The first accurate description of an aurora
NASA Astrophysics Data System (ADS)
Schröder, Wilfried
2006-12-01
As technology has advanced, the scientific study of auroral phenomena has increased by leaps and bounds. A look back at the earliest descriptions of aurorae offers an interesting look into how medieval scholars viewed the subjects that we study.Although there are earlier fragmentary references in the literature, the first accurate description of the aurora borealis appears to be that published by the German Catholic scholar Konrad von Megenberg (1309-1374) in his book Das Buch der Natur (The Book of Nature). The book was written between 1349 and 1350.
"Influence Method". Detailed mathematical description
NASA Astrophysics Data System (ADS)
Rios, I. J.; Mayer, R. E.
2015-07-01
A new method for the absolute determination of nuclear particle flux in the absence of known detector efficiency, the "Influence Method", was recently published (I.J. Rios and R.E. Mayer, Nuclear Instruments & Methods in Physics Research A 775 (2015) 99-104). The method defines an estimator for the population and another estimator for the efficiency. In this article we present a detailed mathematical description which yields the conditions for its application, the probability distributions of the estimators and their characteristic parameters. An analysis of the different cases leads to expressions of the estimators and their uncertainties.
NASA Astrophysics Data System (ADS)
Kim, Jibeom; Jeon, Joonhyeon
2015-01-01
Recently, related studies on Equation Of State (EOS) have reported that generalized van der Waals (GvdW) shows poor representations in the near critical region for non-polar and non-sphere molecules. Hence, there are still remains a problem of GvdW parameters to minimize loss in describing saturated vapor densities and vice versa. This paper describes a recursive model GvdW (rGvdW) for an accurate representation of pure fluid materials in the near critical region. For the performance evaluation of rGvdW in the near critical region, other EOS models are also applied together with two pure molecule group: alkane and amine. The comparison results show rGvdW provides much more accurate and reliable predictions of pressure than the others. The calculating model of EOS through this approach gives an additional insight into the physical significance of accurate prediction of pressure in the nearcritical region.
Mathematical Description of Bacterial Traveling Pulses
Bournaveas, Nikolaos; Buguin, Axel; Silberzan, Pascal; Perthame, Benoît
2010-01-01
The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on Escherichia coli have shown the precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at the macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition, we can capture quantitatively the traveling speed of the pulse as well as its characteristic length. This work opens several experimental and theoretical perspectives since coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance, the particular response of a single cell to chemical cues turns out to have a strong effect on collective motion. Furthermore, the bottom-up scaling allows us to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion. PMID:20808878
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.
Fernández-Colino, A; Bermudez, J M; Arias, F J; Quinteros, D; Gonzo, E
2016-04-01
Transversality between mathematical modeling, pharmacology, and materials science is essential in order to achieve controlled-release systems with advanced properties. In this regard, the area of biomaterials provides a platform for the development of depots that are able to achieve controlled release of a drug, whereas pharmacology strives to find new therapeutic molecules and mathematical models have a connecting function, providing a rational understanding by modeling the parameters that influence the release observed. Herein we present a mechanism which, based on reasonable assumptions, explains the experimental data obtained very well. In addition, we have developed a simple and accurate “lumped” kinetics model to correctly fit the experimentally observed drug-release behavior. This lumped model allows us to have simple analytic solutions for the mass and rate of drug release as a function of time without limitations of time or mass of drug released, which represents an important step-forward in the area of in vitro drug delivery when compared to the current state of the art in mathematical modeling. As an example, we applied the mechanism and model to the release data for acetazolamide from a recombinant polymer. Both materials were selected because of a need to develop a suitable ophthalmic formulation for the treatment of glaucoma. The in vitro release model proposed herein provides a valuable predictive tool for ensuring product performance and batch-to-batch reproducibility, thus paving the way for the development of further pharmaceutical devices. PMID:26838852
FRESHMAN MATHEMATICS COURSE DESCRIPTIONS, TEXAS COLLEGES AND UNIVERSITIES.
ERIC Educational Resources Information Center
Texas Education Agency, Austin.
FOR EACH OF 84 TEXAS COLLEGES AND UNIVERSITIES, THE FOLLOWING INFORMATION IS PRESENTED--(1) ENTRANCE REQUIREMENTS, WITH EMPHASIS ON TESTS AND MATHEMATICS COURSES, (2) GENERAL ORGANIZATION, WITH STATEMENTS OF GRADUATION REQUIREMENTS IN MATHEMATICS FOR BOTH GENERAL STUDENTS AND THOSE WITH MAJORS IN SPECIALIZED FIELDS, (3) A BRIEF DESCRIPTION OF EACH…
Towards a Bernsteinian Language of Description for Mathematics Classroom Discourse
ERIC Educational Resources Information Center
Straehler-Pohl, Hauke; Gellert, Uwe
2013-01-01
This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein's conceptualisation of power in classification, we develop a three-dimensional model that operationalises the…
Connecting Intonation Labels to Mathematical Descriptions of Fundamental Frequency
ERIC Educational Resources Information Center
Grabe, Esther; Kochanski, Greg; Coleman, John
2007-01-01
The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In…
Santolini, Marc; Mora, Thierry; Hakim, Vincent
2014-01-01
The identification of transcription factor binding sites (TFBSs) on genomic DNA is of crucial importance for understanding and predicting regulatory elements in gene networks. TFBS motifs are commonly described by Position Weight Matrices (PWMs), in which each DNA base pair contributes independently to the transcription factor (TF) binding. However, this description ignores correlations between nucleotides at different positions, and is generally inaccurate: analysing fly and mouse in vivo ChIPseq data, we show that in most cases the PWM model fails to reproduce the observed statistics of TFBSs. To overcome this issue, we introduce the pairwise interaction model (PIM), a generalization of the PWM model. The model is based on the principle of maximum entropy and explicitly describes pairwise correlations between nucleotides at different positions, while being otherwise as unconstrained as possible. It is mathematically equivalent to considering a TF-DNA binding energy that depends additively on each nucleotide identity at all positions in the TFBS, like the PWM model, but also additively on pairs of nucleotides. We find that the PIM significantly improves over the PWM model, and even provides an optimal description of TFBS statistics within statistical noise. The PIM generalizes previous approaches to interdependent positions: it accounts for co-variation of two or more base pairs, and predicts secondary motifs, while outperforming multiple-motif models consisting of mixtures of PWMs. We analyse the structure of pairwise interactions between nucleotides, and find that they are sparse and dominantly located between consecutive base pairs in the flanking region of TFBS. Nonetheless, interactions between pairs of non-consecutive nucleotides are found to play a significant role in the obtained accurate description of TFBS statistics. The PIM is computationally tractable, and provides a general framework that should be useful for describing and predicting TFBSs beyond
Researchers' Descriptions and the Construction of Mathematical Thinking
ERIC Educational Resources Information Center
Barwell, Richard
2009-01-01
Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing,…
Connecting intonation labels to mathematical descriptions of fundamental frequency.
Grabe, Esther; Kochanski, Greg; Coleman, John
2007-01-01
The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In this paper, we explore the interface between the disciplines, in search of bridges between intonational phonology and speech technology. In a corpus of speech data from seven dialects of English, we hand-labeled over 700 sentences and identified seven nuclear accent types. Then we fitted a third-order polynomial to the fundamental frequency (F0) contour in the region around the accent mark. The polynomial captures the local shape (time-dependence) of F0 in a few numbers, in our case, four coefficients. The coefficients were subjected to statistical analysis. Nineteen of the 21 pairs of accent types differed significantly in one or more coefficients. Our approach bridges the gap between intonational phonology and speech technology. It provides quantitative, empirically testable models of intonation labels that can be implemented in applications. PMID:17974321
Chemically accurate description of aromatic rings interaction using quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Azadi, Sam
We present an accurate study of interactions between benzene molecules using wave function based quantum Monte Carlo (QMC) methods. We compare our QMC results with density functional theory (DFT) using various van der Waals (vdW) functionals. This comparison enables us to tune vdW functionals. We show that highly optimizing the wave function and introducing more dynamical correlation into the wave function are crucial to calculate the weak chemical binding energy between benzene molecules. The good agreement among our results, experiments and quantum chemistry methods, is an important sign of the capability of the wave function based QMC methods to provide accurate description of very weak intermolecular interactions based on vdW dispersive forces.
Xiao, Suzhi; Tao, Wei; Zhao, Hui
2016-01-01
In order to acquire an accurate three-dimensional (3D) measurement, the traditional fringe projection technique applies complex and laborious procedures to compensate for the errors that exist in the vision system. However, the error sources in the vision system are very complex, such as lens distortion, lens defocus, and fringe pattern nonsinusoidality. Some errors cannot even be explained or rendered with clear expressions and are difficult to compensate directly as a result. In this paper, an approach is proposed that avoids the complex and laborious compensation procedure for error sources but still promises accurate 3D measurement. It is realized by the mathematical model extension technique. The parameters of the extended mathematical model for the ’phase to 3D coordinates transformation’ are derived using the least-squares parameter estimation algorithm. In addition, a phase-coding method based on a frequency analysis is proposed for the absolute phase map retrieval to spatially isolated objects. The results demonstrate the validity and the accuracy of the proposed flexible fringe projection vision system on spatially continuous and discontinuous objects for 3D measurement. PMID:27136553
Short description of mathematical support programs for space experiments in the Interkosmos program
NASA Technical Reports Server (NTRS)
Elyasberg, P. Y.
1979-01-01
A synopsis of programs of mathematical support designed at the Institute for Cosmic Research of the USSR Academy of Sciences for cosmic experiments being conducted in the Interkosmos Program is presented. A short description of the appropriate algorithm is given.
Descriptions of Free and Freeware Software in the Mathematics Teaching
NASA Astrophysics Data System (ADS)
Antunes de Macedo, Josue; Neves de Almeida, Samara; Voelzke, Marcos Rincon
2016-05-01
This paper presents the analysis and the cataloging of free and freeware mathematical software available on the internet, a brief explanation of them, and types of licenses for use in teaching and learning. The methodology is based on the qualitative research. Among the different types of software found, it stands out in algebra, the Winmat, that works with linear algebra, matrices and linear systems. In geometry, the GeoGebra, which can be used in the study of functions, plan and spatial geometry, algebra and calculus. For graphing, can quote the Graph and Graphequation. With Graphmatica software, it is possible to build various graphs of mathematical equations on the same screen, representing cartesian equations, inequalities, parametric among other functions. The Winplot allows the user to build graphics in two and three dimensions functions and mathematical equations. Thus, this work aims to present the teachers some free math software able to be used in the classroom.
Mathematical description of human body constitution and fatness.
Sheikh-Zade, Yu R; Galenko-Yaroshevskii, P A; Cherednik, I L
2014-02-01
Using mathematical modeling of human body, we demonstrated logical drawbacks of body mass index (BMI1 = M/H(2); A. Quetelet, 1832) and proposed more precise body mass index (BMI2 = M/H(3)) as well as body constitution index (BCI = (M/H(3))(1/2)) and fatness index (FI = M/HC(2)), where M, H, and C are body weight, height, and wrist circumference of the individual. PMID:24771443
Maudlin, P.J.; Stout, M.G.
1996-09-01
Strength and fracture constitutive relationships containing strain rate dependence and thermal softening are important for accurate simulation of metal cutting. The mechanical behavior of a hardened 4340 steel was characterized using the von Mises yield function, the Mechanical Threshold Stress model and the Johnson- Cook fracture model. This constitutive description was implemented into the explicit Lagrangian FEM continuum-mechanics code EPIC, and orthogonal plane-strain metal cutting calculations were performed. Heat conduction and friction at the toolwork-piece interface were included in the simulations. These transient calculations were advanced in time until steady state machining behavior (force) was realized. Experimental cutting force data (cutting and thrust forces) were measured for a planning operation and compared to the calculations. 13 refs., 6 figs.
Accurate Energies and Orbital Description in Semi-Local Kohn-Sham DFT
NASA Astrophysics Data System (ADS)
Lindmaa, Alexander; Kuemmel, Stephan; Armiento, Rickard
2015-03-01
We present our progress on a scheme in semi-local Kohn-Sham density-functional theory (KS-DFT) for improving the orbital description while still retaining the level of accuracy of the usual semi-local exchange-correlation (xc) functionals. DFT is a widely used tool for first-principles calculations of properties of materials. A given task normally requires a balance of accuracy and computational cost, which is well achieved with semi-local DFT. However, commonly used semi-local xc functionals have important shortcomings which often can be attributed to features of the corresponding xc potential. One shortcoming is an overly delocalized representation of localized orbitals. Recently a semi-local GGA-type xc functional was constructed to address these issues, however, it has the trade-off of lower accuracy of the total energy. We discuss the source of this error in terms of a surplus energy contribution in the functional that needs to be accounted for, and offer a remedy for this issue which formally stays within KS-DFT, and, which does not harshly increase the computational effort. The end result is a scheme that combines accurate total energies (e.g., relaxed geometries) with an improved orbital description (e.g., improved band structure).
Elvira, L; Hernandez, F; Cuesta, P; Cano, S; Gonzalez-Martin, J-V; Astiz, S
2013-06-01
Although the intensive production system of Lacaune dairy sheep is the only profitable method for producers outside of the French Roquefort area, little is known about this type of systems. This study evaluated yield records of 3677 Lacaune sheep under intensive management between 2005 and 2010 in order to describe the lactation curve of this breed and to investigate the suitability of different mathematical functions for modeling this curve. A total of 7873 complete lactations during a 40-week lactation period corresponding to 201 281 pieces of weekly yield data were used. First, five mathematical functions were evaluated on the basis of the residual mean square, determination coefficient, Durbin Watson and Runs Test values. The two better models were found to be Pollott Additive and fractional polynomial (FP). In the second part of the study, the milk yield, peak of milk yield, day of peak and persistency of the lactations were calculated with Pollot Additive and FP models and compared with the real data. The results indicate that both models gave an extremely accurate fit to Lacaune lactation curves in order to predict milk yields (P = 0.871), with the FP model being the best choice to provide a good fit to an extensive amount of real data and applicable on farm without specific statistical software. On the other hand, the interpretation of the parameters of the Pollott Additive function helps to understand the biology of the udder of the Lacaune sheep. The characteristics of the Lacaune lactation curve and milk yield are affected by lactation number and length. The lactation curves obtained in the present study allow the early identification of ewes with low milk yield potential, which will help to optimize farm profitability. PMID:23257242
Description of a tilt wing mathematical model for piloted simulation
NASA Technical Reports Server (NTRS)
Totah, Joseph J.
1991-01-01
A tilt-wing mathematical model that was used in a piloted six-deg-of-freedom flight simulation application is presented. Two types of control systems developed for the model - a conventional programmed-flap wing-tilt control system and a geared-flap wing-tilt control system - are discussed. The objective of this effort was to develop the capability to study tilt-wing aircraft. Experienced tilt-wing pilots subjectively evaluated the model using programmed-flap control to assess the quality of the simulation. The objective was met and the model was then applied to study geared-flap control to investigate the possibility of eliminating the need for auxiliary pitch control devices. This was performed in the moving-base simulation environment, and the vehicle responses with programmed-flap and geared-flap control were compared.
NASA Astrophysics Data System (ADS)
Glazachev, A. V.; Dementyev, Yu. N.; Negodin, K. N.; Umursakova, A. D.
2016-02-01
The article gives the mathematical description of an asynchronous motor with the indirect control of the output mechanical variables of an asynchronous motor in the electric drive. To determine the electromagnetic torque and angular velocity of the asynchronous motor in the electric drive the mathematical description is used in which the values are determined by the readings of the motor and easily measured values by means of known in practice devices. The proposed in the article the mathematical description for the indirect measuring the electromagnetic torque and angular velocity of the asynchronous motor in the electric drive does not contain the integral components that introduce the great error into the value of the controlled electromagnetic torque and angular velocity.
a Mathematical Description of the Critical Point in Phase Transitions
NASA Astrophysics Data System (ADS)
Bilge, Ayse Humeyra; Pekcan, Onder
2013-10-01
Let y(x) be a smooth sigmoidal curve, y(n) be its nth derivative and {xm,i} and {xa,i}, i = 1,2,…, be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {xm,i} and {xa,i} are both convergent and they have a common limit xc that we characterize as the critical point of the phase transition. In this study, we examine the logistic growth curve and the Susceptible-Infected-Removed (SIR) epidemic model as typical examples of symmetrical and asymmetrical transition curves. Numerical computations indicate that the critical point of the logistic growth curve that is symmetrical about the point (x0, y0) is always the point (x0, y0) but the critical point of the asymmetrical SIR model depends on the system parameters. We use the description of the sol-gel phase transition of polyacrylamide-sodium alginate (SA) composite (with low SA concentrations) in terms of the SIR epidemic model, to compare the location of the critical point as described above with the "gel point" determined by independent experiments. We show that the critical point tc is located in between the zero of the third derivative ta and the inflection point tm of the transition curve and as the strength of activation (measured by the parameter k/η of the SIR model) increases, the phase transition occurs earlier in time and the critical point, tc, moves toward ta.
NASA Technical Reports Server (NTRS)
Lennington, R. K.; Rassbach, M. E.
1979-01-01
Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.
ERIC Educational Resources Information Center
Friedman, Lee; Harvey, Robert J.
1986-01-01
Job-naive raters provided with job descriptive information made Position Analysis Questionnaire (PAQ) ratings which were validated against ratings of job analysts who were also job content experts. None of the reduced job descriptive information conditions enabled job-naive raters to obtain either acceptable levels of convergent validity with…
A simple mathematical description of an off-grid hybrid solar-wind power generating system
NASA Astrophysics Data System (ADS)
Blasone, M.; Dell'Anno, F.; De Luca, R.; Torre, G.
2013-05-01
We give a detailed description of the energy balance equation for a stand-alone hybrid solar-wind power generating system. The dimensions of the power generator and the energy capacity of a buffer battery (used as an energy storage system) are chosen to suit a known consumer's profile. Future applications of the mathematical model developed and analogies with a similar hydrodynamic problem are discussed.
Physical and Mathematical Description of Nuclear Weapons Identification System (NWIS) Signatures
Mattingly, J.K.; Mihalczo, J.T.; Mullens, J.A.; Valentine, T.E.
1997-09-26
This report describes all time and frequency analysis parameters measured with the new Nuclear Weapons Identification System (NWIS) processor with three input channels: (1) the 252Cf source ionization chamber (2) a detection channel; and (3) a second detection channel for active measurements. An intuitive and physical description of the various functions is given as well as a brief mathematical description and a brief description of how the data are acquired. If the fill five channel capability is used, the number of functions increases in number but not in type. The parameters provided by this new NWIS processor can be divided into two general classes: time analysis signatures including multiplicities and frequency analysis signatures. Data from measurements with an 18.75 kg highly enriched uranium (93.2 wt 0/0, 235U) metai casting for storage are presented to illustrate the various time and frequency analysis parameters.
A mathematical description of inhaled particle behavior suitable for analysis of factors affecting deposition in the human upper respiratory tract (nasopharyngeal and oropharyngeal compartments), larynx, and ciliated airways is presented. When upper respiratory tract and larynx f...
Mathematical model accurately predicts protein release from an affinity-based delivery system.
Vulic, Katarina; Pakulska, Malgosia M; Sonthalia, Rohit; Ramachandran, Arun; Shoichet, Molly S
2015-01-10
Affinity-based controlled release modulates the delivery of protein or small molecule therapeutics through transient dissociation/association. To understand which parameters can be used to tune release, we used a mathematical model based on simple binding kinetics. A comprehensive asymptotic analysis revealed three characteristic regimes for therapeutic release from affinity-based systems. These regimes can be controlled by diffusion or unbinding kinetics, and can exhibit release over either a single stage or two stages. This analysis fundamentally changes the way we think of controlling release from affinity-based systems and thereby explains some of the discrepancies in the literature on which parameters influence affinity-based release. The rate of protein release from affinity-based systems is determined by the balance of diffusion of the therapeutic agent through the hydrogel and the dissociation kinetics of the affinity pair. Equations for tuning protein release rate by altering the strength (KD) of the affinity interaction, the concentration of binding ligand in the system, the rate of dissociation (koff) of the complex, and the hydrogel size and geometry, are provided. We validated our model by collapsing the model simulations and the experimental data from a recently described affinity release system, to a single master curve. Importantly, this mathematical analysis can be applied to any single species affinity-based system to determine the parameters required for a desired release profile. PMID:25449806
McKee, J K; Molnar, S
1988-01-01
The ability to describe dental arch shape is necessary for biomechanical studies of occlusion as well as for anthropological studies of human and primate dental variation. A mathematical method of describing and classifying human dental arch shape was used to assess the nature of individual variability. The method involved the calculation of a series of third-degree polynomials which were fitted to coordinate points along the dental arcade. The slopes of the polynomials, evaluated at these coordinate points, provided a multivariate description of shape, independent of arch size. Graphic representations of arch shape could be constructed from the polynomial equations. These mathematical techniques were used in association with multivariate and univariate statistics to explore the types of variability in dental arch shape among a population of Australian aborigines. The results illustrated the ambiguities of conventional subjective classifications. PMID:3256297
Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth
Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip
2014-01-01
Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199
Models in biology: ‘accurate descriptions of our pathetic thinking’
2014-01-01
In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as ‘predictive’, in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders. PMID:24886484
2011-01-01
Background Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor. Results We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise. Conclusions The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling. Reviewers This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck). PMID:22185645
NASA Astrophysics Data System (ADS)
Chung, H. Y.; Guo, G. Y.; Chiang, H.-P.; Tsai, D. P.; Leung, P. T.
2010-10-01
The optical response of a multilayered spherical system of unlimited number of layers (a “matryushka”) in the long wavelength limit can be accounted for from the knowledge of the static multipole polarizability of the system to first-order accuracy. However, for systems of ultrasmall dimensions or systems with sizes not-too-small compared to the wavelength, this ordinary quasistatic long wavelength approximation (LWA) becomes inaccurate. Here we introduce two significant modifications of the LWA for such a nanomatryushka in each of the two limits: the nonlocal optical response for ultrasmall systems (<10nm) , and the “finite-wavelength corrections” for systems ˜100nm . This is accomplished by employing the previous work for a single-layer shell, in combination with a certain effective-medium approach formulated recently in the literature. Numerical calculations for the extinction cross sections for such a system of different dimensions are provided as illustrations for these effects. This formulation thus provides significant improvements on the ordinary LWA, yielding enough accuracy for the description of the optical response of these nanoshell systems over an appreciable range of sizes, without resorting to more involved quantum mechanical or fully electrodynamic calculations.
Bauer, Sebastian; Mathias, Gerald; Tavan, Paul
2014-03-14
We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ{sub i} of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ{sub i}. A summarizing discussion highlights the achievements of the new theory and of its approximate solution
NASA Astrophysics Data System (ADS)
Bauer, Sebastian; Mathias, Gerald; Tavan, Paul
2014-03-01
We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ɛ(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by
Bauer, Sebastian; Mathias, Gerald; Tavan, Paul
2014-03-14
We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by
Argudo, David; Bethel, Neville P; Marcoline, Frank V; Grabe, Michael
2016-07-01
Biological membranes deform in response to resident proteins leading to a coupling between membrane shape and protein localization. Additionally, the membrane influences the function of membrane proteins. Here we review contributions to this field from continuum elastic membrane models focusing on the class of models that couple the protein to the membrane. While it has been argued that continuum models cannot reproduce the distortions observed in fully-atomistic molecular dynamics simulations, we suggest that this failure can be overcome by using chemically accurate representations of the protein. We outline our recent advances along these lines with our hybrid continuum-atomistic model, and we show the model is in excellent agreement with fully-atomistic simulations of the nhTMEM16 lipid scramblase. We believe that the speed and accuracy of continuum-atomistic methodologies will make it possible to simulate large scale, slow biological processes, such as membrane morphological changes, that are currently beyond the scope of other computational approaches. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov. PMID:26853937
Accurate description of phase diagram of clathrate hydrates at the molecular level
NASA Astrophysics Data System (ADS)
Belosludov, Rodion V.; Subbotin, Oleg S.; Mizuseki, Hiroshi; Kawazoe, Yoshiyuki; Belosludov, Vladimir R.
2009-12-01
In order to accurately estimate the thermodynamic properties of hydrogen clathrate hydrates, we developed a method based on the solid solution theory of van der Waals and Platteeuw. This model allows one to take into account the influence of guest molecules on the host lattice and guest-guest interactions—especially when more than one guest molecule occupies a cage. The free energies, equations of state, and chemical potentials of hydrogen and mixed propane-hydrogen clathrate hydrates of cubic structure II with different cage fillings have been estimated using this approach. Moreover, the proposed theory has been used for construction p -T phase diagrams of hydrogen hydrate and mixed hydrogen-propane hydrates in a wide range of pressures and temperatures. For the systems with well defined interactions the calculated curves of "guest gas-hydrate-ice Ih" equilibrium agree with the available experimental data. We also believe that the present model allows one not only to calculate the hydrogen storage ability of known hydrogen hydrate but also predict this value for structures that have not yet been realized by experiment.
Description and Application of a Mathematical Method for the Analysis of Harmony
Zuo, Qiting; Jin, Runfang; Ma, Junxia; Cui, Guotao
2015-01-01
Harmony issues are widespread in human society and nature. To analyze these issues, harmony theory has been proposed as the main theoretical approach for the study of interpersonal relationships and relationships between humans and nature. Therefore, it is of great importance to study harmony theory. After briefly introducing the basic concepts of harmony theory, this paper expounds the five elements that are essential for the quantitative description of harmony issues in water resources management: harmony participant, harmony objective, harmony regulation, harmony factor, and harmony action. A basic mathematical equation for the harmony degree, that is, a quantitative expression of harmony issues, is introduced in the paper: HD = ai − bj, where a is the uniform degree, b is the difference degree, i is the harmony coefficient, and j is the disharmony coefficient. This paper also discusses harmony assessment and harmony regulation and introduces some application examples. PMID:26167535
2014-01-01
Predicting the binding affinities of large sets of diverse molecules against a range of macromolecular targets is an extremely challenging task. The scoring functions that attempt such computational prediction are essential for exploiting and analyzing the outputs of docking, which is in turn an important tool in problems such as structure-based drug design. Classical scoring functions assume a predetermined theory-inspired functional form for the relationship between the variables that describe an experimentally determined or modeled structure of a protein–ligand complex and its binding affinity. The inherent problem of this approach is in the difficulty of explicitly modeling the various contributions of intermolecular interactions to binding affinity. New scoring functions based on machine-learning regression models, which are able to exploit effectively much larger amounts of experimental data and circumvent the need for a predetermined functional form, have already been shown to outperform a broad range of state-of-the-art scoring functions in a widely used benchmark. Here, we investigate the impact of the chemical description of the complex on the predictive power of the resulting scoring function using a systematic battery of numerical experiments. The latter resulted in the most accurate scoring function to date on the benchmark. Strikingly, we also found that a more precise chemical description of the protein–ligand complex does not generally lead to a more accurate prediction of binding affinity. We discuss four factors that may contribute to this result: modeling assumptions, codependence of representation and regression, data restricted to the bound state, and conformational heterogeneity in data. PMID:24528282
NASA Astrophysics Data System (ADS)
Nold, Andreas; Goddard, Ben; Sibley, David; Kalliadasis, Serafim
2014-03-01
Multiscale effects play a predominant role in wetting phenomena such as the moving contact line. An accurate description is of paramount interest for a wide range of industrial applications, yet it is a matter of ongoing research, due to the difficulty of incorporating different physical effects in one model. Important small-scale phenomena are corrections to the attractive fluid-fluid and wall-fluid forces in inhomogeneous density distributions, which often previously have been accounted for by the disjoining pressure in an ad-hoc manner. We systematically derive a novel model for the description of a single-component liquid-vapor multiphase system which inherently incorporates these nonlocal effects. This derivation, which is inspired by statistical mechanics in the framework of colloidal density functional theory, is critically discussed with respect to its assumptions and restrictions. The model is then employed numerically to study a moving contact line of a liquid fluid displacing its vapor phase. We show how nonlocal physical effects are inherently incorporated by the model and describe how classical macroscopic results for the contact line motion are retrieved. We acknowledge financial support from ERC Advanced Grant No. 247031 and Imperial College through a DTG International Studentship.
ERIC Educational Resources Information Center
Jansen, Amanda; Spitzer, Sandy M.
2009-01-01
In this study, we examined prospective middle school mathematics teachers' reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers' descriptions of students' thinking and frequency of their…
Explosion-proof fiber optic fire detector: design and mathematical description
NASA Astrophysics Data System (ADS)
Kazakov, V. I.; Moskaletz, O. D.
2014-10-01
The problem of early fire detection in areas classified as potentially explosive is considered in this paper. These include, for example, some types of facilities and plants, which may cause environmental disasters in case of fires. Hard safety requirements impose serious terms for the technical performance the detectors for the protection of such objects from the fire. Detector itself should not cause a fire. The main danger is open conductive parts in the construction of the sensitive elements of detectors, which can lead to the generation of sparks and fire. The using of fiber-optic technology allows creating smoke and heating fire detectors, which only the sensors will be located in the protected area, and all electronic components generate signals and their processing may be removed at considerable distances measured by kilometers. The block diagram of the fire smoke point detector based on fiber-optic technology is considered, the mathematical description of the propagation of optical radiation through the sensing element of the detector is provided, sensitivity is analyzed.
A computerized method for mathematical description of three-dimensional root canal axis.
Dobó-Nagy, C; Keszthelyi, G; Szabó, J; Sulyok, P; Ledeczky, G; Szabó, J
2000-11-01
Knowledge of the three-dimensional (3D) morphology of root canals is important for successful endodontic treatment. The objective of the present study was to determine the 3D root canal axis mathematically. Two views (mesiodistal and buccolingual) of digitized images were taken from extracted natural human teeth. Geometric reconstruction to standardize projection geometry was conducted on images. Because 90-degree turn-around image pairs are Monge images of a given root canal, these Monge images were positioned using photogrammetric methods. Each well-ordered axis pair of a given root canal was put into a common coordinate system resulting in 3D polynomial function of the actual root canal. On the basis of the results gained using 10 samples evaluated with the Friedman statistical test, this description seems to be reproducible. The 3D representation of the root canal may help the clinicians in choosing the optimal instruments and shaping techniques. The root canal axis that is described by the 3D function forms a basis for determination of curvature values and torsion values in each of the axis points. Evaluating these values may also yield a new type of classification. PMID:11469291
Mui, K W; Wong, L T; Chung, L Y
2009-11-01
Atmospheric visibility impairment has gained increasing concern as it is associated with the existence of a number of aerosols as well as common air pollutants and produces unfavorable conditions for observation, dispersion, and transportation. This study analyzed the atmospheric visibility data measured in urban and suburban Hong Kong (two selected stations) with respect to time-matched mass concentrations of common air pollutants including nitrogen dioxide (NO(2)), nitrogen monoxide (NO), respirable suspended particulates (PM(10)), sulfur dioxide (SO(2)), carbon monoxide (CO), and meteorological parameters including air temperature, relative humidity, and wind speed. No significant difference in atmospheric visibility was reported between the two measurement locations (p > or = 0.6, t test); and good atmospheric visibility was observed more frequently in summer and autumn than in winter and spring (p < 0.01, t test). It was also found that atmospheric visibility increased with temperature but decreased with the concentrations of SO(2), CO, PM(10), NO, and NO(2). The results showed that atmospheric visibility was season dependent and would have significant correlations with temperature, the mass concentrations of PM(10) and NO(2), and the air pollution index API (correlation coefficients mid R: R mid R: > or = 0.7, p < or = 0.0001, t test). Mathematical expressions catering to the seasonal variations of atmospheric visibility were thus proposed. By comparison, the proposed visibility prediction models were more accurate than some existing regional models. In addition to improving visibility prediction accuracy, this study would be useful for understanding the context of low atmospheric visibility, exploring possible remedial measures, and evaluating the impact of air pollution and atmospheric visibility impairment in this region. PMID:18951139
Kim, David; Farthing, Matthew W; Miller, Cass T; Nylander-French, Leena A
2008-05-30
The objective of this research was to develop a mathematical description of uptake of aromatic and aliphatic hydrocarbons into the stratum corneum of human skin in vivo. A simple description based on Fick's laws of diffusion was used to predict the spatiotemporal variation of naphthalene, 1- and 2-methylnaphthalene, undecane, and dodecane in the stratum corneum of human volunteers. The estimated values of the diffusion coefficients for each chemical were comparable to values predicted using in vitro skin systems and biomonitoring studies. These results demonstrate the value of measuring dermal exposure using the tape-strip technique and the importance of quantifying of dermal uptake. PMID:18423910
Kim, David; Farthing, Matthew W.; Miller, Cass T.; Nylander-French, Leena A.
2008-01-01
The objective of this research was to develop a mathematical description of uptake of aromatic and aliphatic hydrocarbons into the stratum corneum of human skin in vivo. A simple description based on Fick’s Laws of diffusion was used to predict the spatiotemporal variation of naphthalene, 1- and 2-methylnaphthalene, undecane, and dodecane in the stratum corneum of human volunteers. The estimated values of the diffusion coefficients for each chemical were comparable to values predicted using in vitro skin systems and biomonitoring studies. These results demonstrate the value of measuring dermal exposure using the tape-strip technique and the importance of quantifying of dermal uptake. PMID:18423910
Cross-National Variations in Rural Mathematics Achievement: A Descriptive Overview
ERIC Educational Resources Information Center
Williams, James H.
2005-01-01
Using PISA 2000 data, this article examines cross-national variation in rural mathematics achievement among 15-year-olds in 24 industrialized nations. Rural mathematics scores were significantly lower than scores in urban and medium-size communities in 14 of 24 countries. However, patterns were complex. Most commonly, a linear relationship…
Cross-National Variations in Rural Mathematics Achievement: A Descriptive Overview
ERIC Educational Resources Information Center
Williams, James H.
2005-01-01
Using PISA 2000 data, this article examines cross-national variation in rural mathematics achievement among 15-year olds in 24 industrialized nations. Rural mathematics scores were significantly lower than scores in urban and medium-size communities in 14 of 24 countries. However, patterns were complex. Most commonly, a linear relationship…
Mathematical description of the structure of a capillary-porous body
NASA Astrophysics Data System (ADS)
Lyashkevich, I. M.; Volchenok, V. F.; Raptunovich, G. S.
1981-02-01
The properties of a capillary-porous disperse body are described and a mathematical model of its structure is constructed. As the model body, gypsum stone, which hardens under conditions of oriented mass transfer involving the liquid phase, is selected.
NASA Astrophysics Data System (ADS)
Sadrtdinov, A. R.; Safin, R. G.; Gerasimov, M. K.; Petrov, V. I.; Gilfanov, K. K.
2016-04-01
The article presents the scheme of processing of plant biomass in the gasification installation with a plasma heat source to produce synthesis gas suitable for chemical industry. The analyzed physical picture of raw materials' recycling process underlies a mathematical description of the process set out in the form of the basic differential equations with boundary conditions. The received mathematical description allows calculating of the main parameters of equipment for biomass recycling and to determine the optimal modes of its operation.
A Description and Characterization of Student Activity in an Open, Online, Mathematics Help Forum
ERIC Educational Resources Information Center
van de Sande, Carla
2011-01-01
Free, open, online, calculus forums are websites where students from around the world can post course-related queries that may be viewed and responded to by anonymous others. These sites are an emergent resource for students seeking help and have become a part of many students' mathematical experience. The purpose of this paper is to introduce and…
The mathematical description of the body centre of mass 3D path in human and animal locomotion.
Minetti, Alberto E; Cisotti, Caterina; Mian, Omar S
2011-05-17
Although the 3D trajectory of the body centre of mass during ambulation constitutes the 'locomotor signature' at different gaits and speeds for humans and other legged species, no quantitative method for its description has been proposed in the literature so far. By combining the mathematical discoveries of Jean Baptiste Joseph Fourier (1768-1830, analysis of periodic events) and of Jules Antoine Lissajous (1822-1880, parametric equation for closed loops) we designed a method simultaneously capturing the spatial and dynamical features of that 3D trajectory. The motion analysis of walking and running humans, and the re-processing of previously published data on trotting and galloping horses, as moving on a treadmill, allowed to obtain closed loops for the body centre of mass showing general and individual locomotor characteristics. The mechanical dynamics due to the different energy exchange, the asymmetry along each 3D axis, and the sagittal and lateral energy recovery, among other parameters, were evaluated for each gait according to the present methodology. The proposed mathematical description of the 3D trajectory of the body centre of mass could be used to better understand the physiology and biomechanics of normal locomotion, from monopods to octopods, and to evaluate individual deviations with respect to average values as resulting from gait pathologies and the restoration of a normal pattern after pharmacological, physiotherapeutic and surgical treatments. PMID:21463861
NASA Astrophysics Data System (ADS)
Wang, Li-yong; Li, Le; Zhang, Zhi-hua
2016-07-01
Hot compression tests of Ti-6Al-4V alloy in a wide temperature range of 1023-1323 K and strain rate range of 0.01-10 s-1 were conducted by a servo-hydraulic and computer-controlled Gleeble-3500 machine. In order to accurately and effectively characterize the highly nonlinear flow behaviors, support vector regression (SVR) which is a machine learning method was combined with genetic algorithm (GA) for characterizing the flow behaviors, namely, the GA-SVR. The prominent character of GA-SVR is that it with identical training parameters will keep training accuracy and prediction accuracy at a stable level in different attempts for a certain dataset. The learning abilities, generalization abilities, and modeling efficiencies of the mathematical regression model, ANN, and GA-SVR for Ti-6Al-4V alloy were detailedly compared. Comparison results show that the learning ability of the GA-SVR is stronger than the mathematical regression model. The generalization abilities and modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model < ANN < GA-SVR. The stress-strain data outside experimental conditions were predicted by the well-trained GA-SVR, which improved simulation accuracy of the load-stroke curve and can further improve the related research fields where stress-strain data play important roles, such as speculating work hardening and dynamic recovery, characterizing dynamic recrystallization evolution, and improving processing maps.
Sutton, Christopher; Gray, Matthew T.; Brunsfeld, Max; Parrish, Robert M.; Sherrill, C. David; Sears, John S.; Brédas, Jean-Luc E-mail: thomas.koerzdoerfer@uni-potsdam.de; Körzdörfer, Thomas E-mail: thomas.koerzdoerfer@uni-potsdam.de
2014-02-07
We investigate the torsion potentials in two prototypical π-conjugated polymers, polyacetylene and polydiacetylene, as a function of chain length using different flavors of density functional theory. Our study provides a quantitative analysis of the delocalization error in standard semilocal and hybrid density functionals and demonstrates how it can influence structural and thermodynamic properties. The delocalization error is quantified by evaluating the many-electron self-interaction error (MESIE) for fractional electron numbers, which allows us to establish a direct connection between the MESIE and the error in the torsion barriers. The use of non-empirically tuned long-range corrected hybrid functionals results in a very significant reduction of the MESIE and leads to an improved description of torsion barrier heights. In addition, we demonstrate how our analysis allows the determination of the effective conjugation length in polyacetylene and polydiacetylene chains.
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Singhal, A. K.; Tam, L. T.
1984-01-01
The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.
Garcia Sestafe, J V; García Paez, J M; Carrera San Martín, A; Jorge-Herrero, E; Navidad, R; Candela, I; Castillo-Olivares, J L
1994-06-01
A material subjected to traction stress increases in length; if we maintain the elongation constant, the stress varies over a period of time. This phenomenon has been referred to as relaxation. The purpose of this study was to define a mathematical law that relates the variation in stress to time when elongation remains constant in bovine pericardium. The mathematical function obtained after assaying 34 samples to the point of relaxation, subjected to initial stresses ranging from 0.17-10.07 MPa, responds to the following equation: y = -0.0252 + 0.953 alpha - (0.0165 + 0.015 alpha)lnt, where y is the stress withstood at an instant in time, t, after initial stress alpha. A normogram, validated by assays of up to 6,340 min duration (4.40 days), is presented for graphic calculation, permitting the computation of the loss of stress due to relaxation of this biomaterial, with initial stresses ranging from 1-10 MPa. PMID:8071387
Mavandadi, Sam; Feng, Steve; Yu, Frank; Dimitrov, Stoyan; Nielsen-Saines, Karin; Prescott, William R; Ozcan, Aydogan
2012-01-01
We propose a methodology for digitally fusing diagnostic decisions made by multiple medical experts in order to improve accuracy of diagnosis. Toward this goal, we report an experimental study involving nine experts, where each one was given more than 8,000 digital microscopic images of individual human red blood cells and asked to identify malaria infected cells. The results of this experiment reveal that even highly trained medical experts are not always self-consistent in their diagnostic decisions and that there exists a fair level of disagreement among experts, even for binary decisions (i.e., infected vs. uninfected). To tackle this general medical diagnosis problem, we propose a probabilistic algorithm to fuse the decisions made by trained medical experts to robustly achieve higher levels of accuracy when compared to individual experts making such decisions. By modelling the decisions of experts as a three component mixture model and solving for the underlying parameters using the Expectation Maximisation algorithm, we demonstrate the efficacy of our approach which significantly improves the overall diagnostic accuracy of malaria infected cells. Additionally, we present a mathematical framework for performing 'slide-level' diagnosis by using individual 'cell-level' diagnosis data, shedding more light on the statistical rules that should govern the routine practice in examination of e.g., thin blood smear samples. This framework could be generalized for various other tele-pathology needs, and can be used by trained experts within an efficient tele-medicine platform. PMID:23071544
Mavandadi, Sam; Dimitrov, Stoyan; Nielsen-Saines, Karin; Prescott, William R.; Ozcan, Aydogan
2012-01-01
We propose a methodology for digitally fusing diagnostic decisions made by multiple medical experts in order to improve accuracy of diagnosis. Toward this goal, we report an experimental study involving nine experts, where each one was given more than 8,000 digital microscopic images of individual human red blood cells and asked to identify malaria infected cells. The results of this experiment reveal that even highly trained medical experts are not always self-consistent in their diagnostic decisions and that there exists a fair level of disagreement among experts, even for binary decisions (i.e., infected vs. uninfected). To tackle this general medical diagnosis problem, we propose a probabilistic algorithm to fuse the decisions made by trained medical experts to robustly achieve higher levels of accuracy when compared to individual experts making such decisions. By modelling the decisions of experts as a three component mixture model and solving for the underlying parameters using the Expectation Maximisation algorithm, we demonstrate the efficacy of our approach which significantly improves the overall diagnostic accuracy of malaria infected cells. Additionally, we present a mathematical framework for performing ‘slide-level’ diagnosis by using individual ‘cell-level’ diagnosis data, shedding more light on the statistical rules that should govern the routine practice in examination of e.g., thin blood smear samples. This framework could be generalized for various other tele-pathology needs, and can be used by trained experts within an efficient tele-medicine platform. PMID:23071544
Petin, Vladislav G; Kim, Jin Kyu; Kritsky, Roman O; Komarova, Ludmila N
2008-06-01
The potential ability of various physical or chemical agents to enhance their effect when they are applied simultaneously with each other is well-known. The purpose of this study was to adjust a simple mathematical model to describe, optimize and predict a synergistic interaction between fluoride and xylitol on acid production by mutans streptococci. The model suggests that the synergism is caused by the additional effective damage arising from an interaction of sublesions induced by each agent. These sublesions are considered to be ineffective when each agent is used individually. The predictions of the model were verified by comparison with experimental data published by other researchers. It was shown that the model describes the experimental data, predicts the greatest value of the synergistic effect and the condition under which it can be achieved. The synergistic effect appeared to decline with any deviation from the optimal value of the ratio of effective damages produced by each agent alone. PMID:18367232
Mathematical description and measurement of refractive parameters of freeform spectacle lenses.
Yu, Jing; Qiu, Zhongjun; Fang, Fengzhou
2014-08-01
Refractive parameters are the main design and evaluation parameters of freeform spectacle lenses. In this paper, the mathematical model of refractive parameters is established, and the refractive power distribution on the whole surface is drawn with a radial basis function. The measurement methods are analyzed, and typical freeform spectacle lenses are measured with a freeform verifier. The refractive power distribution on the whole surface, the cylinder view, and the refractive power curve along the progressive corridor are drawn up. There are no evident image changes on the whole surface. The refractive power smoothly varies along the progressive corridor. In comparing the results with the analysis, measurement results are in agreement with the calculation. PMID:25090322
[Mathematical description of the three-dimensional axis of the root canal of human teeth].
Dobó, Nagy Csaba; Keszthelyi, Gusztáv; Sulyok, Péter; Ledeczky, Gábor; Szabó, József
2002-08-01
The objective of the present study was to describe root canal axes of natural human teeth mathematically. Two views (clinical and proximal) radiographs were taken from extracted human teeth. Geometry defines the 90-degree turn-around image pairs as Monge images. These Monge images of the root canals were positioned using photogrammetric methods. Each well-ordered axis pair of a given root canal was put into a common coordinate system resulting in three-dimensional polynomial function of the actual root canal. Testing differences between determined and repeatedly determined axes of ten samples by statistical analysis did not show any significant differences. Evaluation of data gained on a large number of samples may also yield a new type of classification. PMID:12236090
ERIC Educational Resources Information Center
Ringer, Catharina W.
2013-01-01
In today's mathematics education, there is an increasing emphasis on students' understanding of the mathematics set forth in standards documents such as the "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics, 2000) and, most recently, the "Common Core State Standards for Mathematics"…
SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY
2016-01-01
In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain.
Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes
NASA Technical Reports Server (NTRS)
Bittker, D. A.
1993-01-01
A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.
Mathematical description of complex chemical kinetics and application to CFD modeling codes
NASA Technical Reports Server (NTRS)
Bittker, D. A.
1993-01-01
A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.
ERIC Educational Resources Information Center
Fowler, Crystal Nicole
2013-01-01
This qualitative descriptive case study explored the perceptions of parents and teachers of the academic achievement gap in mathematics between African-American middle school males and their White counterparts. Ten parents, both African-American and White, with students attending middle school in the Cherokee County School District and 5 teachers…
A 3-year program was conducted to examine the ecology of Cladophora glomerata and to develop a mathematical model useful in evaluating various management strategies for the control of this nuisance alga. This manuscript provides a detailed description of the field program and stu...
Friesner, Richard A.; Baik, Mu-Hyun; Gherman, Benjamin F.; Guallar, Victor; Wirstam, Maria E.; Murphy, Robert B.; Lippard, Stephen J.
2003-03-01
Over the past several years, rapid advances in computational hardware, quantum chemical methods, and mixed quantum mechanics/molecular mechanics (QM/MM) techniques have made it possible to model accurately the interaction of ligands with metal-containing proteins at an atomic level of detail. In this paper, we describe the application of our computational methodology, based on density functional (DFT) quantum chemical methods, to two diiron-containing proteins that interact with dioxygen: methane monooxygenase (MMO) and hemerythrin (Hr). Although the active sites are structurally related, the biological function differs substantially. MMO is an enzyme found in methanotrophic bacteria and hydroxylates aliphatic C-H bonds, whereas Hr is a carrier protein for dioxygen used by a number of marine invertebrates. Quantitative descriptions of the structures and energetics of key intermediates and transition states involved in the reaction with dioxygen are provided, allowing their mechanisms to be compared and contrasted in detail. An in-depth understanding of how the chemical identity of the first ligand coordination shell, structural features, electrostatic and van der Waals interactions of more distant shells control ligand binding and reactive chemistry is provided, affording a systematic analysis of how iron-containing proteins process dioxygen. Extensive contact with experiment is made in both systems, and a remarkable degree of accuracy and robustness of the calculations is obtained from both a qualitative and quantitative perspective.
ERIC Educational Resources Information Center
Kritzer, Karen L.
2009-01-01
This study examined young deaf children's early informal/formal mathematical knowledge as measured by the Test of Early Mathematics Ability (TEMA-3). Findings from this study suggest that prior to the onset of formal schooling, young deaf children might already demonstrate evidence of academic delays. Of these 28 participants (4-6 years of age),…
ERIC Educational Resources Information Center
Tsatsaroni, Anna; Lerman, Stephen; Xu, Guo-Rong
This paper presents aspects of a study that aims to describe and make sense of changes over time in the intellectual field of mathematics education research. Drawing on the work of B. Bernstein, especially his essay on intellectual fields and knowledge structures, the paper seeks to raise questions about the fields standing in the wider field of…
NASA Astrophysics Data System (ADS)
Ribeiro, Vitor B.; Silva, Flávio A.; Oliveira, Julio C. R. F.; Franz, Lucas V.; Schneider, Eduardo O.; Moretti, Cleber; Ranzini, Stenio M.
2013-01-01
Today and next generation optical coherent systems rely more and more in DSP algorithms to improve capacity, spectral efficiency and fiber impairments mitigation. The amount of signal processing is remarkable, and because of that ASICs are preferable in order to comply with cost, power consumption and size, required in OIF 100G optical module standards. One important step in the ASIC development process is the validation of the DSP algorithms mathematical models in a high level language that consider HW characteristics and constrains. In this work we present, compare and evaluate in experimental data the mathematical model developed in Matlab and the SystemC model developed in C++. The DSP algorithms functionalities implemented were orthonormalization, CD equalizer, clock recovery, dynamic equalizer, frequency offset and phase estimation. The SystemC model considers clock signals, reset/enable structures, parallelization, finite fixed-point operations and structures that are closer to the ASIC HW implementation; due to these restrictions the performance is not as good as the mathematical modeling. The DSP algorithms models are evaluated in two 112 Gbit/s DP-QPSK experimental scenarios. In the first scenario the models are evaluated in back-to-back with ASE noise loading; in the second scenario the models are compared in a 226km optical fiber recirculation loop, with 80x112 Gbit/s DP-QPSK channels (8.96 Tbit/s). In the back-to-back experiment the OSNR penalty from the mathematical model to the SystemC model is only 1,0dB and in the recirculation loop the maximum reach is 2,600 km and 2,200 km for the Matlab and SystemC models respectively.
Gray, W.G.
2001-01-25
This project has contributed to the improved understanding and precise physical description of multiphase subsurface flow by combining theoretical derivation of equations, lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and simplification of field-scale equations to assess the advantages and disadvantages of the complete theory.
NASA Technical Reports Server (NTRS)
Fortenbaugh, R. L.
1980-01-01
A mathematical model of a high performance airplane capable of vertical attitude takeoff and landing (VATOL) was developed. An off line digital simulation program incorporating this model was developed to provide trim conditions and dynamic check runs for the piloted simulation studies and support dynamic analyses of proposed VATOL configuration and flight control concepts. Development details for the various simulation component models and the application of the off line simulation program, Vertical Attitude Take-Off and Landing Simulation (VATLAS), to develop a baseline control system for the Vought SF-121 VATOL airplane concept are described.
Kritzer, Karen L
2009-01-01
This study examined young deaf children's early informal/formal mathematical knowledge as measured by the Test of Early Mathematics Ability (TEMA-3). Findings from this study suggest that prior to the onset of formal schooling, young deaf children might already demonstrate evidence of academic delays. Of these 28 participants (4-6 years of age), for whom data were analyzed, none received a score on the TEMA-3, indicating above-"average" ability according to normative ranking. More than half of participants received scores substantially below average with 11 participants receiving scores a year or more behind normative age-equivalent scores. Upon more focused analysis, specific areas of difficulty were found to include word/story problems, skip counting (i.e., counting by twos, threes, etc.), number comparisons, the reading/writing of two to three digit numbers, and addition/subtraction number facts. A qualitative analysis of the answers participants gave and the behaviors they demonstrated while answering the test items was conducted and revealed possible explanations for why specific test items may have been challenging. Implications of findings for parents, early interventionists, and teachers of young deaf children are discussed. PMID:19596725
Günther, T; Büttner, C; Käsbohrer, A; Filter, M
2015-01-01
Mathematical models on properties and behavior of harmful organisms in the food chain are an increas- ingly relevant approach of the agriculture and food industry. As a consequence, there are many efforts to develop biological models in science, economics and risk assessment nowadays. However, there is a lack of international harmonized standards on model annotation and model formats, which would be neces- sary to set up efficient tools supporting broad model application and information exchange. There are some established standards in the field of systems biology, but there is currently no corresponding provi- sion in the area of plant protection. This work therefore aimed at the development of an annotation scheme using domain-specific metadata. The proposed scheme has been validated in a prototype implementation of a web-database model repository. This prototypic community resource currently contains models on aflatoxin secreting fungal Aspergillus flavus in maize, as these models have a high relevance to food safety and economic impact. Specifically, models describing biological processes of the fungus (growth, Aflatoxin secreting), as well as dose-response- and carry over models were included. Furthermore, phenological models for maize were integrated as well. The developed annotation scheme is based on the well-established data exchange format SBML, which is broadly applied in the field of systems biology. The identified example models were annotated according to the developed scheme and entered into a Web-table (Google Sheets), which was transferred to a web based demonstrator available at https://sites.google.com/site/test782726372685/. By implementation of a software demonstrator it became clear that the proposed annotation scheme can be applied to models on plant pathogens and that broad adoption within the domain could promote communication and application of mathematical models. PMID:27141756
Bagnasco, Annamaria; Galaverna, Lucia; Aleo, Giuseppe; Grugnetti, Anna Maria; Rosa, Francesca; Sasso, Loredana
2016-01-01
In the literature we found many studies that confirmed our concerns about nursing students' poor maths skills that directly impact on their ability to correctly calculate drug dosages with very serious consequences for patient safety. The aim of our study was to explore where students had most difficulty and identify appropriate educational interventions to bridge their mathematical knowledge gaps. This was a quali-quantitative descriptive study that included a sample of 726 undergraduate nursing students. We identified exactly where students had most difficulty and identified appropriate educational interventions to bridge their mathematical knowledge gaps. We found that the undergraduate nursing students mainly had difficulty with basic maths principles. Specific learning interventions are needed to improve their basic maths skills and their dosage calculation skills. For this purpose, we identified safeMedicate and eDose (Authentic World Ltd.), only that they are only available in English. In the near future we hope to set up a partnership to work together on the Italian version of these tools. PMID:26347449
NASA Astrophysics Data System (ADS)
Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal
2013-01-01
A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.
Marinho, M M F; Dagosta, F C P; Camelier, P; Oyakawa, O T
2016-07-01
A new species of Hyphessobrycon is described from a tributary of the upper Rio Tapajós, Amazon basin, Mato Grosso, Brazil. Its exuberant colour in life, with blue to purple body and red fins, is appreciated in the aquarium trade. Characters to diagnose the new species from all congeners are the presence of a single humeral blotch, absence of a distinct caudal-peduncle blotch, absence of a well-defined dark mid-lateral stripe on body, the presence of 16-18 branched anal-fin rays, nine branched dorsal-fin rays and six branched pelvic-fin rays. A brief comment on fish species descriptions solely based on aquarium material and its consequence for conservation policies is provided. PMID:27245763
NASA Astrophysics Data System (ADS)
de Vicente, S.; Galiano, G.; Velasco, J.; Aróstegui, J. M.
Two-phase systems where a dense phase of small particles is fluidized with a gas flow appear in many industrial applications, among which the fluidized bed combustors are probably the most important. A homogenization technique allows us to formulate the mathematical model in form of the compressible Navier-Stokes system type with some particularities: 1) the volumetric fraction of the dense phase (analogous to the density in the Navier-Stokes equations) may vanish, 2) the constitutive viscosity law may depend in a nonlinear form on this density, 3) the source term is nonlinear and coupled with state equations involving drag forces and hydrodynamic pressure, and 4) the state equation for the collision pressure of dense phase blows up for finite values of the density. We develop a rigorous theory for a special kind of solutions we call stationary clouds. Such solutions exist only under restrictions on the geometry of combustor and on the boundary conditions that usually meet in engineering applications. In return, these solutions have a stationary one-dimensional structure very simple and, from them, it is possible to reconstruct much of the dynamics of the whole system, responding to most of the practical issues of interest. Finally, we study the linear stability for the trivial solutions corresponding to uniform fluidized states injecting plane wave perturbations in our equations. Depending on the parameters of the equations of state describing the collisions between solid particles, hydrodynamic pressure, and the values of blowing boundary condition, we can draw detailed abacus separating stable regions of unstable regions where bubbles appear. Then, we use the dispersion relations of this multidimensional linearized model, combined with the stationary phase theorem, to approach the profiles and the evolution of the bubbles appearing in unstable regimes, and verify that the obtained results adjust to the observations.
Rural Mathematics Educator, 2002.
ERIC Educational Resources Information Center
Rural Mathematics Educator, 2002
2002-01-01
This document contains the two issues of "Rural Mathematics Educator" published in 2002. This newsletter of the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM) includes articles on rural mathematics education, as well as information and descriptions of professional development opportunities for…
Mathematical morphology for shape description
NASA Astrophysics Data System (ADS)
Schmitt, M.
2002-03-01
We first examine the measurements one can perform on the space of compact and convex sets. A famous theorem, due to Hadwiger (1957), shows that any measurement with nice properties, namely additivity, is a linear combination of Minkowski functionals. Then, some useful formulae, linking measurements in different dimensions of space are derived.In the second step, we make use of the morphological operations transforming sets into sets. These sets are then measured using the previous measurements. The most famous attempt yields the concept of granulomerties and their extensions.In the last part, we examine a way to build morphological random sets which are compatible with morphological operators like erosions or openings and apply it to the most famous example in morphology, the Boolean model, describing objects located at random.
What Counts as Mathematical Discourse?
ERIC Educational Resources Information Center
Moschkovich, Judit
2003-01-01
In this paper I use situated and socio-cultural perspective (Gee, 1996 & 1999) to examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. Using this example, I discuss how the distinction between everyday and mathematical discourse can help or hinder us in hearing the mathematical content in…
ERIC Educational Resources Information Center
Locklear, Tonja Motley
2012-01-01
The Sources of Middle School Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) was adapted for use in this study investigating the impact that gender, race, sexual orientation, hometown location (rural, suburban, or urban), high school GPA, college GPA and letter grade of a mathematics course in the previous semester had on the four…
Changing Mathematics Education in Mozambique.
ERIC Educational Resources Information Center
Gerdes, Paulus
1981-01-01
A brief description and analysis of mathematics education in different phases of the history of Mozambique are provided. Particular attention is given to teacher training and the first National Seminar on the Teaching of Mathematics. (MP)
NASA Technical Reports Server (NTRS)
Gliese, U.; Avanov, L. A.; Barrie, A. C.; Kujawski, J. T.; Mariano, A. J.; Tucker, C. J.; Chornay, D. J.; Cao, N. T.; Gershman, D. J.; Dorelli, J. C.; Zeuch, M. A.; Pollock, C. J.; Jacques, A. D.
2015-01-01
system calibration method that enables accurate and repeatable measurement and calibration of MCP gain, MCP efficiency, signal loss due to variation in gain and efficiency, crosstalk from effects both above and below the MCP, noise margin, and stability margin in one single measurement. More precise calibration is highly desirable as the instruments will produce higher quality raw data that will require less post-acquisition data correction using results from in-flight pitch angle distribution measurements and ground calibration measurements. The detection system description and the fundamental concepts of this new calibration method, named threshold scan, will be presented. It will be shown how to derive all the individual detection system parameters and how to choose the optimum detection system operating point. This new method has been successfully applied to achieve a highly accurate calibration of the DESs and DISs of the MMS mission. The practical application of the method will be presented together with the achieved calibration results and their significance. Finally, it will be shown that, with further detailed modeling, this method can be extended for use in flight to achieve and maintain a highly accurate detection system calibration across a large number of instruments during the mission.
Cooper, D.K.; Cooper, J.A.; Ferson, S.
1999-01-21
Calculating safety and reliability probabilities with functions of uncertain variables can yield incorrect or misleading results if some precautions are not taken. One important consideration is the application of constrained mathematics for calculating probabilities for functions that contain repeated variables. This paper includes a description of the problem and develops a methodology for obtaining an accurate solution.
Langley Atmospheric Information Retrieval System (LAIRS): System description and user's guide
NASA Technical Reports Server (NTRS)
Boland, D. E., Jr.; Lee, T.
1982-01-01
This document presents the user's guide, system description, and mathematical specifications for the Langley Atmospheric Information Retrieval System (LAIRS). It also includes a description of an optimal procedure for operational use of LAIRS. The primary objective of the LAIRS Program is to make it possible to obtain accurate estimates of atmospheric pressure, density, temperature, and winds along Shuttle reentry trajectories for use in postflight data reduction.
Student Nurses and Mathematics.
ERIC Educational Resources Information Center
Hutton, B. Meriel
For the safety of the public, it is essential that nurses are competent at least in the mathematics that enables them to calculate medications accurately. From a survey by G. Hek (1994), it is apparent that mathematics is not universally included in the nursing curricula, nor asked for as a pre-requisite to entry. Changes in the profile of the…
NNLOPS accurate associated HW production
NASA Astrophysics Data System (ADS)
Astill, William; Bizon, Wojciech; Re, Emanuele; Zanderighi, Giulia
2016-06-01
We present a next-to-next-to-leading order accurate description of associated HW production consistently matched to a parton shower. The method is based on reweighting events obtained with the HW plus one jet NLO accurate calculation implemented in POWHEG, extended with the MiNLO procedure, to reproduce NNLO accurate Born distributions. Since the Born kinematics is more complex than the cases treated before, we use a parametrization of the Collins-Soper angles to reduce the number of variables required for the reweighting. We present phenomenological results at 13 TeV, with cuts suggested by the Higgs Cross section Working Group.
NASA Technical Reports Server (NTRS)
Zolotukhin, V. G.; Kolosov, B. I.; Usikov, D. A.; Borisenko, V. I.; Mosin, S. T.; Gorokhov, V. N.
1980-01-01
A description of a batch of programs for the YeS-1040 computer combined into an automated system for processing photo (and video) images of the Earth's surface, taken from spacecraft, is presented. Individual programs with the detailed discussion of the algorithmic and programmatic facilities needed by the user are presented. The basic principles for assembling the system, and the control programs are included. The exchange format within whose framework the cataloging of any programs recommended for the system of processing will be activated in the future is displayed.
Goddard trajectory determination subsystem: Mathematical specifications
NASA Technical Reports Server (NTRS)
Wagner, W. E. (Editor); Velez, C. E. (Editor)
1972-01-01
The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.
I Learn Mathematics from My Students--Multiculturalism in Action.
ERIC Educational Resources Information Center
Henderson, David W.
1996-01-01
Gives examples of new mathematics theorems and proofs shown to the author by his students. Reflects on the notion of proof and discusses issues of multiculturalism in mathematics and descriptions of mathematics. (MKR)
Gray, W.G.; Tompson, A.; Soll, W.E.
1998-06-01
'Improved capabilities for modeling multiphase flow in the subsurface requires that several aspects of the system which impact the flow and transport processes be more properly accounted for. A distinguishing feature of multiphase flow in comparison to single phase flow is the existence of interfaces between fluids. At the microscopic (pore) scale, these interfaces are known to influence system behavior by supporting non-zero stresses such that the pressures in adjacent phases are not equal. In problems of interphase transport at the macroscopic (core) scale, knowledge of the total amount of interfacial area in the system provides a clue to the effectiveness of the communication between phases. Although interfacial processes are central to multiphase flow physics, their treatment in traditional porous-media theories has been implicit rather than explicit; and no attempts have been made to systematically account for the evolution of the interfacial area in dynamic systems or to include the dependence of constitutive functions, such as capillary pressure, on the interfacial area. This project implements a three-pronged approach to assessing the importance of various features of multiphase flow to its description. The research contributes to the improved understanding and precise physical description of multiphase subsurface flow by combining: (1) theoretical derivation of equations, (2) lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and (3) solution of the field-scale equations using a discrete numerical method to assess the advantages and disadvantages of the complete theory. This approach includes both fundamental scientific inquiry and a path for inclusion of the scientific results obtained in a technical tool that will improve assessment capabilities for multiphase flow situations that have arisen due to the introduction of organic materials in the natural environment. This report summarizes work after 1.5 years of a 3
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
The Dilemma of Descriptive Geometry
ERIC Educational Resources Information Center
Boleslavski, Moshe
1977-01-01
Proposes that engineering students undergo a preparatory summer school training program in fundamentals of engineering drawing, descriptive geometry, and mathematics prior to being admitted to regular engineering studies. (SL)
A mathematical approach to human pterygium shape
Pajic, Bojan; Vastardis, Iraklis; Rajkovic, Predrag; Pajic-Eggspuehler, Brigitte; Aebersold, Daniel M; Cvejic, Zeljka
2016-01-01
Purpose Pterygium is a common lesion affecting the population in countries with high levels of ultraviolet exposure. The final shape of a pterygium is the result of a growth pattern, which remains poorly understood. This manuscript provides a mathematical analysis as a tool to determine the shape of human pterygia. Materials and methods Eighteen patients, all affected by nasal unilateral pterygia, were randomly selected from our patient database independently of sex, origin, or race. We included all primary or recurrent pterygia with signs of proliferation, dry eye, and induction of astigmatism. Pseudopterygia were excluded from this study. Pterygia were outlined and analyzed mathematically using a Cartesian coordinate system with two axes (X, Y) and five accurate landmarks of the pterygium. Results In 13 patients (72%), the shape of the pterygia was hyperbolic and in five patients (28%), the shape was rather elliptical. Conclusion This analysis gives a highly accurate mathematical description of the shape of human pterygia. This might help to better assess the clinical results and outcome of the great variety of therapeutic approaches concerning these lesions. PMID:27555741
Computation and graphics in mathematical research
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
Mathematical representations of turbulent mixing
NASA Technical Reports Server (NTRS)
Farmer, R. C.; Audeh, B.
1973-01-01
A basic description is given of the mathematical tools and models which are presently used to represent turbulent, free shear layers. Recommendations are included for ways in which current modeling techniques can be improved.
Mathematical epidemiology is not an oxymoron
2009-01-01
A brief description of the importance of communicable diseases in history and the development of mathematical modelling of disease transmission is given. This includes reasons for mathematical modelling, the history of mathematical modelling from the foundations laid in the late nineteenth century to the present, some of the accomplishments of mathematical modelling, and some challenges for the future. Our purpose is to demonstrate the importance of mathematical modelling for the understanding and management of infectious disease transmission. PMID:19922686
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
The Mathematics of Global Change
ERIC Educational Resources Information Center
Kreith, Kurt
2011-01-01
This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…
Fostering Creativity Through Mathematics.
ERIC Educational Resources Information Center
Lichtenberg, Betty K., Ed.; Troutman, Andria P., Ed.
The 26 activities described in this volume deal with a wide variety of mathematical ideas. Most of the activities are appropriate for grades 6-9; many could be used with older or younger groups as well. All activities are described in detail; some descriptions include sample worksheets, and several provide suggestions for followup activities. The…
Assessment Mathematics Teacher's Competencies
ERIC Educational Resources Information Center
Alnoor, A. G.; Yuanxiang, Guo; Abudhuim, F. S.
2007-01-01
This paper aimed to identifying the professional efficiencies for the intermediate schools mathematics teachers and tries to know at what level the math teachers experience those competencies. The researcher used a descriptive research approach, the study data collected from specialist educators and teacher's experts and previous studies to…
Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern.
Sommargren, G E; Weaver, H J
1990-11-01
In this paper we discuss the diffraction pattern resulting from the propagation of light past an opaque obstacle with a circular cross section. A mathematical description of the diffraction pattern is obtained in the Fresnel region using scalar diffraction theory and is presented in terms of the Lommel functions. This description is shown experimentally to be quite accurate, not only for near axis points within the shadow region but also well past the shadow's edge into the directly illuminated region. The mathematical description is derived for spherical wave illumination and an isomorphic relation is developed relating it to plane wave illumination. The size of the central bright spot (as well as the subsequent diffraction rings), the axial intensity, and the intensity along the geometric shadow are characterized in terms of point source location and the distance of propagation past the circular obstacle. PMID:20577447
Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern
Sommargren, G.E. ); Weaver, H.J. )
1990-11-01
In this paper we discuss the diffraction pattern resulting from the propagation of light past an opaque obstacle with a circular cross section. A mathematical description of the diffraction pattern is obtained in the Fresnel region using scalar diffraction theory and is presented in terms of the Lommel functions. This description is shown experimentally to be quite accurate, not only for near axis points within the shadow region but also well past the shadow's edge into the directly illuminated region. The mathematical description is derived for spherical wave illumination and an isomorphic relation is developed relating it to plane wave illumination. The size of the central bright spot (as well as the subsequent diffraction rings), the axial intensity, and the intensity along the geometric shadow are characterized in terms of point source location and the distance of propagation past the circular obstacle. Key words: Spherical diffraction, isomorphic propagation theory, Lommel functions.
Golibrzuch, Kai; Shirhatti, Pranav R.; Kandratsenka, Alexander; Wodtke, Alec M.; Bartels, Christof; Max Planck Institute for Biophysical Chemistry, Göttingen 37077 ; Rahinov, Igor; Auerbach, Daniel J.; Max Planck Institute for Biophysical Chemistry, Göttingen 37077; Department of Chemistry and Biochemistry, University of California Santa Barbara, Santa Barbara, California 93106
2014-01-28
We present a combined experimental and theoretical study of NO(v = 3 → 3, 2, 1) scattering from a Au(111) surface at incidence translational energies ranging from 0.1 to 1.2 eV. Experimentally, molecular beam–surface scattering is combined with vibrational overtone pumping and quantum-state selective detection of the recoiling molecules. Theoretically, we employ a recently developed first-principles approach, which employs an Independent Electron Surface Hopping (IESH) algorithm to model the nonadiabatic dynamics on a Newns-Anderson Hamiltonian derived from density functional theory. This approach has been successful when compared to previously reported NO/Au scattering data. The experiments presented here show that vibrational relaxation probabilities increase with incidence energy of translation. The theoretical simulations incorrectly predict high relaxation probabilities at low incidence translational energy. We show that this behavior originates from trajectories exhibiting multiple bounces at the surface, associated with deeper penetration and favored (N-down) molecular orientation, resulting in a higher average number of electronic hops and thus stronger vibrational relaxation. The experimentally observed narrow angular distributions suggest that mainly single-bounce collisions are important. Restricting the simulations by selecting only single-bounce trajectories improves agreement with experiment. The multiple bounce artifacts discovered in this work are also present in simulations employing electronic friction and even for electronically adiabatic simulations, meaning they are not a direct result of the IESH algorithm. This work demonstrates how even subtle errors in the adiabatic interaction potential, especially those that influence the interaction time of the molecule with the surface, can lead to an incorrect description of electronically nonadiabatic vibrational energy transfer in molecule-surface collisions.
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
CARE 3 phase 2 report - mathematical description
NASA Technical Reports Server (NTRS)
Stiffler, J. J.; Bryant, L. A.
1982-01-01
CARE III (Computer-Aided Reliability Estimation, version three) a computer program designed to help estimate the reliability of complex, redundant systems is described. Although the program can model a wide variety of redundant structures, it was developed specifically for fault tolerant avionics systems. CARE III generalizes the class of system structures that can be modeled and greatly expands the coverage model to take into account such effects as intermittent and transient faults, latent faults, and error propagation.
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Beauty as Fit: A Metaphor in Mathematics?
ERIC Educational Resources Information Center
Raman, Manya; Öhman, Lars-Daniel
2013-01-01
Beauty, which plays a central role in the practice of mathematics (Sinclair 2002), is almost absent in discussions of school mathematics (Dreyfus and Eisenberg 1986). This is problematic, because students will decide whether or not to continue their studies in mathematics without having an accurate picture of what the subject is about. In order to…
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Matalas, N.C.
1991-01-01
What constitutes a comprehensive description of drought, a description forming a basis for answering why a drought occurred is outlined. The description entails two aspects that are "naturally" coupled, named physical and economic, and treats the set of hydrologic measures of droughts in terms of their multivariate distribution, rather than in terms of a collection of the marginal distributions. ?? 1991 Springer-Verlag.
Self-Efficacy Beliefs of Prospective Primary Mathematics Teachers about Mathematical Literacy
ERIC Educational Resources Information Center
Yavuz, Gunes; Gunhan, Berna Canturk; Ersoy, Esen; Narli, Serkan
2013-01-01
The aim of this study was to examine the self-efficacy beliefs about mathematical literacy among teachers of primary school mathematics and the relationship between the self-efficacy beliefs and attitudes towards mathematics. To that end, a descriptive research study was conducted with 550 prospective teachers studying primary school mathematics…
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Siskiyou County Superintendent of Schools, Yreka, CA.
The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
ERIC Educational Resources Information Center
Rom, Mark Carl
2011-01-01
Grades matter. College grading systems, however, are often ad hoc and prone to mistakes. This essay focuses on one factor that contributes to high-quality grading systems: grading accuracy (or "efficiency"). I proceed in several steps. First, I discuss the elements of "efficient" (i.e., accurate) grading. Next, I present analytical results…
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.
ERIC Educational Resources Information Center
Johnson, Jerry
1997-01-01
Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)
ERIC Educational Resources Information Center
Gardner, Martin
1978-01-01
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
Accurate monotone cubic interpolation
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1991-01-01
Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.
Accurate Finite Difference Algorithms
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1996-01-01
Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.
Computer-Game-Based Tutoring of Mathematics
ERIC Educational Resources Information Center
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
Mathematics Teachers' Criteria of Dimension
ERIC Educational Resources Information Center
Ural, Alattin
2014-01-01
The aim of the study is to determine mathematics teachers' decisions about dimensions of the geometric figures, criteria of dimension and consistency of decision-criteria. The research is a qualitative research and the model applied in the study is descriptive method on the basis of general scanning model. 15 mathematics teachers attended the…
On the Role of Mathematics in Physics
ERIC Educational Resources Information Center
Quale, Andreas
2011-01-01
I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a…
Teaching Mathematics with Computers 9-12.
ERIC Educational Resources Information Center
New York State Education Dept., Albany.
This publication is designed to show how computers can be used effectively in secondary school mathematics curricula. Section I provides a description of the various types of software that could be incorporated into the secondary school mathematics curriculum. Procedures for evaluating the software and using it in a classroom or laboratory…
Secondary School Mathematics Curriculum Improvement Study.
ERIC Educational Resources Information Center
Secondary School Mathematics Curriculum Improvement Study, New York, NY.
This bulletin contains: (1) a summary and conclusions of a study of mathematics curricula in Europe and Japan, and (2) a description of beginning efforts to evaluate the Secondary School Mathematics Curriculum Improvement Study (SSMCIS) project. Some of the conclusions of the European and Japanese study are: (1) the study of Euclidean synthetic…
Analysis of Physiological Systems via Mathematical Models.
ERIC Educational Resources Information Center
Hazelrig, Jane B.
1983-01-01
Discusses steps to be executed when studying physiological systems with theoretical mathematical models. Steps considered include: (1) definition of goals; (2) model formulation; (3) mathematical description; (4) qualitative evaluation; (5) parameter estimation; (6) model fitting; (7) evaluation; and (8) design of new experiments based on the…
The First Mathematics Olympiads in Mozambique.
ERIC Educational Resources Information Center
Gerdes, Paulus
1984-01-01
Explains why mathematics olympiads were introduced in Mozambique. A description and analysis of results (scores, type of problems, social background, and composition by sex of participants and winners) and short biographies of winners are given to offer insight into the social aspects of the development of their mathematical talent. (Author/JN)
Shi, Runhua; McLarty, Jerry W
2009-10-01
In this article, we introduced basic concepts of statistics, type of distributions, and descriptive statistics. A few examples were also provided. The basic concepts presented herein are only a fraction of the concepts related to descriptive statistics. Also, there are many commonly used distributions not presented herein, such as Poisson distributions for rare events and exponential distributions, F distributions, and logistic distributions. More information can be found in many statistics books and publications. PMID:19891281
Malkevitch, J. ); McCarthy, D. )
1990-01-01
The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Enhancing Mathematical Communication: "Bag of Tricks" Game
ERIC Educational Resources Information Center
Patahuddin, Sitti Maesuri; Ramful, Ajay; Greenlees, Jane
2015-01-01
An engaging activity which prompts students to listen, talk, reason and write about geometrical properties. The "Bag of Tricks" encourages students to clarify their thoughts and communicate precisely using accurate mathematical language.
Applied mathematical problems in modern electromagnetics
NASA Astrophysics Data System (ADS)
Kriegsman, Gregory
1994-05-01
We have primarily investigated two classes of electromagnetic problems. The first contains the quantitative description of microwave heating of dispersive and conductive materials. Such problems arise, for example, when biological tissue are exposed, accidentally or purposefully, to microwave radiation. Other instances occur in ceramic processing, such as sintering and microwave assisted chemical vapor infiltration and other industrial drying processes, such as the curing of paints and concrete. The second class characterizes the scattering of microwaves by complex targets which possess two or more disparate length and/or time scales. Spatially complex scatterers arise in a variety of applications, such as large gratings and slowly changing guiding structures. The former are useful in developing microstrip energy couplers while the later can be used to model anatomical subsystems (e.g., the open guiding structure composed of two legs and the adjoining lower torso). Temporally complex targets occur in applications involving dispersive media whose relaxation times differ by orders of magnitude from thermal and/or electromagnetic time scales. For both cases the mathematical description of the problems gives rise to complicated ill-conditioned boundary value problems, whose accurate solutions require a blend of both asymptotic techniques, such as multiscale methods and matched asymptotic expansions, and numerical methods incorporating radiation boundary conditions, such as finite differences and finite elements.
ERIC Educational Resources Information Center
ROSEN, ELLEN F.; STOLUROW, LAWRENCE M.
MANIPULATION OF FRAMES WITHIN PROGRAMED MATHEMATICS TEXTS IN ORDER TO STUDY FOUR VARIABLES YIELDED, IN A PREVIOUSLY REPORTED PAPER, CORRELATIONAL DATA (FOR RELATIVELY SMALL TREATMENT GROUPS) THAT ARE PRESENTED HERE. FIRST, THE ORDER OF PRESENTATION OF PROGRAMED MATERIAL (BEFORE, AFTER, AND WITHOUT CONVENTIONAL INSTRUCTION) HAD NO EFFECT ON…
ERIC Educational Resources Information Center
Britton, Edward; Raizen, Senta; Kaser, Joyce; Porter, Andrew
When entering this new millennium, educators and researchers need to know much more about how to address the increasingly acute diversity and equity issues in educating children in mathematics and science. This headline was the conclusion of the over 200 distinguished panelists, chairs, discussants, featured speakers, and participants who…
Accurate ab Initio Spin Densities
2012-01-01
We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740]. PMID:22707921
NASA Astrophysics Data System (ADS)
Itano, Wayne M.; Ramsey, Norman F.
1993-07-01
The paper discusses current methods for accurate measurements of time by conventional atomic clocks, with particular attention given to the principles of operation of atomic-beam frequency standards, atomic hydrogen masers, and atomic fountain and to the potential use of strings of trapped mercury ions as a time device more stable than conventional atomic clocks. The areas of application of the ultraprecise and ultrastable time-measuring devices that tax the capacity of modern atomic clocks include radio astronomy and tests of relativity. The paper also discusses practical applications of ultraprecise clocks, such as navigation of space vehicles and pinpointing the exact position of ships and other objects on earth using the GPS.
Educational assessment of mathematics skills and abilities.
Bryant, B R; Rivera, D P
1997-01-01
Mathematics assessments play a valuable role in identifying students' strengths and weaknesses and in developing and monitoring instructional practice. Over the last century, mathematics assessment has been refined as math content has changed as a result of curriculum reform. Today, researchers and practitioners use various assessment techniques to (a) identify students who have mathematics learning disabilities (LD), (b) target individual strengths and weaknesses across mathematics areas, (c) document the effects of mathematics instruction in a remedial or special program, (d) identify strategies that students employ during math activities, (e) conduct research about the characteristics of students with math LD, and (f) examine the technical characteristics of mathematics tests. This article provides an historical overview of the development of mathematics assessment and a description of specific strategies for conducting math evaluations. PMID:9009875
Accurate quantum chemical calculations
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.
1989-01-01
An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.
Elementary Statistics I--Mathematics 274 Course Syllabus, Fall 2001.
ERIC Educational Resources Information Center
Clark, Deborah L.
This document features the syllabus for a course in Elementary Statistics/Mathematics at Southern University in Baton Rouge, LA. The course textbook, a course description, readings, goals, and course requirements are presented. Basic descriptive analysis and mathematical concepts commonly used in statistics are emphasized in the course. Topics…
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
ERIC Educational Resources Information Center
Lapointe, Archie E.; And Others
In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
A HALF CENTURY OF TEACHING SCIENCE AND MATHEMATICS.
ERIC Educational Resources Information Center
ISENBARGER, KATHARINE U.; AND OTHERS
MAJOR DEVELOPMENTS IN SCIENCE AND MATHEMATICS EDUCATION DURING THE PERIOD 1900-50 ARE REVIEWED. AN EARLY CHAPTER IS DEVOTED TO A DETAILED DESCRIPTION OF THE FORMATION AND SUBSEQUENT DEVELOPMENT OF THE CENTRAL ASSOCIATION OF SCHOOL SCIENCE AND MATHEMATICS TEACHERS AND THE JOURNAL, "SCHOOL SCIENCE AND MATHEMATICS." OTHER SECTIONS INCLUDE (1)…
Development of the Database "Mathematical Web-resources"
NASA Astrophysics Data System (ADS)
Barakhnin, V. B.
The development and creation technology of the mathematical web-resources portal is offered. Basic components of this portal are the mathematical Internet-resources catalogue and the mathematical sciences ontology. The description of resources is carried according to the international standards (DC and GILS) by means of structural metadata.
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
New model accurately predicts reformate composition
Ancheyta-Juarez, J.; Aguilar-Rodriguez, E. )
1994-01-31
Although naphtha reforming is a well-known process, the evolution of catalyst formulation, as well as new trends in gasoline specifications, have led to rapid evolution of the process, including: reactor design, regeneration mode, and operating conditions. Mathematical modeling of the reforming process is an increasingly important tool. It is fundamental to the proper design of new reactors and revamp of existing ones. Modeling can be used to optimize operating conditions, analyze the effects of process variables, and enhance unit performance. Instituto Mexicano del Petroleo has developed a model of the catalytic reforming process that accurately predicts reformate composition at the higher-severity conditions at which new reformers are being designed. The new AA model is more accurate than previous proposals because it takes into account the effects of temperature and pressure on the rate constants of each chemical reaction.
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
Mathematical String Sculptures: A Case Study in Computationally-Enhanced Mathematical Crafts
ERIC Educational Resources Information Center
Eisenberg, Michael
2007-01-01
Mathematical string sculptures constitute an extremely beautiful realm of mathematical crafts. This snapshot begins with a description of a marvelous (and no longer manufactured) toy called Space Spider, which provided a framework with which children could experiment with string sculptures. Using a computer-controlled laser cutter to create frames…
ERIC Educational Resources Information Center
Gafoor, Kunnathodi Abdul; Sarabi, M. K.
2015-01-01
This study relates factors in nature of Mathematics and its teaching learning to student difficulties for diverse mathematics tasks. Descriptive survey was done on a sample of 300 high school students in Kerala with a questionnaire on difficulties in learning. Student perception of difficulty on 26 types of tasks, under five heads that students…
Symmetry in Mathematics and Art: An Exploration of an Art Venue for Mathematics Learning
ERIC Educational Resources Information Center
Stylianou, Despina A.; Grzegorczyk, Ivona
2005-01-01
Symmetry is an aspect of mathematics that is strongly linked to art and design. We chose to explore this connection in the context of a liberal arts mathematics course. Here we present a brief description of this course, including an outline of the curriculum and specific features of the course. We subsequently present the results of a study we…
NASA Astrophysics Data System (ADS)
Baader, Franz
Description Logics (DLs) are a well-investigated family of logic-based knowledge representation formalisms, which can be used to represent the conceptual knowledge of an application domain in a structured and formally well-understood way. They are employed in various application domains, such as natural language processing, configuration, and databases, but their most notable success so far is the adoption of the DL-based language OWL as standard ontology language for the semantic web.
SKYMAP system description: Star catalog data base generation and utilization
NASA Technical Reports Server (NTRS)
Gottlieb, D. M.
1979-01-01
The specifications, design, software description, and use of the SKYMAP star catalog system are detailed. The SKYMAP system was developed to provide an accurate and complete catalog of all stars with blue or visual magnitudes brighter than 9.0 for use by attitude determination programs. Because of the large number of stars which are brighter than 9.0 magnitude, efficient techniques of manipulating and accessing the data were required. These techniques of staged distillation of data from a Master Catalog to a Core Catalog, and direct access of overlapping zone catalogs, form the basis of the SKYMAP system. The collection and tranformation of data required to produce the Master Catalog data base is described. The data flow through the main programs and levels of star catalogs is detailed. The mathematical and logical techniques for each program and the format of all catalogs are documented.
Three essays in mathematical finance
NASA Astrophysics Data System (ADS)
Wang, Ruming
This dissertation uses mathematical techniques to solve three problems in mathematical finance. The first two problems are on model-independent pricing and hedging of financial derivatives. We use asymptotic expansions to express derivative prices and implied volatilities. Then just by using the first few terms in the expansions, we get simple and accurate formulas, which can also help us find connections between different products. The last problem is on optimal trading strategies in a limit order book. Under a very general setup, we solve explicitly for a dynamic decision problem involving choosing between limit order and market order.
Mathematical Models of Gene Regulation
NASA Astrophysics Data System (ADS)
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena
NASA Astrophysics Data System (ADS)
Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.
2008-02-01
Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Edwards, A W F
2011-03-01
Ernst Mayr called the first part of the evolutionary synthesis the 'Fisherian synthesis' on account of the dominant role played by R.A. Fisher in forging a mathematical theory of natural selection together with J.B.S. Haldane and Sewall Wright in the decade 1922-1932. It is here argued that Fisher's contribution relied on a close reading of Darwin's work to a much greater extent than did the contributions of Haldane and Wright, that it was synthetic in contrast to their analytic approach and that it was greatly influenced by his friendship with the Darwin family, particularly with Charles's son Leonard. PMID:21423339
Accurate calculation of diffraction-limited encircled and ensquared energy.
Andersen, Torben B
2015-09-01
Mathematical properties of the encircled and ensquared energy functions for the diffraction-limited point-spread function (PSF) are presented. These include power series and a set of linear differential equations that facilitate the accurate calculation of these functions. Asymptotic expressions are derived that provide very accurate estimates for the relative amount of energy in the diffraction PSF that fall outside a square or rectangular large detector. Tables with accurate values of the encircled and ensquared energy functions are also presented. PMID:26368873
Accurate modeling of parallel scientific computations
NASA Technical Reports Server (NTRS)
Nicol, David M.; Townsend, James C.
1988-01-01
Scientific codes are usually parallelized by partitioning a grid among processors. To achieve top performance it is necessary to partition the grid so as to balance workload and minimize communication/synchronization costs. This problem is particularly acute when the grid is irregular, changes over the course of the computation, and is not known until load time. Critical mapping and remapping decisions rest on the ability to accurately predict performance, given a description of a grid and its partition. This paper discusses one approach to this problem, and illustrates its use on a one-dimensional fluids code. The models constructed are shown to be accurate, and are used to find optimal remapping schedules.
Mathematical modelling in MHD technology
Scheindlin, A.E.; Medin, S.A. )
1990-01-01
The technological scheme and the general parameters of the commercial scale pilot MHD power plant are described. The characteristics of the flow train components and the electrical equipment are discussed. The basic ideas of the mathematical modelling of the processes and the devices operation in MHD systems are considered. The application of different description levels in computer simulation is analyzed and the examples of typical solutions are presented.
Mathematical modeling of ligaments and tendons.
Woo, S L; Johnson, G A; Smith, B A
1993-11-01
Ligaments and tendons serve a variety of important functions in maintaining the structure of the human body. Although abundant literature exists describing experimental investigations of these tissues, mathematical modeling of ligaments and tendons also contributes significantly to understanding their behavior. This paper presents a survey of developments in mathematical modeling of ligaments and tendons over the past 20 years. Mathematical descriptions of ligaments and tendons are identified as either elastic or viscoelastic, and are discussed in chronological order. Elastic models assume that ligaments and tendons do not display time dependent behavior and thus, they focus on describing the nonlinear aspects of their mechanical response. On the other hand, viscoelastic models incorporate time dependent effects into their mathematical description. In particular, two viscoelastic models are discussed in detail; quasi-linear viscoelasticity (QLV), which has been widely used in the past 20 years, and the recently proposed single integral finite strain (SIFS) model. PMID:8302027
A Multifaceted Mathematical Approach for Complex Systems
Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.
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 significant 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.
Examining Classroom Interactions & Mathematical Discourses
ERIC Educational Resources Information Center
Grant, Melva R.
2009-01-01
This investigation examined interactions in three classrooms to determine how they influenced Discourses related to mathematics learning and teaching. Mathematics education literature suggests that effective mathematics instruction includes mathematical Discourses. However, effective mathematical Discourses within mathematics classrooms vary…
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…
NASA Astrophysics Data System (ADS)
Ford, David; Huntsman, Steven
2006-06-01
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. Whereas conventionally, the systems investigated require this form of data reduction in order to facilitate prediction, a different problem also occurs, in the context of communication networks, markets, etc. Such “empirically accessible” systems typically overwhelm observers with the sort of information that in the case of (say) a gas is effectively unobtainable. What is required for such complex interacting systems is not prediction (this may be impossible when humans besides the observer are responsible for the interactions) but rather, description as a route to understanding. Still, the need for a thermodynamical data reduction scheme remains. In this paper, we show how an empirical temperature can be computed for finite, empirically accessible systems, and further outline how this construction allows the age-old science of thermodynamics to be fruitfully applied to them.
NASA Astrophysics Data System (ADS)
Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew
2013-06-01
Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.
NASA Astrophysics Data System (ADS)
Kasturirangan, Rajesh
2014-07-01
Mathematics is a human pursuit. Whether the truths of mathematics lie outside the human mind or emerge out of it, the actual practice of mathematics is conducted by human beings. In other words, human mathematics is the only kind of mathematics that we can pursue and human mathematics has to be built on top of cognitive capacities that are possessed by all human beings. Another way of stating the same claim is that mathematics is experienced by human beings using their cognitive capacities. This paper argues that exploring the experience of mathematics is a useful way to make headway on the foundations of mathematics. Focusing on the experience of mathematics is an empirical approach to the study of mathematics that sidesteps some of the thorniest debates from an earlier era about Platonism and Formalism in the foundations of mathematics.
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Mathematical Language and Advanced Mathematics Learning
ERIC Educational Resources Information Center
Ferrari, Pier Luigi
2004-01-01
This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Mathematics for Life: Sustainable Mathematics Education
ERIC Educational Resources Information Center
Renert, Moshe
2011-01-01
Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…
Mathematical Story: A Metaphor for Mathematics Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
Computation and graphics in mathematical research. Progress report, June 1, 1991--May 31, 1992
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
Katsnelson, Boris A; Panov, Vladimir G; Minigaliyeva, Ilzira A; Varaksin, Anatoly N; Privalova, Larisa I; Slyshkina, Tatyana V; Grebenkina, Svetlana V
2015-08-01
For characterizing the three-factorial toxicity, we proposed a new health risk-oriented approach, the gist of which is a classification of effects depending on whether a binary combined toxicity's type remains virtually the same or appears to be either more or less adverse when modeled against the background of a third toxic. To explore possibilities of this approach, we used results of an experiment in which rats had been injected ip 3 times a week (up to 20 injections) with a water solution of either one of the toxics (Mn, Ni or Cr-VI salts) in a dose equivalent to 0.05 LD50, or any two of them, or all the three in the same doses, the controls receiving injections of the same volume of distilled water (4mL per rat). Judging by more than 30 indices for the organism's status, all exposures caused subchronic intoxication of mild to moderate strength. For each two-factorial exposure, we found by mathematical modeling based on the isobolograms that the binary combined subchronic toxicity either was of additive type or departed from it (predominantly toward subadditivity) depending on the effect assessed, dose, and effect level. For the three-factorial combination, different classes of effects were observed rather consistently: class A - those regarding which the third toxic's addition made the binary toxicity type more unfavorable for the organism, class B - those regarding which the result was opposite, and class C - those regarding which the type of binary combined toxicity on the background of a third toxic virtually remained the same as in its absence. We found a complicated reciprocal influence of combined metals on their retention in kidneys, liver, spleen and brain which might presumably be one of the possible mechanisms of combined toxicity, but the lack of an explicit correspondence between the above influence and the influence on toxicity effects suggests that this mechanism is not always the most important one. The relevance of the proposed classification
The reasonable effectiveness of mathematics in the natural sciences
NASA Astrophysics Data System (ADS)
Harvey, Alex
2011-12-01
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.
The College Entrance Examination Board and Mathematics Education.
ERIC Educational Resources Information Center
Jones, Chancey O.; Valentine, John A.
1984-01-01
To help explain the relationship between board activities and mathematics education today, the creation and evolution of the College Board are described. The development of the Advanced Placement computer science course description and examination are noted particularly. (MNS)
Values taught, values learned, attitude and performance in mathematics
NASA Astrophysics Data System (ADS)
Limbaco, K. S. A.
2015-03-01
The purpose of the study was to identify, describe and find the relationship among values taught, values learned, attitude and performance in mathematics. The researcher used descriptive-correlational method of research to gather information and to describe the nature of situation. The following instruments were used in this study: Math Attitude Inventory, Inventory of Values Taught and Learned which were content validated by experts in the field of Mathematics, Values and Education. Generally, most of the values were taught by the teachers. All of the values were learned by the students. The following got the highest mean ratings for values taught: moral strength, sharing, charity, valuing life, love of God, truth and honesty, reason, alternativism and articulation. The following got highest mean ratings for values learned: patience/tolerance, sharing, charity, valuing life, faith, love of God, truth and honesty, analogical thinking, confidence and individual liberty. Majority of the respondents have moderately positive attitude towards mathematics. Positive statements in the Mathematics Attitude Inventory are "Generally true" while negative statements are "Neutral." In conclusion, values were taught by mathematics teacher, thus, learned by the students. Therefore, mathematics is very much related to life. Values can be learned and strengthened through mathematics; there is a significant relationship between values taught by the teachers and values learned by the students and attitude towards mathematics and performance in mathematics; values taught does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance in mathematics even if the mathematics teacher did not teach values; values learned does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance
How to accurately bypass damage
Broyde, Suse; Patel, Dinshaw J.
2016-01-01
Ultraviolet radiation can cause cancer through DNA damage — specifically, by linking adjacent thymine bases. Crystal structures show how the enzyme DNA polymerase η accurately bypasses such lesions, offering protection. PMID:20577203
Accurate Evaluation of Quantum Integrals
NASA Technical Reports Server (NTRS)
Galant, David C.; Goorvitch, D.
1994-01-01
Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schr\\"{o}dinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.
Multidimensional wave field signal theory: Mathematical foundations
NASA Astrophysics Data System (ADS)
Baddour, Natalie
2011-06-01
Many important physical phenomena are described by wave or diffusion-wave type equations. Since these equations are linear, it would be useful to be able to use tools from the theory of linear signals and systems in solving related forward or inverse problems. In particular, the transform domain signal description from linear system theory has shown concrete promise for the solution of problems that are governed by a multidimensional wave field. The aim is to develop a unified framework for the description of wavefields via multidimensional signals. However, certain preliminary mathematical results are crucial for the development of this framework. This first paper on this topic thus introduces the mathematical foundations and proves some important mathematical results. The foundation of the framework starts with the inhomogeneous Helmholtz or pseudo-Helmholtz equation, which is the mathematical basis of a large class of wavefields. Application of the appropriate multi-dimensional Fourier transform leads to a transfer function description. To return to the physical spatial domain, certain mathematical results are necessary and these are presented and proved here as six fundamental theorems. These theorems are crucial for the evaluation of a certain class of improper integrals which arise in the evaluation of inverse multi-dimensional Fourier and Hankel transforms, upon which the framework is based. Subsequently, applications of these theorems are demonstrated, in particular for the derivation of Green's functions in different coordinate systems.
Transforming Primary Mathematics
ERIC Educational Resources Information Center
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
Mathematical Epistemologies at Work.
ERIC Educational Resources Information Center
Noss, Richard
2002-01-01
Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…
NASA Astrophysics Data System (ADS)
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…
Mathematics Lessons without ...
ERIC Educational Resources Information Center
Cross, Kath; Hibbs, John
2006-01-01
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
Student Teachers' Views about Assessment and Evaluation Methods in Mathematics
ERIC Educational Resources Information Center
Dogan, Mustafa
2011-01-01
This study aimed to find out assessment and evaluation approaches in a Mathematics Teacher Training Department based on the views and experiences of student teachers. The study used a descriptive survey method, with the research sample consisting of 150 third- and fourth-year Primary Mathematics student teachers. Data were collected using a…
Success of Online Mathematics Courses at the Community College Level
ERIC Educational Resources Information Center
Lee, Lisa S.
2011-01-01
Low success rates in online mathematics courses at the community college level have raised concerns. The purpose of this study was to investigate the factors that contribute to student success in online mathematics courses at community colleges. The non-experimental quantitative design began with descriptive statistics to explore the quantitative…
Mathematics Education and the Objectivist Programme in HPS
ERIC Educational Resources Information Center
Glas, Eduard
2013-01-01
Using history of mathematics for studying concepts, methods, problems and other internal features of the discipline may give rise to a certain tension between descriptive adequacy and educational demands. Other than historians, educators are concerned with mathematics as a "normatively defined" discipline. Teaching cannot but be based on a…
Motivational Classroom Climate for Learning Mathematics: A Reversal Theory Perspective
ERIC Educational Resources Information Center
Lewis, Gareth
2015-01-01
In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…
The Necessary Teaching Competences for Mathematics Teachers in Middle Schools
ERIC Educational Resources Information Center
Alnoor, A. G.; xiang, G. Y.
2007-01-01
The professional competences of middle school mathematics teachers has been identified, also the significance extent of such competences for chinese and yemenies mathematics teachers has been studied. The researcher used descriptive research approach. The study data collected from Specialist educators and teachers experts to determine the…
NLSMA Reports, No. 33, Intercorrelations of Mathematical and Psychological Variables.
ERIC Educational Resources Information Center
Wilson, James W., Ed.; Begle, Edward G., Ed.
This is one of a series of reports on the National Longitudinal Study of Mathematical Abilities (NLSMA). It is a listing of correlation coefficients where each mathematical scale has been paired with each psychological scale. (See NLSMA Reports Nos. 4-6 for a description of these scales.) Besides each correlation matrix, a rotated factor matrix is…
[Cambridge Conference on School Mathematics Feasibility Studies 9-13.
ERIC Educational Resources Information Center
Cambridge Conference on School Mathematics, Newton, MA.
These materials are a part of a series of studies sponsored by the Cambridge Conference on School Mathematics which reflects the ideas of CCSM regarding the goals and objectives for school mathematics K-12. Feasibility Studies 9-13 contain a wide range of topics. The following are the titles and brief descriptions of these studies. Number…
Water wave model with accurate dispersion and vertical vorticity
NASA Astrophysics Data System (ADS)
Bokhove, Onno
2010-05-01
Cotter and Bokhove (Journal of Engineering Mathematics 2010) derived a variational water wave model with accurate dispersion and vertical vorticity. In one limit, it leads to Luke's variational principle for potential flow water waves. In the another limit it leads to the depth-averaged shallow water equations including vertical vorticity. Presently, focus will be put on the Hamiltonian formulation of the variational model and its boundary conditions.
Mathematical and Statistical Software Index. Final Report.
ERIC Educational Resources Information Center
Black, Doris E., Comp.
Brief descriptions are provided of general-purpose mathematical and statistical software, including 27 "stand-alone" programs, three subroutine systems, and two nationally recognized statistical packages, which are available in the Air Force Human Resources Laboratory (AFHRL) software library. This index was created to enable researchers to…
Teaching Mathematics from a Chemist's Viewpoint.
ERIC Educational Resources Information Center
DeLorenzo, Ronald A.
This paper describes a chemistry professor's approach to teaching mathematics in the college classroom. Based on the assumption that the four main goals of the educational process in general are to teach students to communicate clearly, study regularly, master basic math skills, and think logically, a description is provided of the manner in which…
Qualitative Graphing: A Construction in Mathematics.
ERIC Educational Resources Information Center
Narode, Ronald
This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…
Classroom Instruction and Students' Attitudes Towards Mathematics
ERIC Educational Resources Information Center
Tessema, Taddesse G.
2010-01-01
This quantitative study examined the association between classroom instruction and students' attitudes towards mathematics at the secondary level. Data were collected through a Likert-type survey of Hope High School students and then analyzed for statistical significance by utilizing descriptive statistics, tests of significance, and correlation…
MATHEMATICAL MODEL FOR THE SELECTIVE DEPOSITION OF INHALED PHARMACEUTICALS
To accurately assess the potential therapeutic effects of airborne drugs, the deposition sites of inhaled particles must be known. erein, an original theory is presented for physiologically based pharmacokinetic modeling and related prophylaxis of airway diseases. he mathematical...
Accurate basis set truncation for wavefunction embedding
NASA Astrophysics Data System (ADS)
Barnes, Taylor A.; Goodpaster, Jason D.; Manby, Frederick R.; Miller, Thomas F.
2013-07-01
Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)], 10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.
Accurate pose estimation for forensic identification
NASA Astrophysics Data System (ADS)
Merckx, Gert; Hermans, Jeroen; Vandermeulen, Dirk
2010-04-01
In forensic authentication, one aims to identify the perpetrator among a series of suspects or distractors. A fundamental problem in any recognition system that aims for identification of subjects in a natural scene is the lack of constrains on viewing and imaging conditions. In forensic applications, identification proves even more challenging, since most surveillance footage is of abysmal quality. In this context, robust methods for pose estimation are paramount. In this paper we will therefore present a new pose estimation strategy for very low quality footage. Our approach uses 3D-2D registration of a textured 3D face model with the surveillance image to obtain accurate far field pose alignment. Starting from an inaccurate initial estimate, the technique uses novel similarity measures based on the monogenic signal to guide a pose optimization process. We will illustrate the descriptive strength of the introduced similarity measures by using them directly as a recognition metric. Through validation, using both real and synthetic surveillance footage, our pose estimation method is shown to be accurate, and robust to lighting changes and image degradation.
Cardiovascular response to dynamic aerobic exercise: a mathematical model.
Magosso, E; Ursino, M
2002-11-01
An original mathematical model of the cardiovascular response to dynamic exercise is presented. It includes the pulsating heart, the pulmonary and systemic circulation, a separate description of the vascular bed in active tissues, the local metabolic vasodilation in these tissues and the mechanical effects of muscular contractions on venous return. Moreover, the model provides a description of the ventilatory response to exercise and various neural regulatory mechanisms working on cardiovascular parameters. These mechanisms embrace the so-called central command, the arterial baroreflex and the lung inflation reflex. All parameters in the model have been given in accordance with physiological data from the literature. In this work, the model has been used to simulate the steady-state value of the main cardiorespiratory quantities at different levels of aerobic exercise and the temporal pattern in the transient phase from rest to moderate exercise. Results suggest that, with suitable parameter values the model is able accurately to simulate the cardiorespiratory response in the overall range of aerobic exercise. This response is characterised by a moderate hypertension (10-30%) and by a conspicuous increase in systemic conductance (80-130%), heart rate (64-150%) and cardiac output (100-200%). The transient pattern exhibits three distinct phases (lasting approximately 5s, 15s and 2 min), that reflect the temporal heterogeneity of the mechanisms involved. The model may be useful to improve understanding of exercise physiology and as an educational tool to analyse the complexity of cardiovascular and respiratory regulation. PMID:12507317
Mathematics of Information Processing and the Internet
ERIC Educational Resources Information Center
Hart, Eric W.
2010-01-01
The mathematics of information processing and the Internet can be organized around four fundamental themes: (1) access (finding information easily); (2) security (keeping information confidential); (3) accuracy (ensuring accurate information); and (4) efficiency (data compression). In this article, the author discusses each theme with reference to…
Mathematical Modelling: A New Approach to Teaching Applied Mathematics.
ERIC Educational Resources Information Center
Burghes, D. N.; Borrie, M. S.
1979-01-01
Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)
ERIC Educational Resources Information Center
Silver, Edward A.; Lane, Suzanne
Recent reports on mathematics education reform have focused the attention of educational practitioners and policymakers on new goals for mathematics education and new descriptions of mathematical proficiency. QUASAR is a national project (Quantitative Understanding: Amplifying Student Achievement and Reasoning) designed to improve the mathematics…
Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics
ERIC Educational Resources Information Center
Große, Cornelia S.
2014-01-01
Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2015-01-01
The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…
ERIC Educational Resources Information Center
Salani, End
2013-01-01
Lesson starts are transitional events which may cause management problems for teachers. This study sought junior secondary school mathematics teachers' beliefs about calculator use in mathematics instruction in Botswana and was descriptive in nature adopting a survey design. The sample of seventeen (17) mathematics teachers from four (4) junior…
Mathematics Coursework Regulates Growth in Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; Wilkins, Jesse L. M.
2007-01-01
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…
Preparatory Mathematics Programs in Departments of Mathematics.
ERIC Educational Resources Information Center
Lindberg, Karl
This paper reports on a survey of remedial mathematics programs offered at the college level. The paper is divided into five sections. Section I describes the sampling procedures used in the study. In Section II, the occurrence of remedial mathematics programs in the various types of institutions and some general characteristics of these programs…
Negotiation of Mathematical Meaning and Learning Mathematics.
ERIC Educational Resources Information Center
Voigt, Jorg
1994-01-01
Presents a case study of a first-grade class and their teacher who were observed as they ascribed mathematical meanings of numbers and of numerical operations to empirical phenomena. Differences in ascriptions led to negotiation of meanings. Discusses some indirect relations between social interaction and mathematics learning. (Contains 60…
Mathematical and statistical analysis
NASA Technical Reports Server (NTRS)
Houston, A. Glen
1988-01-01
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
Mathematics. [SITE 2001 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics" (Kathy R. Autrey and Leigh…
Making Mathematics Culturally Relevant.
ERIC Educational Resources Information Center
Moyer, Patricia
2001-01-01
Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…
ERIC Educational Resources Information Center
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
ERIC Educational Resources Information Center
Clary, Joseph R.; Nery, Karen P.
This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…
ERIC Educational Resources Information Center
Martin, Tami S.; Speer, William R.
2009-01-01
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Abraham, Ralph
2015-12-01
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination. PMID:26278644
ERIC Educational Resources Information Center
Pratt, Dave
2012-01-01
Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…
Applying Mathematical Processes (AMP)
ERIC Educational Resources Information Center
Kathotia, Vinay
2011-01-01
This article provides insights into the "Applying Mathematical Processes" resources, developed by the Nuffield Foundation. It features Nuffield AMP activities--and related ones from Bowland Maths--that were designed to support the teaching and assessment of key processes in mathematics--representing a situation mathematically, analysing,…
Mathematical Epistemologies at Work.
ERIC Educational Resources Information Center
Noss, Richard
In this paper, I draw together a corpus of findings derived from two sources: studies of students using computers to learn mathematics, and research into the use of mathematics in professional practice. Using this as a basis, I map some elements of a theoretical framework for understanding the nature of mathematical knowledge in use, and how it is…
Revisiting Mathematics Manipulative Materials
ERIC Educational Resources Information Center
Swan, Paul; Marshall, Linda
2010-01-01
It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative…
Mathematics in Masons' Workplace
ERIC Educational Resources Information Center
Moreira, Darlinda; Pardal, Eugénia
2012-01-01
This paper presents masons' professional practices, which are related to mathematics. It aims to contribute to the area of adult mathematics education and to enlarge knowledge about how mathematics is used at the workplace. Methodologically it was followed an ethnographic approach. The key informants of the study were four masons aged between 40…
ERIC Educational Resources Information Center
Ortiz-Franco, Luis
An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…
Mathenger Hunt: Mathematics Matters.
ERIC Educational Resources Information Center
Falba, Christy J.; Weiss, Maria J.
1991-01-01
Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)
Mathematics and Global Survival.
ERIC Educational Resources Information Center
Schwartz, Richard H.
This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
ERIC Educational Resources Information Center
Darlington, Ellie
2014-01-01
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Applied Vocational Mathematics.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
Developed for use in teaching a two-semester, one-unit course, this course guide is intended to aid the high school instructor in teaching mathematical problem-solving and computational skills to vocational education students. The state-adopted textbook for general mathematics III, "Applied General Mathematics" serves as the major resource…
A "Mathematics Background Check"
ERIC Educational Resources Information Center
Hubisz, John
2009-01-01
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…
ERIC Educational Resources Information Center
Nisbet, Steven
1991-01-01
The relationship between mathematics and music has been investigated for thousands of years. Presented are the mathematical features of music through a study of melody, harmony, and rhythm, and the musical features of mathematics through a study of pattern, ratio, modular arithmetic, Pythagorean triples, and number sequences. (MDH)
The Creative Mathematics Teacher.
ERIC Educational Resources Information Center
Ediger, Marlow
The creative mathematics teacher who has love and enthusiasm for mathematics as a curriculum area should be in great demand in all schools. This paper discusses the characteristics of creative mathematics teachers, including those who guide students to engage in divergent thinking; have learners do much creative writing; and integrate creative…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
Sayed, Fayez
2015-01-01
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
ERIC Educational Resources Information Center
Posey, Johnsie Jo, Ed.; And Others
This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…
ERIC Educational Resources Information Center
Gallian, Joseph A., Ed.
2010-01-01
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Mathematical Friends and Relations
ERIC Educational Resources Information Center
Tomalin, Jo
2012-01-01
The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…
Dense Granular Avalanches: Mathematical Description and Experimental Validation
NASA Astrophysics Data System (ADS)
Tai, Y.-C.; Hutter, K.; Gray, J. M. N. T.
Snow avalanches, landslides, rock falls and debris flows are extremely dangerous and destructive natural phenomena. The frequency of occurrence and amplitudes of these disastrous events appear to have increased in recent years perhaps due to recent climate warming. The events endanger the personal property and infra-structure in mountainous regions. For example, from the winters 1940/41 to 1987/88 more than 7000 snow avalanches occurred in Switzerland with damaged property leading to a total of 1269 deaths. In February 1999, 36 people were buried by a single avalanche in Galtür, Austria. In August 1996, a very large debris flow in middle Taiwan resulted in 51 deaths, 22 lost and an approximate property damage of more than 19 billion NT dollars (ca. 600 million US dollars) [18]. In Europe, a suddenly released debris flow in North Italy in August 1998 buried 5 German tourists on the Superhighway "Brenner-Autobahn". The topic has gained so much significance that in 1990 the United Nations declared the International Decade for Natural Disasters Reduction (IDNDR); Germany has its own Deutsches IDNDR-Komitee für Katastrophenvorbeugung e.V. Special conferences are devoted to the theme, e.g., the CALAR conference on Avalanches, Landslides, Rock Falls and Debris Flows (Vienna, January 2000), INTERPRAEVENT, annual conferences on the protection of habitants from floods, debris flows and avalanches, special conferences on debris flow hazard mi tigation and those exclusively on Avalanches.
ERIC Educational Resources Information Center
Barwell, Richard
2013-01-01
Climate change is one of the most pressing issues of the 21st Century. Mathematics is involved at every level of understanding climate change, including the description, prediction and communication of climate change. As a highly complex issue, climate change is an example of "post-normal" science -- it is urgent, complex and involves a…
Qualitative and quantitative descriptions of glenohumeral motion.
Hill, A M; Bull, A M J; Wallace, A L; Johnson, G R
2008-02-01
Joint modelling plays an important role in qualitative and quantitative descriptions of both normal and abnormal joints, as well as predicting outcomes of alterations to joints in orthopaedic practice and research. Contemporary efforts in modelling have focussed upon the major articulations of the lower limb. Well-constrained arthrokinematics can form the basis of manageable kinetic and dynamic mathematical predictions. In order to contain computation of shoulder complex modelling, glenohumeral joint representations in both limited and complete shoulder girdle models have undergone a generic simplification. As such, glenohumeral joint models are often based upon kinematic descriptions of inadequate degrees of freedom (DOF) for clinical purposes and applications. Qualitative descriptions of glenohumeral motion range from the parody of a hinge joint to the complex realism of a spatial joint. In developing a model, a clear idea of intention is required in order to achieve a required application. Clinical applicability of a model requires both descriptive and predictive output potentials, and as such, a high level of validation is required. Without sufficient appreciation of the clinical intention of the arthrokinematic foundation to a model, error is all too easily introduced. Mathematical description of joint motion serves to quantify all relevant clinical parameters. Commonly, both the Euler angle and helical (screw) axis methods have been applied to the glenohumeral joint, although concordance between these methods and classical anatomical appreciation of joint motion is limited, resulting in miscommunication between clinician and engineer. Compounding these inconsistencies in motion quantification is gimbal lock and sequence dependency. PMID:17509885
An Accurate Model for Biomolecular Helices and Its Application to Helix Visualization
Wang, Lincong; Qiao, Hui; Cao, Chen; Xu, Shutan; Zou, Shuxue
2015-01-01
Helices are the most abundant secondary structural elements in proteins and the structural forms assumed by double stranded DNAs (dsDNA). Though the mathematical expression for a helical curve is simple, none of the previous models for the biomolecular helices in either proteins or DNAs use a genuine helical curve, likely because of the complexity of fitting backbone atoms to helical curves. In this paper we model a helix as a series of different but all bona fide helical curves; each one best fits the coordinates of four consecutive backbone Cα atoms for a protein or P atoms for a DNA molecule. An implementation of the model demonstrates that it is more accurate than the previous ones for the description of the deviation of a helix from a standard helical curve. Furthermore, the accuracy of the model makes it possible to correlate deviations with structural and functional significance. When applied to helix visualization, the ribbon diagrams generated by the model are less choppy or have smaller side chain detachment than those by the previous visualization programs that typically model a helix as a series of low-degree splines. PMID:26126117
Salt Block II: description and results
Hohlfelder, J.J.
1980-06-01
A description of and results from the Salt Block II experiment, which involved the heating of and measurement of water transport within a large sample of rock salt, are presented. These results include the measurement of water released into a heated borehole in the sample as well as measured temperatures within the salt. Measured temperatures are compared with the results of a mathematical model of the experiment.
Scaffolding students' opportunities to learn mathematics through social interactions
NASA Astrophysics Data System (ADS)
Bell, Clare V.; Pape, Stephen J.
2012-12-01
In this study, we take a sociocultural perspective on teaching and learning to examine how teachers in an urban Algebra 1 classroom constructed opportunities to learn. Drawing on analyses of discourse practices, including videotaped classroom lessons as well as other classroom artifacts and telephone interviews, we describe ways that two teachers and their students interacted to develop mathematical understanding. Through descriptive narrative, we highlight practices that positioned students as competent mathematical thinkers and provided evidence of students' mathematical agency. This study suggests that critical awareness of discourse practices in conjunction with teacher mediation of other affordances for learning within the classroom environment might engage students in mathematical practices such as problem solving, explaining mathematical ideas, arguing for or against specific solutions to problems, and justifying mathematical thinking.
Predict amine solution properties accurately
Cheng, S.; Meisen, A.; Chakma, A.
1996-02-01
Improved process design begins with using accurate physical property data. Especially in the preliminary design stage, physical property data such as density viscosity, thermal conductivity and specific heat can affect the overall performance of absorbers, heat exchangers, reboilers and pump. These properties can also influence temperature profiles in heat transfer equipment and thus control or affect the rate of amine breakdown. Aqueous-amine solution physical property data are available in graphical form. However, it is not convenient to use with computer-based calculations. Developed equations allow improved correlations of derived physical property estimates with published data. Expressions are given which can be used to estimate physical properties of methyldiethanolamine (MDEA), monoethanolamine (MEA) and diglycolamine (DGA) solutions.
Accurate thickness measurement of graphene
NASA Astrophysics Data System (ADS)
Shearer, Cameron J.; Slattery, Ashley D.; Stapleton, Andrew J.; Shapter, Joseph G.; Gibson, Christopher T.
2016-03-01
Graphene has emerged as a material with a vast variety of applications. The electronic, optical and mechanical properties of graphene are strongly influenced by the number of layers present in a sample. As a result, the dimensional characterization of graphene films is crucial, especially with the continued development of new synthesis methods and applications. A number of techniques exist to determine the thickness of graphene films including optical contrast, Raman scattering and scanning probe microscopy techniques. Atomic force microscopy (AFM), in particular, is used extensively since it provides three-dimensional images that enable the measurement of the lateral dimensions of graphene films as well as the thickness, and by extension the number of layers present. However, in the literature AFM has proven to be inaccurate with a wide range of measured values for single layer graphene thickness reported (between 0.4 and 1.7 nm). This discrepancy has been attributed to tip-surface interactions, image feedback settings and surface chemistry. In this work, we use standard and carbon nanotube modified AFM probes and a relatively new AFM imaging mode known as PeakForce tapping mode to establish a protocol that will allow users to accurately determine the thickness of graphene films. In particular, the error in measuring the first layer is reduced from 0.1-1.3 nm to 0.1-0.3 nm. Furthermore, in the process we establish that the graphene-substrate adsorbate layer and imaging force, in particular the pressure the tip exerts on the surface, are crucial components in the accurate measurement of graphene using AFM. These findings can be applied to other 2D materials.
Acquisition of teleological descriptions
NASA Astrophysics Data System (ADS)
Franke, David W.
1992-03-01
Teleology descriptions capture the purpose of an entity, mechanism, or activity with which they are associated. These descriptions can be used in explanation, diagnosis, and design reuse. We describe a technique for acquiring teleological descriptions expressed in the teleology language TeD. Acquisition occurs during design by observing design modifications and design verification. We demonstrate the acquisition technique in an electronic circuit design.
Experimental and Mathematical-Modeling Characterization of Trypanosoma cruzi Epimastigote Motility
Arias-del-Angel, Jorge A.; Dévora-Canales, Diego; Manning-Cela, Rebeca G.; Santana-Solano, Jesús; Santillán, Moisés
2015-01-01
The present work is aimed at characterizing the motility of parasite T. cruzi in its epimastigote form. To that end, we recorded the trajectories of two strains of this parasite (a wild-type strain and a stable transfected strain, which contains an ectopic copy of LYT1 gene and whose motility is known to be affected). We further extracted parasite trajectories from the recorded videos, and statistically analysed the following trajectory-step features: step length, angular change of direction, longitudinal and transverse displacements with respect to the previous step, and mean square displacement. Based on the resulting observations, we developed a mathematical model to simulate parasite trajectories. The fact that the model predictions closely match most of the experimentally observed parasite-trajectory characteristics, allows us to conclude that the model is an accurate description of T. cruzi motility. PMID:26544863
ERIC Educational Resources Information Center
House, Peggy A.
1994-01-01
Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)
Philosophy and mathematics: interactions.
Rashed, Roshdi
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so. PMID:25029825
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Jett, Christopher C.
2014-01-01
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Mathematics for Teaching: A Form of Applied Mathematics
ERIC Educational Resources Information Center
Stylianides, Gabriel J.; Stylianides, Andreas J.
2010-01-01
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics
ERIC Educational Resources Information Center
Wang, Youjun
2009-01-01
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…
Haase, Vitor G.; Júlio-Costa, Annelise; Lopes-Silva, Júlia B.; Starling-Alves, Isabella; Antunes, Andressa M.; Pinheiro-Chagas, Pedro; Wood, Guilherme
2014-01-01
Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties. PMID:24592243
Mathematical modelling of microtumour infiltration based on in vitro experiments.
Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia
2016-08-01
The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment
The emerging and emergent present: a view on the indeterminate nature of mathematics lessons
NASA Astrophysics Data System (ADS)
Roth, Wolff-Michael; Maheux, Jean-François
2014-06-01
The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of emergence. After providing an exemplifying description and analysis of an episode from a second-grade mathematics classroom studying three-dimensional geometry, we discuss implications for theoretical and classroom praxis in mathematics education, especially for the curriculum planning and the preparation, training, and enhancement of teachers of mathematics.
Remedial Mathematics for Quantum Chemistry
ERIC Educational Resources Information Center
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
2008-01-01
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…
Experimenting with Mathematical Biology
ERIC Educational Resources Information Center
Sanft, Rebecca; Walter, Anne
2016-01-01
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
The Relativity of Mathematics.
ERIC Educational Resources Information Center
Kleiner, Israel; Avital, Shmuel
1984-01-01
The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)
The Applied Mathematics Laboratory.
ERIC Educational Resources Information Center
Siegel, Martha J.
This report describes the Applied Mathematics Laboratory (AML) operated by the Department of Mathematics at Towson State University, Maryland. AML is actually a course offered to selected undergraduates who are given the opportunity to apply their skills in investigating industrial and governmental problems. By agreement with sponsoring…
ERIC Educational Resources Information Center
Heck, Andre; Van Gastel, Leendert
2006-01-01
Lowering the dropout rate of incoming mathematics and science students, and enhancing the provision of mathematics support for freshmen are two important aims of the University of Amsterdam. The approach recently adopted to support first year students is to set up a diagnostic pretest and posttest and use these tests to identify students being at…
ERIC Educational Resources Information Center
Hallenberg, Harvey
1995-01-01
Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…
Designing Assessment for Mathematics
ERIC Educational Resources Information Center
Depka, Eileen
2007-01-01
Teaching mathematics in today's world requires practices and procedures integrated with performance tasks that actively involve students. In this second edition of Designing Rubrics for Mathematics, Eileen Depka clarifies the purpose of rubrics in math instruction and illustrates the relationship between assessment, rubrics, and the National…
Modularizing Remedial Mathematics
ERIC Educational Resources Information Center
Wong, Aaron
2013-01-01
As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…
Quality Teaching in Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2012-01-01
The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…
Mathematics. [SITE 2002 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
ERIC Educational Resources Information Center
Dodd, Jennifer
2010-01-01
In this article, the author reports on the findings of her research on what her Year 10 students consider to be "mathematical." The class contains thirteen students who will all sit the higher tier IGCSE next year. The author found out that the students considered things she told them to have a higher mathematical status than work they did…
Mathematics: The Universal Language?
ERIC Educational Resources Information Center
Hoffert, Sharon B.
2009-01-01
Mathematics is considered the universal language, but students who speak languages other than English have difficulty doing mathematics in English. For instance, because of a lack of familiarity with the problem's context, many have trouble understanding exactly what operations to perform. In the United States, approximately one in seven students…
Elementary Mathematics Leaders
ERIC Educational Resources Information Center
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
2013-01-01
Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
ERIC Educational Resources Information Center
Corle, Clyde G.
This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…
Solving Common Mathematical Problems
NASA Technical Reports Server (NTRS)
Luz, Paul L.
2005-01-01
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
Mathematical Graphic Organizers
ERIC Educational Resources Information Center
Zollman, Alan
2009-01-01
As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…
Learning Mathematics while Black
ERIC Educational Resources Information Center
Martin, Danny Bernard
2012-01-01
While research by scholars has contributed greatly to an emerging knowledge base on Black children and mathematics, there continues to be a dire need for insightful research that de-centers longstanding accounts that have contributed to the construction of Black children as mathematically illiterate and as less than ideal learners relative to…
ERIC Educational Resources Information Center
Goldsmith, Lynn T.
2000-01-01
Parents can help ensure that their children are well-equipped with the necessary mathematical skills and understanding for the future by: having high expectations for their children's learning; helping their children see mathematical connections and applications in the world; being curious about their children's thinking; and being enthusiastic…
ERIC Educational Resources Information Center
Stallings, L. Lynn
2007-01-01
This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…
[Collected Papers on Mathematics.
ERIC Educational Resources Information Center
Connell, Michael L., Ed.
This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student Learning and…
Astronomy and Mathematics Education
NASA Astrophysics Data System (ADS)
Ros, Rosa M.
There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.
ERIC Educational Resources Information Center
Fennema, Elizabeth, Ed.; Leder, Gilah C., Ed.
This book reports on various studies that have increased our understanding of why females and males learn different kinds and amounts of mathematics. In particular, this book explicates the Autonomous Learning Behavior model, proposed by Fennema and Peterson, which is a possible explanation of the development of gender differences in mathematics.…
Business Mathematics Curriculum.
ERIC Educational Resources Information Center
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
Strengthen Your Mathematical Muscles
ERIC Educational Resources Information Center
Wohlhuter, Kay A.; Breyfogle, M. Lynn; McDuffie, Amy Roth
2010-01-01
Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…
ERIC Educational Resources Information Center
Sharp, John
2012-01-01
This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…
Genders, Mathematics, and Feminisms.
ERIC Educational Resources Information Center
Damarin, Suzanne
Historical studies reveal that mathematics has been claimed as a private domain by men, while studies of the popular press document that women and girls are considered incompetent in that field. The study of gender and mathematics as viewed through feminism can create a new reading which exposes hidden assumptions, unwarranted conclusions, and…
NASA Astrophysics Data System (ADS)
Rohrlich, Fritz
2011-12-01
Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
Mathematics Projects Handbook.
ERIC Educational Resources Information Center
Hess, Adrien L.
This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entrance in fairs and competitions. The use of projects to…
Developing Mathematical Proficiency
ERIC Educational Resources Information Center
Groves, Susie
2012-01-01
It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as "relational" rather than "instrumental" understanding. More recently, Kilpatrick, Swafford and Findell (2001)…
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The first of three volumes of a mathematics training course for Navy personnel, this document covers a wide range of basic mathematics. The text begins with number systems, signed numbers, fractions, decimals, and percentages and continues into algebra with exponents, polynomials, and linear equations. Early chapters were designed to give insight…
Issues in Teaching Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2013-01-01
In this article, the author states that there are selected issues in mathematics instruction that educators should be well aware of when planning lessons and units of study. These issues provide a basis for thought and discussion when assisting pupils to attain more optimally. Purposeful studying of issues guides mathematics teachers in…
Teaching Mathematics Using Steplets
ERIC Educational Resources Information Center
Bringslid, Odd; Norstein, Anne
2008-01-01
This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory…
Dyslexia, Dyspraxia and Mathematics.
ERIC Educational Resources Information Center
Yeo, Dorian
This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…
Mathematical thinking and origami
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2016-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
Mathematics Education in Argentina
ERIC Educational Resources Information Center
Varsavsky, Cristina; Anaya, Marta
2009-01-01
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
ERIC Educational Resources Information Center
Oldfield, Christine
1996-01-01
Describes aspects of learning the language of mathematics including vocabulary and grammar, the origins of the vocabulary, the pronunciation problem, and translation of English phrases and sentences into mathematical language accompanied by conceptual understanding of the process being described. Gives suggestions for teachers in class and…
Developing Mathematically Promising Students.
ERIC Educational Resources Information Center
Sheffield, Linda Jensen, Ed.
This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…
Mathematical techniques: A compilation
NASA Technical Reports Server (NTRS)
1975-01-01
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
Encouraging Good Mathematical Writing
ERIC Educational Resources Information Center
O'Shea, J.
2006-01-01
This paper is a report on an attempt to teach students in their first and second year of university how to write mathematics. The problems faced by these students are outlined and the system devised to emphasize the importance of communicating mathematics is explained.
ERIC Educational Resources Information Center
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Mathematical models of diabetes progression.
De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels
2008-12-01
Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page. PMID:18780774
Accurate 3D quantification of the bronchial parameters in MDCT
NASA Astrophysics Data System (ADS)
Saragaglia, A.; Fetita, C.; Preteux, F.; Brillet, P. Y.; Grenier, P. A.
2005-08-01
The assessment of bronchial reactivity and wall remodeling in asthma plays a crucial role in better understanding such a disease and evaluating therapeutic responses. Today, multi-detector computed tomography (MDCT) makes it possible to perform an accurate estimation of bronchial parameters (lumen and wall areas) by allowing a quantitative analysis in a cross-section plane orthogonal to the bronchus axis. This paper provides the tools for such an analysis by developing a 3D investigation method which relies on 3D reconstruction of bronchial lumen and central axis computation. Cross-section images at bronchial locations interactively selected along the central axis are generated at appropriate spatial resolution. An automated approach is then developed for accurately segmenting the inner and outer bronchi contours on the cross-section images. It combines mathematical morphology operators, such as "connection cost", and energy-controlled propagation in order to overcome the difficulties raised by vessel adjacencies and wall irregularities. The segmentation accuracy was validated with respect to a 3D mathematically-modeled phantom of a pair bronchus-vessel which mimics the characteristics of real data in terms of gray-level distribution, caliber and orientation. When applying the developed quantification approach to such a model with calibers ranging from 3 to 10 mm diameter, the lumen area relative errors varied from 3.7% to 0.15%, while the bronchus area was estimated with a relative error less than 5.1%.
Technical Mathematics: Restructure of Technical Mathematics.
ERIC Educational Resources Information Center
Flannery, Carol A.
Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…
Towards Accurate Application Characterization for Exascale (APEX)
Hammond, Simon David
2015-09-01
Sandia National Laboratories has been engaged in hardware and software codesign activities for a number of years, indeed, it might be argued that prototyping of clusters as far back as the CPLANT machines and many large capability resources including ASCI Red and RedStorm were examples of codesigned solutions. As the research supporting our codesign activities has moved closer to investigating on-node runtime behavior a nature hunger has grown for detailed analysis of both hardware and algorithm performance from the perspective of low-level operations. The Application Characterization for Exascale (APEX) LDRD was a project concieved of addressing some of these concerns. Primarily the research was to intended to focus on generating accurate and reproducible low-level performance metrics using tools that could scale to production-class code bases. Along side this research was an advocacy and analysis role associated with evaluating tools for production use, working with leading industry vendors to develop and refine solutions required by our code teams and to directly engage with production code developers to form a context for the application analysis and a bridge to the research community within Sandia. On each of these accounts significant progress has been made, particularly, as this report will cover, in the low-level analysis of operations for important classes of algorithms. This report summarizes the development of a collection of tools under the APEX research program and leaves to other SAND and L2 milestone reports the description of codesign progress with Sandia’s production users/developers.
Improving accessibility to mathematical formulas: the Wikipedia Math Accessor
NASA Astrophysics Data System (ADS)
Fuentes Sepúlveda, J.; Ferres, L.
2012-09-01
Mathematics accessibility is an important topic for inclusive education. In this paper, we make Wikipedia's repository of mathematical formulas accessible by providing a natural language description of its more than 420,000 formulas using a well-researched sub-language. We also contribute by targeting Spanish speakers, for whom assistive technologies, particularly domain-specific technologies like the one described here, are scarce. Our focus on the semantics of formulas (rather than their visual appearance) allowed us to generate verbalizations with a precision of approximately 80% of understandable descriptions, as shown in an evaluation with sighted users.
ERIC Educational Resources Information Center
Dede, Yuksel
2013-01-01
This study reported the specific findings of a larger comparative study concerning Turkish and German mathematics teachers' values. The main focus was on the teaching experience of the mathematics teachers. Interactions related to nationality were also of interest. The research methodology employed in this study was a descriptive study. The…
Mathematical 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).
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Multimedia content description framework
NASA Technical Reports Server (NTRS)
Bergman, Lawrence David (Inventor); Kim, Michelle Yoonk Yung (Inventor); Li, Chung-Sheng (Inventor); Mohan, Rakesh (Inventor); Smith, John Richard (Inventor)
2003-01-01
A framework is provided for describing multimedia content and a system in which a plurality of multimedia storage devices employing the content description methods of the present invention can interoperate. In accordance with one form of the present invention, the content description framework is a description scheme (DS) for describing streams or aggregations of multimedia objects, which may comprise audio, images, video, text, time series, and various other modalities. This description scheme can accommodate an essentially limitless number of descriptors in terms of features, semantics or metadata, and facilitate content-based search, index, and retrieval, among other capabilities, for both streamed or aggregated multimedia objects.
Assessing Students Beliefs about Mathematics.
ERIC Educational Resources Information Center
Spangler, Denise A.
1992-01-01
Presents 11 open-ended questions that can be presented to students and teachers at all educational levels in various formats to assess mathematical beliefs. Questions investigate beliefs toward mathematics, the problem-solving process, mathematicians, and mathematical applications. (MDH)
Creating a Differentiated Mathematics Classroom
ERIC Educational Resources Information Center
Strong, Richard; Thomas, Ed; Perini, Matthew; Silver, Harvey
2004-01-01
Student differences in learning mathematics are categorized under four different mathematical learning styles. The names of books providing examples on how mathematics teachers can differentiate their classroom instructions are mentioned.
On canonical cylinder sections for accurate determination of contact angle in microgravity
NASA Technical Reports Server (NTRS)
Concus, Paul; Finn, Robert; Zabihi, Farhad
1992-01-01
Large shifts of liquid arising from small changes in certain container shapes in zero gravity can be used as a basis for accurately determining contact angle. Canonical geometries for this purpose, recently developed mathematically, are investigated here computationally. It is found that the desired nearly-discontinuous behavior can be obtained and that the shifts of liquid have sufficient volume to be readily observed.
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2011-07-01 2011-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
Two pre-Willan descriptions of psoriasis.
De Bersaques, Jean
2012-01-01
Accurate descriptions of skin lesions, and in particular of those of what we now call osiriasis vulgaris, are rare before the book of Willan's On Cutaneous Diseases at the very beginning of the 19th century. Here we present two instances in which such clinical descriptions are given. Benjamin Franklin wrote about his own skin lesions and their evolution. Dr. Willam Falconer, physician in Bath, England, presents the clinical symptoms and his results with 83 patients with 'lepra graecorum' (the name used at that time) treated between 1772 and 1775. One can wonder why such a now frequent, obvious and distinctive disease had not attracted more attention. PMID:22902228
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. PMID:25595115
The FLUKA Code: An Accurate Simulation Tool for Particle Therapy
Battistoni, Giuseppe; Bauer, Julia; Boehlen, Till T.; Cerutti, Francesco; Chin, Mary P. W.; Dos Santos Augusto, Ricardo; Ferrari, Alfredo; Ortega, Pablo G.; Kozłowska, Wioletta; Magro, Giuseppe; Mairani, Andrea; Parodi, Katia; Sala, Paola R.; Schoofs, Philippe; Tessonnier, Thomas; Vlachoudis, Vasilis
2016-01-01
Monte Carlo (MC) codes are increasingly spreading in the hadrontherapy community due to their detailed description of radiation transport and interaction with matter. The suitability of a MC code for application to hadrontherapy demands accurate and reliable physical models capable of handling all components of the expected radiation field. This becomes extremely important for correctly performing not only physical but also biologically based dose calculations, especially in cases where ions heavier than protons are involved. In addition, accurate prediction of emerging secondary radiation is of utmost importance in innovative areas of research aiming at in vivo treatment verification. This contribution will address the recent developments of the FLUKA MC code and its practical applications in this field. Refinements of the FLUKA nuclear models in the therapeutic energy interval lead to an improved description of the mixed radiation field as shown in the presented benchmarks against experimental data with both 4He and 12C ion beams. Accurate description of ionization energy losses and of particle scattering and interactions lead to the excellent agreement of calculated depth–dose profiles with those measured at leading European hadron therapy centers, both with proton and ion beams. In order to support the application of FLUKA in hospital-based environments, Flair, the FLUKA graphical interface, has been enhanced with the capability of translating CT DICOM images into voxel-based computational phantoms in a fast and well-structured way. The interface is capable of importing also radiotherapy treatment data described in DICOM RT standard. In addition, the interface is equipped with an intuitive PET scanner geometry generator and automatic recording of coincidence events. Clinically, similar cases will be presented both in terms of absorbed dose and biological dose calculations describing the various available features. PMID:27242956
The FLUKA Code: An Accurate Simulation Tool for Particle Therapy.
Battistoni, Giuseppe; Bauer, Julia; Boehlen, Till T; Cerutti, Francesco; Chin, Mary P W; Dos Santos Augusto, Ricardo; Ferrari, Alfredo; Ortega, Pablo G; Kozłowska, Wioletta; Magro, Giuseppe; Mairani, Andrea; Parodi, Katia; Sala, Paola R; Schoofs, Philippe; Tessonnier, Thomas; Vlachoudis, Vasilis
2016-01-01
Monte Carlo (MC) codes are increasingly spreading in the hadrontherapy community due to their detailed description of radiation transport and interaction with matter. The suitability of a MC code for application to hadrontherapy demands accurate and reliable physical models capable of handling all components of the expected radiation field. This becomes extremely important for correctly performing not only physical but also biologically based dose calculations, especially in cases where ions heavier than protons are involved. In addition, accurate prediction of emerging secondary radiation is of utmost importance in innovative areas of research aiming at in vivo treatment verification. This contribution will address the recent developments of the FLUKA MC code and its practical applications in this field. Refinements of the FLUKA nuclear models in the therapeutic energy interval lead to an improved description of the mixed radiation field as shown in the presented benchmarks against experimental data with both (4)He and (12)C ion beams. Accurate description of ionization energy losses and of particle scattering and interactions lead to the excellent agreement of calculated depth-dose profiles with those measured at leading European hadron therapy centers, both with proton and ion beams. In order to support the application of FLUKA in hospital-based environments, Flair, the FLUKA graphical interface, has been enhanced with the capability of translating CT DICOM images into voxel-based computational phantoms in a fast and well-structured way. The interface is capable of importing also radiotherapy treatment data described in DICOM RT standard. In addition, the interface is equipped with an intuitive PET scanner geometry generator and automatic recording of coincidence events. Clinically, similar cases will be presented both in terms of absorbed dose and biological dose calculations describing the various available features. PMID:27242956
Mathematization in introductory physics
NASA Astrophysics Data System (ADS)
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
The Greatest Mathematical Discovery?
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.
2001-01-01
In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024
Physics 3204. Course Description.
ERIC Educational Resources Information Center
Newfoundland and Labrador Dept. of Education.
A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…
Descriptive Metadata: Emerging Standards.
ERIC Educational Resources Information Center
Ahronheim, Judith R.
1998-01-01
Discusses metadata, digital resources, cross-disciplinary activity, and standards. Highlights include Standard Generalized Markup Language (SGML); Extensible Markup Language (XML); Dublin Core; Resource Description Framework (RDF); Text Encoding Initiative (TEI); Encoded Archival Description (EAD); art and cultural-heritage metadata initiatives;…
Accurately Determining the Risks of Rising Sea Level
NASA Astrophysics Data System (ADS)
Marbaix, Philippe; Nicholls, Robert J.
2007-10-01
With the highest density of people and the greatest concentration of economic activity located in the coastal regions, sea level rise is an important concern as the climate continues to warm. Subsequent flooding may potentially disrupt industries, populations, and livelihoods, particularly in the long term if the climate is not quickly stabilized [McGranahan et al., 2007; Tol et al., 2006]. To help policy makers understand these risks, a more accurate description of hazards posed by rising sea levels is needed at the global scale, even though the impacts in specific regions are better known.
Math Description Engine Software Development Kit
NASA Technical Reports Server (NTRS)
Shelton, Robert O.; Smith, Stephanie L.; Dexter, Dan E.; Hodgson, Terry R.
2010-01-01
The Math Description Engine Software Development Kit (MDE SDK) can be used by software developers to make computer-rendered graphs more accessible to blind and visually-impaired users. The MDE SDK generates alternative graph descriptions in two forms: textual descriptions and non-verbal sound renderings, or sonification. It also enables display of an animated trace of a graph sonification on a visual graph component, with color and line-thickness options for users having low vision or color-related impairments. A set of accessible graphical user interface widgets is provided for operation by end users and for control of accessible graph displays. Version 1.0 of the MDE SDK generates text descriptions for 2D graphs commonly seen in math and science curriculum (and practice). The mathematically rich text descriptions can also serve as a virtual math and science assistant for blind and sighted users, making graphs more accessible for everyone. The MDE SDK has a simple application programming interface (API) that makes it easy for programmers and Web-site developers to make graphs accessible with just a few lines of code. The source code is written in Java for cross-platform compatibility and to take advantage of Java s built-in support for building accessible software application interfaces. Compiled-library and NASA Open Source versions are available with API documentation and Programmer s Guide at http:/ / prim e.jsc.n asa. gov.
Physical vs. Mathematical Models in Rock Mechanics
NASA Astrophysics Data System (ADS)
Morozov, I. B.; Deng, W.
2013-12-01
One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an
Ferrari, Pier Luigi
2003-07-29
Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful. PMID:12903658
Black African Traditional Mathematics
ERIC Educational Resources Information Center
Zaslavsky, Claudia
1970-01-01
Discusses the traditional number systems and the origin of the number names used by several African peoples living south of the Sahara. Also included are limitations in African mathematical development, and possible topics for research. (RP)
Standards in Mathematics Teaching.
ERIC Educational Resources Information Center
Brookes, Bill
1978-01-01
This article is based on a lecture given at the 1978 Easter Course at Padgate College of Higher Education. The lecture is an analysis of the complexity of mathematics teaching and the setting of teaching standards. (MN)
Mathematics Case Methods Project.
ERIC Educational Resources Information Center
Barnett, Carne S.
1998-01-01
Presents an overview and analysis of the Mathematics Case Methods Project, which uses cases in order to examine and reflect upon teaching. Focuses on a special kind of teacher knowledge, coined pedagogical-content knowledge. (ASK)
Benjamin Banneker's Mathematical Puzzles.
ERIC Educational Resources Information Center
Mahoney, John F.
2003-01-01
Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)
Applications of Secondary School Mathematics: Readings from the "Mathematics Teacher."
ERIC Educational Resources Information Center
Austin, Joe Dan, Ed.
This book provides applications for use in the secondary school mathematics curriculum by selecting related articles appearing in the "Mathematics Teacher" during the last 15 years. The articles are grouped into chapters that reflect the main secondary school mathematics courses and categorized by the highest level of mathematics needed for…
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
ERIC Educational Resources Information Center
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Promoting Critical Mathematics Literacy in Secondary Mathematics Teacher Education
ERIC Educational Resources Information Center
Fish, Michael Charles
2012-01-01
This study examines how critical mathematical literacy teachers conceptualize their practices and how those practices were demonstrated in the classroom. Practices were considered from an ontology of mathematics education, specific to critical mathematical literacy, in which classroom interactions question what it means to do mathematics as an…
Using Mathematics in Science: Working with Your Mathematics Department
ERIC Educational Resources Information Center
Lyon, Steve
2014-01-01
Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…
Handwritten mathematical symbols dataset
Chajri, Yassine; Bouikhalene, Belaid
2016-01-01
Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975
NASA Astrophysics Data System (ADS)
Ligomenides, Panos A.
2009-05-01
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
Handwritten mathematical symbols dataset.
Chajri, Yassine; Bouikhalene, Belaid
2016-06-01
Due to the technological advances in recent years, paper scientific documents are used less and less. Thus, the trend in the scientific community to use digital documents has increased considerably. Among these documents, there are scientific documents and more specifically mathematics documents. In this context, we present our own dataset of handwritten mathematical symbols composed of 10,379 images. This dataset gathers Arabic characters, Latin characters, Arabic numerals, Latin numerals, arithmetic operators, set-symbols, comparison symbols, delimiters, etc. PMID:27006975
Mathematical foundations of neurocomputing
Amari, S. . Faculty of Engineering)
1990-09-01
Neurocomputing makes use of parallel dynamical interactions of modifiable neuron-like elements. It is important to show, by mathematical treatments, the capabilities and limitations of information processing by various architectures of neural networks. This paper, gives mathematical foundations to neurocomputing. It considers the capabilities of transformations by layered networks, statistical neurodynamics, the dynamical characteristics of associative memory, a general theory of neural learning, and self-organization of neural networks.
Landauer, C.; Bellman, K.L.
1996-12-31
In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.
Janssen, Paddy K.C.
2016-01-01
Purpose To find the most accurate mathematical description of the intravaginal ejaculation latency time (IELT) distribution in the general male population. Materials and Methods We compared the fitness of various well-known mathematical distributions with the IELT distribution of two previously published stopwatch studies of the Caucasian general male population and a stopwatch study of Dutch Caucasian men with lifelong premature ejaculation (PE). The accuracy of fitness is expressed by the Goodness of Fit (GOF). The smaller the GOF, the more accurate is the fitness. Results The 3 IELT distributions are gamma distributions, but the IELT distribution of lifelong PE is another gamma distribution than the IELT distribution of men in the general male population. The Lognormal distribution of the gamma distributions most accurately fits the IELT distribution of 965 men in the general population, with a GOF of 0.057. The Gumbel Max distribution most accurately fits the IELT distribution of 110 men with lifelong PE with a GOF of 0.179. There are more men with lifelong PE ejaculating within 30 and 60 seconds than can be extrapolated from the probability density curve of the Lognormal IELT distribution of men in the general population. Conclusions Men with lifelong PE have a distinct IELT distribution, e.g., a Gumbel Max IELT distribution, that can only be retrieved from the general male population Lognormal IELT distribution when thousands of men would participate in a IELT stopwatch study. The mathematical formula of the Lognormal IELT distribution is useful for epidemiological research of the IELT. PMID:26981594
Barton, J.W.; Zhang, X.S.; Klasson, K.T.; Davison, B.H.
1998-03-01
Mathematical models of varying complexity have been proposed in the open literature for describing uptake of volatile organics in trickling bed biofilters. Many simpler descriptions yield relatively accurate solutions, but are limited as predictive tools by numerous assumptions which decrease the utility of the model. Trickle bed operation on the boundary between mass transfer and kinetic limitation regimes serves as one example in which these models may be insufficient. One-dimensional models may also fail to consider important effects/relationships in multiple directions, limiting their usefulness. This paper discusses the use of a predictive, two-dimensional mathematical model to describe microbial uptake, diffusion through a biofilm, and mass transfer of VOCs from gas to liquid. The model is validated by experimental data collected from operating trickle-bed bioreactors designed for removing sparingly soluble gaseous contaminants. Axial and radial (biofilm) concentration profiles are presented, along with validation results. Operation in regimes in which both mass transfer and kinetic factors play significant roles are discussed, along with predictive modeling implications.
Accurate polarimeter with multicapture fitting for plastic lens evaluation
NASA Astrophysics Data System (ADS)
Domínguez, Noemí; Mayershofer, Daniel; Garcia, Cristina; Arasa, Josep
2016-02-01
Due to their manufacturing process, plastic injection molded lenses do not achieve a constant density throughout their volume. This change of density introduces tensions in the material, inducing local birefringence, which in turn is translated into a variation of the ordinary and extraordinary refractive indices that can be expressed as a retardation phase plane using the Jones matrix notation. The detection and measurement of the value of the retardation of the phase plane are therefore very useful ways to evaluate the quality of plastic lenses. We introduce a polariscopic device to obtain two-dimensional maps of the tension distribution in the bulk of a lens, based on detection of the local birefringence. In addition to a description of the device and the mathematical approach used, a set of initial measurements is presented that confirms the validity of the developed system for the testing of the uniformity of plastic lenses.
Mathematical Rigor vs. Conceptual Change: Some Early Results
NASA Astrophysics Data System (ADS)
Alexander, W. R.
2003-05-01
Results from two different pedagogical approaches to teaching introductory astronomy at the college level will be presented. The first of these approaches is a descriptive, conceptually based approach that emphasizes conceptual change. This descriptive class is typically an elective for non-science majors. The other approach is a mathematically rigorous treatment that emphasizes problem solving and is designed to prepare students for further study in astronomy. The mathematically rigorous class is typically taken by science majors. It also fulfills an elective science requirement for these science majors. The Astronomy Diagnostic Test version 2 (ADT 2.0) was used as an assessment instrument since the validity and reliability have been investigated by previous researchers. The ADT 2.0 was administered as both a pre-test and post-test to both groups. Initial results show no significant difference between the two groups in the post-test. However, there is a slightly greater improvement for the descriptive class between the pre and post testing compared to the mathematically rigorous course. There was great care to account for variables. These variables included: selection of text, class format as well as instructor differences. Results indicate that the mathematically rigorous model, doesn't improve conceptual understanding any better than the conceptual change model. Additional results indicate that there is a similar gender bias in favor of males that has been measured by previous investigators. This research has been funded by the College of Science and Mathematics at James Madison University.
A Course in Multicultural Mathematics
ERIC Educational Resources Information Center
Hall, Rachel W.
2007-01-01
The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…
Discrete Mathematics and Curriculum Reform.
ERIC Educational Resources Information Center
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Assessing Innovative Proposals in Mathematics.
ERIC Educational Resources Information Center
Ediger, Marlow
Mathematics is at the apex in priorities pertaining to state-mandated testing of students. With 49 out of 50 states having mandated the testing of students, all of these have mathematics in the testing format. This paper discusses the modern school mathematics movement, recent approaches in improving the teaching of mathematics, and specific…
ERIC Educational Resources Information Center
Gough, John
2008-01-01
It is potentially arresting when a mathematical implication is offered in a non-mathematical book. This author contends that students are encouraged to develop mathematical thinking when they read mathematical challenges in books. Aspects of books such as time-lines, historical relationships, maps, journeys, cause-and-affect, deductive inference,…
Mathematical Modeling: A Structured Process
ERIC Educational Resources Information Center
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Mathematics Is a Spectator Sport
ERIC Educational Resources Information Center
Foster, Colin; Williams, Helen
2007-01-01
This article presents a conversation between two editors of "Mathematics Teaching Incorporating Micromath." Topics discussed include the 2004 Association of Teachers of Mathematics conference, titled "Mathematics is Not a Spectator Sport," and the thought of engaging in mathematics and what that might mean. One of the editors stresses the need to…
Semantic Processing of Mathematical Gestures
ERIC Educational Resources Information Center
Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.
2009-01-01
Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…
A Mathematics Software Database Update.
ERIC Educational Resources Information Center
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Truth & Beauty: Mathematics in Literature
ERIC Educational Resources Information Center
Cohen, Marion D.
2013-01-01
Today there are many categories of mathematics literature, including fiction and poetry. Mathematics fiction appears in such anthologies as "Fantasia Mathematica" (Fadiman 1958, 1997) and "The Mathematical Magpie" (Fadiman 1962, 1997). In addition, mathematics fiction is featured at http://kasmana.people.cofc.edu/MATHFICT.…
Reaching All Students with Mathematics.
ERIC Educational Resources Information Center
Cuevas, Gilbert, Ed.; Driscoll, Mark, Ed.
The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this book was put together…
ERIC Educational Resources Information Center
Simon, Martin A.; Tzur, Ron
2004-01-01
Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning.…
ERIC Educational Resources Information Center
Wang, Yang; O'Dwyer, Laura
2011-01-01
Using data from the Trends in International Mathematics and Science Study (TIMSS) 2003 and 2007 administrations, this study examines international trends in technology use and explores the international patterns in how teacher-directed, student-use of technology is related to eighth grade mathematics achievement. Descriptive patterns in…
ERIC Educational Resources Information Center
Yenilmez, Kursat; Ersoy, Mehmet
2008-01-01
The purpose of this study was to determine opinions of mathematics teacher candidates towards applying 7E instructional model on computer aided instruction environments. The descriptive case study model was used in this study. The sample of the study consists of 52 mathematics teacher candidates which were selected randomly from Eskisehir…
An Investigation of Pre-Service Mathematics Teachers' Skills in the Development of Activities
ERIC Educational Resources Information Center
Özgen, Kemal; Alkan, Hu¨seyin
2014-01-01
The purpose of this research is to determine pre-service mathematics teachers' skills in the development of activities. The research was carried out using the case study which is descriptive method. For the collection of data, 57 pre-service mathematics teachers' in their final year secondary math teachers' education department…
Hidden Disparities: How Courses and Curricula Shape Opportunities in Mathematics during High School
ERIC Educational Resources Information Center
Schiller, Kathryn S.; Schmidt, William H.; Muller, Chandra; Houang, Richard T.
2010-01-01
Efforts to promote academic achievement by increasing access to courses, especially in mathematics, may mask educational disparities if variations in curriculum are not also monitored. A multi-dimensional description of students' mathematics curricula during high school was obtained from analyses of surveys, transcripts, and textbooks collected…
The Applied Mathematics for Power Systems (AMPS)
Chertkov, Michael
2012-07-24
Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxes for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.
A new sensor system for accurate and precise determination of sediment dynamics and position.
NASA Astrophysics Data System (ADS)
Maniatis, Georgios; Hoey, Trevor; Sventek, Joseph; Hodge, Rebecca
2014-05-01
Sediment transport processes control many significant geomorphological changes. Consequently, sediment transport dynamics are studied across a wide range of scales leading to application of a variety of conceptually different mathematical descriptions (models) and data acquisition techniques (sensing). For river sediment transport processes both Eulerian and Lagrangian formulations are used. Data are gathered using a very wide range of sensing techniques that are not always compatible with the conceptual formulation applied. We are concerned with small to medium sediment grain-scale motion in gravel-bed rivers, and other coarse-grained environments, and: a) are developing a customised environmental sensor capable of providing coherent data that reliably record the motion; and, b) provide a mathematical framework in which these data can be analysed and interpreted, this being compatible with current stochastic approaches to sediment transport theory. Here we present results from three different aspects of the above developmental process. Firstly, we present a requirement analysis for the sensor based on the state of the art of the existing technologies. We focus on the factors that enhance data coherence and representativeness, extending the common practice for optimization which is based exclusively on electronics/computing related criteria. This analysis leads to formalization of a method that permits accurate control on the physical properties of the sensor using contemporary rapid prototyping techniques [Maniatis et al. 2013]. Secondly the first results are presented from a series of entrainment experiments in a 5 x 0.8 m flume in which a prototype sensor was deployed to monitor entrainment dynamics under increasing flow conditions (0.037 m3.s-1). The sensor was enclosed in an idealized spherical case (111 mm diameter) and placed on a constructed bed of hemispheres of the same diameter. We measured 3-axial inertial acceleration (as a measure of flow stress
Characterization of high school mathematics and physics language genres
NASA Astrophysics Data System (ADS)
Wallace, Michelle L.
Research indicates that language factors play a critical role in the learning of school mathematics and science. Symbols and language-forms have been created to represent and discuss mathematical ideas. Understanding language factors, therefore, is critical in improving the teaching and learning of school mathematics and science. The specific goal of this research was to characterize language genres found in secondary school mathematics and physics classrooms. The research presented here was conducted in two secondary school classrooms---one algebra and one physics---taught by the same teacher. The focus was on the discourse between the teacher and her students. In both mathematics and physics, the teacher attended to the meaning of mathematical concepts and processes, but the talk differed. Physics talk focused on developing meaning for the physics concepts through activities and discussion, which were accompanied by mathematical calculations and analyses. Algebra talk, on the other hand, was procedural and narrative in nature. Thus physics talk was more descriptive of individual concepts and situation, and was more explanatory and exploratory than algebra talk. All discourse inevitably reflects one's thinking and beliefs about the content of that discourse. Thus talking algebra and talking physics, as observed in this study, both represented the teacher's beliefs about teaching and learning and the nature of the school curriculum. Even for a teacher with a strong academic background in both mathematics and science, integrating across the curriculum can be hindered by the approved school curriculum and by the reality of the particular classroom context. Providing professional development and implementing one of several available integrated curricula would be needed if more integration were to be implemented. This study presents a literature-based description of the conceptual notion of language genre. It additionally presents a conceptualization of mathematics and
Li, Sicheng; Smith, Daniel G A; Patkowski, Konrad
2015-07-01
We assessed the performance of a large variety of modern density functional theory approaches for the adsorption of carbon dioxide on molecular models of pyridinic N-doped graphene. Specifically, we selected eight polyheterocyclic aromatic compounds ranging from pyridine and pyrazine to 1,6-diazacoronene and investigated their complexes with CO2 for a large range of intermolecular distances and including both in-plane and stacked orientations. The benchmark interaction energies were computed at the complete-basis-set limit MP2 level plus a CCSD(T) coupled-cluster correction in a moderate but carefully selected basis set. Using a set of 96 benchmark CCSD(T)-level interaction energies as a reference, we investigated the accuracy of DFT-based approaches as a function of the density functional, the dispersion correction, the basis set, and the counterpoise correction or lack thereof. While virtually all DFT variants exhibit some deterioration of accuracy for distances slightly shorter than the van der Waals minima, we were able to identify several schemes such as B2PLYP-D3 and M05-2X-D3 whose average errors on the entire benchmark data set are in the 5-10% range. The top DFT performers were subsequently used to investigate the energy profile for a carbon dioxide transition through model N-doped graphene pores. All investigated methods confirmed that the largest, N4H4 pore allows for a barrierless CO2 transition to the other side of a graphene sheet. PMID:26055458
The use of experimental bending tests to more accurate numerical description of TBC damage process
NASA Astrophysics Data System (ADS)
Sadowski, T.; Golewski, P.
2016-04-01
Thermal barrier coatings (TBCs) have been extensively used in aircraft engines to protect critical engine parts such as blades and combustion chambers, which are exposed to high temperatures and corrosive environment. The blades of turbine engines are additionally exposed to high mechanical loads. These loads are created by the high rotational speed of the rotor (30 000 rot/min), causing the tensile and bending stresses. Therefore, experimental testing of coated samples is necessary in order to determine strength properties of TBCs. Beam samples with dimensions 50×10×2 mm were used in those studies. The TBC system consisted of 150 μm thick bond coat (NiCoCrAlY) and 300 μm thick top coat (YSZ) made by APS (air plasma spray) process. Samples were tested by three-point bending test with various loads. After bending tests, the samples were subjected to microscopic observation to determine the quantity of cracks and their depth. The above mentioned results were used to build numerical model and calibrate material data in Abaqus program. Brittle cracking damage model was applied for the TBC layer, which allows to remove elements after reaching criterion. Surface based cohesive behavior was used to model the delamination which may occur at the boundary between bond coat and top coat.
The Force-Frequency Relationship: Insights from Mathematical Modeling
ERIC Educational Resources Information Center
Puglisi, Jose L.; Negroni, Jorge A.; Chen-Izu, Ye; Bers, Donald M.
2013-01-01
The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by…
[Mathematical model of baroreflex regulation of hemodynamics in the dog].
Palets, B L
1983-11-01
A non-linear mathematical model of dog hemodynamics regulation was developed including descriptions of the cardiovascular system, the arterial baroreflex and the Beinbridge reflex. Model calculated arterial and venous pressure, blood flow, and heart rate are in good agreement with experimental data. PMID:6653829
101 Environmental Education Activities. Booklet 3--Mathematics Activities.
ERIC Educational Resources Information Center
Schaljo, Roger, Comp.
Each of the 14 environment-related mathematics activities included in this publication by the Upper Mississippi River ECO-Center includes objectives, materials needed, preparation, and activity description. Occasionally, variations and helpful hints are added. Because the student can gain experience to help him with the practical application of…
Mathematics Education Series (Summary of GEMTEP series--15 Modules).
ERIC Educational Resources Information Center
National Education Association, Washington, DC. Project on Utilization of Inservice Education R & D Outcomes.
The inservice learning module described focuses on teaching mathematical concepts at the elementary grade level. Specifically covered in the module are discovery learning, drill activities, understanding number concepts, and introduction to geometry. Information is provided in this descriptive report on the scope and sequencing of topics and the…
Engaging Students in Mathematical Modeling through Service-Learning
ERIC Educational Resources Information Center
Carducci, Olivia M.
2014-01-01
I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…
Angles and Space: MINNEMAST Coordinated Mathematics - Science Series, Unit 21.
ERIC Educational Resources Information Center
Biersteker, Joseph; And Others
This volume is the twenty-first in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by second-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of three groups of lessons. The purposes and…
A Generalized Instructional System for Elementary Mathematical Logic.
ERIC Educational Resources Information Center
Goldberg, Adele
A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving…
Brain Hemisphericity and Mathematics Achievement of High School Students
ERIC Educational Resources Information Center
Fernandez, Sanny F.
2011-01-01
This study aimed to find out the brain hemisphericity and mathematics achievement of high school students. The respondents of the study were the 168 first year high school students of Colegio de San Jose, during school year 2010-2011 who were chosen through stratified random sampling. The descriptive and interview methods of research were used in…
Mathematics Education Is Not an Enigma--Part 2
ERIC Educational Resources Information Center
Williams, Doug
2012-01-01
Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". Here he continues storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that seeks to…
Mathematics Education Is Not an Enigma--Part 1
ERIC Educational Resources Information Center
Williams, Doug
2012-01-01
Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". This is storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that seeks to change…
Cultural Issues in the Communication of Research on Mathematics Education
ERIC Educational Resources Information Center
Bartolini Bussi, Maria G.; Martignone, Francesca
2013-01-01
It might be trite to observe that every research study is framed within a cultural background. In this paper we argue that the description of the cultural background is important for discussing, evaluating and exploiting internationally the findings of local educational studies. This issue is fundamental in every study in mathematics education…
Science and Mathematics Software Opportunities and Needs. Executive Summary.
ERIC Educational Resources Information Center
Technical Education Research Center, Cambridge, MA.
This study examined the extent to which opportunities created by computer technology addresses the needs in school science and mathematics instruction. Information was gathered by obtaining descriptions of most available software; reviewing published software evaluations, grant-supported software development projects, and a broad selection of…
An Annotated Bibliography of Films and Videotapes for College Mathematics.
ERIC Educational Resources Information Center
Schneider, David I.
This document is intended to facilitate the use of mathematics films and videotapes. All materials listed are readily available from film and videotape companies or from film rental libraries. All descriptions provided are excerpts from distributor's brochures. The materials are generally suitable for college students, and are categorized into the…
Eliciting Students' Beliefs about Who Is Good at Mathematics
ERIC Educational Resources Information Center
Morge, Shelby P.
2007-01-01
This article highlights a series of activities designed to elicit students' mathematics-related beliefs, particularly those related to gender. As a result of the activities, females in upper-level classes rated themselves as having less confidence than males, and viewing a movie clip was sufficient for some students to modify their descriptions of…
Harmony between Turkish Early Childhood and Primary Mathematics Education Standards
ERIC Educational Resources Information Center
Caliskan Dedeoglu, Nuray; Alat, Zeynep
2012-01-01
The aim of this study was to explore the spiral relation and the congruency between mathematics standards listed in the Early Childhood and First Grade curricula in Turkey. A descriptive content analysis was conducted on Early Child Education Curriculum (OOEP) for 36-72 months old children and Math Curriculum for the Grades 1-5 (IMOP), both…
Parts and Pieces: MINNEMAST Coordinated Mathematics - Science Series, Unit 22.
ERIC Educational Resources Information Center
Sohre, Beverly, Ed.
This volume is the twenty-second in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by second-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of seven groups of lessons. The purposes and…
Cross-national Retrospective Studies of Mathematics Olympians.
ERIC Educational Resources Information Center
Campbell, James Reed, Ed.
1996-01-01
The eight chapters of this theme issue use quantitative and qualitative methods to explore the nature and nurture of young participants in the mathematics Olympiad from five countries. Parallel studies are presented of winners from China, Taiwan, and the United States, along with descriptions of programs in Japan and Russia. (SLD)
The Teaching of Developmental Mathematics in Community Colleges.
ERIC Educational Resources Information Center
Medin, Julie
Details of the remedial mathematics programs offered by three community colleges in the Washington D.C. area and a short description of programs offered by eight Maryland community colleges are given. Research and studies of remedial programs at the community college level in other parts of the United States are briefly reviewed. (DT)
Natural Systems: MINNEMAST Coordinated Mathematics - Science Series, Unit 29.
ERIC Educational Resources Information Center
Bakke, Jeannette; And Others
This volume is the last in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by third-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of three groups of lessons. The purposes and procedures for…
Mathematical Modeling of Photochemical Air Pollution.
NASA Astrophysics Data System (ADS)
McRae, Gregory John
Air pollution is an environmental problem that is both pervasive and difficult to control. An important element of any rational control approach is a reliable means for evaluating the air quality impact of alternative abatement measures. This work presents such a capability, in the form of a mathematical description of the production and transport of photochemical oxidants within an urban airshed. The combined influences of advection, turbulent diffusion, chemical reaction, emissions and surface removal processes are all incorporated into a series of models that are based on the species continuity equations. A delineation of the essential assumptions underlying the formulation of a three-dimensional, a Lagrangian trajectory, a vertically integrated and single cell air quality model is presented. Since each model employs common components and input data the simpler forms can be used for rapid screening calculations and the more complex ones for detailed evaluations. The flow fields, needed for species transport, are constructed using inverse distance weighted polynomial interpolation techniques that map routine monitoring data onto a regular computational mesh. Variational analysis procedures are then employed to adjust the field so that mass is conserved. Initial concentration and mixing height distributions can be established with the same interpolation algorithms. Subgrid scale turbulent transport is characterized by a gradient diffusion hypothesis. Similarity solutions are used to model the surface layer fluxes. Above this layer different treatments of turbulent diffusivity are required to account for variations in atmospheric stability. Convective velocity scaling is utilized to develop eddy diffusivities for unstable conditions. The predicted mixing times are in accord with results obtained during sulfur hexafluoride (SF(,6)) tracer experiments. Conventional models are employed for neutral and stable conditions. A new formulation for gaseous deposition fluxes
Hardware description languages
NASA Technical Reports Server (NTRS)
Tucker, Jerry H.
1994-01-01
Hardware description languages are special purpose programming languages. They are primarily used to specify the behavior of digital systems and are rapidly replacing traditional digital system design techniques. This is because they allow the designer to concentrate on how the system should operate rather than on implementation details. Hardware description languages allow a digital system to be described with a wide range of abstraction, and they support top down design techniques. A key feature of any hardware description language environment is its ability to simulate the modeled system. The two most important hardware description languages are Verilog and VHDL. Verilog has been the dominant language for the design of application specific integrated circuits (ASIC's). However, VHDL is rapidly gaining in popularity.
ERIC Educational Resources Information Center
Jaji, Gail
Presents a detailed discussion of the data collected on calculator and computer use in schools in 20 countries. The document includes discussion of: (1) school policy on calculator use; (2) description of populations A (8th grade students) and B (12th grade students) in the United States; (3) uses of calculators in subjects other than mathematics;…
ERIC Educational Resources Information Center
Clarkson, P. C.
Descriptions of Papua New Guinea's national high schools, grade 12 major/minor mathematics courses, and an analysis of the 1980 and 1981 major/minor course examination results are presented. The analysis is intended for use by post year 12 lecturers/instructors planning their courses. Findings indicate that topic scores were far too low for these…
Mathematical Models and the Experimental Analysis of Behavior
Mazur, James E
2006-01-01
The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make equally accurate predictions for a large body of data. In such cases, it is important to find and investigate situations for which the competing models make different predictions because, unless two models are actually mathematically equivalent, they are based on different assumptions about the psychological processes that underlie an observed behavior. Mathematical models developed in basic behavioral research have been used to predict and control behavior in applied settings, and they have guided research in other areas of psychology. A good mathematical model can provide a common framework for understanding what might otherwise appear to be diverse and unrelated behavioral phenomena. Because psychologists vary in their quantitative skills and in their tolerance for mathematical equations, it is important for those who develop mathematical models of behavior to find ways (such as verbal analogies, pictorial representations, or concrete examples) to communicate the key premises of their models to nonspecialists. PMID:16673829
A robust and accurate formulation of molecular and colloidal electrostatics.
Sun, Qiang; Klaseboer, Evert; Chan, Derek Y C
2016-08-01
This paper presents a re-formulation of the boundary integral method for the Debye-Hückel model of molecular and colloidal electrostatics that removes the mathematical singularities that have to date been accepted as an intrinsic part of the conventional boundary integral equation method. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional boundary integral method in such a way as to cancel out the singularities associated with the Green's function. This approach better reflects the non-singular physical behavior of the systems on boundaries with the benefits of the following: (i) the surface integrals can be evaluated accurately using quadrature without any need to devise special numerical integration procedures, (ii) being able to use quadratic or spline function surface elements to represent the surface more accurately and the variation of the functions within each element is represented to a consistent level of precision by appropriate interpolation functions, (iii) being able to calculate electric fields, even at boundaries, accurately and directly from the potential without having to solve hypersingular integral equations and this imparts high precision in calculating the Maxwell stress tensor and consequently, intermolecular or colloidal forces, (iv) a reliable way to handle geometric configurations in which different parts of the boundary can be very close together without being affected by numerical instabilities, therefore potentials, fields, and forces between surfaces can be found accurately at surface separations down to near contact, and (v) having the simplicity of a formulation that does not require complex algorithms to handle singularities will result in significant savings in coding effort and in the reduction of opportunities for coding errors. These advantages are illustrated using examples drawn from molecular and colloidal electrostatics. PMID:27497538
A robust and accurate formulation of molecular and colloidal electrostatics
NASA Astrophysics Data System (ADS)
Sun, Qiang; Klaseboer, Evert; Chan, Derek Y. C.
2016-08-01
This paper presents a re-formulation of the boundary integral method for the Debye-Hückel model of molecular and colloidal electrostatics that removes the mathematical singularities that have to date been accepted as an intrinsic part of the conventional boundary integral equation method. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional boundary integral method in such a way as to cancel out the singularities associated with the Green's function. This approach better reflects the non-singular physical behavior of the systems on boundaries with the benefits of the following: (i) the surface integrals can be evaluated accurately using quadrature without any need to devise special numerical integration procedures, (ii) being able to use quadratic or spline function surface elements to represent the surface more accurately and the variation of the functions within each element is represented to a consistent level of precision by appropriate interpolation functions, (iii) being able to calculate electric fields, even at boundaries, accurately and directly from the potential without having to solve hypersingular integral equations and this imparts high precision in calculating the Maxwell stress tensor and consequently, intermolecular or colloidal forces, (iv) a reliable way to handle geometric configurations in which different parts of the boundary can be very close together without being affected by numerical instabilities, therefore potentials, fields, and forces between surfaces can be found accurately at surface separations down to near contact, and (v) having the simplicity of a formulation that does not require complex algorithms to handle singularities will result in significant savings in coding effort and in the reduction of opportunities for coding errors. These advantages are illustrated using examples drawn from molecular and colloidal electrostatics.
The Effect of Mathematics Research on Mathematics Majors' Mathematical Beliefs
ERIC Educational Resources Information Center
Goodson, Joshua E.
2012-01-01
This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics…
Gaber, David; Schlimm, Dirk
2015-01-01
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. PMID:26263425
Experimenting with Impacts in a Conceptual Physics or Descriptive Astronomy Laboratory
ERIC Educational Resources Information Center
LoPresto, Michael C.
2016-01-01
What follows is a description of the procedure for and results of a simple experiment on the formation of impact craters designed for the laboratory portions of lower mathematical-level general education science courses such as conceptual physics or descriptive astronomy. The experiment provides necessary experience with data collection and…
Automatic TLI recognition system, general description
Lassahn, G.D.
1997-02-01
This report is a general description of an automatic target recognition system developed at the Idaho National Engineering Laboratory for the Department of Energy. A user`s manual is a separate volume, Automatic TLI Recognition System, User`s Guide, and a programmer`s manual is Automatic TLI Recognition System, Programmer`s Guide. This system was designed as an automatic target recognition system for fast screening of large amounts of multi-sensor image data, based on low-cost parallel processors. This system naturally incorporates image data fusion, and it gives uncertainty estimates. It is relatively low cost, compact, and transportable. The software is easily enhanced to expand the system`s capabilities, and the hardware is easily expandable to increase the system`s speed. In addition to its primary function as a trainable target recognition system, this is also a versatile, general-purpose tool for image manipulation and analysis, which can be either keyboard-driven or script-driven. This report includes descriptions of three variants of the computer hardware, a description of the mathematical basis if the training process, and a description with examples of the system capabilities.
Mathematical and computational models of plasma flows
NASA Astrophysics Data System (ADS)
Brushlinsky, K. V.
Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.
Nakhleh, Luay
2014-03-12
I proposed to develop computationally efficient tools for accurate detection and reconstruction of microbes' complex evolutionary mechanisms, thus enabling rapid and accurate annotation, analysis and understanding of their genomes. To achieve this goal, I proposed to address three aspects. (1) Mathematical modeling. A major challenge facing the accurate detection of HGT is that of distinguishing between these two events on the one hand and other events that have similar "effects." I proposed to develop a novel mathematical approach for distinguishing among these events. Further, I proposed to develop a set of novel optimization criteria for the evolutionary analysis of microbial genomes in the presence of these complex evolutionary events. (2) Algorithm design. In this aspect of the project, I proposed to develop an array of e cient and accurate algorithms for analyzing microbial genomes based on the formulated optimization criteria. Further, I proposed to test the viability of the criteria and the accuracy of the algorithms in an experimental setting using both synthetic as well as biological data. (3) Software development. I proposed the nal outcome to be a suite of software tools which implements the mathematical models as well as the algorithms developed.
Mathematical Astronomy in India
NASA Astrophysics Data System (ADS)
Plofker, Kim
Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.
Mathematics in modern immunology
Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M.
2016-01-01
Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered. PMID:27051512
Making connections in mathematics.
Engelmann, S; Carnine, D; Steely, D G
1991-05-01
Math textbooks, which usually represent the mathematics curriculum, seem to be linked to the poor math performance of U.S. students. The major shortcomings of math textbooks are described in this article; then an alternative perspective is offered (the sameness analysis), along with research conducted with students with learning disabilities and at-risk students. The article then presents a detailed illustration of the sameness analysis--how to teach the addition-subtraction and multiplication-division relationships and their interrelationships in the context of solving word problems in mathematics. PMID:2045726
Perception determinants in learning mathematics
NASA Astrophysics Data System (ADS)
Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul
2015-05-01
This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.
Elementary School Mathematics: What Parents Should Know About... Estimation.
ERIC Educational Resources Information Center
Reys, Barbara
Parents have many opportunities every day to develop, nurture, and refine their children's mathematics skills. This pamphlet was designed to help parents become aware of these opportunities and to encourage them to participate in their children's learning process. Estimation is the skill of making a reasonably accurate guess and is prominently…
Electrooculography: Connecting Mind, Brain, and Behavior in Mathematics Education Research
ERIC Educational Resources Information Center
Shipulina, Olga V.; Campbell, Stephen R.; Cimen, Arda O.
2009-01-01
This paper reports on the potential roles and importance of electrooculography (EOG) for mathematics educational neuroscience research. EOG enables accurate measurements of eye-related behavior (i.e., blinks & movements) by recording changes in voltage potentials generated by eye-related behavior. We identify and discuss three main uses of EOG.…
Accurate thermoelastic tensor and acoustic velocities of NaCl
NASA Astrophysics Data System (ADS)
Marcondes, Michel L.; Shukla, Gaurav; da Silveira, Pedro; Wentzcovitch, Renata M.
2015-12-01
Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.
Accurate thermoelastic tensor and acoustic velocities of NaCl
Marcondes, Michel L.; Shukla, Gaurav; Silveira, Pedro da; Wentzcovitch, Renata M.
2015-12-15
Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.
Mathematical challenges from theoretical/computational chemistry
1995-12-31
The committee believes that this report has relevance and potentially valuable suggestions for a wide range of readers. Target audiences include: graduate departments in the mathematical and chemical sciences; federal and private agencies that fund research in the mathematical and chemical sciences; selected industrial and government research and development laboratories; developers of software and hardware for computational chemistry; and selected individual researchers. Chapter 2 of this report covers some history of computational chemistry for the nonspecialist, while Chapter 3 illustrates the fruits of some past successful cross-fertilization between mathematical scientists and computational/theoretical chemists. In Chapter 4 the committee has assembled a representative, but not exhaustive, survey of research opportunities. Most of these are descriptions of important open problems in computational/theoretical chemistry that could gain much from the efforts of innovative mathematical scientists, written so as to be accessible introductions to the nonspecialist. Chapter 5 is an assessment, necessarily subjective, of cultural differences that must be overcome if collaborative work is to be encouraged between the mathematical and the chemical communities. Finally, the report ends with a brief list of conclusions and recommendations that, if followed, could promote accelerated progress at this interface. Recognizing that bothersome language issues can inhibit prospects for collaborative research at the interface between distinctive disciplines, the committee has attempted throughout to maintain an accessible style, in part by using illustrative boxes, and has included at the end of the report a glossary of technical terms that may be familiar to only a subset of the target audiences listed above.
The Provision, Use, Study Time and Effectiveness of Media: A Mathematical Model
ERIC Educational Resources Information Center
Burt, Gordon; Lloyd, David
2005-01-01
Many institutions regularly conduct surveys of students. In some cases these provide descriptive statistics about students' actual use of course components and the descriptive statistics are discussed using ordinary language. A number of refinements to these surveys are proposed. It is argued that mathematical modeling as used in the discipline of…
The "Emerging" and "Emergent" Present: A View on the Indeterminate Nature of Mathematics Lessons
ERIC Educational Resources Information Center
Roth, Wolff-Michael; Maheux, Jean-François
2014-01-01
The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of "emergence." After providing an exemplifying description and…
Theoretical Explanations in Mathematical Physics
NASA Astrophysics Data System (ADS)
Rivadulla, Andrés
Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.
ERIC Educational Resources Information Center
Popelka, Susan R.
2011-01-01
Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…
ERIC Educational Resources Information Center
Whitin, Phyllis; Whitin, David J.
2011-01-01
The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…
New Technologies in Mathematics.
ERIC Educational Resources Information Center
Sarmiento, Jorge
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
Mathematics in Indigenous Contexts
ERIC Educational Resources Information Center
Perry, Bob; Howard Peter
2008-01-01
From 1999-2005, the Mathematics in Indigenous Contexts (MIC) project was implemented by the Board of Studies, New South Wales (NSW), in conjunction with the NSW Department of Education and Training, and academics from two universities. MIC project members worked with schools and communities at two sites: a primary school in an urban community in…
Designing a Mathematics Curriculum
ERIC Educational Resources Information Center
Yee, Lee Peng
2010-01-01
A decade of PMRI saw the changes in the classroom in some of the primary schools in Indonesia. Based on observation, we can say that though the mathematics syllabus in Indonesia did not change, its curriculum has changed under the movement of PMRI. In this article, we put in writing some of the experience gained through the involvement in…
ERIC Educational Resources Information Center
Bogdany, Melvin
The curriculum guide offers a course of training in the fundamentals of mathematics as applied to baking. Problems specifically related to the baking trade are included to maintain a practical orientation. The course is designed to help the student develop proficiency in the basic computation of whole numbers, fractions, decimals, percentage,…
Measurement, Mathematics, and Music.
ERIC Educational Resources Information Center
Blackburn, Katie; White, David
The Greek mathematician, Pythagoras, was among the first to undertake a mathematical study of music. His work, resulted in a scale of notes which can produce beautiful melodies and which is easily reproduced in the elementary classroom. In an age when teachers look for an interdisciplinary connection between various aspects of the curriculum, in a…
ERIC Educational Resources Information Center
Woof, K. R.
1975-01-01
Describes an experimental type of science course which involves theoretical and practical approaches to scientific topics by using mathematics to develop and explain scientific problems and theory. Gives an example of such a course applied to the teaching of physical anthropology. (MLH)
Celebrate Mathematical Curiosity
ERIC Educational Resources Information Center
Redford, Christine
2011-01-01
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
ERIC Educational Resources Information Center
Taschow, Horst G.
Difficulties inherent in the reading of mathematics at secondary and college levels are discussed. Special emphasis is placed on the reading of arithmetic numerals, literal numbers, operational symbols, and expressions of relationships, as well as the reading of technical vocabularies and specialized meanings of general words. While each…
Correlating Mathematics and Science
ERIC Educational Resources Information Center
Mireles, Selena Vasquez
2009-01-01
The change from students learning all subjects together in a one-room schoolhouse to learning in classes separated by subject and grade resulted in distinct disciplines such as social studies, mathematics, science, and English. What was lost was the unified, holistic curriculum that a one-room setting required. Since students move from…
Mathematical Student Motivation
ERIC Educational Resources Information Center
Bacon, Alison
2012-01-01
The research project will be conducted with a target focus group of six students who have been identified as struggling students in 3rd grade mathematics. The research project will study the effect of using different teaching strategies and methods to increase motivation and focus among these students. The research project will be conducted at…
Mathematics: Montessori of Traditional?
ERIC Educational Resources Information Center
Woessner, Ruth
1995-01-01
Compares and contrasts the approaches to mathematics in Montessori schools and traditional schools. Suggests that in a traditional curriculum, math is studied as a separate subject and isolated discipline, in an abstract format, with the entire group of children moving together through the prescribed curriculum. In contrast, the Montessori school…
Mathematical Intrusions in Literatures
ERIC Educational Resources Information Center
Modica, Erasmo
2011-01-01
This article describes an activity that can be carried out in one of the final classes of Italian secondary schools. The aim of the activity is to stimulate pupil curiosity, demonstrating that Mathematics is not a barren subject and allowing the students, according to an interdisciplinary point of view, to investigate some literary works and the…
ERIC Educational Resources Information Center
Livingstone, Ian, Ed.; Izard, John, Ed.
1993-01-01
Set: Research Information for Teachers, is published twice a year by the New Zealand Council for Educational Research and the Australian Council for Educational Research. This document draws together 16 articles on mathematics from previous issues grouped into three categories: general, primary, and secondary. The titles are: (1) "Contents and…
Using and Applying Mathematics
ERIC Educational Resources Information Center
Knight, Rupert
2011-01-01
The Nobel prize winning physicist Richard Feynman (2007) famously enthused about "the pleasure of finding things out". In day-to-day classroom life, however, it is easy to lose and undervalue this pleasure in the process, as opposed to products, of mathematics. Finding things out involves a journey and is often where the learning takes place.…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
In this article, the author looks at ways of creating conditions to bring about learning. If one is to "arrange conditions to bring about learning," one needs written guidance and support systems. Two books that discusses how to arrange these conditions are: "Thinking Mathematically" by John Mason with Leone Burton and Kaye Stacey and "Starting…
Elementary School Mathematics Priorities
ERIC Educational Resources Information Center
Wilson, W. Stephen
2009-01-01
This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
White, Tobin; Martin, Lee
2014-01-01
This paper argues for an approach to mobile learning that leverages students' informal digital practices as resources for designing mathematics classrooms activities. We briefly describe two exploratory designs along these lines, one featuring the use of photos taken by students outside class and the other centered on their recording and…
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…
Verbalizing Mathematics Using APL.
ERIC Educational Resources Information Center
Matthews, George E.
The nature of "A Programing Language" (APL) is viewed as unambiguous, consistent, and powerful. It is based on the notion of functions as imperative verbs, and is used by a small but growing number of mathematicians and computer programers. Three areas of mathematical activity are addressed: calculation of arithmetic expressions, evaluation of…
Designing for Mathematical Abstraction
ERIC Educational Resources Information Center
Pratt, Dave; Noss, Richard
2010-01-01
Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…
Personal Achievement Mathematics: Automotive.
ERIC Educational Resources Information Center
Baenziger, Betty
Utilizing word problems relevant to automotive mechanics, this workbook presents a concept-oriented approach to competency development in 13 areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3) scientific notation;…
ERIC Educational Resources Information Center
Noblitt, Bethany A.; Buckley, Brooke E.
2011-01-01
Teams, pit stops, clues, time limits, fast forwards, challenges, and prizes are all components of the CBS hit show "The Amazing Race." They were also elements of the Amazing Mathematical Race sponsored by the Math and Stats Club at Northern Kentucky University in April 2009. Held in recognition of Math Awareness Month, which is advocated by the…
ERIC Educational Resources Information Center
Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen
2015-01-01
Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…
ERIC Educational Resources Information Center
Bruun, Faye; Diaz, Joan M.; Dykes, Valerie J.
2015-01-01
Students may excel in computation, but their ability to apply their skills will suffer if they do not understand the math vocabulary used in instructions and story problems. This action research project examines two methods for strengthening students' ability to communicate mathematically: (1) Journal writing and peer discussion; and (2) The…
ERIC Educational Resources Information Center
Leutzinger, Larry, Ed.
This book contains articles that help to further the process of reform in the middle grades, recognizing that the knowledge acquired during these years greatly affects how well the secondary school curriculum will attain its goals. Critical issues facing middle grade classes in particular and all mathematics classrooms in general are discussed.…
Storytelling + Origami = Storigami Mathematics
ERIC Educational Resources Information Center
Mastin, Marla
2007-01-01
This article presents a way to engage students in mathematics learning by using the innovative instructional method of storigami. The author shares reactions from teachers who have used her storigami techniques in their classes and provides an example of storigami using the Norwegian fable "The Dog and the Mountain." (Contains 6 figures.)
Mathematical Education of Engineers.
ERIC Educational Resources Information Center
Organisation for Economic Cooperation and Development, Paris (France).
The seminar reported in this document examined the university mathematics courses which should be available to future engineers, and was especially concerned with the introduction of computer science education. There are four major sections. The first reports a survey of electrical engineers in the United Kingdom which investigated how often they…
International Mathematical Olympiad.
ERIC Educational Resources Information Center
Dauber, Susan L.
1988-01-01
The history of the International Mathematical Olympiad (IMO) is presented, emphasizing U.S. participation, competitive events leading to selection of an American team, and rewards of the program. Also revealed are results of a survey of 58 American IMO participants and personal views of six American participants to the 1986 IMO. (JDD)
Teaching Mathematics with Technology.
ERIC Educational Resources Information Center
Jensen, Robert J.
1988-01-01
Argues that calculator activities, even in the early grades, can present situations in which basic mathematical thinking processes come into play. The activity described involves developing efficient calculator guess-and-test strategies and requires only an introductory notion of the four basic operations of arithmetic. (PK)
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…
Urban Mathematics Teacher Retention
ERIC Educational Resources Information Center
Hamdan, Kamal
2010-01-01
Mathematics teachers are both more difficult to attract and more difficult to retain than social sciences teachers. This fact is not unique to the United States; it is reported as being a problem in Europe as well (Howson, 2002). In the United States, however, the problem is particularly preoccupying. Because of the chronic teacher shortages and…
Audiovisual Materials in Mathematics.
ERIC Educational Resources Information Center
Raab, Joseph A.
This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…
Mathematics in Vocational Education.
ERIC Educational Resources Information Center
Oregon State Univ., Corvallis. Vocational-Technical Education Dept.
This handbook was developed to help the vocational teacher aid students in solving mathematical problems in vocational education classes. Most of the examples in the handbook were derived from metal-working and industrial mechanics classes; however, the procedures explained through them will work in any vocational class. The handbook is divided…
Communities in University Mathematics
ERIC Educational Resources Information Center
Biza, Irene; Jaworski, Barbara; Hemmi, Kirsti
2014-01-01
This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of "Communities of Practice." From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form…
Mathematics: Common Curriculum Goals.
ERIC Educational Resources Information Center
Oregon State Dept. of Education, Salem.
This document defines what are considered to be the essentials in a strong mathematics program for the state of Oregon for grades K-12. The common curriculum goals are organized into nine content strands: (1) number and numeration; (2) appropriate computational skills; (3) problem solving; (4) geometry and visualization skills; (5) measurement;…
Investigations: Building Mathematics.
ERIC Educational Resources Information Center
Small, Marian S.
1996-01-01
These activities invite students to use mathematics to explore interesting facts about famous buildings. The investigation for grades three to four focuses on the SkyDome, a sports arena in Toronto, Canada, and the investigation for grades five to six discusses the Empire State Building in New York City. Includes reproducible student worksheets.…
A Classroom Mathematics Utility.
ERIC Educational Resources Information Center
Williams, Michael
1984-01-01
Reviews CATUSPLOT, a mathematics utility aimed at high school algebra through college-level calculus. Basic program capabilities include plotting, tabulating, integrating, and locating of intersections of functions composed of combinations of polynomial, trigonometric, and exponential functions. Rated excellent on all areas examined…
ERIC Educational Resources Information Center
Atiyah, Michael
2000-01-01
The 20th century was a period of extraordinary expansion and progress in mathematics. Concentrates on a few key themes that can be discerned such as local to global, increase in dimension, commutative to non-commutative, linear to non-linear, and homology theory, although it is impossible to list all the main achievements. (ASK)
Intensive Intervention in Mathematics
ERIC Educational Resources Information Center
Powell, Sarah R.; Fuchs, Lynn S.
2015-01-01
Students who demonstrate persistent mathematics difficulties and whose performance is severely below grade level require "intensive intervention". Intensive intervention is an individualized approach to instruction that is more demanding and concentrated than Tier 2 intervention efforts. We present the elements of intensive intervention…
Exploratory Problems in Mathematics.
ERIC Educational Resources Information Center
Stevenson, Frederick W.
This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…
Comprehension Tests in Mathematics.
ERIC Educational Resources Information Center
Conradie, Jurie; Frith, John
2000-01-01
Presents an alternative way for testing a student's understanding of theory in a tertiary mathematics course. Provides two sample questions and discusses the advantages and disadvantages of the method. Argues that the method is an acceptable and flexible means of testing students and can be adapted to use in other contexts as well. (Author/ASK)
ERIC Educational Resources Information Center
Barger, Rita H.; Jarrah, Adeeb M.
2012-01-01
March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…
Developing Remedial Mathematics Strategies.
ERIC Educational Resources Information Center
Sadowski, Barbara R.
The paper describes strategies for remediating mathematics difficulties (particularly the process of regrouping or "borrowing" in whole number subtraction) in children. Three interrelated aspects of the process (the meaning of subtraction, understanding of non-standard numerals, and the function of the subtraction algorithm), are considered. The…
Supporting Mathematical Thinking
ERIC Educational Resources Information Center
Houssart, Jenny; Roaf, Caroline; Watson, Anne
2005-01-01
This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The third of three volumes of a mathematics training course for Navy personnel, this text emphasizes topics needed in understanding digital computers and computer programing. The text begins with sequences and series, induction and the binomial theorem, and continues with two chapters on statistics. Arithmetic operations in number systems other…
Mathematics for Commercial Foods.
ERIC Educational Resources Information Center
Wersan, Norman
A review of basic mathematics operations is presented with problems and examples applied to activities in the food service industry. The text is divided into eight units: measurement, fractions, arithmetic operations, money and decimals, percentage, ratio and proportion, wages and taxes, and business records. Each unit contains a series of lessons…
Mathematics as Problem Solving.
ERIC Educational Resources Information Center
Soifer, Alexander
This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)
COMMERCIAL FOODS, MATHEMATICS - I.
ERIC Educational Resources Information Center
DORNFIELD, BLANCHE E.
THE UNDERSTANDING AND MASTERY OF FUNDAMENTAL MATHEMATICS IS A NECESSARY PART OF COMMERCIAL FOODS WORK. THIS STUDENT HANDBOOK WAS DESIGNED TO ACCOMPANY A COMMERCIAL FOODS COURSE AT THE HIGH SCHOOL LEVEL FOR STUDENTS WITH APPROPRIATE APTITUDES AND COMMERCIAL FOOD SERVICE GOALS. THE MATERIAL, TESTED IN VARIOUS INTERESTED CLASSROOMS, WAS PREPARED BY…
Mathematical Formulation of Multilayer Networks
NASA Astrophysics Data System (ADS)
De Domenico, Manlio; Solé-Ribalta, Albert; Cozzo, Emanuele; Kivelä, Mikko; Moreno, Yamir; Porter, Mason A.; Gómez, Sergio; Arenas, Alex
2013-10-01
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.
Ritchie, L.T.; Alpert, D.J.; Burke, R.P.; Johnson, J.D.; Ostmeyer, R.M.; Aldrich, D.C.; Blond, R.M.
1984-03-01
The CRAC2 computer code is a revised version of CRAC (Calculation of Reactor Accident Consequences) which was developed for the Reactor Safety Study. This document provides an overview of the CRAC2 code and a description of each of the models used. Significant improvements incorporated into CRAC2 include an improved weather sequence sampling technique, a new evacuation model, and new output capabilities. In addition, refinements have been made to the atmospheric transport and deposition model. Details of the modeling differences between CRAC2 and CRAC are emphasized in the model descriptions.
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
ERIC Educational Resources Information Center
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Middle School Mathematics Students' Perspectives on the Study of Mathematics
ERIC Educational Resources Information Center
Vaughn, Christy H.
2012-01-01
This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…
Between the Academic Mathematics and the Mathematics Education Worlds.
ERIC Educational Resources Information Center
Moreira, Candida Queiroz
1997-01-01
Investigated stresses confronted by Portuguese secondary mathematics teachers during the first semester in a master's course, Perspectives on Mathematics Education, noting how they negatively affected teachers' self-confidence and morale and discussing fundamental issues teachers addressed in bridging the academic mathematics and mathematics…
Mathematics Teacher Candidates' Metaphors about the Concept of "Mathematics"
ERIC Educational Resources Information Center
Erdogan, Ahmet; Yazlik, Derya Ozlem; Erdik, Cengiz
2014-01-01
The main purpose of this study was to research mathematics teacher candidates' perceptions about the concept of "mathematics" through the use of metaphors. The research is conducted during 2012-2013 academic year, on a group of 111 mathematics teacher candidates at the Education Faculty of a University in Turkey. To collect the research…
Extended Analyses: Promoting Mathematical Inquiry with Preservice Mathematics Teachers
ERIC Educational Resources Information Center
Bloom, Irene
2007-01-01
This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying…
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
ERIC Educational Resources Information Center
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
Mill profiler machines soft materials accurately
NASA Technical Reports Server (NTRS)
Rauschl, J. A.
1966-01-01
Mill profiler machines bevels, slots, and grooves in soft materials, such as styrofoam phenolic-filled cores, to any desired thickness. A single operator can accurately control cutting depths in contour or straight line work.
Remote balance weighs accurately amid high radiation
NASA Technical Reports Server (NTRS)
Eggenberger, D. N.; Shuck, A. B.
1969-01-01
Commercial beam-type balance, modified and outfitted with electronic controls and digital readout, can be remotely controlled for use in high radiation environments. This allows accurate weighing of breeder-reactor fuel pieces when they are radioactively hot.
Understanding the Code: keeping accurate records.
Griffith, Richard
2015-10-01
In his continuing series looking at the legal and professional implications of the Nursing and Midwifery Council's revised Code of Conduct, Richard Griffith discusses the elements of accurate record keeping under Standard 10 of the Code. This article considers the importance of accurate record keeping for the safety of patients and protection of district nurses. The legal implications of records are explained along with how district nurses should write records to ensure these legal requirements are met. PMID:26418404
Overview of Mathematical Social Sciences.
ERIC Educational Resources Information Center
Kim, K. H.; And Others
1992-01-01
Provides a survey of models that use mathematics in a variety of fields of social science. Discusses specifically mathematical applications in demography, economics, management, political science, psychology, sociology, and other areas. Proposes four unsolved problems. (20 references) (MDH)
Integrating Mathematics and Composition Instruction.
ERIC Educational Resources Information Center
Kirtland, Joseph; Hoh, Pau-San
2002-01-01
Describes the development of an integrated approach for teaching mathematics and writing to freshmen. The goals are to strengthen mathematical skills, develop writing competencies, and foster interdisciplinary awareness. (Author/MM)
ERIC Educational Resources Information Center
Brashers, H. C.
1968-01-01
As the inexperienced writer becomes aware of the issues involved in the composition of effective descriptive prose, he also develops a consistent control over his materials. The persona he chooses, if coherently thought out, can function as an index of many choices, helping him to manipulate the tone, intent, and mood of this style; to regulate…
The Secondary School Mathematics Curriculum.
ERIC Educational Resources Information Center
Kolb, John R.; Waters, William M., Jr.
This report begins with a brief historical sketch of the origins of the mathematics curriculum and the responsiveness of mathematics curriculum to the demands of society. The current North Carolina mathematics curriculum is then described and evaluated. A "strands" approach to the development of curriculum and a framework for planning are then…
Mathematical Modeling: Convoying Merchant Ships
ERIC Educational Resources Information Center
Mathews, Susann M.
2004-01-01
This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…
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…
Physical Principles versus Mathematical Rigor.
ERIC Educational Resources Information Center
Patterson, Jim
2000-01-01
While it is most often the case that an understanding of physics can simplify mathematical calculations, occasionally mathematical precision leads directly to a better physical understanding of a situation. Presents an example of a mechanics problem in which careful mathematical derivation can lead directly to a deeper physical understanding of…
Ethical Dimensions of Mathematics Education
ERIC Educational Resources Information Center
Boylan, Mark
2016-01-01
The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…
A Primer for Mathematical Modeling
ERIC Educational Resources Information Center
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Experimental Mathematics and Computational Statistics
Bailey, David H.; Borwein, Jonathan M.
2009-04-30
The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.
Toddlers' Opportunities to Learn Mathematics
ERIC Educational Resources Information Center
Bjorklund, Camilla
2008-01-01
Mathematical knowledge has developed from human activities through thousands of years and is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans' everyday life, an environment where people reach agreement regarding principles in mathematics. Through interaction with worldly phenomena and…
MAPP: A Mathematics Placement Program.
ERIC Educational Resources Information Center
Doblin, Stephen A.
1978-01-01
MAPP (A Mathematics Placement Program) uses two COBOL programs to place entering freshmen in mathematics courses which are commensurate with their backgrounds and abilities. Having been used for three years, the program is considered to be a viable alternative to the traditional mathematics placement process. (Author/JKS)
Flawed Mathematical Conceptualizations: Marlon's Dilemma
ERIC Educational Resources Information Center
Garrett, Lauretta
2013-01-01
Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…
Mathematical History, Philosophy and Education
ERIC Educational Resources Information Center
Otte, Michael
2007-01-01
History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and…
Perceptions of Mathematics in Engineering
ERIC Educational Resources Information Center
Winkelman, Paul
2009-01-01
Students entering engineering programmes are typically expected to be competent in mathematics and science. Design competencies are seldom required. This research focuses on mathematics and investigates how concepts of mathematics may affect perceptions of design. Case studies, consisting of interviews and web-based material, reveal a range of…
STEM Gives Meaning to Mathematics
ERIC Educational Resources Information Center
Hefty, Lukas J.
2015-01-01
The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…
Why Are Mathematical Investigations Important?
ERIC Educational Resources Information Center
Quinnell, Lorna
2010-01-01
"Research studies show that when students discover mathematical ideas and invent mathematical procedures, they have a stronger conceptual understanding of connections between mathematical ideas." Flewelling and Higginson state that inquiry, investigations, and problem solving "give students the opportunity to use their imagination and to get into…
Teaching of Mathematics: Way Forward
ERIC Educational Resources Information Center
Bashir, Taqadus; Shami, Pervez A.
2006-01-01
This paper describes the results of a research study focusing quality improvement in mathematics education and promotion with the use of mathematics laboratory. The primary purpose was to assess the perception of teachers regarding the teaching method through activities and the subsequent need for the mathematics laboratory in schools. This…
Gender Differences in Mathematics Performance.
ERIC Educational Resources Information Center
Porter, Rhonda C.
Since the 1960s, gender differences in mathematics performance have been a major topic in educational and mathematical research. This study entails a gender comparative analysis of students' mathematics performance as determined by the Iowa Test of Basic Skills and by the Tests of Achievement and Proficiency. In a public school system in rural…
Wisconsin's Mathematics Talent Development Project.
ERIC Educational Resources Information Center
Rolland, Al; Schuster, Nancy
1988-01-01
The Mathematics Talent Development Project offers accelerated mathematics to students aged 10-14, on Saturdays at the University of Wisconsin-Eau Claire. Four years of high-school mathematics are covered in two years, including algebra, geometry, trigonometry, and statistics. Described are student selection, importance of homework, and teacher…
Developments in Elementary Mathematics Teaching.
ERIC Educational Resources Information Center
Sawyer, Ann Elisabeth
The rapid introduction of Britain's National Curriculum for Mathematics and its effects upon classroom practice is the main thrust of this book. Chapter titles are: (1) "National Curriculum Implications for Teaching and Learning Mathematics"; (2) "Starting Points for Using and Applying Mathematics: Maths Trails"; (3) "Logo. Some Case Studies of…