepGlu2-) in the pH range of blood plasma (6.80 ≤ pH ≤ 7.40). It is concluded that the Ca2hepGlu2- complex reduces the Ca2+ concentration 107 times more than the Ca2+ complex with pure heparin. The anticoagulant effect of the developed HhepGlu5- complex is confirmed in vitro and in vivo via coagulation tests on the blood plasma of laboratory rats. Additional antithrombotic properties of the developed complex are identified. The new highly active anticoagulant, HhepGlu5- complex with additional antithrombotic properties, is patented.

The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge.

PubMed

Fuchs, Lynn S; Gilbert, Jennifer K; Powell, Sarah R; Cirino, Paul T; Fuchs, Douglas; Hamlett, Carol L; Seethaler, Pamela M; Tolar, Tammy D

2016-12-01

The purpose of this study was to examine child-level pathways in development of prealgebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of Grade 2; calculation accuracy and calculation fluency at end of Grade 2; and prealgebraic knowledge and word-problem solving at end of Grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than prealgebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students' foundational mathematics skills or cognitive processes. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

WAVDRAG- ZERO-LIFT WAVE DRAG OF COMPLEX AIRCRAFT CONFIGURATIONS

NASA Technical Reports Server (NTRS)

Craidon, C. B.

1994-01-01

WAVDRAG calculates the supersonic zero-lift wave drag of complex aircraft configurations. The numerical model of an aircraft is used throughout the design process from concept to manufacturing. WAVDRAG incorporates extended geometric input capabilities to permit use of a more accurate mathematical model. With WAVDRAG, the engineer can define aircraft components as fusiform or nonfusiform in terms of non-intersecting contours in any direction or more traditional parallel contours. In addition, laterally asymmetric configurations can be simulated. The calculations in WAVDRAG are based on Whitcomb's area-rule computation of equivalent-bodies, with modifications for supersonic speed. Instead of using a single equivalent-body, WAVDRAG calculates a series of equivalent-bodies, one for each roll angle. The total aircraft configuration wave drag is the integrated average of the equivalent-body wave drags through the full roll range of 360 degrees. WAVDRAG currently accepts up to 30 user-defined components containing a maximum of 50 contours as geometric input. Each contour contains a maximum of 50 points. The Mach number, angle-of-attack, and coordinates of angle-of-attack rotation are also input. The program warns of any fusiform-body line segments having a slope larger than the Mach angle. WAVDRAG calculates total drag and the wave-drag coefficient of the specified aircraft configuration. WAVDRAG is written in FORTRAN 77 for batch execution and has been implemented on a CDC CYBER 170 series computer with a central memory requirement of approximately 63K (octal) of 60 bit words. This program was developed in 1983.

A mathematical applications into the cells.

PubMed

Tiwari, Manjul

2012-01-01

Biology has become the new "physics" of mathematics, one of the areas of greatest mathematical applications. In turn, mathematics has provided powerful tools and metaphors to approach the astonishing complexity of biological systems. This has allowed the development of sound theoretical frameworks. Here, in this review article, some of the most significant contributions of mathematics to biology, ranging from population genetics, to developmental biology, and to networks of species interactions are summarized.

The transition to formal thinking in mathematics

NASA Astrophysics Data System (ADS)

Tall, David

2008-09-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and mathematical proof. In this paper, the transition in thinking is formulated within a framework of `three worlds of mathematics'- the `conceptual-embodied' world based on perception, action and thought experiment, the `proceptual-symbolic' world of calculation and algebraic manipulation compressing processes such as counting into concepts such as number, and the `axiomatic-formal' world of set-theoretic concept definitions and mathematical proof. Each `world' has its own sequence of development and its own forms of proof that may be blended together to give a rich variety of ways of thinking mathematically. This reveals mathematical thinking as a blend of differing knowledge structures; for instance, the real numbers blend together the embodied number line, symbolic decimal arithmetic and the formal theory of a complete ordered field. Theoretical constructs are introduced to describe how genetic structures set before birth enable the development of mathematical thinking, and how experiences that the individual has met before affect their personal growth. These constructs are used to consider how students negotiate the transition from school to university mathematics as embodiment and symbolism are blended with formalism. At a higher level, structure theorems proved in axiomatic theories link back to more sophisticated forms of embodiment and symbolism, revealing the intimate relationship between the three worlds.

Search for promising compositions for developing new multiphase casting alloys based on Al-Cu-Mg matrix using thermodynamic calculations and mathematic simulation

NASA Astrophysics Data System (ADS)

Zolotorevskii, V. S.; Pozdnyakov, A. V.; Churyumov, A. Yu.

2012-11-01

A calculation-experimental study is carried out to improve the concept of searching for new alloying systems in order to develop new casting alloys using mathematical simulation methods in combination with thermodynamic calculations. The results show the high effectiveness of the applied methods. The real possibility of selecting the promising compositions with the required set of casting and mechanical properties is exemplified by alloys with thermally hardened Al-Cu and Al-Cu-Mg matrices, as well as poorly soluble additives that form eutectic components using mainly the calculation study methods and the minimum number of experiments.

Secondary Teachers' Conception of Various Forms of Complex Numbers

ERIC Educational Resources Information Center

Karakok, Gulden; Soto-Johnson, Hortensia; Dyben, Stephenie Anderson

2015-01-01

This study explores in-service high school mathematics teachers' conception of various forms of complex numbers and ways in which they transition between different representations of these forms. One 90-min interview was conducted with three high school mathematics teachers after they completed three professional development sessions, each 4 h, on…

An Exploratory Framework for Handling the Complexity of Mathematical Problem Posing in Small Groups

ERIC Educational Resources Information Center

Kontorovich, Igor; Koichu, Boris; Leikin, Roza; Berman, Avi

2012-01-01

The paper introduces an exploratory framework for handling the complexity of students' mathematical problem posing in small groups. The framework integrates four facets known from past research: task organization, students' knowledge base, problem-posing heuristics and schemes, and group dynamics and interactions. In addition, it contains a new…

Teachers' Decisions about Mathematics Tasks When Planning

ERIC Educational Resources Information Center

Sullivan, Peter; Clarke, David; Clarke, Doug; Roche, Anne

2013-01-01

At some stage when planning, teachers make decisions about the mathematics tasks they will pose and how they will structure lessons. It seems, though, that these decisions are complex, and that this complexity has been underestimated by curriculum developers and teacher educators. The following is a report of data collection that simulated some of…

Everyday Matters in Science and Mathematics: Studies of Complex Classroom Events

ERIC Educational Resources Information Center

Nemirovsky, Ricardo, Ed.; Rosebery, Ann S., Ed.; Solomon, Jesse, Ed.; Warren, Beth, Ed.

2005-01-01

This book re-examines the dichotomy between the everyday and the disciplinary in mathematics and science education, and explores alternatives to this opposition from points of view grounded in the close examination of complex classroom events. It makes the case that students' everyday experience and knowledge in their entire manifold forms matter…

The Power of Numbers. A Teacher's Guide to Mathematics in a Social Studies Context. An Interdisciplinary Curriculum.

ERIC Educational Resources Information Center

Gross, Fred E.; And Others

This document is the teacher's guide for a curriculum designed to teach mathematics in a social studies context. It provides mathematical experiences in real world contexts that help students interpret, experiment, communicate, and look for multiple solutions to complex problems. The curriculum uses mathematics in context to help students develop…

Similarities and Differences in Classroom Interaction between Remedial and College Mathematics Courses in a Community College

ERIC Educational Resources Information Center

Mesa, V.

2011-01-01

Through an analysis of instruction in mathematics classrooms at a community college, the author describes the nature of the interaction and the complexity of the mathematical activities evident in two types of courses: remedial and science, technology, engineering, and mathematics (STEM) college preparatory courses. Although both types of courses…

Being a Girl Mathematician: Diversity of Positive Mathematical Identities in a Secondary Classroom

ERIC Educational Resources Information Center

Radovic, Darinka; Black, Laura; Salas, Christian E.; Williams, Julian

2017-01-01

The construction of positive mathematical identities (MIs) is a complex and central issue in school mathematics, where girls are usually "counted out" of the field. This study explores positive MIs (high achiever and positive relationship with mathematics) of 3 girls. We employed a nested model of identity based on a case study approach…

Mathematical Investigations for Supporting Pre-Service Primary Teachers Repeating a Mathematics Education Course

ERIC Educational Resources Information Center

Bailey, Judy

2014-01-01

Preparing to become an effective primary school mathematics teacher is a challenging and complex task; and is influenced by one's past experiences, personal knowledge of, and beliefs and attitudes towards mathematics. This paper examines the experiences of a small group of pre-service teachers who did not pass their first year mathematics…

Unpacking Teachers' Moves in the Classroom: Navigating Micro- and Macro-Levels of Mathematical Complexity

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"…

Model of multistep electron transfer in a single-mode polar medium

NASA Astrophysics Data System (ADS)

Feskov, S. V.; Yudanov, V. V.

2017-09-01

A mathematical model of multistep photoinduced electron transfer (PET) in a polar medium with a single relaxation time (Debye solvent) is developed. The model includes the polarization nonequilibrity formed in the vicinity of the donor-acceptor molecular system at the initial steps of photoreaction and its influence on the subsequent steps of PET. It is established that the results from numerical simulation of transient luminescence spectra of photoexcited donor-acceptor complexes (DAC) conform to calculated data obtained on the basis of the familiar experimental technique used to measure the relaxation function of solvent polarization in the vicinity of DAC in the picosecond and subpicosecond ranges.

Quantitative Finance

NASA Astrophysics Data System (ADS)

James, Jessica

2017-01-01

Quantitative finance is a field that has risen to prominence over the last few decades. It encompasses the complex models and calculations that value financial contracts, particularly those which reference events in the future, and apply probabilities to these events. While adding greatly to the flexibility of the market available to corporations and investors, it has also been blamed for worsening the impact of financial crises. But what exactly does quantitative finance encompass, and where did these ideas and models originate? We show that the mathematics behind finance and behind games of chance have tracked each other closely over the centuries and that many well-known physicists and mathematicians have contributed to the field.

Stress state estimation in multilayer support of vertical shafts, considering off-design cross-sectional deformation

NASA Astrophysics Data System (ADS)

Antsiferov, SV; Sammal, AS; Deev, PV

2018-03-01

To determine the stress-strain state of multilayer support of vertical shafts, including cross-sectional deformation of the tubing rings as against the design, the authors propose an analytical method based on the provision of the mechanics of underground structures and surrounding rock mass as the elements of an integrated deformable system. The method involves a rigorous solution of the corresponding problem of elasticity, obtained using the mathematical apparatus of the theory of analytic functions of a complex variable. The design method is implemented as a software program allowing multivariate applied computation. Examples of the calculation are given.

Flip or Flop? Students' Perspectives of a Flipped Lecture in Mathematics

ERIC Educational Resources Information Center

Novak, Julia; Kensington-Miller, Barbara; Evans, Tanya

2017-01-01

This paper describes students' perspectives of a one-off flipped lecture in a large undergraduate mathematics service course. The focus was on calculating matrix determinants and was designed specifically to introduce debate and argumentation into a mathematics lecture. The intention was to promote a deeper learning and understanding through…

Factors That Encourage or Inhibit Computer Use for Secondary Mathematics Teaching

ERIC Educational Resources Information Center

Forgasz, Helen

2006-01-01

Included in contemporary mathematics curricula is the expectation that mathematics teachers will use technology--computers and calculators--in their classrooms. It is widely believed in Australian educational circles and in society at large that students' learning will be enhanced by engaging with these technologies. For children to use computers…

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

ERIC Educational Resources Information Center

Bolte, Linda A.

2002-01-01

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

WMI2, the Student's On-Line Symbolic Calculator

ERIC Educational Resources Information Center

Kovacs, Zoltan

2011-01-01

Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides…

The MATH--Open Source Application for Easier Learning of Numerical Mathematics

ERIC Educational Resources Information Center

Glaser-Opitz, Henrich; Budajová, Kristina

2016-01-01

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Elementary School Quality: The Mathematics Curriculum and the Role of Local Knowledge.

ERIC Educational Resources Information Center

Balfanz, Robert

This report considers how the mathematical knowledge children develop on their own outside of formal school instruction can be used to increase the distribution and level of mathematical knowledge attained by students in grades K-3. Included are preliminary results of an investigation of the counting and calculating abilities brought to…

Analysis of students’ mathematical reasoning

NASA Astrophysics Data System (ADS)

Sukirwan; Darhim; Herman, T.

2018-01-01

The reasoning is one of the mathematical abilities that have very complex implications. This complexity causes reasoning including abilities that are not easily attainable by students. Similarly, studies dealing with reason are quite diverse, primarily concerned with the quality of mathematical reasoning. The objective of this study was to determine the quality of mathematical reasoning based perspective Lithner. Lithner looked at how the environment affects the mathematical reasoning. In this regard, Lithner made two perspectives, namely imitative reasoning and creative reasoning. Imitative reasoning can be memorized and algorithmic reasoning. The Result study shows that although the students generally still have problems in reasoning. Students tend to be on imitative reasoning which means that students tend to use a routine procedure when dealing with reasoning. It is also shown that the traditional approach still dominates on the situation of students’ daily learning.

From Molecules to Life: Quantifying the Complexity of Chemical and Biological Systems in the Universe.

PubMed

Böttcher, Thomas

2018-01-01

Life is a complex phenomenon and much research has been devoted to both understanding its origins from prebiotic chemistry and discovering life beyond Earth. Yet, it has remained elusive how to quantify this complexity and how to compare chemical and biological units on one common scale. Here, a mathematical description of molecular complexity was applied allowing to quantitatively assess complexity of chemical structures. This in combination with the orthogonal measure of information complexity resulted in a two-dimensional complexity space ranging over the entire spectrum from molecules to organisms. Entities with a certain level of information complexity directly require a functionally complex mechanism for their production or replication and are hence indicative for life-like systems. In order to describe entities combining molecular and information complexity, the term biogenic unit was introduced. Exemplified biogenic unit complexities were calculated for ribozymes, protein enzymes, multimeric protein complexes, and even an entire virus particle. Complexities of prokaryotic and eukaryotic cells, as well as multicellular organisms, were estimated. Thereby distinct evolutionary stages in complexity space were identified. The here developed approach to compare the complexity of biogenic units allows for the first time to address the gradual characteristics of prebiotic and life-like systems without the need for a definition of life. This operational concept may guide our search for life in the Universe, and it may direct the investigations of prebiotic trajectories that lead towards the evolution of complexity at the origins of life.

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

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

Plechac, Petr

2016-03-01

The overall objective of this project was to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics and developing rigorous mathematical techniques and computational algorithms to study such models. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals.

Novel in vitro diagnosis of equine allergies using a protein array and mathematical modelling approach: a proof of concept using insect bite hypersensitivity.

PubMed

Marti, E; Wang, X; Jambari, N N; Rhyner, C; Olzhausen, J; Pérez-Barea, J J; Figueredo, G P; Alcocer, M J C

2015-10-15

Insect bite hypersensitivity (IBH) is a seasonal recurrent skin allergy of horses caused by IgE-mediated reactions to allergens present in the saliva of biting insects of the genus Culicoides, and possibly also Simulium and Stomoxys species. In this work we show that protein microarrays containing complex extracts and pure proteins, including recombinant Culicoides allergens, can be used as a powerful technique for the diagnosis of IBH. Besides the obvious advantages such as general profiling and use of few microliters of samples, this microarray technique permits automation and allows the generation of mathematical models with the calculation of individual risk profiles that can support the clinical diagnosis of allergic diseases. After selection of variables on influence on the projection (VIP), the observed values of sensitivity and specificity were 1.0 and 0.967, respectively. This confirms the highly discriminatory power of this approach for IBH and made it possible to attain a robust predictive mathematical model for this disease. It also further demonstrates the specificity of the protein array method on identifying a particular IgE-mediated disease when the sensitising allergen group is known. Copyright © 2015 Elsevier B.V. All rights reserved.

The ‘hit’ phenomenon: a mathematical model of human dynamics interactions as a stochastic process

NASA Astrophysics Data System (ADS)

Ishii, Akira; Arakaki, Hisashi; Matsuda, Naoya; Umemura, Sanae; Urushidani, Tamiko; Yamagata, Naoya; Yoshida, Narihiko

2012-06-01

A mathematical model for the ‘hit’ phenomenon in entertainment within a society is presented as a stochastic process of human dynamics interactions. The model uses only the advertisement budget time distribution as an input, and word-of-mouth (WOM), represented by posts on social network systems, is used as data to make a comparison with the calculated results. The unit of time is days. The WOM distribution in time is found to be very close to the revenue distribution in time. Calculations for the Japanese motion picture market based on the mathematical model agree well with the actual revenue distribution in time.

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.

Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study

PubMed Central

Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y.; Gynku, Elena I.; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

2015-01-01

Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6–9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7–9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age. PMID:25859235

Spatial complexity of character-based writing systems and arithmetic in primary school: a longitudinal study.

PubMed

Rodic, Maja; Tikhomirova, Tatiana; Kolienko, Tatiana; Malykh, Sergey; Bogdanova, Olga; Zueva, Dina Y; Gynku, Elena I; Wan, Sirui; Zhou, Xinlin; Kovas, Yulia

2015-01-01

Previous research has consistently found an association between spatial and mathematical abilities. We hypothesized that this link may partially explain the consistently observed advantage in mathematics demonstrated by East Asian children. Spatial complexity of the character-based writing systems may reflect or lead to a cognitive advantage relevant to mathematics. Seven hundered and twenty one 6-9-year old children from the UK and Russia were assessed on a battery of cognitive skills and arithmetic. The Russian children were recruited from specialist linguistic schools and divided into four different language groups, based on the second language they were learning (i.e., English, Spanish, Chinese, and Japanese). The UK children attended regular schools and were not learning any second language. The testing took place twice across the school year, once at the beginning, before the start of the second language acquisition, and once at the end of the year. The study had two aims: (1) to test whether spatial ability predicts mathematical ability in 7-9 year-old children across the samples; (2) to test whether acquisition and usage of a character-based writing system leads to an advantage in performance in arithmetic and related cognitive tasks. The longitudinal link from spatial ability to mathematics was found only in the Russian sample. The effect of second language acquisition on mathematics or other cognitive skills was negligible, although some effect of Chinese language on mathematical reasoning was suggested. Overall, the findings suggest that although spatial ability is related to mathematics at this age, one academic year of exposure to spatially complex writing systems is not enough to provide a mathematical advantage. Other educational and socio-cultural factors might play a greater role in explaining individual and cross-cultural differences in arithmetic at this age.

The Effects of Cover, Copy, and Compare, Performance Feedback and Rewards on the Mathematical Calculation Skills of Students Identified with Math Difficulty

ERIC Educational Resources Information Center

Benson, Geetal

2013-01-01

This study examined the isolated effects of Cover, Copy and Compare (CCC) and the effects of CCC paired with performance feedback (CCC + PF) and rewards (CCC + RW) on the mathematical calculation skills of first grade students identified with math difficulty. Four research questions were addressed in this study. 1. Does Cover, Copy, and Compare…

Dynamics of inductors for heating of the metal under deformation

NASA Astrophysics Data System (ADS)

Zimin, L. S.; Yeghiazaryan, A. S.; Protsenko, A. N.

2018-01-01

Current issues of creating powerful systems for hot sheet rolling with induction heating application in mechanical engineering and metallurgy were discussed. Electrodynamical and vibroacoustic problems occurring due to the induction heating of objects with complex shapes, particularly the slabs heating prior to rolling, were analysed. The numerical mathematical model using the method of related contours and the principle of virtual displacements is recommended for electrodynamical calculations. For the numerical solution of the vibrational problem, it is reasonable to use the finite element method (FEM). In general, for calculating the distribution forces, the law of Biot-Savart-Laplace method providing the determination of the current density of the skin layer in slab was used. The form of the optimal design of the inductor based on maximum hardness was synthesized while researching the vibrodynamic model of the system "inductor-metal" which provided allowable sound level meeting all established sanitary standards.

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

Steady-state currents in p-n junction filaments or grains in case of large surface recombination velocities at lateral surfaces

NASA Technical Reports Server (NTRS)

Von Roos, O.; Lindholm, F. A.

1985-01-01

Recently it has been pointed out that the saturation current of a semiconductor filament which constitutes part of a p-n junction diverges when the surface recombination velocity at the faces become infinitely large. Here it is pointed out that this is to be expected on physical grounds since, whenever the carrier concentration is kept off equilibrium by an outside agent, and at the same time recombination lifetimes in the bulk or in surface layers tend to zero, concentration gradients tend to infinity. As also previously noted, the situation can be remedied by using realistic (finite) surface recombination velocities in model calculations. However, this procedure leads to mathematical complexities which have been circumvented recently by the introduction of a heuristic approach. It is the aim of this paper to assess the validity of the heuristic approach by means of detailed and exact calculations.

Hydraulic transients in the long diversion-type hydropower station with a complex differential surge tank.

PubMed

Yu, Xiaodong; Zhang, Jian; Zhou, Ling

2014-01-01

Based on the theory of hydraulic transients and the method of characteristics (MOC), a mathematic model of the differential surge tank with pressure-reduction orifices (PROs) and overflow weirs for transient calculation is proposed. The numerical model of hydraulic transients is established using the data of a practical hydropower station; and the probable transients are simulated. The results show that successive load rejection is critical for calculating the maximum pressure in spiral case and the maximum rotating speed of runner when the bifurcated pipe is converging under the surge tank in a diversion-type hydropower station; the pressure difference between two sides of breast wall is large during transient conditions, and it would be more serious when simultaneous load rejections happen after load acceptance; the reasonable arrangement of PROs on breast wall can effectively decrease the pressure difference.

Thermal radiation view factor: Methods, accuracy and computer-aided procedures

NASA Technical Reports Server (NTRS)

Kadaba, P. V.

1982-01-01

The computer aided thermal analysis programs which predicts the result of predetermined acceptable temperature range prior to stationing of these orbiting equipment in various attitudes with respect to the Sun and the Earth was examined. Complexity of the surface geometries suggests the use of numerical schemes for the determination of these viewfactors. Basic definitions and standard methods which form the basis for various digital computer methods and various numerical methods are presented. The physical model and the mathematical methods on which a number of available programs are built are summarized. The strength and the weaknesses of the methods employed, the accuracy of the calculations and the time required for computations are evaluated. The situations where accuracies are important for energy calculations are identified and methods to save computational times are proposed. Guide to best use of the available programs at several centers and the future choices for efficient use of digital computers are included in the recommendations.

Hydraulic Transients in the Long Diversion-Type Hydropower Station with a Complex Differential Surge Tank

PubMed Central

Yu, Xiaodong; Zhang, Jian

2014-01-01

Based on the theory of hydraulic transients and the method of characteristics (MOC), a mathematic model of the differential surge tank with pressure-reduction orifices (PROs) and overflow weirs for transient calculation is proposed. The numerical model of hydraulic transients is established using the data of a practical hydropower station; and the probable transients are simulated. The results show that successive load rejection is critical for calculating the maximum pressure in spiral case and the maximum rotating speed of runner when the bifurcated pipe is converging under the surge tank in a diversion-type hydropower station; the pressure difference between two sides of breast wall is large during transient conditions, and it would be more serious when simultaneous load rejections happen after load acceptance; the reasonable arrangement of PROs on breast wall can effectively decrease the pressure difference. PMID:25133213

Development of computer-aided design system of elastic sensitive elements of automatic metering devices

NASA Astrophysics Data System (ADS)

Kalinkina, M. E.; Kozlov, A. S.; Labkovskaia, R. I.; Pirozhnikova, O. I.; Tkalich, V. L.; Shmakov, N. A.

2018-05-01

The object of research is the element base of devices of control and automation systems, including in its composition annular elastic sensitive elements, methods of their modeling, calculation algorithms and software complexes for automation of their design processes. The article is devoted to the development of the computer-aided design system of elastic sensitive elements used in weight- and force-measuring automation devices. Based on the mathematical modeling of deformation processes in a solid, as well as the results of static and dynamic analysis, the calculation of elastic elements is given using the capabilities of modern software systems based on numerical simulation. In the course of the simulation, the model was a divided hexagonal grid of finite elements with a maximum size not exceeding 2.5 mm. The results of modal and dynamic analysis are presented in this article.

Implementing digital holograms to create and measure complex-plane optical fields

NASA Astrophysics Data System (ADS)

Dudley, Angela; Majola, Nombuso; Chetty, Naven; Forbes, Andrew

2016-02-01

The coherent superposition of a Gaussian beam with an optical vortex can be mathematically described to occupy the complex plane. We provide a simple analogy between the mathematics, in the form of the complex plane, and the visual representation of these two superimposed optical fields. We provide detailed instructions as to how one can experimentally produce, measure, and control these fields with the use of digital holograms encoded on a spatial light modulator.

The Nuances and Complexities of Teaching Mathematics for Cultural Relevance and Social Justice

ERIC Educational Resources Information Center

Leonard, Jacqueline; Brooks, Wanda; Barnes-Johnson, Joy; Berry, Robert Q., III.

2010-01-01

Mathematics is not a race-neutral subject. Access and opportunity in mathematics for students of color in the United States continue to be limited. While a great deal of attention has been given to increasing the number of underrepresented minority students in the mathematics pipeline, there is little consideration of who they are as learners or…

Criticising with Foucault: Towards a Guiding Framework for Socio-Political Studies in Mathematics Education

ERIC Educational Resources Information Center

Kollosche, David

2016-01-01

Socio-political studies in mathematics education often touch complex fields of interaction between education, mathematics and the political. In this paper I present a Foucault-based framework for socio-political studies in mathematics education which may guide research in that area. In order to show the potential of such a framework, I discuss the…

Why Should Mathematics Educators Learn from and about Latina/o Students' In-School and Out-of-School Experiences?

ERIC Educational Resources Information Center

Civil, Marta

2014-01-01

University of Arizona's Marta Civil has been studying the complexities of bridging in-school and out-of-school mathematics for some time, during which she has raised specific questions related to connecting in-school and out-of-school mathematics (Civil, 2002, 2007, 2014). These questions have to do with "What is mathematics?"…

Mathematical Interaction Shaped by Communication, Epistemological Constraints and Enactivism

ERIC Educational Resources Information Center

Steinbring, Heinz

2015-01-01

On the surface, mathematical interaction often appears as an immediately transparent event that could be directly understood by careful observation. Theoretical considerations, however, clearly show that mathematical speaking and conversation in teaching-learning situations are highly complex social structures comprising many preconditions.…

Learning by Preparing to Teach: Fostering Self-Regulatory Processes and Achievement during Complex Mathematics Problem Solving

ERIC Educational Resources Information Center

Muis, Krista R.; Psaradellis, Cynthia; Chevrier, Marianne; Di Leo, Ivana; Lajoie, Susanne P.

2016-01-01

We developed an intervention based on the learning by teaching paradigm to foster self-regulatory processes and better learning outcomes during complex mathematics problem solving in a technology-rich learning environment. Seventy-eight elementary students were randomly assigned to 1 of 2 conditions: learning by preparing to teach, or learning for…

Computational complexity of Boolean functions

NASA Astrophysics Data System (ADS)

Korshunov, Aleksei D.

2012-02-01

Boolean functions are among the fundamental objects of discrete mathematics, especially in those of its subdisciplines which fall under mathematical logic and mathematical cybernetics. The language of Boolean functions is convenient for describing the operation of many discrete systems such as contact networks, Boolean circuits, branching programs, and some others. An important parameter of discrete systems of this kind is their complexity. This characteristic has been actively investigated starting from Shannon's works. There is a large body of scientific literature presenting many fundamental results. The purpose of this survey is to give an account of the main results over the last sixty years related to the complexity of computation (realization) of Boolean functions by contact networks, Boolean circuits, and Boolean circuits without branching. Bibliography: 165 titles.

Validation the use of refractometer and mathematic equations to measure dietary formula contents for clinical application.

PubMed

Chang, W-K; Chao, Y-C; Mcclave, S-A; Yeh, M-K

2005-10-01

Gastric residual volumes are widely used to evaluate gastric emptying for patients receiving enteral feeding, but controversy exists about what constitutes gastric residual volume. We have developed a method by using refractometer and derived mathematical equations to calculate the formula concentration, total residual volume (TRV), and formula volume. In this study, we like to validate these mathematical equations before they can be implemented for clinical patient care. Four dietary formulas were evaluated in two consecutive validation experiments. Firstly, dietary formula volume of 50, 100, 200, and 400 ml were diluted with 50 ml water, and then the Brix value (BV) was measured by the refractometer. Secondly, 50 ml of water, then 100 ml of dietary formula were infused into a beaker, and followed by the BV measurement. After this, 50 ml of water was infused and followed by the second BV measurement. The entire procedure of infusing of dietary formula (100 ml) and waster (50 ml) was repeated twice and followed by the BV measurement. The formula contents (formula concentration, TRV, and formula volume) were calculated by mathematical equations. The calculated formula concentrations, TRVs, and formula volumes measured from mathematic equations were strongly close to the true values in the first and second validation experiments (R2>0.98, P<0.001). Refractometer and the derived mathematical equations may be used to accurately measure the formula concentration, TRV, and formula volume and served as a tool to monitor gastric emptying for patients receiving enteral feeding.

BFEE: A User-Friendly Graphical Interface Facilitating Absolute Binding Free-Energy Calculations.

PubMed

Fu, Haohao; Gumbart, James C; Chen, Haochuan; Shao, Xueguang; Cai, Wensheng; Chipot, Christophe

2018-03-26

Quantifying protein-ligand binding has attracted the attention of both theorists and experimentalists for decades. Many methods for estimating binding free energies in silico have been reported in recent years. Proper use of the proposed strategies requires, however, adequate knowledge of the protein-ligand complex, the mathematical background for deriving the underlying theory, and time for setting up the simulations, bookkeeping, and postprocessing. Here, to minimize human intervention, we propose a toolkit aimed at facilitating the accurate estimation of standard binding free energies using a geometrical route, coined the binding free-energy estimator (BFEE), and introduced it as a plug-in of the popular visualization program VMD. Benefitting from recent developments in new collective variables, BFEE can be used to generate the simulation input files, based solely on the structure of the complex. Once the simulations are completed, BFEE can also be utilized to perform the post-treatment of the free-energy calculations, allowing the absolute binding free energy to be estimated directly from the one-dimensional potentials of mean force in simulation outputs. The minimal amount of human intervention required during the whole process combined with the ergonomic graphical interface makes BFEE a very effective and practical tool for the end-user.

Interdisciplinary education - a predator-prey model for developing a skill set in mathematics, biology and technology

NASA Astrophysics Data System (ADS)

van der Hoff, Quay

2017-08-01

The science of biology has been transforming dramatically and so the need for a stronger mathematical background for biology students has increased. Biological students reaching the senior or post-graduate level often come to realize that their mathematical background is insufficient. Similarly, students in a mathematics programme, interested in biological phenomena, find it difficult to master the complex systems encountered in biology. In short, the biologists do not have enough mathematics and the mathematicians are not being taught enough biology. The need for interdisciplinary curricula that includes disciplines such as biology, physical science, and mathematics is widely recognized, but has not been widely implemented. In this paper, it is suggested that students develop a skill set of ecology, mathematics and technology to encourage working across disciplinary boundaries. To illustrate such a skill set, a predator-prey model that contains self-limiting factors for both predator and prey is suggested. The general idea of dynamics, is introduced and students are encouraged to discover the applicability of this approach to more complex biological systems. The level of mathematics and technology required is not advanced; therefore, it is ideal for inclusion in a senior-level or introductory graduate-level course for students interested in mathematical biology.

Influence of clamping plate permeability and metal screen structures on three-dimensional magnetic field and eddy current loss in end region of a turbo-generator by numerical analysis

NASA Astrophysics Data System (ADS)

Likun, Wang; Weili, Li; Yi, Xue; Chunwei, Guan

2013-11-01

A significant problem of turbogenerators on complex end structures is overheating of local parts caused by end losses in the end region. Therefore, it is important to investigate the 3-D magnetic field and eddy current loss in the end. In end region of operating large turbogenerator at thermal power plants, magnetic leakage field distribution is complex. In this paper, a 3-D mathematical model used for the calculation of the electromagnetic field in the end region of large turbo-generators is given. The influence of spatial locations of end structures, the actual shape and material of end windings, clamping plate, and copper screen are considered. Adopting the time-step finite element (FE) method and taking the nonlinear characteristics of the core into consideration, a 3-D transient magnetic field is calculated. The objective of this paper is to investigate the influence of clamping plate permeability and metal screen structures on 3-D electromagnetic field distribution and eddy current loss in end region of a turbo-generator. To reduce the temperature of copper screen, a hollow metal screen is proposed. The eddy current loss, which is gained from the 3D transient magnetic field, is used as heat source for the thermal field of end region. The calculated temperatures are compared with test data.

An Evaluation of Elementary School Mathematics Programs Utilizing the Mini-Calculator.

ERIC Educational Resources Information Center

Campbell, Patricia; Virgin, A. E.

The purpose of this study was to compare the achievement, attitudes, and teaching/learning experiences in mathematics programs of two groups of elementary-school students in grades 5 and 6. Approximately 150 students in each of two elementary schools were given as a pretest a standardized mathematics achievement test and a questionnaire regarding…

"New Directions for Traditional Lessons": Can Handheld Game Consoles Enhance Mental Mathematics Skills?

ERIC Educational Resources Information Center

Main, Susan; O'Rourke, John

2011-01-01

This paper reports on a pilot study that compared the use of commercial off-the-shelf (COTS) handheld game consoles (HGCs) with traditional teaching methods to develop the automaticity of mathematical calculations and self-concept towards mathematics for year 4 students in two metropolitan schools. One class conducted daily sessions using the HGCs…

UAH mathematical model of the variable polarity plasma ARC welding system calculation

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

Significant advantages of Variable Polarity Plasma Arc (VPPA) welding process include faster welding, fewer repairs, less joint preparation, reduced weldment distortion, and absence of porosity. A mathematical model is presented to analyze the VPPA welding process. Results of the mathematical model were compared with the experimental observation accomplished by the GDI team.

Who's Wrong? Tasks Fostering Understanding of Mathematical Relationships in Word Problems in Elementary Students

ERIC Educational Resources Information Center

Savard, Annie; Polotskaia, Elena

2017-01-01

Mathematical relationships are crucial elements to consider for learning mathematics. However, too often students pay more attention to the calculations to be done rather than the reasons for doing them. Relying on the relational paradigm to support elementary school students, we proposed two specially designed tasks to help students recognize and…

Integrating STEM in Elementary Classrooms Using Model-Eliciting Activities: Responsive Professional Development for Mathematics Coaches and Teachers

ERIC Educational Resources Information Center

Baker, Courtney K.; Galanti, Terrie M.

2017-01-01

Background: This research highlights a school-university collaboration to pilot a professional development framework for integrating STEM in K-6 mathematics classrooms in a mid-Atlantic suburban school division. Because mathematics within STEM integration is often characterized as the calculations or the data representations in science classrooms,…

Closing the Gap between Formalism and Application--PBL and Mathematical Skills in Engineering

ERIC Educational Resources Information Center

Christensen, Ole Ravn

2008-01-01

A common problem in learning mathematics concerns the gap between, on the one hand, doing the formalisms and calculations of abstract mathematics and, on the other hand, applying these in a specific contextualized setting for example the engineering world. The skills acquired through problem-based learning (PBL), in the special model used at…

Private Speech Use in Arithmetical Calculation: Contributory Role of Phonological Awareness in Children with and without Mathematical Difficulties

ERIC Educational Resources Information Center

Ostad, Snorre A.

2013-01-01

The majority of recent studies conclude that children's private speech development (private speech internalization) is related to and important for mathematical development and disabilities. It is far from clear, however, whether private speech internalization itself plays any causal role in the development of mathematical competence. The main…

Mathematics. Unit 6: A Core Curriculum of Related Instruction for Apprentices.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of Occupational and Career Curriculum Development.

The mathematics unit is presented to assist apprentices to acquire a general knowledge of mathematic skills. The unit consists of nine modules: (1) basic addition, subtraction, multiplication, and division; (2) conventional linear measure; (3) using the metric system, (4) steps to take in solving problems, (5) how to calculate areas and volumes,…

A Cross-Cultural Investigation into How Tasks Influence Seatwork Activities in Mathematics Lessons

ERIC Educational Resources Information Center

Serrano, Ana M.

2012-01-01

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…

A Five-Dimensional Mathematical Model for Regional and Global Changes in Cardiac Uptake and Motion

NASA Astrophysics Data System (ADS)

Pretorius, P. H.; King, M. A.; Gifford, H. C.

2004-10-01

The objective of this work was to simultaneously introduce known regional changes in contraction pattern and perfusion to the existing gated Mathematical Cardiac Torso (MCAT) phantom heart model. We derived a simple integral to calculate the fraction of the ellipsoidal volume that makes up the left ventricle (LV), taking into account the stationary apex and the moving base. After calculating the LV myocardium volume of the existing beating heart model, we employed the property of conservation of mass to manipulate the LV ejection fraction to values ranging between 13.5% and 68.9%. Multiple dynamic heart models that differ in degree of LV wall thickening, base-to-apex motion, and ejection fraction, are thus available for use with the existing MCAT methodology. To introduce more complex regional LV contraction and perfusion patterns, we used composites of dynamic heart models to create a central region with little or no motion or perfusion, surrounded by a region in which the motion and perfusion gradually reverts to normal. To illustrate this methodology, the following gated cardiac acquisitions for different clinical situations were simulated analytically: 1) reduced regional motion and perfusion; 2) same perfusion as in (1) without motion intervention; and 3) washout from the normal and diseased myocardial regions. Both motion and perfusion can change dynamically during a single rotation or multiple rotations of a simulated single-photon emission computed tomography acquisition system.

Improved Algorithms Speed It Up for Codes

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

Hazi, A

2005-09-20

Huge computers, huge codes, complex problems to solve. The longer it takes to run a code, the more it costs. One way to speed things up and save time and money is through hardware improvements--faster processors, different system designs, bigger computers. But another side of supercomputing can reap savings in time and speed: software improvements to make codes--particularly the mathematical algorithms that form them--run faster and more efficiently. Speed up math? Is that really possible? According to Livermore physicist Eugene Brooks, the answer is a resounding yes. ''Sure, you get great speed-ups by improving hardware,'' says Brooks, the deputy leadermore » for Computational Physics in N Division, which is part of Livermore's Physics and Advanced Technologies (PAT) Directorate. ''But the real bonus comes on the software side, where improvements in software can lead to orders of magnitude improvement in run times.'' Brooks knows whereof he speaks. Working with Laboratory physicist Abraham Szoeke and others, he has been instrumental in devising ways to shrink the running time of what has, historically, been a tough computational nut to crack: radiation transport codes based on the statistical or Monte Carlo method of calculation. And Brooks is not the only one. Others around the Laboratory, including physicists Andrew Williamson, Randolph Hood, and Jeff Grossman, have come up with innovative ways to speed up Monte Carlo calculations using pure mathematics.« less

Analysis of laser remote fusion cutting based on a mathematical model

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

Matti, R. S.; Department of Mechanical Engineering, College of Engineering, University of Mosul, Mosul; Ilar, T.

Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, lasermore » remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.« less

Analysis of laser remote fusion cutting based on a mathematical model

NASA Astrophysics Data System (ADS)

Matti, R. S.; Ilar, T.; Kaplan, A. F. H.

2013-12-01

Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, laser remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.

Prospects of a mathematical theory of human behavior in complex man-machine systems tasks. [time sharing computer analogy of automobile driving

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.

Modeling the magnetoelectric effect in laminated composites using Hamilton’s principle

NASA Astrophysics Data System (ADS)

Zhang, Shengyao; Zhang, Ru; Jiang, Jiqing

2018-01-01

Mathematical modeling of the magnetoelectric (ME) effect has been established for some rectangular and disk laminate structures. However, these methods are difficult in other cases, particularly for complex structures. In this work, a new method for the analysis of the ME effect is proposed using a generalized Hamilton’s principle, which is conveniently applicable to various laminate structures. As an example, the performance of the rectangular ME laminated composite is analyzed and the equivalent circuit model for the laminate is obtained directly from the analysis. The experimental data is also obtained to compare with the theoretical calculations and to validate the new method. Compared with Dong’s method, the new method is more accurate and convenient. In particular, the equivalent circuit for the rectangular laminated composite can be obtained more easily by the proposed method as it does not require the complex treatment used in Dong’s method.

Hidden Figures Tour Kennedy Space Center Visitor Complex

NASA Image and Video Library

2016-12-12

In the IMAX Theater of the Kennedy Space Center Visitor Complex Cast and crew members of the upcoming motion picture "Hidden Figures" participate in a question and answer session. From the left are Ted Melfi, writer and director of “Hidden Figures,” Octavia Spencer, who portrays Dorothy Vaughan in the film, Taraji P. Henson, who portrays Katherine Johnson, Pharrell Williams, musician and producer of “Hidden Figures," and Janelle Monáe, who portrays Mary Jackson. The movie is based on the book of the same title, by Margot Lee Shetterly. It chronicles the lives of Katherine Johnson, Dorothy Vaughan and Mary Jackson, three African-American women who worked for NASA as human "computers.” Their mathematical calculations were crucial to the success of Project Mercury missions including John Glenn’s orbital flight aboard Friendship 7 in 1962. The film is due in theaters in January 2017.

Hidden Figures Tour Kennedy Space Center Visitor Complex

NASA Image and Video Library

2016-12-12

In the IMAX Theater of the Kennedy Space Center Visitor Complex Cast and crew members of the upcoming motion picture "Hidden Figures" participate in a question and answer session. From the left are Octavia Spencer, who portrays Dorothy Vaughan in the film, Taraji P. Henson, who portrays Katherine Johnson, Janelle Monáe, who portrays Mary Jackson, Pharrell Williams, musician and producer of “Hidden Figures," Ted Melfi, writer and director of “Hidden Figures,” center director Bob Cabana, and Janet Petro, deputy center director. The movie is based on the book of the same title, by Margot Lee Shetterly. It chronicles the lives of Katherine Johnson, Dorothy Vaughan and Mary Jackson, three African-American women who worked for NASA as human "computers.” Their mathematical calculations were crucial to the success of Project Mercury missions including John Glenn’s orbital flight aboard Friendship 7 in 1962. The film is due in theaters in January 2017.

Seizures induced by music.

PubMed

Ogunyemi, A O; Breen, H

1993-01-01

Musicogenic epilepsy is a rare disorder. Much remains to be learned about the electroclinical features. This report describes a patient who has been followed at our institution for 17 years, and was investigated with long-term telemetered simultaneous video-EEG recordings. She began to have seizures at the age of 10 years. She experienced complex partial seizures, often preceded by elementary auditory hallucination and complex auditory illusion. The seizures occurred in relation to singing, listening to music or thinking about music. She also had occasional generalized tonic clonic seizures during sleep. There was no significant antecedent history. The family history was negative for epilepsy. The physical examination was unremarkable. CT and MRI scans of the brain were normal. During long-term simultaneous video-EEG recordings, clinical and electrographic seizure activities were recorded in association with singing and listening to music. Mathematical calculation, copying or viewing geometric patterns and playing the game of chess failed to evoke seizures.

Making the Learning of Mathematics More Meaningful

NASA Technical Reports Server (NTRS)

Ward, Robin A.

1998-01-01

In the early 1980's, the National Commission on Excellence in Education responded to the call for reform in the teaching and learning of mathematics. In particular, the Commission developed a document addressing the consensus that all students need to learn more, and often different, mathematics and that instruction in mathematics must be significantly revised. In a response to these calls for mathematics education reform, the National Council of Teachers of Mathematics (NCTM) developed its Curriculum and Evaluation Standards (1989) with a two-fold purpose: 1) to create a coherent vision of what it means to be mathematically literate in a world that relies on calculators and computers, and 2) to create a set of standards to guide the revisions of school mathematics curriculum.

Understanding the Complexities of Student Motivations in Mathematics Learning

ERIC Educational Resources Information Center

Walter, Janet G.; Hart, Janelle

2009-01-01

Student motivation has long been a concern of mathematics educators. However, commonly held distinctions between intrinsic and extrinsic motivations may be insufficient to inform our understandings of student motivations in learning mathematics or to appropriately shape pedagogical decisions. Here, motivation is defined, in general, as an…

Illustrations of mathematical modeling in biology: epigenetics, meiosis, and an outlook.

PubMed

Richards, D; Berry, S; Howard, M

2012-01-01

In the past few years, mathematical modeling approaches in biology have begun to fulfill their promise by assisting in the dissection of complex biological systems. Here, we review two recent examples of predictive mathematical modeling in plant biology. The first involves the quantitative epigenetic silencing of the floral repressor gene FLC in Arabidopsis, mediated by a Polycomb-based system. The second involves the spatiotemporal dynamics of telomere bouquet formation in wheat-rye meiosis. Although both the biology and the modeling framework of the two systems are different, both exemplify how mathematical modeling can help to accelerate discovery of the underlying mechanisms in complex biological systems. In both cases, the models that developed were relatively minimal, including only essential features, but both nevertheless yielded fundamental insights. We also briefly review the current state of mathematical modeling in biology, difficulties inherent in its application, and its potential future development.

Complexity analysis and mathematical tools towards the modelling of living systems.

PubMed

Bellomo, N; Bianca, C; Delitala, M

2009-09-01

This paper is a review and critical analysis of the mathematical kinetic theory of active particles applied to the modelling of large living systems made up of interacting entities. The first part of the paper is focused on a general presentation of the mathematical tools of the kinetic theory of active particles. The second part provides a review of a variety of mathematical models in life sciences, namely complex social systems, opinion formation, evolution of epidemics with virus mutations, and vehicular traffic, crowds and swarms. All the applications are technically related to the mathematical structures reviewed in the first part of the paper. The overall contents are based on the concept that living systems, unlike the inert matter, have the ability to develop behaviour geared towards their survival, or simply to improve the quality of their life. In some cases, the behaviour evolves in time and generates destructive and/or proliferative events.

Workspace Program for Complex-Number Arithmetic

NASA Technical Reports Server (NTRS)

Patrick, M. C.; Howell, Leonard W., Jr.

1986-01-01

COMPLEX is workspace program designed to empower APL with complexnumber capabilities. Complex-variable methods provide analytical tools invaluable for applications in mathematics, science, and engineering. COMPLEX written in APL.

Dosimetry in x-ray-based breast imaging

PubMed Central

Dance, David R; Sechopoulos, Ioannis

2016-01-01

The estimation of the mean glandular dose to the breast (MGD) for x-ray based imaging modalities forms an essential part of quality control and is needed for risk estimation and for system design and optimisation. This review considers the development of methods for estimating the MGD for mammography, digital breast tomosynthesis (DBT) and dedicated breast CT (DBCT). Almost all of the methodology used employs Monte Carlo calculated conversion factors to relate the measurable quantity, generally the incident air kerma, to the MGD. After a review of the size and composition of the female breast, the various mathematical models used are discussed, with particular emphasis on models for mammography. These range from simple geometrical shapes, to the more recent complex models based on patient DBCT examinations. The possibility of patient-specific dose estimates is considered as well as special diagnostic views and the effect of breast implants. Calculations using the complex models show that the MGD for mammography is overestimated by about 30% when the simple models are used. The design and uses of breast-simulating test phantoms for measuring incident air kerma are outlined and comparisons made between patient and phantom-based dose estimates. The most widely used national and international dosimetry protocols for mammography are based on different simple geometrical models of the breast, and harmonisation of these protocols using more complex breast models is desirable. PMID:27617767

Dosimetry in x-ray-based breast imaging

NASA Astrophysics Data System (ADS)

Dance, David R.; Sechopoulos, Ioannis

2016-10-01

The estimation of the mean glandular dose to the breast (MGD) for x-ray based imaging modalities forms an essential part of quality control and is needed for risk estimation and for system design and optimisation. This review considers the development of methods for estimating the MGD for mammography, digital breast tomosynthesis (DBT) and dedicated breast CT (DBCT). Almost all of the methodology used employs Monte Carlo calculated conversion factors to relate the measurable quantity, generally the incident air kerma, to the MGD. After a review of the size and composition of the female breast, the various mathematical models used are discussed, with particular emphasis on models for mammography. These range from simple geometrical shapes, to the more recent complex models based on patient DBCT examinations. The possibility of patient-specific dose estimates is considered as well as special diagnostic views and the effect of breast implants. Calculations using the complex models show that the MGD for mammography is overestimated by about 30% when the simple models are used. The design and uses of breast-simulating test phantoms for measuring incident air kerma are outlined and comparisons made between patient and phantom-based dose estimates. The most widely used national and international dosimetry protocols for mammography are based on different simple geometrical models of the breast, and harmonisation of these protocols using more complex breast models is desirable.

Preschool predictors of mathematics in first grade children with autism spectrum disorder.

PubMed

Titeca, Daisy; Roeyers, Herbert; Josephy, Haeike; Ceulemans, Annelies; Desoete, Annemie

2014-11-01

Up till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5-6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6-7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Modeling of Pressure Drop During Refrigerant Condensation in Pipe Minichannels

NASA Astrophysics Data System (ADS)

Sikora, Małgorzata; Bohdal, Tadeusz

2017-12-01

Investigations of refrigerant condensation in pipe minichannels are very challenging and complicated issue. Due to the multitude of influences very important is mathematical and computer modeling. Its allows for performing calculations for many different refrigerants under different flow conditions. A large number of experimental results published in the literature allows for experimental verification of correctness of the models. In this work is presented a mathematical model for calculation of flow resistance during condensation of refrigerants in the pipe minichannel. The model was developed in environment based on conservation equations. The results of calculations were verified by authors own experimental investigations results.

MATHEMATICAL MANIPULATIONS OF ENANTIOMERIC DATA

EPA Science Inventory

The oral presentation describes the alternative method of peak fitting for the measurement of enantiomeric parameters such as enantiomeric ratio (ER) and enantiomer fraction (EF). The talk describes the disadvantage of using typical integrators, mathematical calculations such as...

Learning with Calculators: Doing More with Less

ERIC Educational Resources Information Center

Kissane, Barry

2017-01-01

It seems that calculators continue to be misunderstood as devices solely for calculation, although the likely contributions to learning mathematics with modern calculators arise from other characteristics. A four-part model to understand the educational significance of calculators underpins this paper. Each of the four components (representation,…

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

Gravitational orientation of the orbital complex, Salyut-6--Soyuz

NASA Technical Reports Server (NTRS)

Grecho, G. M.; Sarychev, V. A.; Legostayev, V. P.; Sazonov, V. V.; Gansvind, I. N.

1983-01-01

A simple mathematical model is proposed for the Salyut-6-Soyuz orbital complex motion with respect to the center of mass under the one-axis gravity-gradient orientation regime. This model was used for processing the measurements of the orbital complex motion parameters when the above orientation region was implemented. Some actual satellite motions are simulated and the satellite's aerodynamic parameters are determined. Estimates are obtained for the accuracy of measurements as well as that of the mathematical model.

Exploring Bilingual Teachers' Beliefs about Academic Language Development in Mathematics Teaching: Implications for Bilingual Teachers' Professional Development

ERIC Educational Resources Information Center

Canales-Vela, Viola

2017-01-01

The achievement of mathematics within Hispanic youth is of great concern across the nation. In order to improve student achievement in mathematics, the nature of a mathematics teacher's complex belief system must be understood (McGee & Wang, 2014). The purpose of this exploratory qualitative study is to investigate the K-5 bilingual teachers'…

Trends in International Mathematics and Science Study and Gendered Math Teaching in Kuwait

ERIC Educational Resources Information Center

Ahmad, Fatimah; Greenhalgh-Spencer, Heather

2017-01-01

This paper argues for a more complex literature around gender and math performance. In order to argue for this complexity, we present a small portion of data from a case study examining the performance of Kuwaiti students on the Trends in International Mathematics and Science Study and on Kuwait national math tests. Westernized discourses suggest…

Using Multiple Calibration Indices in Order to Capture the Complex Picture of What Affects Students' Accuracy of Feeling of Confidence

ERIC Educational Resources Information Center

Boekaerts, Monique; Rozendaal, Jeroen S.

2010-01-01

The present study used multiple calibration indices to capture the complex picture of fifth graders' calibration of feeling of confidence in mathematics. Specifically, the effects of gender, type of mathematical problem, instruction method, and time of measurement (before and after problem solving) on calibration skills were investigated. Fourteen…

Enhancing Students' Written Mathematical Arguments

ERIC Educational Resources Information Center

Lepak, Jerilynn

2014-01-01

Writing in mathematics is complex. The purpose of this article is to share how one teacher, Ms. Hill, used peer-review activities involving rubrics to explicitly communicate mathematical resources that students could draw from when justifying a claim. She found that helping students understand which type of statements could be used in…

Where Are the Quadratic's Complex Roots?

ERIC Educational Resources Information Center

Páll-Szabó, Ágnes Orsolya

2015-01-01

A picture is worth more than a thousand words--in mathematics too. Many students fail in learning mathematics because, in some cases, teachers do not offer the necessary visualization. Nowadays technology overcomes this problem: computer aided instruction is one of the most efficients methods in teaching mathematics. In this article we try to…

Equitable Mathematics Teaching and Learning in Practice: Exploring Students' Negotiations of Identity and Power

ERIC Educational Resources Information Center

Harper, Frances Kay

2017-01-01

This dissertation builds on and extends research on the relationship between equity-minded mathematics teaching, specifically teaching mathematics for social justice, complex instruction, and project-based learning, and students' learning and identity development. Although different in their structures and strategies, equity-minded mathematics…

The Object Metaphor and Synecdoche in Mathematics Classroom Discourse

ERIC Educational Resources Information Center

Font, Vicenc; Godino, Juan D.; Planas, Nuria; Acevedo, Jorge I.

2010-01-01

This article describes aspects of classroom discourse, illustrated through vignettes, that reveal the complex relationship between the forms in which mathematical objects exist and their ostensive representations. We illustrate various aspects of the process through which students come to consider the reality of mathematical objects that are…

Enhancing Undergraduate Mathematics Curriculum via Coding Theory and Cryptography

ERIC Educational Resources Information Center

Aydin, Nuh

2009-01-01

The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the…

Chaos and insect ecology

Treesearch

Jesse A. Logan; Fred P. Hain

1990-01-01

Recent advances in applied mathematical analysis have uncovered a fascinating and unexpected dynamical richness that underlies behavior of even the simplest non-linear mathematical models. Due to the complexity of solutions to these non-linear equations, a new mathematical term, chaos, has been coined to describe the resulting dynamics. This term captures the notion...

Conceptual Complexity and Apparent Contradictions in Mathematics Language

ERIC Educational Resources Information Center

Gough, John

2007-01-01

Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…

Using Mental Computation Training to Improve Complex Mathematical Performance

ERIC Educational Resources Information Center

Liu, Allison S.; Kallai, Arava Y.; Schunn, Christian D.; Fiez, Julie A.

2015-01-01

Mathematical fluency is important for academic and mathematical success. Fluency training programs have typically focused on fostering retrieval, which leads to math performance that does not reliably transfer to non-trained problems. More recent studies have focused on training number understanding and representational precision, but few have…

Precalculus teachers' perspectives on using graphing calculators: an example from one curriculum

NASA Astrophysics Data System (ADS)

Karadeniz, Ilyas; Thompson, Denisse R.

2018-01-01

Graphing calculators are hand-held technological tools currently used in mathematics classrooms. Teachers' perspectives on using graphing calculators are important in terms of exploring what teachers think about using such technology in advanced mathematics courses, particularly precalculus courses. A descriptive intrinsic case study was conducted to analyse the perspectives of 11 teachers using graphing calculators with potential Computer Algebra System (CAS) capability while teaching Functions, Statistics, and Trigonometry, a precalculus course for 11th-grade students developed by the University of Chicago School Mathematics Project. Data were collected from multiple sources as part of a curriculum evaluation study conducted during the 2007-2008 school year. Although all teachers were using the same curriculum that integrated CAS into the instructional materials, teachers had mixed views about the technology. Graphing calculator features were used much more than CAS features, with many teachers concerned about the use of CAS because of pressures from external assessments. In addition, several teachers found it overwhelming to learn a new technology at the same time they were learning a new curriculum. The results have implications for curriculum developers and others working with teachers to update curriculum and the use of advanced technologies simultaneously.

Mathematical figures.

PubMed

Fara, Patricia

2009-06-01

Renaissance philosophers believed that God had created a harmonious cosmos bonded together mathematically. This intellectual approach was also embraced by some artists, who incorporated complex numerical and geometrical symbolism within their portraits.

A Comprehensive Software and Database Management System for Glomerular Filtration Rate Estimation by Radionuclide Plasma Sampling and Serum Creatinine Methods.

PubMed

Jha, Ashish Kumar

2015-01-01

Glomerular filtration rate (GFR) estimation by plasma sampling method is considered as the gold standard. However, this method is not widely used because the complex technique and cumbersome calculations coupled with the lack of availability of user-friendly software. The routinely used Serum Creatinine method (SrCrM) of GFR estimation also requires the use of online calculators which cannot be used without internet access. We have developed user-friendly software "GFR estimation software" which gives the options to estimate GFR by plasma sampling method as well as SrCrM. We have used Microsoft Windows(®) as operating system and Visual Basic 6.0 as the front end and Microsoft Access(®) as database tool to develop this software. We have used Russell's formula for GFR calculation by plasma sampling method. GFR calculations using serum creatinine have been done using MIRD, Cockcroft-Gault method, Schwartz method, and Counahan-Barratt methods. The developed software is performing mathematical calculations correctly and is user-friendly. This software also enables storage and easy retrieval of the raw data, patient's information and calculated GFR for further processing and comparison. This is user-friendly software to calculate the GFR by various plasma sampling method and blood parameter. This software is also a good system for storing the raw and processed data for future analysis.

Finite Dimensional Approximations for Continuum Multiscale Problems

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

Berlyand, Leonid

2017-01-24

The completed research project concerns the development of novel computational techniques for modeling nonlinear multiscale physical and biological phenomena. Specifically, it addresses the theoretical development and applications of the homogenization theory (coarse graining) approach to calculation of the effective properties of highly heterogenous biological and bio-inspired materials with many spatial scales and nonlinear behavior. This theory studies properties of strongly heterogeneous media in problems arising in materials science, geoscience, biology, etc. Modeling of such media raises fundamental mathematical questions, primarily in partial differential equations (PDEs) and calculus of variations, the subject of the PI’s research. The focus of completed researchmore » was on mathematical models of biological and bio-inspired materials with the common theme of multiscale analysis and coarse grain computational techniques. Biological and bio-inspired materials offer the unique ability to create environmentally clean functional materials used for energy conversion and storage. These materials are intrinsically complex, with hierarchical organization occurring on many nested length and time scales. The potential to rationally design and tailor the properties of these materials for broad energy applications has been hampered by the lack of computational techniques, which are able to bridge from the molecular to the macroscopic scale. The project addressed the challenge of computational treatments of such complex materials by the development of a synergistic approach that combines innovative multiscale modeling/analysis techniques with high performance computing.« less

Methodology and Results of Mathematical Modelling of Complex Technological Processes

NASA Astrophysics Data System (ADS)

Mokrova, Nataliya V.

2018-03-01

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

Personal Finance Calculations.

ERIC Educational Resources Information Center

Argo, Mark

1982-01-01

Contains explanations and examples of mathematical calculations for a secondary level course on personal finance. How to calculate total monetary cost of an item, monthly payments, different types of interest, annual percentage rates, and unit pricing is explained. (RM)

Partial Support of Meeting of the Board on Mathematical Sciences and Their Applications

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

Weidman, Scott

2014-08-31

During the performance period, BMSA released the following major reports: Transforming Combustion Research through Cyberinfrastructure (2011); Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (2012); Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century (2012); Aging and the Macroeconomy: Long-Term Implications of an Older Population (2012); The Mathematical Sciences in 2025 (2013); Frontiers in Massive Data Analysis (2013); and Developing a 21st Century Global Library for Mathematics Research (2014).

Mathematical modeling of ignition of woodlands resulted from accident on the pipeline

NASA Astrophysics Data System (ADS)

Perminov, V. A.; Loboda, E. L.; Reyno, V. V.

2014-11-01

Accidents occurring at the sites of pipelines, accompanied by environmental damage, economic loss, and sometimes loss of life. In this paper we calculated the sizes of the possible ignition zones in emergency situations on pipelines located close to the forest, accompanied by the appearance of fireballs. In this paper, using the method of mathematical modeling calculates the maximum size of the ignition zones of vegetation as a result of accidental releases of flammable substances. The paper suggested in the context of the general mathematical model of forest fires give a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. The dependences of the size of the forest fuel for different amounts of leaked flammable substances and moisture content of vegetation.

The Views of Preservice Teachers about the Strengths and Limitations of the Use of Graphing Calculators in Mathematics Instruction

ERIC Educational Resources Information Center

Ozgun-Koca, S. Asli

2009-01-01

Handheld graphing technologies have fundamentally been utilized in the teaching and learning of many secondary school and college mathematics concepts. In order to observe the effects of these new kinds of technologies on students' learning of mathematics, their teachers need to decide whether it is reasonable to do, learn, and teach mathematics…

[Mathematical apparatus of the circuit theory in modeling of heat transfer upon extreme heating of an organism].

PubMed

2010-01-01

The mathematical model of heat transfer in whole-body hyperthermia, developed earlier by the author, has been refined using the mathematical apparatus of the circuit theory. The model can be used to calculate the temperature of each organ, which can increase the efficacy and safety of the immersion-convection technique of whole-body hyperthermia.

Grade 9 Pilot Test. Mathematics. June 1988 = 9e Annee Test Pilote. Mathematiques. Juin 1988.

ERIC Educational Resources Information Center

Alberta Dept. of Education, Edmonton.

This pilot test for ninth grade mathematics is written in both French and English. The test consists of 75 multiple-choice items. Students are given 90 minutes to complete the examination and the use of a calculator is highly recommended. The test content covers a wide range of mathematical topics including: decimals; exponents; arithmetic word…

A Caribbean Pre-Service Mathematics Teacher's Impetus to Integrate Computer Technology in His Practice

ERIC Educational Resources Information Center

Clarke, Pier Junor

2009-01-01

This article presents a case study of one pre-service secondary school mathematics (PSSM) teacher taken from a larger study within an English-speaking Caribbean context. The major goal of the larger study was to investigate the experiences and perceptions of the PSSM teachers as they explored the graphing calculator and mathematics software in…

What Mathematics Education May Prepare Students for the Society of the Future?

ERIC Educational Resources Information Center

Gravemeijer, Koeno; Stephan, Michelle; Julie, Cyril; Lin, Fou-Lai; Ohtani, Minoru

2017-01-01

This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what…

Individual differences in mathematical competence predict parietal brain activation during mental calculation.

PubMed

Grabner, Roland H; Ansari, Daniel; Reishofer, Gernot; Stern, Elsbeth; Ebner, Franz; Neuper, Christa

2007-11-01

Functional neuroimaging studies have revealed that parietal brain circuits subserve arithmetic problem solving and that their recruitment dynamically changes as a function of training and development. The present study investigated whether the brain activation during mental calculation is also modulated by individual differences in mathematical competence. Twenty-five adult students were selected from a larger pool based on their performance on standardized tests of intelligence and arithmetic and divided into groups of individuals with relatively lower and higher mathematical competence. These groups did not differ in their non-numerical intelligence or age. In an fMRI block-design, participants had to verify the correctness of single-digit and multi-digit multiplication problems. Analyses revealed that the individuals with higher mathematical competence displayed stronger activation of the left angular gyrus while solving both types of arithmetic problems. Additional correlational analyses corroborated the association between individual differences in mathematical competence and angular gyrus activation, even when variability in task performance was controlled for. These findings demonstrate that the recruitment of the left angular gyrus during arithmetic problem solving underlies individual differences in mathematical ability and suggests a stronger reliance on automatic, language-mediated processes in more competent individuals.

Role of shielding in modulating the effects of solar particle events: Monte Carlo calculation of absorbed dose and DNA complex lesions in different organs

NASA Technical Reports Server (NTRS)

Ballarini, F.; Biaggi, M.; De Biaggi, L.; Ferrari, A.; Ottolenghi, A.; Panzarasa, A.; Paretzke, H. G.; Pelliccioni, M.; Sala, P.; Scannicchio, D.;

Role of shielding in modulating the effects of solar particle events: Monte Carlo calculation of absorbed dose and DNA complex lesions in different organs

NASA Astrophysics Data System (ADS)

Ballarini, F.; Biaggi, M.; De Biaggi, L.; Ferrari, A.; Ottolenghi, A.; Panzarasa, A.; Paretzke, H. G.; Pelliccioni, M.; Sala, P.; Scannicchio, D.; Zankl, M.

2004-01-01

Distributions of absorbed dose and DNA clustered damage yields in various organs and tissues following the October 1989 solar particle event (SPE) were calculated by coupling the FLUKA Monte Carlo transport code with two anthropomorphic phantoms (a mathematical model and a voxel model), with the main aim of quantifying the role of the shielding features in modulating organ doses. The phantoms, which were assumed to be in deep space, were inserted into a shielding box of variable thickness and material and were irradiated with the proton spectra of the October 1989 event. Average numbers of DNA lesions per cell in different organs were calculated by adopting a technique already tested in previous works, consisting of integrating into "condensed-history" Monte Carlo transport codes - such as FLUKA - yields of radiobiological damage, either calculated with "event-by-event" track structure simulations, or taken from experimental works available in the literature. More specifically, the yields of "Complex Lesions" (or "CL", defined and calculated as a clustered DNA damage in a previous work) per unit dose and DNA mass (CL Gy -1 Da -1) due to the various beam components, including those derived from nuclear interactions with the shielding and the human body, were integrated in FLUKA. This provided spatial distributions of CL/cell yields in different organs, as well as distributions of absorbed doses. The contributions of primary protons and secondary hadrons were calculated separately, and the simulations were repeated for values of Al shielding thickness ranging between 1 and 20 g/cm 2. Slight differences were found between the two phantom types. Skin and eye lenses were found to receive larger doses with respect to internal organs; however, shielding was more effective for skin and lenses. Secondary particles arising from nuclear interactions were found to have a minor role, although their relative contribution was found to be larger for the Complex Lesions than for the absorbed dose, due to their higher LET and thus higher biological effectiveness.

Mathematical calculation skills required for drug administration in undergraduate nursing students to ensure patient safety: A descriptive study: Drug calculation skills in nursing students.

PubMed

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. Copyright © 2015 Elsevier Ltd. All rights reserved.

Investigation of the torsional stiffness of flexible disc coupling

NASA Astrophysics Data System (ADS)

Buryy, A.; Simonovsky, V.; Obolonik, V.

2017-08-01

Calculation of flexible coupling torsional stiffness is required when analyzing the torsional vibrations of the reciprocating machinery train. While having the lowest torsional stiffness of all the elements of the train, flexible coupling has a significant influence on the natural frequencies of torsional vibration. However, considering structural complexity of coupling, precise definition of its torsional stiffness is quite a difficult task. The paper presents a method for calculating the torsional stiffness of flexible disc coupling based on the study of its finite element model response under the action of torque. The analysis of the basic parameters that quantitatively and qualitatively affect the coupling torsional stiffness has been also provided. The results of the calculation as well as model adequacy, sufficient for practical application, have been confirmed at the experimental measurement of flexible disc coupling torsional stiffness. The obtained elastic characteristics (dependences of applied torque and torsional stiffness versus twist angle) are nonlinear in the initial stage of loading. This feature should be taken into account when creating reliable mathematical models of torsional vibrations of reciprocating machinery trains containing flexible disc couplings.

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the fourth of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

Nursing mathematics: the importance of application.

PubMed

Hutton, B M

This study explores the effectiveness of a revision programme in nursing mathematics for student nurses. Students who took the revision programme achieved a marked improvement in test results, although some still scored low in written tests. When interviewed, the students reported that they had difficulty applying written work in the classroom to actual calculations in the workplace. They found that only by 'doing' mathematics did the theory make sense. The author recommends that students should be encouraged to maximise the opportunities to practise mathematics in the clinical setting.

Effective Connectivity Reveals Strategy Differences in an Expert Calculator

PubMed Central

Minati, Ludovico; Sigala, Natasha

2013-01-01

Mathematical reasoning is a core component of cognition and the study of experts defines the upper limits of human cognitive abilities, which is why we are fascinated by peak performers, such as chess masters and mental calculators. Here, we investigated the neural bases of calendrical skills, i.e. the ability to rapidly identify the weekday of a particular date, in a gifted mental calculator who does not fall in the autistic spectrum, using functional MRI. Graph-based mapping of effective connectivity, but not univariate analysis, revealed distinct anatomical location of “cortical hubs” supporting the processing of well-practiced close dates and less-practiced remote dates: the former engaged predominantly occipital and medial temporal areas, whereas the latter were associated mainly with prefrontal, orbitofrontal and anterior cingulate connectivity. These results point to the effect of extensive practice on the development of expertise and long term working memory, and demonstrate the role of frontal networks in supporting performance on less practiced calculations, which incur additional processing demands. Through the example of calendrical skills, our results demonstrate that the ability to perform complex calculations is initially supported by extensive attentional and strategic resources, which, as expertise develops, are gradually replaced by access to long term working memory for familiar material. PMID:24086291

Intelligent control system for continuous technological process of alkylation

NASA Astrophysics Data System (ADS)

Gebel, E. S.; Hakimov, R. A.

2018-01-01

Relevance of intelligent control for complex dynamic objects and processes are shown in this paper. The model of a virtual analyzer based on a neural network is proposed. Comparative analysis of mathematical models implemented in MathLab software showed that the most effective from the point of view of the reproducibility of the result is the model with seven neurons in the hidden layer, the training of which was performed using the method of scaled coupled gradients. Comparison of the data from the laboratory analysis and the theoretical model are showed that the root-mean-square error does not exceed 3.5, and the calculated value of the correlation coefficient corresponds to a "strong" connection between the values.

Numerical image manipulation and display in solar astronomy

NASA Technical Reports Server (NTRS)

Levine, R. H.; Flagg, J. C.

1977-01-01

The paper describes the system configuration and data manipulation capabilities of a solar image display system which allows interactive analysis of visual images and on-line manipulation of digital data. Image processing features include smoothing or filtering of images stored in the display, contrast enhancement, and blinking or flickering images. A computer with a core memory of 28,672 words provides the capacity to perform complex calculations based on stored images, including computing histograms, selecting subsets of images for further analysis, combining portions of images to produce images with physical meaning, and constructing mathematical models of features in an image. Some of the processing modes are illustrated by some image sequences from solar observations.

"I Believe the Most Helpful Thing Was Him Skipping over the Proof": Examining PCK in a Senior Secondary Mathematics Lesson

ERIC Educational Resources Information Center

Maher, Nicole; Chick, Helen; Muir, Tracey

2016-01-01

Pedagogical content knowledge is widely considered an essential and complex facet of mathematics teacher knowledge, but little research has focused on PCK at the senior secondary level. This study explores some of the complexities of PCK in a teacher's lesson for senior secondary students by analysing data from lesson observation, the teacher's…

Students' Use of Mathematical Representations in Problem Solving.

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

2002-01-01

Documents the experiences of 25 first-year university students with regard to the kinds of tasks calculus instructors should design in order to engage students in mathematical practices that often require the use of a graphing calculator. (MM)

Snapshots of Applications in Mathematics: Thermal Systems and the Solar Oven.

ERIC Educational Resources Information Center

Callas, Dennis, Ed.; Hildreth, David J., Ed.; Bickford, Carl

1998-01-01

Showcases applications of mathematics designed to demonstrate to students how the topics under study are used in the real world or to solve problems. Presents an activity on thermal systems using spreadsheets or graphing calculators. (ASK)

The Mathematics of High School Physics

NASA Astrophysics Data System (ADS)

Kanderakis, Nikos

2016-10-01

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students' difficulties with the mathematics of high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations' symbols represent magnitudes with empirical meaning and units instead of pure numbers). Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world.

Complex Listening: Supporting Students to Listen as Mathematical Sense-Makers

ERIC Educational Resources Information Center

Hintz, Allison; Tyson, Kersti

2015-01-01

Participating in reform-oriented mathematical discussion calls on teachers and students to listen to one another in new and different ways. However, listening is an understudied dimension of teaching and learning mathematics. In this analysis, we draw on a sociocultural perspective and a conceptual framing of three types of listening--evaluative,…

Understanding Student Achievement in Mathematics and Science: The Case of Trinidad and Tobago

ERIC Educational Resources Information Center

Alexander, Vivian; Maeda, Yukiko

2015-01-01

This study aims to disentangle the complex relationships among student attributes, school context, and student performance in mathematics and science in Trinidad and Tobago, using the PISA 2009 data. Our findings reveal that schools account for a substantial amount of variation in students' mathematics and science performances. School…

Labelling Angles: Care, Indifference and Mathematical Symbols

ERIC Educational Resources Information Center

Long, Julie

2011-01-01

In this article, I explore tensions of care in the context of school mathematics by examining two accounts of a classroom moment involving labelling an angle. In particular, I draw attention to how caring for students and caring for mathematical ideas interplay in complex ways by inquiring into the two accounts through ideas of care and…

The Complexity of the Affordance-Ability Relationship When Second-Grade Children Interact with Mathematics Virtual Manipulative Apps

ERIC Educational Resources Information Center

Tucker, Stephen I.; Moyer-Packenham, Patricia S.; Westenskow, Arla; Jordan, Kerry E.

2016-01-01

The purpose of this study was to explore relationships between app affordances and user abilities in second graders' interactions with mathematics virtual manipulative touchscreen tablet apps. The research questions focused on varying manifestations of affordance-ability relationships during children's interactions with mathematics virtual…

Making It Count: Strategies for Improving Mathematics Instruction for Students in Short-Term Facilities. Strategy Guide

ERIC Educational Resources Information Center

Leone, Peter; Wilson, Michael; Mulcahy, Candace

2010-01-01

This guide is designed to support the development of mathematics proficiency for youth in short-term juvenile correctional facilities. Mathematics proficiency includes mastery and fluency in foundational numeracy; an understanding of complex, grade-appropriate concepts and procedures; and application of those competencies to solve relevant,…

Differentiated Instruction: Effects on Primary Students' Mathematics Achievement

ERIC Educational Resources Information Center

Maxey, Katherine S.

2013-01-01

Low mathematics achievement is a concern of educators and the general public because many Americans are emerging from school without the requisite mathematics skills to function well in our complex, quickly changing society. Individuals with low math abilities are more likely to be unemployed and be a burden to fellow taxpayers. Educators and…

Jabberwocky: The Complexities of Mathematical English

ERIC Educational Resources Information Center

Carter, Merilyn; Quinnell, Lorna

2012-01-01

Students find it hard to interpret mathematical problem texts. Mathematics is a unique language with its own symbols (grapho-phonics), vocabulary (lexicon), grammar (syntax), semantics and literature. As in any other language, to make meaning of the text, the student must learn: (1) signs and symbols (for example: [division], x, [not equal to]);…

Mathematical Rigor in the Common Core

ERIC Educational Resources Information Center

Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin

2013-01-01

A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

Student nurses need more than maths to improve their drug calculating skills.

PubMed

Wright, Kerri

2007-05-01

Nurses need to be able to calculate accurate drug calculations in order to safely administer drugs to their patients (NMC, 2002). Studies have shown however that nurses do not always have the necessary skills to calculate accurate drug dosages and are potentially administering incorrect dosages of drugs to their patients (Hutton, M. 1998. Nursing Mathematics: the importance of application. Nursing Standard 13(11), 35-38; Kapborg, I. 1994. Calculation and administration of drug dosage by Swedish nurses, Student Nurses and Physicians. International Journal for Quality in Health Care 6(4), 389-395; O'Shea, E. 1999. Factors contributing to medication errors: a literature review. Journal of Advanced Nursing 8, 496-504; Wilson, A. 2003. Nurses maths: researching a practical approach. Nursing Standard 17(47), 33-36). The literature indicates that in order to improve drug calculations strategies need to focus on both the mathematical skills and conceptual skills of student nurses so they can interpret clinical data into drug calculations to be solved. A study was undertaken to investigate the effectiveness of implementing several strategies which focussed on developing the mathematical and conceptual skills of student nurses to improve their drug calculation skills. The study found that implementing a range of strategies which addressed these two developmental areas significantly improved the drug calculation skills of nurses. The study also indicates that a range of strategies has the potential ensuring that the skills taught are retained by the student nurses. Although the strategies significantly improved the drug calculation skills of student nurses, the fact that only 2 students were able to achieve 100% in their drug calculation test indicates a need for further research into this area.

Mathematical model for gyroscope effects

NASA Astrophysics Data System (ADS)

Usubamatov, Ryspek

2015-05-01

Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).

[Differential diagnosis of primary and secondary mathematical learning disability – indications from the dyscalculia test Basis-Math 4–8].

PubMed

Krinzinger, Helga

2016-09-01

Studies in children with AD(H)D without mathematical learning disability (MLD) as well as studies on the effects of methylphenidate on arithmetic have shown that most deficits in mathematics and most error types commonly described as specific to developmental dyscalculia (e. g., finger-counting, fact-retrieval deficit, complex counting, difficulties with carry/borrow procedures, self-corrections) cannot be classified as such and should thus not be used for the differential diagnosis of primary dyscalculia and secondary MLD. This article proposes using the overall score in the dyscalculia test Basis-Math 4-8 (Moser Opitz et al., 2010) as well as implausible subtraction errors as a marker for dyscalculia and the number of self-corrections made during the test as a cognitive marker for attention deficits. Hierarchical cluster analyses were calculated in a sample of 51 clinically referred children with normal IQ and suspicion of MLD, using IQ, years of schooling, overall score of the Basis-Math 4–8 and number of self-corrections in this test as variables. The results revealed a subgroup with primary dyscalculia as well as three subgroups with secondary MLD (two with attention deficit hyperactivity disorder, one with depression and one small subgroup with high IQ). In conclusion, the Basis-Math 4–8 (Moser Opitz et al., 2010) can offer substantial information for the differential diagnosis of dyscalculia and secondary deficits in mathematics due to attention problems and enable optimization of treatment decisions for the different groups.

Indirect Lightning Safety Assessment Methodology

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

Ong, M M; Perkins, M P; Brown, C G

2009-04-24

Lightning is a safety hazard for high-explosives (HE) and their detonators. In the However, the current flowing from the strike point through the rebar of the building The methodology for estimating the risk from indirect lighting effects will be presented. It has two parts: a method to determine the likelihood of a detonation given a lightning strike, and an approach for estimating the likelihood of a strike. The results of these two parts produce an overall probability of a detonation. The probability calculations are complex for five reasons: (1) lightning strikes are stochastic and relatively rare, (2) the quality ofmore » the Faraday cage varies from one facility to the next, (3) RF coupling is inherently a complex subject, (4) performance data for abnormally stressed detonators is scarce, and (5) the arc plasma physics is not well understood. Therefore, a rigorous mathematical analysis would be too complex. Instead, our methodology takes a more practical approach combining rigorous mathematical calculations where possible with empirical data when necessary. Where there is uncertainty, we compensate with conservative approximations. The goal is to determine a conservative estimate of the odds of a detonation. In Section 2, the methodology will be explained. This report will discuss topics at a high-level. The reasons for selecting an approach will be justified. For those interested in technical details, references will be provided. In Section 3, a simple hypothetical example will be given to reinforce the concepts. While the methodology will touch on all the items shown in Figure 1, the focus of this report is the indirect effect, i.e., determining the odds of a detonation from given EM fields. Professor Martin Uman from the University of Florida has been characterizing and defining extreme lightning strikes. Using Professor Uman's research, Dr. Kimball Merewether at Sandia National Laboratory in Albuquerque calculated the EM fields inside a Faraday-cage type facility, when the facility is struck by lightning. In the following examples we will use Dr. Merewether's calculations from a poor quality Faraday cage as the input for the RF coupling analysis. coupling of radio frequency (RF) energy to explosive components is an indirect effect of currents [1]. If HE is adequately separated from the walls of the facility that is struck by disassembled have been turned into Faraday-cage structures to protect against lightning is initiation of the HE. last couple of decades, DOE facilities where HE is manufactured, assembled, stored or lightning. The most sensitive component is typically a detonator, and the safety concern lightning, electrons discharged from the clouds should not reach the HE components. radio receiver, the metal cable of a detonator can extract energy from the EM fields. This to the earth will create electromagnetic (EM) fields in the facility. Like an antenna in a« less

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

PubMed

Kim, Sangdan; Han, Suhee

2010-01-01

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

Drawing Nomograms with R: applications to categorical outcome and survival data.

PubMed

Zhang, Zhongheng; Kattan, Michael W

2017-05-01

Outcome prediction is a major task in clinical medicine. The standard approach to this work is to collect a variety of predictors and build a model of appropriate type. The model is a mathematical equation that connects the outcome of interest with the predictors. A new patient with given clinical characteristics can be predicted for outcome with this model. However, the equation describing the relationship between predictors and outcome is often complex and the computation requires software for practical use. There is another method called nomogram which is a graphical calculating device allowing an approximate graphical computation of a mathematical function. In this article, we describe how to draw nomograms for various outcomes with nomogram() function. Binary outcome is fit by logistic regression model and the outcome of interest is the probability of the event of interest. Ordinal outcome variable is also discussed. Survival analysis can be fit with parametric model to fully describe the distributions of survival time. Statistics such as the median survival time, survival probability up to a specific time point are taken as the outcome of interest.

Mathematics, anxiety, and the brain.

PubMed

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

Nursing students' mathematic calculation skills.

PubMed

Rainboth, Lynde; DeMasi, Chris

2006-12-01

This mixed method study used a pre-test/post-test design to evaluate the efficacy of a teaching strategy in improving beginning nursing student learning outcomes. During a 4-week student teaching period, a convenience sample of 54 sophomore level nursing students were required to complete calculation assignments, taught one calculation method, and mandated to attend medication calculation classes. These students completed pre- and post-math tests and a major medication mathematic exam. Scores from the intervention student group were compared to those achieved by the previous sophomore class. Results demonstrated a statistically significant improvement from pre- to post-test and the students who received the intervention had statistically significantly higher scores on the major medication calculation exam than did the students in the control group. The evaluation completed by the intervention group showed that the students were satisfied with the method and outcome.

Mathematical Knowledge and Understanding for Effective Participation in Australian Society. A National Statement on Mathematics for Australian Schools.

ERIC Educational Resources Information Center

Australian Association of Mathematics Teachers, Adelaide.

In a multicultural society such as Australia, it can be difficult to acquire a strong mathematics education because of language, locale, or other differences including access to technology. The widespread use of devices such as calculators and computers has changed the nature of work. It has become more important for students to have the…

Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Reddy, C. J.

2011-01-01

This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.

Mathematical modeling of high and low temperature heat pipes

NASA Technical Reports Server (NTRS)

Chi, S. W.

1971-01-01

Mathematical models are developed for calculating heat-transfer limitations of high-temperature heat pipes and heat-transfer limitations and temperature gradient of low temperature heat pipes. Calculated results are compared with the available experimental data from various sources to increase confidence in the present math models. Complete listings of two computer programs for high- and low-temperature heat pipes respectively are appended. These programs enable the performance of heat pipes with wrapped-screen, rectangular-groove or screen-covered rectangular-groove wick to be predicted.

Formal methods in computer system design

NASA Astrophysics Data System (ADS)

Hoare, C. A. R.

1989-12-01

This note expounds a philosophy of engineering design which is stimulated, guided and checked by mathematical calculations and proofs. Its application to software engineering promises the same benifits as those derived from the use of mathematics in all other branches of modern science.

Mathematics and Demography.

ERIC Educational Resources Information Center

Schwartz, Richard

1992-01-01

Suggests that teachers use mathematics problems related to the "1992 World Population Data Sheet" to teach students about such population-related issues as hunger, resource scarcity, poverty, and pollution. Offers sample problems involving percents, ratios, basic calculations, sequences, variability, graphs, averages, and correlation. Includes a…

Comparison of the calculation QRS angle for bundle branch block detection

NASA Astrophysics Data System (ADS)

Goeirmanto, L.; Mengko, R.; Rajab, T. L.

2016-04-01

QRS angle represent condition of blood circulation in the heart. Normally QRS angle is between -30 until 90 degree. Left Axis Defiation (LAD) and Right Axis Defiation (RAD) are abnormality conditions that lead to Bundle Branch Block. QRS angle is calculated using common method from physicians and compared to mathematical method using difference amplitudos and difference areas. We analyzed the standard 12 lead electrocardiogram data from MITBIH physiobank database. All methods using lead I and lead avF produce similar QRS angle and right QRS axis quadrant. QRS angle from mathematical method using difference areas is close to common method from physician. Mathematical method using difference areas can be used as a trigger for detecting heart condition.

Concentrator optical characterization using computer mathematical modelling and point source testing

NASA Technical Reports Server (NTRS)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

Rescheduling nursing shifts: scoping the challenge and examining the potential of mathematical model based tools.

PubMed

Clark, Alistair; Moule, Pam; Topping, Annie; Serpell, Martin

2015-05-01

To review research in the literature on nursing shift scheduling / rescheduling, and to report key issues identified in a consultation exercise with managers in four English National Health Service trusts to inform the development of mathematical tools for rescheduling decision-making. Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives from scheduling. Poor rescheduling decisions can have quality, cost and morale implications. A systematic critical literature review identified rescheduling issues and existing mathematic modelling tools. A consultation exercise with nursing managers examined the complex challenges associated with rescheduling. Minimal research exists on rescheduling compared with scheduling. Poor rescheduling can result in greater disruption to planned nursing shifts and may impact negatively on the quality and cost of patient care, and nurse morale and retention. Very little research examines management challenges or mathematical modelling for rescheduling. Shift rescheduling is a complex and frequent management activity that is more challenging than scheduling. Mathematical modelling may have potential as a tool to support managers to minimise rescheduling disruption. The lack of specific methodological support for rescheduling that takes into account its complexity, increases the likelihood of harm for patients and stress for nursing staff and managers. © 2013 John Wiley & Sons Ltd.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

PubMed

Morgan, Paul L; Farkas, George; Maczuga, Steve

2015-06-01

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1 st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement-three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1 st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ES s = .05-.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ES s = .03-.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD.

Integrated Modeling of Complex Optomechanical Systems

NASA Astrophysics Data System (ADS)

Andersen, Torben; Enmark, Anita

2011-09-01

Mathematical modeling and performance simulation are playing an increasing role in large, high-technology projects. There are two reasons; first, projects are now larger than they were before, and the high cost calls for detailed performance prediction before construction. Second, in particular for space-related designs, it is often difficult to test systems under realistic conditions beforehand, and mathematical modeling is then needed to verify in advance that a system will work as planned. Computers have become much more powerful, permitting calculations that were not possible before. At the same time mathematical tools have been further developed and found acceptance in the community. Particular progress has been made in the fields of structural mechanics, optics and control engineering, where new methods have gained importance over the last few decades. Also, methods for combining optical, structural and control system models into global models have found widespread use. Such combined models are usually called integrated models and were the subject of this symposium. The objective was to bring together people working in the fields of groundbased optical telescopes, ground-based radio telescopes, and space telescopes. We succeeded in doing so and had 39 interesting presentations and many fruitful discussions during coffee and lunch breaks and social arrangements. We are grateful that so many top ranked specialists found their way to Kiruna and we believe that these proceedings will prove valuable during much future work.

An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.

PubMed

Dannemann, Martin; Kucher, Michael; Kirsch, Jasmin; Binkowski, Alexander; Modler, Niels; Hannig, Christian; Weber, Marie-Theres

2017-04-01

Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals. Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model. The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry. With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

The Programmable Calculator in the Classroom.

ERIC Educational Resources Information Center

Stolarz, Theodore J.

The uses of programable calculators in the mathematics classroom are presented. A discussion of the "microelectronics revolution" that has brought programable calculators into our society is also included. Pointed out is that the logical or mental processes used to program the programable calculator are identical to those used to program…

Assessing pediatrics residents' mathematical skills for prescribing medication: a need for improved training.

PubMed

Glover, Mark L; Sussmane, Jeffrey B

2002-10-01

To evaluate residents' skills in performing basic mathematical calculations used for prescribing medications to pediatric patients. In 2001, a test of ten questions on basic calculations was given to first-, second-, and third-year residents at Miami Children's Hospital in Florida. Four additional questions were included to obtain the residents' levels of training, specific pediatrics intensive care unit (PICU) experience, and whether or not they routinely double-checked doses and adjusted them for each patient's weight. The test was anonymous and calculators were permitted. The overall score and the score for each resident class were calculated. Twenty-one residents participated. The overall average test score and the mean test score of each resident class was less than 70%. Second-year residents had the highest mean test scores, although there was no significant difference between the classes of residents (p =.745) or relationship between the residents' PICU experiences and their exam scores (p =.766). There was no significant difference between residents' levels of training and whether they double-checked their calculations (p =.633) or considered each patient's weight relative to the dose prescribed (p =.869). Seven residents committed tenfold dosing errors, and one resident committed a 1,000-fold dosing error. Pediatrics residents need to receive additional education in performing the calculations needed to prescribe medications. In addition, residents should be required to demonstrate these necessary mathematical skills before they are allowed to prescribe medications.

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)

Dispositions in the Field: Viewing Mathematics Teacher Education through the Lens of Bourdieu's Social Field Theory

ERIC Educational Resources Information Center

Nolan, Kathleen

2012-01-01

Mathematics teacher educators are confronted with numerous challenges and complexities as they work to inspire prospective teachers to embrace inquiry-based pedagogies. The research study described in this paper asks what a teacher educator and faculty advisor can learn from prospective secondary mathematics teachers as they construct (and are…

Teaching Mathematics in Two Languages: A Teaching Dilemma of Malaysian Chinese Primary Schools

ERIC Educational Resources Information Center

Lim, Chap Sam; Presmeg, Norma

2011-01-01

This paper discusses a teaching dilemma faced by mathematics teachers in the Malaysian Chinese primary schools in coping with the latest changes in language policy. In 2003, Malaysia launched a new language policy of teaching mathematics using English as the language of instruction in all schools. However, due to the complex sociocultural demands…

How to Combine Collaboration Scripts and Heuristic Worked Examples to Foster Mathematical Argumentation--When Working Memory Matters

ERIC Educational Resources Information Center

Schwaighofer, Matthias; Vogel, Freydis; Kollar, Ingo; Ufer, Stefan; Strohmaier, Anselm; Terwedow, Ilka; Ottinger, Sarah; Reiss, Kristina; Fischer, Frank

2017-01-01

Mathematical argumentation skills (MAS) are considered an important outcome of mathematics learning, particularly in secondary and tertiary education. As MAS are complex, an effective way of supporting their acquisition may require combining different scaffolds. However, how to combine different scaffolds is a delicate issue, as providing learners…

About the Complexities of Video-Based Assessments: Theoretical and Methodological Approaches to Overcoming Shortcomings of Research on Teachers' Competence

ERIC Educational Resources Information Center

Kaiser, Gabriele; Busse, Andreas; Hoth, Jessica; König, Johannes; Blömeke, Sigrid

2015-01-01

Research on the evaluation of the professional knowledge of mathematics teachers (comprising for example mathematical content knowledge, mathematics pedagogical content knowledge and general pedagogical knowledge) has become prominent in the last decade; however, the development of video-based assessment approaches is a more recent topic. This…

Validity-Supporting Evidence of the Self-Efficacy for Teaching Mathematics Instrument

ERIC Educational Resources Information Center

McGee, Jennifer R.; Wang, Chuang

2014-01-01

The purpose of this study is to provide evidence of reliability and validity of the Self-Efficacy for Teaching Mathematics Instrument (SETMI). Self-efficacy, as defined by Bandura, was the theoretical framework for the development of the instrument. The complex belief systems of mathematics teachers, as touted by Ernest provided insights into the…

A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

The Priorities and Challenges of Primary Teachers' Knowledge in Their Mathematics Planning

ERIC Educational Resources Information Center

Davidson, Aylie

2016-01-01

There is growing consensus that the process of planning mathematics lessons is as complex as teaching them, yet there is limited research on this. This paper reports on one aspect of a project examining issues in primary teachers' mathematics planning. The results, taken from a questionnaire completed by 62 primary teachers, indicate that when…

Shifting More than the Goal Posts: Developing Classroom Norms of Inquiry-Based Learning in Mathematics

ERIC Educational Resources Information Center

Makar, Katie; Fielding-Wells, Jill

2018-01-01

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex…

Entering into Dialogue about the Mathematical Value of Contextual Mathematising Tasks

ERIC Educational Resources Information Center

Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng

2018-01-01

Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for…

How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling

ERIC Educational Resources Information Center

Johnston, Peter R.

2013-01-01

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

Dosimetry for nonuniform activity distributions: a method for the calculation of 3D absorbed-dose distribution without the use of voxel S-values, point kernels, or Monte Carlo simulations.

PubMed

Traino, A C; Marcatili, S; Avigo, C; Sollini, M; Erba, P A; Mariani, G

2013-04-01

Nonuniform activity within the target lesions and the critical organs constitutes an important limitation for dosimetric estimates in patients treated with tumor-seeking radiopharmaceuticals. The tumor control probability and the normal tissue complication probability are affected by the distribution of the radionuclide in the treated organ/tissue. In this paper, a straightforward method for calculating the absorbed dose at the voxel level is described. This new method takes into account a nonuniform activity distribution in the target/organ. The new method is based on the macroscopic S-values (i.e., the S-values calculated for the various organs, as defined in the MIRD approach), on the definition of the number of voxels, and on the raw-count 3D array, corrected for attenuation, scatter, and collimator resolution, in the lesion/organ considered. Starting from these parameters, the only mathematical operation required is to multiply the 3D array by a scalar value, thus avoiding all the complex operations involving the 3D arrays. A comparison with the MIRD approach, fully described in the MIRD Pamphlet No. 17, using S-values at the voxel level, showed a good agreement between the two methods for (131)I and for (90)Y. Voxel dosimetry is becoming more and more important when performing therapy with tumor-seeking radiopharmaceuticals. The method presented here does not require calculating the S-values at the voxel level, and thus bypasses the mathematical problems linked to the convolution of 3D arrays and to the voxel size. In the paper, the results obtained with this new simplified method as well as the possibility of using it for other radionuclides commonly employed in therapy are discussed. The possibility of using the correct density value of the tissue/organs involved is also discussed.

A mathematical method for verifying the validity of measured information about the flows of energy resources based on the state estimation theory

NASA Astrophysics Data System (ADS)

Pazderin, A. V.; Sof'in, V. V.; Samoylenko, V. O.

2015-11-01

Efforts aimed at improving energy efficiency in all branches of the fuel and energy complex shall be commenced with setting up a high-tech automated system for monitoring and accounting energy resources. Malfunctions and failures in the measurement and information parts of this system may distort commercial measurements of energy resources and lead to financial risks for power supplying organizations. In addition, measurement errors may be connected with intentional distortion of measurements for reducing payment for using energy resources on the consumer's side, which leads to commercial loss of energy resource. The article presents a universal mathematical method for verifying the validity of measurement information in networks for transporting energy resources, such as electricity and heat, petroleum, gas, etc., based on the state estimation theory. The energy resource transportation network is represented by a graph the nodes of which correspond to producers and consumers, and its branches stand for transportation mains (power lines, pipelines, and heat network elements). The main idea of state estimation is connected with obtaining the calculated analogs of energy resources for all available measurements. Unlike "raw" measurements, which contain inaccuracies, the calculated flows of energy resources, called estimates, will fully satisfy the suitability condition for all state equations describing the energy resource transportation network. The state equations written in terms of calculated estimates will be already free from residuals. The difference between a measurement and its calculated analog (estimate) is called in the estimation theory an estimation remainder. The obtained large values of estimation remainders are an indicator of high errors of particular energy resource measurements. By using the presented method it is possible to improve the validity of energy resource measurements, to estimate the transportation network observability, to eliminate the energy resource flows measurement imbalances, and to filter invalid measurements at the data acquisition and processing stage in performing monitoring of an automated energy resource monitoring and accounting system.

Connecting mathematics learning through spatial reasoning

NASA Astrophysics Data System (ADS)

Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

2018-03-01

Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new pathways for mathematics learning, pedagogy and curriculum. Novel analytical tools will map the unknown complex systems linking spatial and mathematical concepts. It will involve the design, implementation and evaluation of a Spatial Reasoning Mathematics Program (SRMP) in Grades 3 to 5. Benefits will be seen through development of critical spatial skills for students, increased teacher capability and informed policy and curriculum across STEM education.

Quantitative assessment model for gastric cancer screening

PubMed Central

Chen, Kun; Yu, Wei-Ping; Song, Liang; Zhu, Yi-Min

2005-01-01

AIM: To set up a mathematic model for gastric cancer screening and to evaluate its function in mass screening for gastric cancer. METHODS: A case control study was carried on in 66 patients and 198 normal people, then the risk and protective factors of gastric cancer were determined, including heavy manual work, foods such as small yellow-fin tuna, dried small shrimps, squills, crabs, mothers suffering from gastric diseases, spouse alive, use of refrigerators and hot food, etc. According to some principles and methods of probability and fuzzy mathematics, a quantitative assessment model was established as follows: first, we selected some factors significant in statistics, and calculated weight coefficient for each one by two different methods; second, population space was divided into gastric cancer fuzzy subset and non gastric cancer fuzzy subset, then a mathematic model for each subset was established, we got a mathematic expression of attribute degree (AD). RESULTS: Based on the data of 63 patients and 693 normal people, AD of each subject was calculated. Considering the sensitivity and specificity, the thresholds of AD values calculated were configured with 0.20 and 0.17, respectively. According to these thresholds, the sensitivity and specificity of the quantitative model were about 69% and 63%. Moreover, statistical test showed that the identification outcomes of these two different calculation methods were identical (P>0.05). CONCLUSION: The validity of this method is satisfactory. It is convenient, feasible, economic and can be used to determine individual and population risks of gastric cancer. PMID:15655813

The Mathematics of Computer Error.

ERIC Educational Resources Information Center

Wood, Eric

1988-01-01

Why a computer error occurred is considered by analyzing the binary system and decimal fractions. How the computer stores numbers is then described. Knowledge of the mathematics behind computer operation is important if one wishes to understand and have confidence in the results of computer calculations. (MNS)

46 CFR 162.060-26 - Land-based testing requirements.

Code of Federal Regulations, 2012 CFR

2012-10-01

.... (iv) The manufacturer of the BWMS must demonstrate by using mathematical modeling, computational fluid dynamics modeling, and/or by calculations, that any downscaling will not affect the ultimate functioning... mathematical and computational fluid dynamics modeling) must be clearly identified in the Experimental Design...

46 CFR 162.060-26 - Land-based testing requirements.

Code of Federal Regulations, 2014 CFR

2014-10-01

.... (iv) The manufacturer of the BWMS must demonstrate by using mathematical modeling, computational fluid dynamics modeling, and/or by calculations, that any downscaling will not affect the ultimate functioning... mathematical and computational fluid dynamics modeling) must be clearly identified in the Experimental Design...

46 CFR 162.060-26 - Land-based testing requirements.

Code of Federal Regulations, 2013 CFR

2013-10-01

.... (iv) The manufacturer of the BWMS must demonstrate by using mathematical modeling, computational fluid dynamics modeling, and/or by calculations, that any downscaling will not affect the ultimate functioning... mathematical and computational fluid dynamics modeling) must be clearly identified in the Experimental Design...

Recent advances in mathematical criminology. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Rodríguez, Nancy

2015-03-01

The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].

A mathematical model for calculation of 90Sr absorbed dose in dental tissues: elaboration and comparison to EPR measurements.

PubMed

Shishkina, E A; Lyubashevskii, N M; Tolstykh, E I; Ignatiev, E A; Betenekova, T A; Nikiforov, S V

2001-09-01

A mathematical model for calculation of the 90Sr absorbed doses in dental tissues is presented. The results of the Monte-Carlo calculations are compared to the data obtained by EPR measurements of dental tissues. Radiometric measurements of the 90Sr concentrations. TLD and EPR dosimetry investigations were performed in animal (dog) study. The importance of the irregular 90Sr distribution in the dentine for absorbed dose formation has been shown. The dominant dose formation factors (main source-tissues) were identified for the crown dentine and enamel. The model has shown agreement with experimental data which allows to determine further directions of the human tooth model development.

Estimation of true serum thyroglobulin concentration using simultaneous measurement of serum antithyroglobulin antibody.

PubMed

Ahn, Byeong-Cheol; Lee, Won Kee; Jeong, Shin Young; Lee, Sang-Woo; Lee, Jaetae

2013-01-01

We investigated the analytical interference of antithyroglobulin antibody (TgAb) to thyroglobulin (Tg) measurement and tried to convert measured Tg concentration to true Tg concentration using a mathematical equation which includes a concentration of TgAb. Methods. Tg was measured by immunoradiometric assay and TgAb by radioimmunoassy. Experimental samples were produced by mixing Tg and TgAb standard solutions or mixing patients' serum with high Tg or high TgAb. Mathematical equations for prediction of expected Tg concentration with measured Tg and TgAb concentrations were deduced. The Tg concentration calculated using the equations was compared with the expected Tg concentration. Results. Measured Tg concentrations of samples having high TgAb were significantly lower than their expected Tg concentration. Magnitude of TgAb interference with the Tg assay showed a positive correlation with concentration of TgAb. Mathematical equations for estimation of expected Tg concentration using measured Tg and TgAb concentrations were successfully deduced and the calculated Tg concentration showed excellent correlation with expected Tg concentration. Conclusions. A mathematic equation for estimation of true Tg concentration using measured Tg and TgAb concentration was deduced. Tg concentration calculated by use of the equation might be more valuable than measured Tg concentration in patients with differentiated thyroid cancer.

Development of structural model of adaptive training complex in ergatic systems for professional use

NASA Astrophysics Data System (ADS)

Obukhov, A. D.; Dedov, D. L.; Arkhipov, A. E.

2018-03-01

The article considers the structural model of the adaptive training complex (ATC), which reflects the interrelations between the hardware, software and mathematical model of ATC and describes the processes in this subject area. The description of the main components of software and hardware complex, their interaction and functioning within the common system are given. Also the article scrutinizers a brief description of mathematical models of personnel activity, a technical system and influences, the interactions of which formalize the regularities of ATC functioning. The studies of main objects of training complexes and connections between them will make it possible to realize practical implementation of ATC in ergatic systems for professional use.

Early Career Teachers' Ability to Focus on Typical Students Errors in Relation to the Complexity of a Mathematical Topic

ERIC Educational Resources Information Center

Pankow, Lena; Kaiser, Gabriele; Busse, Andreas; König, Johannes; Blömeke, Sigrid; Hoth, Jessica; Döhrmann, Martina

2016-01-01

The paper presents results from a computer-based assessment in which 171 early career mathematics teachers from Germany were asked to anticipate typical student errors on a given mathematical topic and identify them under time constraints. Fast and accurate perception and knowledge-based judgments are widely accepted characteristics of teacher…

Teacher and Student Use of Gesture and Access to Secondary Mathematics for Students with Learning Disabilities: An Exploratory Study

ERIC Educational Resources Information Center

Hord, Casey; Marita, Samantha; Walsh, Jennifer B.; Tomaro, Taylor-Marie; Gordon, Kiyana; Saldanha, Rene L.

2016-01-01

The researchers conducted an exploratory qualitative case study to describe the gesturing processes of tutors and students when engaging in secondary mathematics. The use of gestures ranged in complexity from simple gestures, such as pointing and moving the pointing finger in an arching motion to demonstrate mathematics relationships within…

Activities for Calculators.

ERIC Educational Resources Information Center

Hiatt, Arthur A.

1987-01-01

Ten activities that give learners in grades 5-8 a chance to explore mathematics with calculators are provided. The activity cards involve such topics as odd addends, magic squares, strange projects, and conjecturing rules. (MNS)

Towards a Definition of Basic Numeracy

ERIC Educational Resources Information Center

Girling, Michael

1977-01-01

The author redefines basic numeracy as the ability to use a four-function calculator sensibly. He then defines "sensibly" and considers the place of algorithms in the scheme of mathematical calculations. (MN)

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study*

PubMed Central

Huang, Jian; Du, Feng-lei; Yao, Yuan; Wan, Qun; Wang, Xiao-song; Chen, Fei-yan

2015-01-01

Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation. PMID:26238541

The analysis of isotherms of radionuclides sorption by inorganic sorbents

NASA Astrophysics Data System (ADS)

Bykova, E. P.; Nedobukh, T. A.

2017-09-01

The isotherm of cesium sorption by an inorganic sorbent based on granulated glauconite obtained in a wide cesium concentrations range was mathematically treated using Langmuir, Freundlich and Redlich-Peterson sorption models. The algorithms of mathematical treatment of experimental data using these models were described; parameters of all isotherms were determined. It was shown that estimating the correctness of various sorption models relies not only on the correlation coefficient values but also on the closeness of the calculated and experimental data. Various types of sorption sites were found as a result of mathematical treatment of the isotherm of cesium sorption. The algorithm was described and calculation of parameters of the isotherm was performed under the assumption that simultaneous sorption on all three types of sorption sites occurs in accordance with Langmuir isotherm.

Mathematical Modeling of Loop Heat Pipes

NASA Technical Reports Server (NTRS)

Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.

1998-01-01

The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

Mathematical concepts for modeling human behavior in complex man-machine systems

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1979-01-01

Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.

Modelling dynamics of atmosphere ventilation and industrial city’s air pollution analysis: New approach

NASA Astrophysics Data System (ADS)

Glushkov, A. V.; Khetselius, O. Yu; Agayar, E. V.; Buyadzhi, V. V.; Romanova, A. V.; Mansarliysky, V. F.

2017-10-01

We present a new effective approach to analysis and modelling the natural air ventilation in an atmosphere of the industrial city, which is based on the Arakawa-Schubert and Glushkov models, modified to calculate the current involvement of the ensemble of clouds, and advanced mathematical methods of modelling an unsteady turbulence in the urban area. For the first time the methods of a plane complex field and spectral expansion algorithms are applied to calculate the air circulation for the cloud layer arrays, penetrating into the territory of the industrial city. We have also taken into account for the mechanisms of transformation of the cloud system advection over the territory of the urban area. The results of test computing the air ventilation characteristics are presented for the Odessa city. All above cited methods and models together with the standard monitoring and management systems can be considered as a basis for comprehensive “Green City” construction technology.

Numerical investigation of cryogen re-gasification in a plate heat exchanger

NASA Astrophysics Data System (ADS)

Malecha, Ziemowit; Płuszka, Paweł; Brenk, Arkadiusz

2017-12-01

The efficient re-gasification of cryogen is a crucial process in many cryogenic installations. It is especially important in the case of LNG evaporators used in stationary and mobile applications (e.g. marine and land transport). Other gases, like nitrogen or argon can be obtained at highest purity after re-gasification from their liquid states. Plate heat exchangers (PHE) are characterized by a high efficiency. Application of PHE for liquid gas vaporization processes can be beneficial. PHE design and optimization can be significantly supported by numerical modelling. Such calculations are very challenging due to very high computational demands and complexity related to phase change modelling. In the present work, a simplified mathematical model of a two phase flow with phase change was introduced. To ensure fast calculations a simplified two-dimensional (2D) numerical model of a real PHE was developed. It was validated with experimental measurements and finally used for LNG re-gasification modelling. The proposed numerical model showed to be orders of magnitude faster than its full 3D original.

Application of geologic-mathematical 3D modeling for complex structure deposits by the example of Lower- Cretaceous period depositions in Western Ust - Balykh oil field (Khanty-Mansiysk Autonomous District)

NASA Astrophysics Data System (ADS)

Perevertailo, T.; Nedolivko, N.; Prisyazhnyuk, O.; Dolgaya, T.

2015-11-01

The complex structure of the Lower-Cretaceous formation by the example of the reservoir BC101 in Western Ust - Balykh Oil Field (Khanty-Mansiysk Autonomous District) has been studied. Reservoir range relationships have been identified. 3D geologic- mathematical modeling technique considering the heterogeneity and variability of a natural reservoir structure has been suggested. To improve the deposit geological structure integrity methods of mathematical statistics were applied, which, in its turn, made it possible to obtain equal probability models with similar input data and to consider the formation conditions of reservoir rocks and cap rocks.

Children's construction task performance and spatial ability: controlling task complexity and predicting mathematics performance.

PubMed

Richardson, Miles; Hunt, Thomas E; Richardson, Cassandra

2014-12-01

This paper presents a methodology to control construction task complexity and examined the relationships between construction performance and spatial and mathematical abilities in children. The study included three groups of children (N = 96); ages 7-8, 10-11, and 13-14 years. Each group constructed seven pre-specified objects. The study replicated and extended previous findings that indicated that the extent of component symmetry and variety, and the number of components for each object and available for selection, significantly predicted construction task difficulty. Results showed that this methodology is a valid and reliable technique for assessing and predicting construction play task difficulty. Furthermore, construction play performance predicted mathematical attainment independently of spatial ability.

Assessing Students' Mathematical Problem Posing

ERIC Educational Resources Information Center

Silver, Edward A.; Cai, Jinfa

2005-01-01

Specific examples are used to discuss assessment, an integral part of mathematics instruction, with problem posing and assessment of problem posing. General assessment criteria are suggested to evaluate student-generated problems in terms of their quantity, originality, and complexity.

Test item linguistic complexity and assessments for deaf students.

PubMed

Cawthon, Stephanie

2011-01-01

Linguistic complexity of test items is one test format element that has been studied in the context of struggling readers and their participation in paper-and-pencil tests. The present article presents findings from an exploratory study on the potential relationship between linguistic complexity and test performance for deaf readers. A total of 64 students completed 52 multiple-choice items, 32 in mathematics and 20 in reading. These items were coded for linguistic complexity components of vocabulary, syntax, and discourse. Mathematics items had higher linguistic complexity ratings than reading items, but there were no significant relationships between item linguistic complexity scores and student performance on the test items. The discussion addresses issues related to the subject area, student proficiency levels in the test content, factors to look for in determining a "linguistic complexity effect," and areas for further research in test item development and deaf students.

Canonical partition functions: ideal quantum gases, interacting classical gases, and interacting quantum gases

NASA Astrophysics Data System (ADS)

Zhou, Chi-Chun; Dai, Wu-Sheng

2018-02-01

In statistical mechanics, for a system with a fixed number of particles, e.g. a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases are calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases are calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

Use of CAS in secondary school: a factor influencing the transition to university-level mathematics?

NASA Astrophysics Data System (ADS)

Varsavsky, Cristina

2012-01-01

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one where students learn and are examined with a computer algebra system (CAS) and another where students can only use scientific calculators. This study compares the performance of 1240 students as they transitioned to traditional university-level mathematics and according to whether they learned intermediate mathematics with or without the assistance of a CAS. This study concludes that students without CAS show a slight advantage, but the most important factor affecting student performance is the uptake of advanced-level mathematics studies in secondary school.

Predicting First Graders' Development of Calculation versus Word-Problem Performance: The Role of Dynamic Assessment.

PubMed

Seethaler, Pamela M; Fuchs, Lynn S; Fuchs, Douglas; Compton, Donald L

2012-02-01

The purpose of this study was to assess the value of dynamic assessment (DA; degree of scaffolding required to learn unfamiliar mathematics content) for predicting 1(st)-grade calculations (CA) and word problems (WP) development, while controlling for the role of traditional assessments. Among 184 1(st) graders, predictors (DA, Quantity Discrimination, Test of Mathematics Ability, language, and reasoning) were assessed near the start of 1(st) grade. CA and WP were assessed near the end of 1(st) grade. Planned regression and commonality analyses indicated that for forecasting CA development, Quantity Discrimination, which accounted for 8.84% of explained variance, was the single most powerful predictor, followed by Test of Mathematics Ability and DA; language and reasoning were not uniquely predictive. By contrast, for predicting WP development, DA was the single most powerful predictor, which accounted for 12.01% of explained variance, with Test of Mathematics Ability, Quantity Discrimination, and language also uniquely predictive. Results suggest that different constellations of cognitive resources are required for CA versus WP development and that DA may be useful in predicting 1(st)-grade mathematics development, especially WP.

Predicting First Graders’ Development of Calculation versus Word-Problem Performance: The Role of Dynamic Assessment

PubMed Central

Seethaler, Pamela M.; Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.

2012-01-01

The purpose of this study was to assess the value of dynamic assessment (DA; degree of scaffolding required to learn unfamiliar mathematics content) for predicting 1st-grade calculations (CA) and word problems (WP) development, while controlling for the role of traditional assessments. Among 184 1st graders, predictors (DA, Quantity Discrimination, Test of Mathematics Ability, language, and reasoning) were assessed near the start of 1st grade. CA and WP were assessed near the end of 1st grade. Planned regression and commonality analyses indicated that for forecasting CA development, Quantity Discrimination, which accounted for 8.84% of explained variance, was the single most powerful predictor, followed by Test of Mathematics Ability and DA; language and reasoning were not uniquely predictive. By contrast, for predicting WP development, DA was the single most powerful predictor, which accounted for 12.01% of explained variance, with Test of Mathematics Ability, Quantity Discrimination, and language also uniquely predictive. Results suggest that different constellations of cognitive resources are required for CA versus WP development and that DA may be useful in predicting 1st-grade mathematics development, especially WP. PMID:22347725

Geometric modeling of subcellular structures, organelles, and multiprotein complexes

PubMed Central

Feng, Xin; Xia, Kelin; Tong, Yiying; Wei, Guo-Wei

2013-01-01

SUMMARY Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multi-protein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes. PMID:23212797

Mathematical Model of Nonstationary Separation Processes Proceeding in the Cascade of Gas Centrifuges in the Process of Separation of Multicomponent Isotope Mixtures

NASA Astrophysics Data System (ADS)

Orlov, A. A.; Ushakov, A. A.; Sovach, V. P.

2017-03-01

We have developed and realized on software a mathematical model of the nonstationary separation processes proceeding in the cascades of gas centrifuges in the process of separation of multicomponent isotope mixtures. With the use of this model the parameters of the separation process of germanium isotopes have been calculated. It has been shown that the model adequately describes the nonstationary processes in the cascade and is suitable for calculating their parameters in the process of separation of multicomponent isotope mixtures.

Mathematical modelling of risk reduction in reinsurance

NASA Astrophysics Data System (ADS)

Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

2017-01-01

The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

Simplified mathematical model of losses in a centrifugal compressor stage

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

Seleznev, K.P.; Galerkin, Yu.B.; Popova, E.Yu.

1988-05-01

A mathematical model was developed for optimizing the parameters of the stage which does not require calculation of the flow around grids. The loss coefficients of the stage elements were considered as functions of the flow-through section, the angle of incidence, the compressibility criterion, and the Reynolds number. The relationships were used to calculate losses in all blade components, including blade diffusers, deflectors, and rotors. The model is implemented in a microcomputer and will compute the efficiency of one variant of the flow-through section of a stage in 60 minutes.

Ranking of options of real estate use by expert assessments mathematical processing

NASA Astrophysics Data System (ADS)

Lepikhina, O. Yu; Skachkova, M. E.; Mihaelyan, T. A.

2018-05-01

The article is devoted to the development of the real estate assessment concept. In conditions of multivariate using of the real estate method based on calculating, the integral indicator of each variant’s efficiency is proposed. In order to calculate weights of criteria of the efficiency expert method, Analytic hierarchy process and its mathematical support are used. The method allows fulfilling ranking of alternative types of real estate use in dependence of their efficiency. The method was applied for one of the land parcels located on Primorsky district in Saint Petersburg.

Mathematics--A Search for Harmony.

ERIC Educational Resources Information Center

Arnold, Stephen

1991-01-01

The harmonic mean, neglected in favor of arithmetic and geometric means in modern mathematics, is defined and its historical relationship to music as presented by Pythagoras is described. Two geometric constructions present a picture of harmony, and an application in calculating the square root of a number is given. (MDH)