Colour by Numbers

ERIC Educational Resources Information Center

Wetherell, Chris

2017-01-01

This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

Mathematical correlation of modal-parameter-identification methods via system-realization theory

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan

1987-01-01

A unified approach is introduced using system-realization theory to derive and correlate modal-parameter-identification methods for flexible structures. Several different time-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal-parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research toward the unification of the many possible approaches for modal-parameter identification.

Structural Model of the Relationships among Cognitive Processes, Visual Motor Integration, and Academic Achievement in Students with Mild Intellectual Disability (MID)

ERIC Educational Resources Information Center

Taha, Mohamed Mostafa

2016-01-01

This study aimed to test a proposed structural model of the relationships and existing paths among cognitive processes (attention and planning), visual motor integration, and academic achievement in reading, writing, and mathematics. The study sample consisted of 50 students with mild intellectual disability or MID. The average age of these…

Sensorimotor coordination and the structure of space.

PubMed

McCollum, Gin

2003-01-01

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

Mathematical theory of a relaxed design problem in structural optimization

NASA Technical Reports Server (NTRS)

Kikuchi, Noboru; Suzuki, Katsuyuki

1990-01-01

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Mathematical correlation of modal parameter identification methods via system realization theory

NASA Technical Reports Server (NTRS)

Juang, J. N.

1986-01-01

A unified approach is introduced using system realization theory to derive and correlate modal parameter identification methods for flexible structures. Several different time-domain and frequency-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research towards the unification of the many possible approaches for modal parameter identification.

PREFACE: Mathematical Aspects of Generalized Entropies and their Applications

NASA Astrophysics Data System (ADS)

Suyari, Hiroki; Ohara, Atsumi; Wada, Tatsuaki

2010-01-01

In the recent increasing interests in power-law behaviors beyond the usual exponential ones, there have been some concrete attempts in statistical physics to generalize the standard Boltzmann-Gibbs statistics. Among such generalizations, nonextensive statistical mechanics has been well studied for about the last two decades with many modifications and refinements. The generalization has provided not only a theoretical framework but also many applications such as chaos, multi-fractal, complex systems, nonequilibrium statistical mechanics, biophysics, econophysics, information theory and so on. At the same time as the developments in the generalization of statistical mechanics, the corresponding mathematical structures have also been required and uncovered. In particular, some deep connections to mathematical sciences such as q-analysis, information geometry, information theory and quantum probability theory have been revealed recently. These results obviously indicate an existence of the generalized mathematical structure including the mathematical framework for the exponential family as a special case, but the whole structure is still unclear. In order to make an opportunity to discuss the mathematical structure induced from generalized entropies by scientists in many fields, the international workshop 'Mathematical Aspects of Generalized Entropies and their Applications' was held on 7-9 July 2009 at Kyoto TERRSA, Kyoto, Japan. This volume is the proceedings of the workshop which consisted of 6 invited speakers, 14 oral presenters, 7 poster presenters and 63 other participants. The topics of the workshop cover the nonextensive statistical mechanics, chaos, cosmology, information geometry, divergence theory, econophysics, materials engineering, molecular dynamics and entropy theory, information theory and so on. The workshop was organized as the first attempt to discuss these mathematical aspects with leading experts in each area. We would like to express special thanks to all the invited speakers, the contributors and the participants at the workshop. We are also grateful to RIMS (Research Institute for Mathematical Science) in Kyoto University and the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B), 18300003, 2009 for their support. Organizing Committee Editors of the Proceedings Hiroki Suyari (Chiba University, Japan) Atsumi Ohara (Osaka University, Japan) Tatsuaki Wada (Ibaraki University, Japan) Conference photograph

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Member and Affiliate Contact Directory. Triangle Coalition for Science and Technology Education. Second Edition.

ERIC Educational Resources Information Center

Triangle Coalition for Science and Technology Education, College Park, MD.

This directory is designed to assist local action groups (existing local alliances; science mathematics, and technology teachers; superintendents, principals, and supervisors; guidance counselors and resource specialists; and university and college professors) in making contact with the local structure of the Triangle Coalition for Science and…

Teacher Learning in the Digital Age: Online Professional Development in STEM Education

ERIC Educational Resources Information Center

Dede, Chris, Ed.; Eisenkraft, Arthur, Ed.; Frumin, Kim, Ed.; Hartley, Alex, Ed.

2016-01-01

With an emphasis on science, technology, engineering, and mathematics (STEM) training, "Teacher Learning in the Digital Age" examines exemplary models of online and blended teacher professional development, including information on the structure and design of each model, intended audience, and existing research and evaluation data. From…

Mathematical formula recognition using graph grammar

NASA Astrophysics Data System (ADS)

Lavirotte, Stephane; Pottier, Loic

1998-04-01

This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.

The Abstraction Ability in Constructing Relation Within Triangles by The Seventh Grade Students of Junior High School

NASA Astrophysics Data System (ADS)

Annas, Suwardi; Djadir; Mutmainna Hasma, Sitti

2018-01-01

on is an activity to organize a mathematical concept that has been previously owned into a new mathematical structure. Activites in abstraction are recognizing, organizing and constructing. Recognizing is a process of identifying a mathematical structure that had existed before. Organizing is a process of using structural knowledge to be assembled into a solution of a problem and constructing is a process of organizing the characteristics of the object into a new structure that does not exist. In abstraction process, the students use attributes to address the object, including routine attribute, nonroutine attributes, and meaningless attributes. This research applied descriptive qualitative research which aimed to describe the abstraction ability of students from high, moderate, and low groups to construct a relation within triangle. In collecting the data, this research used students’ pre-ability math test, abstraction test, and guided interview. The sampling technique in this research was based on the students’ scores in pre-ability math test, which were divided into three groups. Two students from each group were opted as the subjects of this research. Questions of the test are based on the indicators of steps in abstraction activity. Thus, based on the data gained in this research, researcher determined the tendency of attributes used in each abstraction activity. The result of this research revealed that students from high, moderate and low groups were prone to use routine attributes in recognizing triangles. In organizing the characteristics within triangles, high group tended to organize the triangle correctly, while the moderate and low groups tended to organize the triangle incorrectly. In constructing relation within triangles, students in high, moderate and low groups construct it incompletely.

Neuroscience from a mathematical perspective: key concepts, scales and scaling hypothesis, universality.

PubMed

van Hemmen, J Leo

2014-10-01

This article analyzes the question of whether neuroscience allows for mathematical descriptions and whether an interaction between experimental and theoretical neuroscience can be expected to benefit both of them. It is argued that a mathematization of natural phenomena never happens by itself. First, appropriate key concepts must be found that are intimately connected with the phenomena one wishes to describe and explain mathematically. Second, the scale on, and not beyond, which a specific description can hold must be specified. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis. Third, can a mathematical description be universally valid and, if so, how? Here we put forth the argument that universals also exist in theoretical neuroscience, that evolution proves the rule, and that theoretical neuroscience is a domain with still lots of space for new developments initiated by an intensive interaction with experiment. Finally, major insight is provided by a careful analysis of the way in which particular brain structures respond to perceptual input and in so doing induce action in an animal's surroundings.

Deformations of the gyroid and Lidinoid minimal surfaces using flat structures

NASA Astrophysics Data System (ADS)

Weyhaupt, Adam

2015-03-01

Mathematically, the challenge in proving the existence of a purported triply periodic minimal surface is in computing parameter values that depend on a system of equations defined by elliptic integrals. This is generally very difficult. In the presence of some symmetry, however, a technique developed by Weber and Wolf can reduce these elliptic integrals to basic algebra and geometry of polygons. These techniques can easily prove the existence of some surfaces and the presence of a family of solutions. Families of surfaces are important mathematically, but recent work by Seddon, et. al., experimentally confirms that these families of surfaces can occur physically as well. In this talk, we give a brief overview of the technique and show how it can be applied to prove the existence of several families of surfaces, including lower symmetry variants of the gyroid and Lidinoid such as the rG, rPD, tG, and rL. We also conjecture a map of the moduli space of triply periodic minimal surfaces of genus 3.

Initial singularity and pure geometric field theories

NASA Astrophysics Data System (ADS)

Wanas, M. I.; Kamal, Mona M.; Dabash, Tahia F.

2018-01-01

In the present article we use a modified version of the geodesic equation, together with a modified version of the Raychaudhuri equation, to study initial singularities. These modified equations are used to account for the effect of the spin-torsion interaction on the existence of initial singularities in cosmological models. Such models are the results of solutions of the field equations of a class of field theories termed pure geometric. The geometric structure used in this study is an absolute parallelism structure satisfying the cosmological principle. It is shown that the existence of initial singularities is subject to some mathematical (geometric) conditions. The scheme suggested for this study can be easily generalized.

Mathematical modeling of the process of determining the standards for process losses in the transfer of thermal energy of the coolant

NASA Astrophysics Data System (ADS)

Akhmetova, I. G.; Chichirova, N. D.

2017-11-01

Currently the actual problem is a precise definition of the normative and actual heat loss. Existing methods - experimental, on metering devices, on the basis of mathematical modeling methods are not without drawbacks. Heat losses establishing during the heat carrier transport has an impact on the tariff structure of heat supply organizations. This quantity determination also promotes proper choice of main and auxiliary equipment power, temperature chart of heat supply networks, as well as the heating system structure choice with the decentralization. Calculation of actual heat loss and their comparison with standard values justifies the performance of works on improvement of the heat networks with the replacement of piping or its insulation. To determine the cause of discrepancies between normative and actual heat losses thermal tests on the magnitude of the actual heat losses in the 124 sections of heat networks in Kazan. As were carried out the result mathematical model of the regulatory definition of heat losses is developed and tested. This model differ from differs the existing according the piping insulation type. The application of this factor will bring the value of calculative normative losses heat energy to their actual value. It is of great importance for enterprises operating distribution networks and because of the conditions of their configuration and extensions do not have the technical ability to produce thermal testing.

Expectancy-Value and Cognitive Process Outcomes in Mathematics Learning: A Structural Equation Analysis

ERIC Educational Resources Information Center

Phan, Huy P.

2014-01-01

Existing research has yielded evidence to indicate that the expectancy-value theoretical model predicts students' learning in various achievement contexts. Achievement values and self-efficacy expectations, for example, have been found to exert positive effects on cognitive process and academic achievement outcomes. We tested a conceptual model…

Improving STEM Program Quality in Out-of-School-Time: Tool Development and Validation

ERIC Educational Resources Information Center

Shah, Ashima Mathur; Wylie, Caroline; Gitomer, Drew; Noam, Gil

2018-01-01

In and out-of-school time (OST) experiences are viewed as complementary in contributing to students' interest, engagement, and performance in science, technology, engineering, and mathematics (STEM). While tools exist to measure quality in general afterschool settings and others to measure structured science classroom experiences, there is a need…

Mathematical concepts for modeling human behavior in complex man-machine systems

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1979-01-01

Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.

Decentralized control of Markovian decision processes: Existence Sigma-admissable policies

NASA Technical Reports Server (NTRS)

Greenland, A.

1980-01-01

The problem of formulating and analyzing Markov decision models having decentralized information and decision patterns is examined. Included are basic examples as well as the mathematical preliminaries needed to understand Markov decision models and, further, to superimpose decentralized decision structures on them. The notion of a variance admissible policy for the model is introduced and it is proved that there exist (possibly nondeterministic) optional policies from the class of variance admissible policies. Directions for further research are explored.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

PubMed

Mohan, B M; Sinha, Arpita

2008-07-01

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

Evaluating Mathematics Achievement of Middle School Students in a Looping Environment

ERIC Educational Resources Information Center

Franz, Dana Pomykal; Thompson, Nicole L.; Fuller, Bob; Hare, R. Dwight; Miller, Nicole C.; Walker, Jacob

2010-01-01

Looping, a school structure where students remain with one group of teachers for two or more school years, is used by middle schools to meet the diverse needs of young adolescents. However, little research exists on how looping effects the academic performance of students. This study was designed to determine if looping influenced middle school…

Markov model of the loan portfolio dynamics considering influence of management and external economic factors

NASA Astrophysics Data System (ADS)

Bozhalkina, Yana; Timofeeva, Galina

2016-12-01

Mathematical model of loan portfolio in the form of a controlled Markov chain with discrete time is considered. It is assumed that coefficients of migration matrix depend on corrective actions and external factors. Corrective actions include process of receiving applications, interaction with existing solvent and insolvent clients. External factors are macroeconomic indicators, such as inflation and unemployment rates, exchange rates, consumer price indices, etc. Changes in corrective actions adjust the intensity of transitions in the migration matrix. The mathematical model for forecasting the credit portfolio structure taking into account a cumulative impact of internal and external changes is obtained.

Mathematical Methods of System Analysis in Construction Materials

NASA Astrophysics Data System (ADS)

Garkina, Irina; Danilov, Alexander

2017-10-01

System attributes of construction materials are defined: complexity of an object, integrity of set of elements, existence of essential, stable relations between elements defining integrative properties of system, existence of structure, etc. On the basis of cognitive modelling (intensive and extensive properties; the operating parameters) materials (as difficult systems) and creation of the cognitive map the hierarchical modular structure of criteria of quality is under construction. It actually is a basis for preparation of the specification on development of material (the required organization and properties). Proceeding from a modern paradigm (model of statement of problems and their decisions) of development of materials, levels and modules are specified in structure of material. It when using the principles of the system analysis allows to considered technological process as the difficult system consisting of elements of the distinguished specification level: from atomic before separate process. Each element of system depending on an effective objective is considered as separate system with more detailed levels of decomposition. Among them, semantic and qualitative analyses of an object (are considered a research objective, decomposition levels, separate elements and communications between them come to light). Further formalization of the available knowledge in the form of mathematical models (structural identification) is carried out; communications between input and output parameters (parametrical identification) are defined. Hierarchical structures of criteria of quality are under construction for each allocated level. On her the relevant hierarchical structures of system (material) are under construction. Regularities of structurization and formation of properties, generally are considered at the levels from micro to a macrostructure. The mathematical model of material is represented as set of the models corresponding to private criteria by which separate modules and their levels (the mathematical description, a decision algorithm) are defined. Adequacy is established (compliance of results of modelling to experimental data; is defined by the level of knowledge of process and validity of the accepted assumptions). The global criterion of quality of material is considered as a set of private criteria (properties). Synthesis of material is carried out on the basis of one-criteria optimization on each of the chosen private criteria. Results of one-criteria optimization are used at multicriteria optimization. The methods of developing materials as single-purpose, multi-purpose, including contradictory, systems are indicated. The scheme of synthesis of composite materials as difficult systems is developed. The specified system approach effectively was used in case of synthesis of composite materials with special properties.

The Mathematics Textbook as a Story: A Novel Approach to the Interrogation of Mathematics Curriculum

ERIC Educational Resources Information Center

Dietiker, Leslie C.

2012-01-01

Both the purpose and overarching goal of this dissertation can be summarized with this quote by Buckminster Fuller: "You never change things by fighting the existing reality. To change something, build a new model that makes the existing model obsolete." That is, to enable substantive positive change in mathematics education, this…

Reprint of "Mathematics as verbal behavior".

PubMed

Marr, M Jackson

2015-05-01

"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. Copyright © 2015 Elsevier B.V. All rights reserved.

Mathematics as verbal behavior.

PubMed

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. Copyright © 2015 Elsevier B.V. All rights reserved.

Gender, culture, and mathematics performance

PubMed Central

Hyde, Janet S.; Mertz, Janet E.

2009-01-01

Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the second question, studies find more males than females scoring above the 95th or 99th percentile, but this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Furthermore, data from several studies indicate that greater male variability with respect to mathematics is not ubiquitous. Rather, its presence correlates with several measures of gender inequality. Thus, it is largely an artifact of changeable sociocultural factors, not immutable, innate biological differences between the sexes. Responding to the third question, we document the existence of females who possess profound mathematical talent. Finally, we review mounting evidence that both the magnitude of mean math gender differences and the frequency of identification of gifted and profoundly gifted females significantly correlate with sociocultural factors, including measures of gender equality across nations. PMID:19487665

Gender, culture, and mathematics performance.

PubMed

Hyde, Janet S; Mertz, Janet E

2009-06-02

Using contemporary data from the U.S. and other nations, we address 3 questions: Do gender differences in mathematics performance exist in the general population? Do gender differences exist among the mathematically talented? Do females exist who possess profound mathematical talent? In regard to the first question, contemporary data indicate that girls in the U.S. have reached parity with boys in mathematics performance, a pattern that is found in some other nations as well. Focusing on the second question, studies find more males than females scoring above the 95th or 99th percentile, but this gender gap has significantly narrowed over time in the U.S. and is not found among some ethnic groups and in some nations. Furthermore, data from several studies indicate that greater male variability with respect to mathematics is not ubiquitous. Rather, its presence correlates with several measures of gender inequality. Thus, it is largely an artifact of changeable sociocultural factors, not immutable, innate biological differences between the sexes. Responding to the third question, we document the existence of females who possess profound mathematical talent. Finally, we review mounting evidence that both the magnitude of mean math gender differences and the frequency of identification of gifted and profoundly gifted females significantly correlate with sociocultural factors, including measures of gender equality across nations.

Combinatorial explosion in model gene networks

NASA Astrophysics Data System (ADS)

Edwards, R.; Glass, L.

2000-09-01

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such networks are extremely rich and they offer novel ways to think about how mutations can alter dynamics.

Combinatorial explosion in model gene networks.

PubMed

Edwards, R.; Glass, L.

2000-09-01

The explosive growth in knowledge of the genome of humans and other organisms leaves open the question of how the functioning of genes in interacting networks is coordinated for orderly activity. One approach to this problem is to study mathematical properties of abstract network models that capture the logical structures of gene networks. The principal issue is to understand how particular patterns of activity can result from particular network structures, and what types of behavior are possible. We study idealized models in which the logical structure of the network is explicitly represented by Boolean functions that can be represented by directed graphs on n-cubes, but which are continuous in time and described by differential equations, rather than being updated synchronously via a discrete clock. The equations are piecewise linear, which allows significant analysis and facilitates rapid integration along trajectories. We first give a combinatorial solution to the question of how many distinct logical structures exist for n-dimensional networks, showing that the number increases very rapidly with n. We then outline analytic methods that can be used to establish the existence, stability and periods of periodic orbits corresponding to particular cycles on the n-cube. We use these methods to confirm the existence of limit cycles discovered in a sample of a million randomly generated structures of networks of 4 genes. Even with only 4 genes, at least several hundred different patterns of stable periodic behavior are possible, many of them surprisingly complex. We discuss ways of further classifying these periodic behaviors, showing that small mutations (reversal of one or a few edges on the n-cube) need not destroy the stability of a limit cycle. Although these networks are very simple as models of gene networks, their mathematical transparency reveals relationships between structure and behavior, they suggest that the possibilities for orderly dynamics in such networks are extremely rich and they offer novel ways to think about how mutations can alter dynamics. (c) 2000 American Institute of Physics.

Assessing non-uniqueness: An algebraic approach

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

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Development of a Short Form of the Attitudes toward Mathematics Inventory

ERIC Educational Resources Information Center

Lim, Siew Yee; Chapman, Elaine

2013-01-01

Existing instruments designed to measure mathematics attitudes were too long, dated, or assessed with only western samples. To address this issue, a shortened version of the Attitudes Toward Mathematics Inventory (short ATMI) which measures four subscales--;enjoyment of mathematics, motivation to do mathematics, self-confidence in mathematics, and…

Has Progress in Mathematics Slowed Down?

ERIC Educational Resources Information Center

Halmos, Paul R.

1990-01-01

Reported is whether and how mathematics has changed during the 75 years of the Mathematical Association of America's (MAA) existence. The progress of mathematics is organized into 9 concepts, 2 explosions, and 11 developments. (KR)

Calling for Research Collaborations and the Use of Dis/ability Studies in Mathematics Education

ERIC Educational Resources Information Center

Tan, Paulo; Kastberg, Signe

2017-01-01

In this commentary, the authors find that despite discussions of "mathematics for all," opportunities that support the development of mathematical reasoning and understanding of mathematics as a human endeavor often do not exist for mathematics learners identified in schools as having dis/abilities. Indeed, mathematics for all is…

Mathematical analysis of an age-structured population model with space-limited recruitment.

PubMed

Kamioka, Katumi

2005-11-01

In this paper, we investigate structured population model of marine invertebrate whose life stage is composed of sessile adults and pelagic larvae, such as barnacles contained in a local habitat. First we formulate the basic model as an Cauchy problem on a Banach space to discuss the existence and uniqueness of non-negative solution. Next we define the basic reproduction number R0 to formulate the invasion condition under which the larvae can successfully settle down in the completely vacant habitat. Subsequently we examine existence and stability of steady states. We show that the trivial steady state is globally asymptotically stable if R0 < or = 1, whereas it is unstable if R0 > 1. Furthermore, we show that a positive (non-trivial) steady state uniquely exists if R0 > 1 and it is locally asymptotically stable as far as absolute value of R0 - 1 is small enough.

Mathematical analysis of a multiple strain, multi-locus-allele system for antigenically variable infectious diseases revisited.

PubMed

Cherif, Alhaji

2015-09-01

Many important pathogens such as HIV/AIDS, influenza, malaria, dengue and meningitis generally exist in phenotypically distinct serotypes that compete for hosts. Models used to study these diseases appear as meta-population systems. Herein, we revisit one of the multiple strain models that have been used to investigate the dynamics of infectious diseases with co-circulating serotypes or strains, and provide analytical results underlying the numerical investigations. In particular, we establish the necessary conditions for the local asymptotic stability of the steady states and for the existence of oscillatory behaviors via Hopf bifurcation. In addition, we show that the existence of discrete antigenic forms among pathogens can either fully or partially self-organize, where (i) strains exhibit no strain structures and coexist or (ii) antigenic variants sort into non-overlapping or minimally overlapping clusters that either undergo the principle of competitive exclusion exhibiting discrete strain structures, or co-exist cyclically. Copyright © 2015. Published by Elsevier Inc.

Modeling small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models.

PubMed

Salgia, Ravi; Mambetsariev, Isa; Hewelt, Blake; Achuthan, Srisairam; Li, Haiqing; Poroyko, Valeriy; Wang, Yingyu; Sattler, Martin

2018-05-25

Mathematical cancer models are immensely powerful tools that are based in part on the fractal nature of biological structures, such as the geometry of the lung. Cancers of the lung provide an opportune model to develop and apply algorithms that capture changes and disease phenotypes. We reviewed mathematical models that have been developed for biological sciences and applied them in the context of small cell lung cancer (SCLC) growth, mutational heterogeneity, and mechanisms of metastasis. The ultimate goal is to develop the stochastic and deterministic nature of this disease, to link this comprehensive set of tools back to its fractalness and to provide a platform for accurate biomarker development. These techniques may be particularly useful in the context of drug development research, such as combination with existing omics approaches. The integration of these tools will be important to further understand the biology of SCLC and ultimately develop novel therapeutics.

Adapting the academic motivation scale for use in pre-tertiary mathematics classrooms

NASA Astrophysics Data System (ADS)

Lim, Siew Yee; Chapman, Elaine

2015-09-01

The Academic Motivation Scale ( ams) is a comprehensive and widely used instrument for assessing motivation based on the self-determination theory. Currently, no such comprehensive instrument exists to assess the different domains of motivation (stipulated by the self-determination theory) in mathematics education at the pre-tertiary level (grades 11 and 12) in Asia. This study adapted the ams for this use and assessed the properties of the adapted instrument with 1610 students from Singapore. Exploratory and confirmatory factor analyses indicated a five-factor structure for the modified instrument (the three original ams intrinsic subscales collapsed into a single factor). Additionally, the modified instrument exhibited good internal consistency (mean α = .88), and satisfactory test-retest reliability over a 1-month interval (mean r xx = .73). The validity of the modified ams was further demonstrated through correlational analyses among scores on its subscales, and with scores on other instruments measuring mathematics attitudes, anxiety and achievement.

Mathematics: Self-Efficacy, Identity, and Achievement among African American Males from the High School Longitudinal Study

ERIC Educational Resources Information Center

Briggs, Calvin

2014-01-01

The purpose of this study was to determine if a relationship existed between mathematics self-efficacy and mathematics identity to mathematics achievement among African American males from High School Longitudinal Study of 2009 (HSLS:09). Subsequently, the extent to which mathematics self-efficacy and mathematics identity accounted for low and…

An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

ERIC Educational Resources Information Center

Powell, Sarah R.; Nelson, Gena

2017-01-01

Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education

ERIC Educational Resources Information Center

Sriraman, Bharath, Ed.

2012-01-01

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

Student’s scheme in solving mathematics problems

NASA Astrophysics Data System (ADS)

Setyaningsih, Nining; Juniati, Dwi; Suwarsono

2018-03-01

The purpose of this study was to investigate students’ scheme in solving mathematics problems. Scheme are data structures for representing the concepts stored in memory. In this study, we used it in solving mathematics problems, especially ratio and proportion topics. Scheme is related to problem solving that assumes that a system is developed in the human mind by acquiring a structure in which problem solving procedures are integrated with some concepts. The data were collected by interview and students’ written works. The results of this study revealed are students’ scheme in solving the problem of ratio and proportion as follows: (1) the content scheme, where students can describe the selected components of the problem according to their prior knowledge, (2) the formal scheme, where students can explain in construct a mental model based on components that have been selected from the problem and can use existing schemes to build planning steps, create something that will be used to solve problems and (3) the language scheme, where students can identify terms, or symbols of the components of the problem.Therefore, by using the different strategies to solve the problems, the students’ scheme in solving the ratio and proportion problems will also differ.

An Application of the Theory of Moments to Euclidean Relativistic Quantum Mechanical Scattering

NASA Astrophysics Data System (ADS)

Aiello, Gordon J.

One recipe for mathematically formulating a relativistic quantum mechanical scattering theory utilizes a two-Hilbert space approach, denoted by H and H0, upon each of which a unitary representation of the Poincare Lie group is given. Physically speaking, H models a complicated interacting system of particles one wishes to understand, and H 0 an associated simpler (i.e., free/noninteracting) structure one uses to construct "asymptotic boundary conditions" on so-called scattering states in H. Simply put, H 0 is an attempted idealization of H one hopes to realize in the large time limits t → +/-infinity. The above considerations lead to the study of the existence of strong limits of operators of the form eiHtJeiH 0t, where H and H0 are self-adjoint generators of the time translation subgroup of the unitary representations of the Poincare group on H and H0, and J is a contrived mapping from H0 into H that provides the internal structure of the scattering asymptotes. The existence of said limits in the context of Euclidean quantum theories (satisfying precepts known as the Osterwalder-Schrader axioms) depends on the choice of J and leads to a marvelous connection between this formalism and a beautiful area of classical mathematical analysis known as the Stieltjes moment problem, which concerns the relationship between numerical sequences {mun}n=0infinity and the existence/uniqueness of measures alpha(x) on the half-line satisfying (n/a).

The Effect of Syllabus on Mathematical Knowledge

ERIC Educational Resources Information Center

Belsom, C. G. H.; Elton, L. R. B.

1974-01-01

Item analysis of a mathematics preknowledge test given to physics students revealed that significant differences existed on certain items between groups of students who had followed different mathematics syllabuses. (MLH)

Information Dynamics in Networks: Models and Algorithms

DTIC Science & Technology

2016-09-13

Twitter ; we investigated how to detect spam accounts on Facebook and other social networks by graph analytics; and finally we investigated how to design...networks. We investigated the appropriateness of existing mathematical models for explaining the structure of retweet cascades on Twitter ; we investigated...Received Paper 1.00 2.00 3.00 . A Note on Modeling Retweet Cascades on Twitter , Workshop on Algorithms and Models for the Web Graph. 09-DEC-15

Algorithms and Array Design Criteria for Robust Imaging in Interferometry

DTIC Science & Technology

2016-04-01

Interferometry 1.1 Chapter Overview In this Section, we introduce the physics -based principles of optical interferometry, thereby providing a foundation for...particular physical structure (i.e. the existence of a certain type of loop in the interferometric graph), and provide a simple algorithm for identifying...mathematical conditions for wrap invariance to a physical condition on aperture placement is more intuitive when considering the raw phase measurements as

Dynamics of two-strain influenza model with cross-immunity and no quarantine class.

PubMed

Chung, K W; Lui, Roger

2016-12-01

The question about whether a periodic solution can exists for a given epidemiological model is a complicated one and has a long history (Hethcote and Levin, Applied math. ecology, biomathematics, vol 18. Springer, Berlin, pp 193-211, 1989). For influenza models, it is well known that a periodic solution can exists for a single-strain model with periodic contact rate (Aron and Schwartz, J Math Biol 110:665-679, 1984; Kuznetsov and Piccardi, J Math Biol 32:109-121, 1994), or a multiple-strain model with cross-immunity and quarantine class or age-structure (Nuño et al., Mathematical epidemiology. Lecture notes in mathematics, vol 1945. Springer, Berlin, 2008, chapter 13). In this paper, we prove the local asymptotic stability of the interior steady-state of a two-strain influenza model with sufficiently close cross-immunity and no quarantine class or age-structure. We also show that if the cross-immunity between two strains are far apart; then it is possible for the interior steady-state to lose its stability and bifurcation of periodic solutions can occur. Our results extend those obtained by Nuño et.al. (SIAM J Appl Math 65:964-982, 2005). This problem is important because understanding the reasons behind periodic outbreaks of seasonal flu is an important issue in public health.

A two-level structure for advanced space power system automation

NASA Technical Reports Server (NTRS)

Loparo, Kenneth A.; Chankong, Vira

1990-01-01

The tasks to be carried out during the three-year project period are: (1) performing extensive simulation using existing mathematical models to build a specific knowledge base of the operating characteristics of space power systems; (2) carrying out the necessary basic research on hierarchical control structures, real-time quantitative algorithms, and decision-theoretic procedures; (3) developing a two-level automation scheme for fault detection and diagnosis, maintenance and restoration scheduling, and load management; and (4) testing and demonstration. The outlines of the proposed system structure that served as a master plan for this project, work accomplished, concluding remarks, and ideas for future work are also addressed.

A Case Study of the Attitudes and Preparedness of a Group of Secondary Mathematics Teachers towards Statistics

ERIC Educational Resources Information Center

Marshman, Margaret; Dunn, Peter K.; McDougall, Robert; Wiegand, Aaron

2015-01-01

The new secondary Australian mathematics curricula have more statistics than the existing Queensland senior mathematics curricula. This paper discusses the attitudes to, and preparedness for, aspects of the implementation of the Australian Senior Mathematics Curricula within a group of Sunshine Coast (Queensland) mathematics educators. We found on…

A nonlinear vibration isolator achieving high-static-low-dynamic stiffness and tunable anti-resonance frequency band

NASA Astrophysics Data System (ADS)

Sun, Xiuting; Jing, Xingjian

2016-12-01

This study investigates theoretically and experimentally a vibration isolator constructed by an n-layer Scissor-Like Structure (SLS), focusing on the analysis and design of nonlinear stiffness and damping characteristics for advantageous isolation performance in both orthogonal directions. With the mathematical modeling, the influence incurred by different structural parameters on system isolation performance is studied. It is shown that, (a) nonlinear high-static-low-dynamic stiffness and damping characteristics can be seen such that the system can achieve good isolation performance in both directions, (b) an anti-resonance frequency band exists due to the coupling effect between the linear and nonlinear stiffness in the two orthogonal directions within the structure, and (c) all these performances are designable with several structural parameters. The advantages of the proposed system are shown through comparisons with an existing quasi-zero-stiffness vibration isolator (QZS-VI) and a traditional mass-spring-damper vibration isolator (MSD-VI), and further validated by experimental results.

Multiscale structure in eco-evolutionary dynamics

NASA Astrophysics Data System (ADS)

Stacey, Blake C.

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, "more is different," and I address this from several perspectives. Spatial host--consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory. The idea of natural selection "acting at multiple levels" has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.

The correlation structure of several popular pseudorandom number generators

NASA Technical Reports Server (NTRS)

Neuman, F.; Merrick, R.; Martin, C. F.

1973-01-01

One of the desirable properties of a pseudorandom number generator is that the sequence of numbers it generates should have very low autocorrelation for all shifts except for zero shift and those that are multiples of its cycle length. Due to the simple methods of constructing random numbers, the ideal is often not quite fulfilled. A simple method of examining any random generator for previously unsuspected regularities is discussed. Once they are discovered it is often easy to derive the mathematical relationships, which describe the mathematical relationships, which describe the regular behavior. As examples, it is shown that high correlation exists in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle lengths.

Pre-Service Teachers' Free and Structured Mathematical Problem Posing

ERIC Educational Resources Information Center

Silber, Steven; Cai, Jinfa

2017-01-01

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

On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2016-03-01

Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.

Collegiate Mathematics Teaching: An Unexamined Practice

ERIC Educational Resources Information Center

Speer, Natasha M.; Smith, John P., III; Horvath, Aladar

2010-01-01

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…

What Students Say about Their Mathematical Thinking When They Listen

ERIC Educational Resources Information Center

Kosko, Karl W.

2014-01-01

Mathematical listening is an important aspect of mathematical communication. Yet there are relatively few examinations of this phenomenon. Further, existing studies of students' mathematical listening come from observational data, lacking the student perspective. This study examined student replies to an open-response question regarding what…

Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics

ERIC Educational Resources Information Center

Oehrtman, Michael; Lawson, Anton E.

2008-01-01

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and…

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

ERIC Educational Resources Information Center

Lee, Hye Jung; Kim, Jihyun

2016-01-01

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

Developing an Actuarial Track Utilizing Existing Resources

ERIC Educational Resources Information Center

Rodgers, Kathy V.; Sarol, Yalçin

2014-01-01

Students earning a degree in mathematics often seek information on how to apply their mathematical knowledge. One option is to follow a curriculum with an actuarial emphasis designed to prepare students as an applied mathematician in the actuarial field. By developing only two new courses and utilizing existing courses for Validation by…

Scientific Visualization in Mathematics and Science Teaching.

ERIC Educational Resources Information Center

Thomas, David A., Ed.

Science and mathematics educators are expected to use existing educational technologies effectively and to keep informed about emerging technologies that might become important educational tools in the not-so-distant future. This monograph offers some help in that regard by highlighting a number of existing and emerging educational technologies.…

Building Knowledge Structures by Testing Helps Children with Mathematical Learning Difficulty

ERIC Educational Resources Information Center

Zhang, Yiyun; Zhou, Xinlin

2016-01-01

Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by…

Hierarchical Safety Cases

NASA Technical Reports Server (NTRS)

Denney, Ewen W.; Whiteside, Iain J.

2012-01-01

We introduce hierarchical safety cases (or hicases) as a technique to overcome some of the difficulties that arise creating and maintaining industrial-size safety cases. Our approach extends the existing Goal Structuring Notation with abstraction structures, which allow the safety case to be viewed at different levels of detail. We motivate hicases and give a mathematical account of them as well as an intuition, relating them to other related concepts. We give a second definition which corresponds closely to our implementation of hicases in the AdvoCATE Assurance Case Editor and prove the correspondence between the two. Finally, we suggest areas of future enhancement, both theoretically and practically.

eText, Mathematics, and Students with Visual Impairments: "What Teachers Need to Know"

ERIC Educational Resources Information Center

Bouck, Emily C.; Meyer, Nancy K.

2012-01-01

Mathematics is an important educational component for students with visual impairments, and technology to support the access to and success of students with visual impairments in mathematics is essential. However, little research exists. This particular paper explores one aspect of technology and mathematics education for students with visual…

Prospective Elementary Teachers' Perceptions of Gender Differences in Children's Attitudes toward Mathematics

ERIC Educational Resources Information Center

Schwartz, Catherine S.; Sinicrope, Rose

2013-01-01

Prospective elementary teachers hold preconceived ideas about elementary school students' attitudes toward mathematics. We found that there exists a gender bias with prospective teachers expecting girls to have negative attitudes toward mathematics and boys more likely to have positive attitudes toward mathematics. We found that these…

Student-Teachers in Higher Education Institutions' (HEIs) Emotional Intelligence and Mathematical Competencies

ERIC Educational Resources Information Center

Eustaquio, William Rafael

2015-01-01

As manifested by various studies conducted, the present state of Mathematics education in the teaching-learning process is relatively declining and the existing effort to identify emotional intelligence and mathematics competencies of Mathematics major student-teachers at Higher Education Institutions in Isabela is an attempt to help alleviate the…

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

ERIC Educational Resources Information Center

Niss, Martin

2017-01-01

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

Behind the Numbers: The Preliminary Findings of a Mixed Methods Study Investigating the Existence of Mathematics Anxiety among Mature Students

ERIC Educational Resources Information Center

Ryan, Maria; Fitzmaurice, Olivia

2017-01-01

Admitting that one is "no good at mathematics" or "hates mathematics" is a common admission among student cohorts. For mature students who harbour a strong dislike of mathematics, these feelings can be exacerbated when they are faced with having to do an obligatory service mathematics module as part of a programme of study. For…

Infusing Alcohol and Drug Prevention with Existing Classroom Study Units: Mathematics.

ERIC Educational Resources Information Center

Valencia Community Coll., Orlando, FL.

This curriculum module, one of seven in "Infusion Project", offers information and lessons on drug use prevention for integration into an existing seventh-grade middle school mathematics curriculum. The module, based on a type of interactive learning called infusion learning, contains eight lessons each providing objectives, a list of…

Social activity method (SAM): A fractal language for mathematics

NASA Astrophysics Data System (ADS)

Dowling, Paul

2013-09-01

In this paper I shall present and develop my organisational language, social activity method (SAM), and illustrate some of its applications. I shall introduce a new scheme for modes of recontextualisation that enables the analysis of the ways in which one activity - which might be school mathematics or social research or any empirically observed regularity of practice - recontextualises the practice of another and I shall also present, deploy, and develop an existing scheme - domains of action - in an analysis of school mathematics examination papers and in the structuring of what I refer to as the esoteric domain. This domain is here conceived as a hybrid domain of, first, linguistic and extralinguistic resources that are unambiguously mathematical in terms of both expression and content and, second, pedagogic theory - often tacit - that enables the mathematical gaze onto other practices and so recontextualises them. A second and more general theme that runs through the paper is the claim that there is nothing that is beyond semiosis, that there is nothing to which we have direct access, unmediated by interpretation. This state of affairs has implications for mathematics education. Specifically, insofar as an individual's mathematical semiotic system is under continuous development - the curriculum never being graspable all at once - understanding - as a stable semiotic moment - of any aspect or object of mathematics is always localised to the individual and is at best transient, and the sequencing of such moments may well also be more individualised than consistent in some correspondence with the sequencing of the curriculum. This being the case, a concentration on understanding as a goal may well serve to inhibit the pragmatic acquisition and deployment of mathematical technologies, which should be the principal aim of mathematics teaching and learning. The paper is primarily concerned with mathematics education. SAM, however, is a language that is available for recruiting and deploying in potentially any context as I have attempted to illustrate with some of the secondary illustrations in the text.

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

NASA Astrophysics Data System (ADS)

Peshkov, Ilya; Pavelka, Michal; Romenski, Evgeniy; Grmela, Miroslav

2018-01-01

Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

Mitigating the Mathematical Knowledge Gap between High School and First Year University Chemical Engineering Mathematics Course

ERIC Educational Resources Information Center

Basitere, Moses; Ivala, Eunice

2015-01-01

This paper reports on a study carried out at a University of Technology, South Africa, aimed at identifying the existence of the mathematical knowledge gap and evaluating the intervention designed to bridge the knowledge gap amongst students studying first year mathematics at the Chemical Engineering Extended Curriculum Program (ECP). In this…

Removing Visual Bias in Filament Identification: A New Goodness-of-fit Measure

NASA Astrophysics Data System (ADS)

Green, C.-E.; Cunningham, M. R.; Dawson, J. R.; Jones, P. A.; Novak, G.; Fissel, L. M.

2017-05-01

Different combinations of input parameters to filament identification algorithms, such as disperse and filfinder, produce numerous different output skeletons. The skeletons are a one-pixel-wide representation of the filamentary structure in the original input image. However, these output skeletons may not necessarily be a good representation of that structure. Furthermore, a given skeleton may not be as good of a representation as another. Previously, there has been no mathematical “goodness-of-fit” measure to compare output skeletons to the input image. Thus far this has been assessed visually, introducing visual bias. We propose the application of the mean structural similarity index (MSSIM) as a mathematical goodness-of-fit measure. We describe the use of the MSSIM to find the output skeletons that are the most mathematically similar to the original input image (the optimum, or “best,” skeletons) for a given algorithm, and independently of the algorithm. This measure makes possible systematic parameter studies, aimed at finding the subset of input parameter values returning optimum skeletons. It can also be applied to the output of non-skeleton-based filament identification algorithms, such as the Hessian matrix method. The MSSIM removes the need to visually examine thousands of output skeletons, and eliminates the visual bias, subjectivity, and limited reproducibility inherent in that process, representing a major improvement upon existing techniques. Importantly, it also allows further automation in the post-processing of output skeletons, which is crucial in this era of “big data.”

USSR and Eastern Europe Scientific Abstracts, Physics and Mathematics, Number 39

DTIC Science & Technology

1978-01-17

examination of a monoclinic single crystal has revealed a U022+ iön, and helical polyphosphate chains with six PO4 tetrahedra per link. Corrugated uranyl...mean mass temperature and local Nusselt number. Figures 5; references 13: 3 Russian, 10 Western. USSR UDC 535.334 DETERMINATION OF THE PARAMETERS...Nuclear Research [Abstract] The theory of pion condensation predicts the existence of super- dense nuclei, on the basis of the structure of the

Finiteness of corner vortices

NASA Astrophysics Data System (ADS)

Kalita, Jiten C.; Biswas, Sougata; Panda, Swapnendu

2018-04-01

Till date, the sequence of vortices present in the solid corners of steady internal viscous incompressible flows was thought to be infinite. However, the already existing and most recent geometric theories on incompressible viscous flows that express vortical structures in terms of critical points in bounded domains indicate a strong opposition to this notion of infiniteness. In this study, we endeavor to bridge the gap between the two opposing stream of thoughts by diagnosing the assumptions of the existing theorems on such vortices. We provide our own set of proofs for establishing the finiteness of the sequence of corner vortices by making use of the continuum hypothesis and Kolmogorov scale, which guarantee a nonzero scale for the smallest vortex structure possible in incompressible viscous flows. We point out that the notion of infiniteness resulting from discrete self-similarity of the vortex structures is not physically feasible. Making use of some elementary concepts of mathematical analysis and our own construction of diametric disks, we conclude that the sequence of corner vortices is finite.

A discrete structure of the brain waves.

NASA Astrophysics Data System (ADS)

Dabaghian, Yuri; Perotti, Luca; oscillons in biological rhythms Collaboration; physics of biological rhythms Team

A physiological interpretation of the biological rhythms, e.g., of the local field potentials (LFP) depends on the mathematical approaches used for the analysis. Most existing mathematical methods are based on decomposing the signal into a set of ``primitives,'' e.g., sinusoidal harmonics, and correlating them with different cognitive and behavioral phenomena. A common feature of all these methods is that the decomposition semantics is presumed from the onset, and the goal of the subsequent analysis reduces merely to identifying the combination that best reproduces the original signal. We propose a fundamentally new method in which the decomposition components are discovered empirically, and demonstrate that it is more flexible and more sensitive to the signal's structure than the standard Fourier method. Applying this method to the rodent LFP signals reveals a fundamentally new structure of these ``brain waves.'' In particular, our results suggest that the LFP oscillations consist of a superposition of a small, discrete set of frequency modulated oscillatory processes, which we call ``oscillons''. Since these structures are discovered empirically, we hypothesize that they may capture the signal's actual physical structure, i.e., the pattern of synchronous activity in neuronal ensembles. Proving this hypothesis will help to advance our principal understanding of the neuronal synchronization mechanisms and reveal new structure within the LFPs and other biological oscillations. NSF 1422438 Grant, Houston Bioinformatics Endowment Fund.

Building Pre-Service Teacher's Mathematical Knowledge for Teaching of High School Geometry

ERIC Educational Resources Information Center

Somayajulu, Ravi Bhamidipati

2012-01-01

There were two primary goals of the research conducted for this dissertation study. Firstly, to fill a gap in the research literature and begin a discussion around secondary pre-service teachers Mathematical Knowledge for Teaching (MKT) as it pertains to geometry. Although a multitude of studies exist for elementary teachers' MKT, few exist at the…

The Popularization of China's Higher Education and Its Influence on University Mathematics Education

ERIC Educational Resources Information Center

Jing, Tang

2007-01-01

This paper introduces the current situation of the popular Chinese university education, points out the impact of popularized Chinese higher education on its university mathematics education, and presents the actualities and existing problems of university mathematics education research in China.

Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.

2011-01-01

This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…

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

ERIC Educational Resources Information Center

Melius, Joyce

2012-01-01

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

Findings and Implications from the Mathematics Support Center at Cornell University.

ERIC Educational Resources Information Center

Rosamond, Frances

The nature and use of the Cornell Mathematics Support Center (MSC) is discussed. It is viewed as significantly different from other existing support programs in that it is part of the Department of Mathematics and offers encouragement and support to any interested student, no matter what that pupil's mathematics level is. The MSC is based on the…

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

Bradonjic, Milan; Hagberg, Aric; Hengartner, Nick

We analyze component evolution in general random intersection graphs (RIGs) and give conditions on existence and uniqueness of the giant component. Our techniques generalize the existing methods for analysis on component evolution in RIGs. That is, we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts from the study on component evolution in Erdos-Renyi graphs. The main challenge becomes from the underlying structure of RIGs, when the number of offsprings follows a binomial distribution with a different number of nodes andmore » different rate at each step during the evolution. RIGs can be interpreted as a model for large randomly formed non-metric data sets. Besides the mathematical analysis on component evolution, which we provide in this work, we perceive RIGs as an important random structure which has already found applications in social networks, epidemic networks, blog readership, or wireless sensor networks.« less

Statistical Properties of Lorenz-like Flows, Recent Developments and Perspectives

NASA Astrophysics Data System (ADS)

Araujo, Vitor; Galatolo, Stefano; Pacifico, Maria José

We comment on the mathematical results about the statistical behavior of Lorenz equations and its attractor, and more generally on the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer-assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statistical behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated with the existence of physical measures: in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors: (1) there exists an invariant foliation whose leaves are forward contracted by the flow (and further properties which are useful to understand the statistical properties of the dynamics); (2) there exists a positive Lyapunov exponent at every orbit; (3) there is a unique physical measure whose support is the whole attractor and which is the equilibrium state with respect to the center-unstable Jacobian; (4) this measure is exact dimensional; (5) the induced measure on a suitable family of cross-sections has exponential decay of correlations for Lipschitz observables with respect to a suitable Poincaré return time map; (6) the hitting time associated to Lorenz-like attractors satisfy a logarithm law; (7) the geometric Lorenz flow satisfies the Almost Sure Invariance Principle (ASIP) and the Central Limit Theorem (CLT); (8) the rate of decay of large deviations for the volume measure on the ergodic basin of a geometric Lorenz attractor is exponential; (9) a class of geometric Lorenz flows exhibits robust exponential decay of correlations; (10) all geometric Lorenz flows are rapidly mixing and their time-1 map satisfies both ASIP and CLT.

Towards Understanding the Origins of Children's Difficulties in Mathematics Learning

ERIC Educational Resources Information Center

Mulligan, Joanne

2011-01-01

Contemporary research from a psychology of mathematics education perspective has turned increasing attention to the structural development of mathematics as an explanation for the wide differences in mathematical competence shown upon school entry and in the early school years. Patterning, multiplicative reasoning and spatial structuring are three…

Bottle Caps as Prekindergarten Mathematical Tools

ERIC Educational Resources Information Center

Raisor, Jill M.; Hudson, Rick A.

2018-01-01

Early childhood provides a time of crucial growth in all developmental domains. Prekindergarten is an optimal time for young children to use objects of play as a medium to explore new cognitive concepts, including mathematical structure. Mathematical structure plays an important role in providing students a means to reason about mathematics,…

Colliding with the Speed of Light, Using Low-Energy Photon-Photon Collision Study the Nature of Matter and the universe

NASA Astrophysics Data System (ADS)

Zhang, Meggie

2013-03-01

Our research discovered logical inconsistence in physics and mathematics. Through reviewing the entire history of physics and mathematics we gained new understanding about our earlier assumptions, which led to a new interpretation of the wave function and quantum physics. We found the existing experimental data supported a 4-dimensional fractal structure of matter and the universe, we found the formation of wave, matter and the universe through the same process started from a single particle, and the process itself is a fractal that contributed to the diversity of matter. We also found physical evidence supporting a not-continuous fractal space structure. The new understanding also led to a reinterpretation of nuclear collision theories, based on this we succeeded a room-temperature low-energy photon-photon collision (RT-LE-PPC), this method allowed us to observe a topological disconnected fractal structure and succeeded a simulation of the formation of matter and the universe which provided evidences for the nature of light and matter and led to a quantum structure interpretation, and we found the formation of the universe started from two particles. However this work cannot be understood with current physics theories due to the logical problems in the current physics theories.

Probability Explorations in a Multicultural Context

ERIC Educational Resources Information Center

Naresh, Nirmala; Harper, Suzanne R.; Keiser, Jane M.; Krumpe, Norm

2014-01-01

Mathematical ideas exist and develop in many different cultures. From this multicultural perspective, teachers can use a variety of approaches to acknowledge the role of culture in the teaching and learning of mathematics. Curricular materials that "emphasize both the mathematical and sociocultural aspects" not only help teachers achieve…

Equity Implications for Mathematics Learning Outcomes

ERIC Educational Resources Information Center

Reznichenko, Nataliya

2013-01-01

The call for "mathematics for all" reaffirms the belief that all students should have equal access, equal educational experiences, and equal educational outcomes. Existing gap in students' mathematics achievement have long been coupled with the demographic categories of race and ethnicity, culture and language, SES and social class,…

Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling.

PubMed

Powathil, Gibin G; Swat, Maciej; Chaplain, Mark A J

2015-02-01

The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. Copyright © 2014 Elsevier Ltd. All rights reserved.

The digital implementation of control compensators: The coefficient wordlength issue

NASA Technical Reports Server (NTRS)

Moroney, P.; Willsky, A. S.; Houpt, P. K.

1979-01-01

There exists a number of mathematical procedures for designing discrete-time compensators. However, the digital implementation of these designs, with a microprocessor for example, has not received nearly as thorough an investigation. The finite-precision nature of the digital hardware makes it necessary to choose an algorithm (computational structure) that will perform 'well-enough' with regard to the initial objectives of the design. This paper describes a procedure for estimating the required fixed-point coefficient wordlength for any given computational structure for the implementation of a single-input single-output LOG design. The results are compared to the actual number of bits necessary to achieve a specified performance index.

A review on principles, theory and practices of 2D-QSAR.

PubMed

Roy, Kunal; Das, Rudra Narayan

2014-01-01

The central axiom of science purports the explanation of every natural phenomenon using all possible logics coming from pure as well as mixed scientific background. The quantitative structure-activity relationship (QSAR) analysis is a study correlating the behavioral manifestation of compounds with their structures employing the interdisciplinary knowledge of chemistry, mathematics, biology as well as physics. Several studies have attempted to mathematically correlate the chemistry and property (physicochemical/ biological/toxicological) of molecules using various computationally or experimentally derived quantitative parameters termed as descriptors. The dimensionality of the descriptors depends on the type of algorithm employed and defines the nature of QSAR analysis. The most interesting feature of predictive QSAR models is that the behavior of any new or even hypothesized molecule can be predicted by the use of the mathematical equations. The phrase "2D-QSAR" signifies development of QSAR models using 2D-descriptors. Such predictor variables are the most widely practised ones because of their simple and direct mathematical algorithmic nature involving no time consuming energy computations and having reproducible operability. 2D-descriptors have a deluge of contributions in extracting chemical attributes and they are also capable of representing the 3D molecular features to some extent; although in no case they should be considered as the ultimate one, since they often suffer from the problems of intercorrelation, insufficient chemical information as well as lack of interpretation. However, by following rational approaches, novel 2D-descriptors may be developed to obviate various existing problems giving potential 2D-QSAR equations, thereby solving the innumerable chemical mysteries still unexplored.

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic

ERIC Educational Resources Information Center

Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.

2016-01-01

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

DOEpatents

Van Benthem, Mark H.; Keenan, Michael R.

2008-11-11

A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

New symmetries and ghost structure of covariant string theories

NASA Astrophysics Data System (ADS)

Neveu, A.; Nicolai, H.; West, P.

1986-02-01

It is shown that there exists an infinite set of new symmetries of the previously given covariant string formulations. These symmetries have themselves an infinite set of hidden local symmetries and so on. A new physically equivalent further extended string action is given in which the infinite set of symmetries is most easily displayed. A quantization involving gauge fixing and ghosts of the various covariant string actions is given. permanent address: Kings College, Mathematics Department, London WC2R 2LS, UK.

Error Correcting Codes and Related Designs

DTIC Science & Technology

1990-09-30

Theory, IT-37 (1991), 1222-1224. 6. Codes and designs, existence and uniqueness, Discrete Math ., to appear. 7. (with R. Brualdi and N. Cai), Orphan...structure of the first order Reed-Muller codes, Discrete Math ., to appear. 8. (with J. H. Conway and N.J.A. Sloane), The binary self-dual codes of length up...18, 1988. 4. "Codes and Designs," Mathematics Colloquium, Technion, Haifa, Israel, March 6, 1989. 5. "On the Covering Radius of Codes," Discrete Math . Group

On the Social Nature of Mathematical Reasoning

ERIC Educational Resources Information Center

Roth, Wolff-Michael

2016-01-01

It has become a truism to state that mathematical knowledge or "meaning" and the norms and practices of (school) mathematical communities are negotiated and socially constructed before individuals construct (internalize) them for themselves. In this study I suggest that the social in existing conceptualizations is based on a trivial…

ICT and Constructivist Strategies Instruction for Science and Mathematics Education

ERIC Educational Resources Information Center

Kong, Ng Wai; Lai, Kong Sow

2005-01-01

Concept learning in science and mathematics had often times been taught based on assumptions of alternative concepts or even in some instances based on misconceptions. Some educational researchers favour a constructivist approach in teaching science and mathematics. The constructivist literature existing makes use of alternative conceptions as…

Teachers and Textbooks: On Statistical Definitions in Senior Secondary Mathematics

ERIC Educational Resources Information Center

Dunn, Peter K.; Marshman, Margaret; McDougall, Robert; Wiegand, Aaron

2015-01-01

The new "Australian Senior Secondary Curriculum: Mathematics" contains more statistics than the existing Australian Curricula. This case study examines how a group of Queensland mathematics teachers define the word "statistics" and five statistical terms from the new curricula. These definitions are compared to those used in…

The Object Metaphor and Synecdoche in Mathematics Classroom Discourse

ERIC Educational Resources Information Center

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

2010-01-01

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

Designing Cognitive Complexity in Mathematical Problem-Solving Items

ERIC Educational Resources Information Center

Daniel, Robert C.; Embretson, Susan E.

2010-01-01

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

Teaching and Learning Mathematics: Translating Research for Elementary School Teachers

ERIC Educational Resources Information Center

Lester, Frank

2010-01-01

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

The Relation between Patterning, Executive Function, and Mathematics

ERIC Educational Resources Information Center

Schmerold, Katrina Lea

2015-01-01

Patterning, or the ability to understand patterns, is a skill commonly taught to young children as part of school mathematics curricula. While a number of studies have demonstrated that patterning is beneficial for young children acquiring mathematical skills, little research exists that examines the cognitive components of the skill. It seems…

Improving Elementary Mathematics and Science Teaching and Learning: Lessons from a School-University Partnership

ERIC Educational Resources Information Center

Norman, Patricia J.; Nordine, Jeffrey

2016-01-01

The challenges of teaching elementary mathematics and science, particularly in urban settings, have been well documented. While evidence exists that sustained professional development in mathematics and science can promote inquiry-oriented instruction and bolster student achievement, little has been written about the particular challenges…

Preservice to Inservice: Does Mathematics Anxiety Change with Teaching Experience?

ERIC Educational Resources Information Center

Gresham, Gina

2018-01-01

Inservice teachers, participants in a prior study on mathematics anxiety, were revisited to determine whether their levels of mathematics anxiety still existed and/or continued to change after 5 years teaching experience. A 98-item Likert-type survey, informal discussions, informal interviews, and questionnaire-guided narrative interviews were…

Seventies, Eighties, Nineties, Noughties.... a Sequence of Concerns

ERIC Educational Resources Information Center

Jackson, Elizabeth

2007-01-01

This paper outlines small scale research regarding mathematics anxiety and potential links to confidence and mathematics subject knowledge for primary teacher education (QTS) students in a HE institution, where the author is a Senior Lecturer in Primary Mathematics Education. The purpose is to establish the existence of such anxiety and related…

Teaching and Learning Mathematics: Translating Research for Secondary School Teachers

ERIC Educational Resources Information Center

Lester, Frank

2010-01-01

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…

Are Mathematics Problems a Problem for Women and Girls?

ERIC Educational Resources Information Center

Schonberger, Ann K.

The primary questions investigated are: Is it true that males excel in mathematical problem solving and, if so, when does this superiority develop? An examination of recent research showed that sex-related differences did exist, although small, even after controlling for mathematics background. Differences appeared in early adolescence and were…

Attending to Precision with Secret Messages

ERIC Educational Resources Information Center

Starling, Courtney; Whitacre, Ian

2016-01-01

Mathematics is a language that is characterized by words and symbols that have precise definitions. Many opportunities exist for miscommunication in mathematics if the words and symbols are interpreted incorrectly or used in imprecise ways. In fact, it is found that imprecision is a common source of mathematical disagreements and misunderstandings…

Connectivity of glass structure. Oxygen number

NASA Astrophysics Data System (ADS)

Medvedev, E. F.; Min'ko, N. I.

2018-03-01

With reference to mathematics, crystal chemistry and chemical technology of synthesis of glass structures in the solution (sol-gel technology), the paper is devoted to the study of the degree of connectivity of a silicon-oxygen backbone (fSi) and the oxygen number (R) [1]. It reveals logical contradictions and uncertainty of mathematical expressions of parameters, since fSi is not similar to the oxygen number. The connectivity of any structure is a result of various types of bonds: ion-covalent, donor-acceptor, hydrogen bonds, etc. Besides, alongside with SiO2, many glass compositions contain other glass-forming elements due to tetrahedral sites thus formed. The connectivity function of a glassy network with any set of glass-forming elements is roughly ensured by connectivity factor Y [2], which has monovalent elements loosening a glassy network. The paper considers the existence of various structural motives in hydrogen-impermeable glasses containing B2O3, Al2O3, PbO, Na2O, K2O and rare-earth elements. Hence, it also describes gradual nucleation, change of crystal forms, and structure consolidation in the process of substance intake from a matrix solution according to sol-gel technology. The crystal form varied from two-dimensional plates to three-dimensional and dendritical ones [3]. Alternative parameters, such as the oxygen number (O) and the structure connectivity factor (Y), were suggested. Functional dependence of Y=f(O) to forecast the generated structures was obtained for two- and multicomponent glass compositions.

Structuring an Undergraduate Mathematics Seminar Dealing with Options and Hedging

ERIC Educational Resources Information Center

Prevot, K. J.

2006-01-01

Offering mathematics majors the opportunity to engage in current, real-world applications can be an important enhancement to their undergraduate course curriculum. Instead of focusing on the traditional topic areas in pure and/or applied mathematics, one may structure a seminar course for senior mathematics majors by concentrating on a specific…

More than Motivation: The Combined Effects of Critical Motivational Variables on Middle School Mathematics Achievement

ERIC Educational Resources Information Center

Middleton, James A.

2013-01-01

The role of mathematical interest, identity, utility, self-efficacy, and effort was examined as a set of interdependent factors leading to students' mathematics achievement. A structural equations model, testing a hypothesized structure of motivation variables and their impact on middle school mathematics achievement was developed utilizing the…

Updates on attention-deficit/hyperactivity disorder and learning disorders.

PubMed

Semrud-Clikeman, Margaret; Bledsoe, Jesse

2011-10-01

The relationship of attention-deficit/hyperactivity disorder (ADHD) to learning disorders was reviewed and included reading disability, mathematics learning disability, and nonverbal learning disability. Genetic, neuroimaging, and neuropsychological functioning were examined for each disorder, along with a discussion of any existing literature when ADHD co-occurred with the disorder. All the disorders were found to frequently co-occur with ADHD. A review of the underlying neuroanatomic and neurofunctional data found specific structures that frequently co-occur in these disorders with others that are specific to the individual diagnosis. Aberrations in structure and/or function were found for the caudate, corpus callosum, and cerebellum, making these structures sensitive for the disorder but not specific. Suggestions for future research, particularly in relation to intervention, are provided.

A necessary condition for dispersal driven growth of populations with discrete patch dynamics.

PubMed

Guiver, Chris; Packman, David; Townley, Stuart

2017-07-07

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Predicted carbonation of existing concrete building based on the Indonesian tropical micro-climate

NASA Astrophysics Data System (ADS)

Hilmy, M.; Prabowo, H.

2018-03-01

This paper is aimed to predict the carbonation progress based on the previous mathematical model. It shortly explains the nature of carbonation including the processes and effects. Environmental humidity and temperature of the existing concrete building are measured and compared to data from local Meteorological, Climatological, and Geophysical Agency. The data gained are expressed in the form of annual hygrothermal values which will use as the input parameter in carbonation model. The physical properties of the observed building such as its location, dimensions, and structural material used are quantified. These data then utilized as an important input parameter for carbonation coefficients. The relationships between relative humidity and the rate of carbonation established. The results can provide a basis for repair and maintenance of existing concrete buildings and the sake of service life analysis of them.

The (kinetic) theory of active particles applied to learning dynamics. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

NASA Astrophysics Data System (ADS)

Nieto, J.

2016-03-01

The learning phenomena, their complexity, concepts, structure, suitable theories and models, have been extensively treated in the mathematical literature in the last century, and [4] contains a very good introduction to the literature describing the many approaches and lines of research developed about them. Two main schools have to be pointed out [5] in order to understand the two -not exclusive- kinds of existing models: the stimulus sampling models and the stochastic learning models. Also [6] should be mentioned as a survey where two methods of learning are pointed out, the cognitive and the social, and where the knowledge looks like a mathematical unknown. Finally, as the authors do, we refer to the works [9,10], where the concept of population thinking was introduced and which motivate the game theory rules as a tool (both included in [4] to develop their theory) and [7], where the ideas of developing a mathematical kinetic theory of perception and learning were proposed.

Using emergent order to shape a space society

NASA Technical Reports Server (NTRS)

Graps, Amara L.

1993-01-01

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Structure and Typical Profiles of Elementary Teacher Students' View of Mathematics

ERIC Educational Resources Information Center

Hannula, Markku S.; Kaasila, Raimo; Laine, Anu; Pehkonen, Erkki

2005-01-01

The elementary school teachers' view of mathematics is important because it will influence the way they will teach mathematics. Based on a survey study in three Finnish universities we explored the structure of student teachers view of mathematics and also the different belief profiles that they had. The core of student teachers' view consisted of…

Equilibrium econophysics: A unified formalism for neoclassical economics and equilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Sousa, Tânia; Domingos, Tiago

2006-11-01

We develop a unified conceptual and mathematical structure for equilibrium econophysics, i.e., the use of concepts and tools of equilibrium thermodynamics in neoclassical microeconomics and vice versa. Within this conceptual structure the results obtained in microeconomic theory are: (1) the definition of irreversibility in economic behavior; (2) the clarification that the Engel curve and the offer curve are not descriptions of real processes dictated by the maximization of utility at constant endowment; (3) the derivation of a relation between elasticities proving that economic elasticities are not all independent; (4) the proof that Giffen goods do not exist in a stable equilibrium; (5) the derivation that ‘economic integrability’ is equivalent to the generalized Le Chatelier principle and (6) the definition of a first order phase transition, i.e., a transition between separate points in the utility function. In thermodynamics the results obtained are: (1) a relation between the non-dimensional isothermal and adiabatic compressibilities and the increase or decrease in the thermodynamic potentials; (2) the distinction between mathematical integrability and optimization behavior and (3) the generalization of the Clapeyron equation.

Transforming Teacher Preparation to Ensure Long-Term Improvement in STEM Teaching

ERIC Educational Resources Information Center

Hiebert, James

2013-01-01

An alternative mathematics preparation program for K-8 teachers is described as an existence proof that steadily increasing effectiveness of STEM (science, technology, engineering, and mathematics) preparation is possible. The program is based on treating every lesson in each of five mathematics content and methods courses as objects of study.…

Stories from the Classroom: The Developing Beliefs and Practices of Beginning Primary Mathematics Teachers

ERIC Educational Resources Information Center

Brady, Kathy

2012-01-01

This study examines the developing beliefs and practices of six beginning primary teachers. Their accounts reveal practices indicative of contemporary approaches to teaching and learning in mathematics. Additionally, a consistency appears to exist between the beliefs and practices of the beginning teachers, and the ideals for mathematics teaching…

Use of Open-Ended Problems in Mathematics Classroom. Research Report 176.

ERIC Educational Resources Information Center

Pehkonen, Erkki, Ed.

During the years 1993-96, there has existed an active discussion group entitled "Using Open-Ended Problems in Mathematics" as a part of the scientific program of the Psychology of Mathematics Education (PME) conference. This report contains revised versions of presentations given in the discussion group. Since the PME is an international…

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

ERIC Educational Resources Information Center

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to…

A Reconceptualized Framework for "Opportunity to Learn" in School Mathematics

ERIC Educational Resources Information Center

Walkowiak, Temple A.; Pinter, Holly H.; Berry, Robert Q.

2017-01-01

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

Utilizing Marzano's Summarizing and Note Taking Strategies on Seventh Grade Students' Mathematics Performance

ERIC Educational Resources Information Center

Jeanmarie-Gardner, Charmaine

2013-01-01

A quasi-experimental research study was conducted that investigated the academic impact of utilizing Marzano's summarizing and note taking strategies on mathematic achievement. A sample of seventh graders from a middle school located on Long Island's North Shore was tested to determine whether significant differences existed in mathematic test…

Oral Assessment in Mathematics: Implementation and Outcomes

ERIC Educational Resources Information Center

Iannone, P.; Simpson, A.

2012-01-01

In this article, we report the planning and implementation of an oral assessment component in a first-year pure mathematics module of a degree course in mathematics. Our aim was to examine potential barriers to using oral assessments, explore the advantages and disadvantages compared to existing common assessment methods and document the outcomes…

Relationship between Pedagogical Strategies and Teachers' Content Knowledge of Mathematics

ERIC Educational Resources Information Center

Kanyongo, Gibbs Y.; Brown, Launcelot I.

2013-01-01

This study employed regression analysis to investigate the relationship between primary school teachers' pedagogical practices and their knowledge of mathematics. The sample composed of 606 Grade 6 mathematics teachers in Namibia, i.e. 304 (50.2%) males and 302 (49.8%) females. The study utilized existing questionnaire data collected by the…

Assessing Journal Quality in Mathematics Education

ERIC Educational Resources Information Center

Nivens, Ryan Andrew; Otten, Samuel

2017-01-01

In this Research Commentary, we describe 3 journal metrics--the Web of Science's Impact Factor, Scopus's SCImago Journal Rank, and Google Scholar Metrics' h5-index--and compile the rankings (if they exist) for 69 mathematics education journals. We then discuss 2 paths that the mathematics education community should consider with regard to these…

Creativity, Mathematizing, and Didactizing: Leen Streefland's Work Continues

ERIC Educational Resources Information Center

Presmeg, Norma

2003-01-01

This reaction to the papers in this PME Special Issue of "Educational Studies in Mathematics" draws a wider perspective on the issues addressed and some of the constructs used in research in Realistic Mathematics Education (RME). In particular, it tries to show that while the problems addressed existed within the world-wide arena of…

A Mixed Methods Analysis of Students' Understanding of Slope and Derivative Concepts and Students' Mathematical Dispositions

ERIC Educational Resources Information Center

Patel, Rita Manubhai

2013-01-01

This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…

Investigation of Mathematics Teacher Candidates' Conceptual Structures about "Measurement" through Word Association Test: The Example of Turkey

ERIC Educational Resources Information Center

Erdogan, Ahmet

2017-01-01

The purpose of this research is to determine mathematics teacher candidates' conceptual structures about the concept of "measurement" that is the one of the important learning fields of mathematics. Qualitative research method was used in this study. Participants of this study were 58 mathematics teacher candidates studying in one of the…

Pre-service mathematics teachers’ ability in solving well-structured problem

NASA Astrophysics Data System (ADS)

Paradesa, R.

2018-01-01

This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

ERIC Educational Resources Information Center

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

Using Factors of Socioeconomic Status, Family Support, and Academic Preparation to Explain the Black-White Gap in Mathematics Achievement and Participation

ERIC Educational Resources Information Center

Watson, Charity Noel

2012-01-01

The Black-White achievement and participation gap in mathematics is a major concern for educators in America. In order to understand why these gaps exist and have continued to exist over the years, it is important to identify some of the factors that may contribute to them. However, one of the limitations in identifying factors that influence the…

An Evaluation of Integrated Curriculum as It Exists in Mathematics and Science SSS as Well as the Subsequent Supportive Presentation of Those Standards in Eighth Grade Mathematics and Science Textbooks

ERIC Educational Resources Information Center

Gill, Clara Joanne Schneberger

2010-01-01

This study attempted to verify points of intersection (POIs) between mathematics and science in the eighth grade Sunshine State Standards (SSS), and to develop a valid and reliable instrument to evaluate these POIs as they were presented in the respective mathematics and science textbooks approved for use in Florida public schools. Shannon and…

Mathematical modeling of the aerodynamics of high-angle-of-attack maneuvers

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Tobak, M.; Malcolm, G. N.

1980-01-01

This paper is a review of the current state of aerodynamic mathematical modeling for aircraft motions at high angles of attack. The mathematical model serves to define a set of characteristic motions from whose known aerodynamic responses the aerodynamic response to an arbitrary high angle-of-attack flight maneuver can be predicted. Means are explored of obtaining stability parameter information in terms of the characteristic motions, whether by wind-tunnel experiments, computational methods, or by parameter-identification methods applied to flight-test data. A rationale is presented for selecting and verifying the aerodynamic mathematical model at the lowest necessary level of complexity. Experimental results describing the wing-rock phenomenon are shown to be accommodated within the most recent mathematical model by admitting the existence of aerodynamic hysteresis in the steady-state variation of the rolling moment with roll angle. Interpretation of the experimental results in terms of bifurcation theory reveals the general conditions under which aerodynamic hysteresis must exist.

Characterizing Interaction with Visual Mathematical Representations

ERIC Educational Resources Information Center

Sedig, Kamran; Sumner, Mark

2006-01-01

This paper presents a characterization of computer-based interactions by which learners can explore and investigate visual mathematical representations (VMRs). VMRs (e.g., geometric structures, graphs, and diagrams) refer to graphical representations that visually encode properties and relationships of mathematical structures and concepts.…

Evolutionary dynamics on any population structure

NASA Astrophysics Data System (ADS)

Allen, Benjamin; Lippner, Gabor; Chen, Yu-Ting; Fotouhi, Babak; Momeni, Naghmeh; Yau, Shing-Tung; Nowak, Martin A.

2017-03-01

Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve. Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours. The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm. Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times of random walks. We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure—graph surgery—affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.

Are Different Students Expected to Learn Norms Differently in the Mathematics Classroom?

ERIC Educational Resources Information Center

Planas, Nuria; Gorgorio, Nuria

2004-01-01

We analyse social interactions during the first days of class in a secondary mathematics classroom (15 and 16-year-olds) with a high percentage of immigrant students. Our analyses show the co-existence of different models for both the interpretation and the use of classroom social norms and socio-mathematical norms. Valorising some behaviours over…

A Modular Approach to Teaching Mathematical Modeling in Biotechnology in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Larripa, Kamila R.; Mazzag, Borbala

2016-01-01

Our paper describes a solution we found to a still existing need to develop mathematical modeling courses for undergraduate biology majors. Some challenges of such courses are: (i) relatively limited exposure of biology students to higher-level mathematical and computational concepts; (ii) availability of texts that can give a flavor of how…

Mathematical Fiction for Senior Students and Undergraduates: Novels, Plays, and Film

ERIC Educational Resources Information Center

Padula, Janice

2006-01-01

Mathematical fiction has probably existed since ideas have been written down and certainly as early as 414 BC (Kasman, 2000). Mathematical fiction is a recently rediscovered and growing literature, as sales of the novels: "The Curious Incident of the Dog in the Night-time" (Haddon, 2003) and "The Da Vinci Code" (Brown, 2004) attest. Science…

Using Video Prompting to Teach Mathematical Problem Solving of Real-World Video-Simulation Problems

ERIC Educational Resources Information Center

Saunders, Alicia F.; Spooner, Fred; Ley Davis, Luann

2018-01-01

Mathematical problem solving is necessary in many facets of everyday life, yet little research exists on how to teach students with more severe disabilities higher order mathematics like problem solving. Using a multiple probe across participants design, three middle school students with moderate intellectual disability (ID) were taught to solve…

Developing Mathematical Understanding and Students with Emotional and Behavioural Disorders: A Review of the Literature

ERIC Educational Resources Information Center

Tan, Paulo

2016-01-01

Recent shifts in focus on academic interventions for students diagnosed with emotional and behavioural disorders (EBD) create a need to evaluate existing interventional research in content areas such as mathematics. Literature reviews in the area of mathematics interventions for students with EBD have mostly focused on the outcomes and the rigour…

Bias Factors in Mathematics Achievement Tests among Israeli Students from the Former Soviet Union

ERIC Educational Resources Information Center

Levi-Keren, Michal

2016-01-01

This study explains mathematical difficulties of students who immigrated from the Former Soviet Union (FSU) vis-à-vis Israeli students, by identifying the existing bias factors in achievement tests. These factors are irrelevant to the mathematical knowledge being measured, and therefore threaten the test results. The bias factors were identified…

Mathematical intelligence developed in math learning with classical backsound music of the classical era

NASA Astrophysics Data System (ADS)

Karlimah

2018-05-01

This study examines the application of classical music backsound in mathematics learning. The method used is quasi experimental design nonequivalent pretest-posttest control group in elementary school students in Tasikmalaya city, Indonesia. The results showed that classical music contributed significantly to the mathematical intelligence of elementary school students. The mathematical intelligence shown is in the cognitive ability ranging from the level of knowledge to evaluation. High level mathematical intelligence is shown by students in reading and writing integers with words and numbers. The low level of mathematical intelligence exists in projecting the story into a mathematical problem. The implication of this research is the use of classical music backsound on learning mathematics should pay attention to the level of difficulty of mathematics material being studied.

Hierarchical Bayesian models to assess between- and within-batch variability of pathogen contamination in food.

PubMed

Commeau, Natalie; Cornu, Marie; Albert, Isabelle; Denis, Jean-Baptiste; Parent, Eric

2012-03-01

Assessing within-batch and between-batch variability is of major interest for risk assessors and risk managers in the context of microbiological contamination of food. For example, the ratio between the within-batch variability and the between-batch variability has a large impact on the results of a sampling plan. Here, we designed hierarchical Bayesian models to represent such variability. Compatible priors were built mathematically to obtain sound model comparisons. A numeric criterion is proposed to assess the contamination structure comparing the ability of the models to replicate grouped data at the batch level using a posterior predictive loss approach. Models were applied to two case studies: contamination by Listeria monocytogenes of pork breast used to produce diced bacon and contamination by the same microorganism on cold smoked salmon at the end of the process. In the first case study, a contamination structure clearly exists and is located at the batch level, that is, between batches variability is relatively strong, whereas in the second a structure also exists but is less marked. © 2012 Society for Risk Analysis.

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

NASA Technical Reports Server (NTRS)

Cragin, B. L.

1986-01-01

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

Time-evolving bubbles in two-dimensional stokes flow

NASA Technical Reports Server (NTRS)

Tanveer, Saleh; Vasconcelos, Giovani L.

1994-01-01

A general class of exact solutions is presented for a time evolving bubble in a two-dimensional slow viscous flow in the presence of surface tension. These solutions can describe a bubble in a linear shear flow as well as an expanding or contracting bubble in an otherwise quiescent flow. In the case of expanding bubbles, the solutions have a simple behavior in the sense that for essentially arbitrary initial shapes the bubble will asymptote an expanding circle. Contracting bubbles, on the other hand, can develop narrow structures ('near-cusps') on the interface and may undergo 'break up' before all the bubble-fluid is completely removed. The mathematical structure underlying the existence of these exact solutions is also investigated.

The Mathematics of Dispatchability, Revisited

NASA Technical Reports Server (NTRS)

Morris, Paul

2016-01-01

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently, it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, dispatchability has considerable theoretical as well as practical significance. One thing that hampers further work in this area is the underdeveloped theory. Moreover, the existing foundation is inadequate in certain respects. In this paper, we develop a new mathematical theory of dispatchability and its relationship to execution. We also provide several characterizations of dispatchability, including characterizations in terms of the structural properties of the STN graph. This facilitates the potential application of the theory to other areas.

The Mathematics of Dispatchability Revisited

NASA Technical Reports Server (NTRS)

Morris, Paul

2016-01-01

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, the dispatchability property has both theoretical and practical interest. One thing that hampers further work in this area is the underdeveloped theory. The existing definitions are expressed in terms of algorithms, and are less suitable for mathematical proofs. In this paper, we develop a new formal theory of dispatchability in terms of execution sequences. We exploit this to prove a characterization of dispatchability involving the structural properties of the STN graph. This facilitates the potential application of the theory to uncertainty reasoning.

Integrating spatial and numerical structure in mathematical patterning

NASA Astrophysics Data System (ADS)

Ni’mah, K.; Purwanto; Irawan, E. B.; Hidayanto, E.

2018-03-01

This paper reports a study monitoring the integrating spatial and numerical structure in mathematical patterning skills of 30 students grade 7th of junior high school. The purpose of this research is to clarify the processes by which learners construct new knowledge in mathematical patterning. Findings indicate that: (1) students are unable to organize the structure of spatial and numerical, (2) students were only able to organize the spatial structure, but the numerical structure is still incorrect, (3) students were only able to organize numerical structure, but its spatial structure is still incorrect, (4) students were able to organize both of the spatial and numerical structure.

Fadeout in an Early Mathematics Intervention: Constraining Content or Pre-existing Differences?

PubMed Central

Bailey, Drew H.; Nguyen, Tutrang; Jenkins, Jade Marcus; Domina, Thurston; Clements, Douglas H.; Sarama, Julie S.

2016-01-01

A robust finding across research on early childhood educational interventions is that the treatment effect diminishes over time, with children not receiving the intervention eventually catching up to children who did. One popular explanation for fadeout of early mathematics interventions is that elementary school teachers may not teach the kind of advanced content that children are prepared for after receiving the intervention, so lower-achieving children in the control groups of early mathematics interventions catch up to the higher-achieving children in the treatment groups. An alternative explanation is that persistent individual differences in children’s long-term mathematical development result more from relatively stable pre-existing differences in their skills and environments than from the direct effects of previous knowledge on later knowledge. We tested these two hypotheses using data from an effective preschool mathematics intervention previously known to show a diminishing treatment effect over time. We compared the intervention group to a matched subset of the control group with a similar mean and variance of scores at the end of treatment. We then tested the relative contributions of factors that similarly constrain learning in children from treatment and control groups with the same level of post-treatment achievement and pre-existing differences between these two groups to the fadeout of the treatment effect over time. We found approximately 72% of the fadeout effect to be attributable to pre-existing differences between children in treatment and control groups with the same level of achievement at post-test. These differences were fully statistically attenuated by children’s prior academic achievement. PMID:27505700

User's manual for the Macintosh version of PASCO

NASA Technical Reports Server (NTRS)

Lucas, S. H.; Davis, Randall C.

1991-01-01

A user's manual for Macintosh PASCO is presented. Macintosh PASCO is an Apple Macintosh version of PASCO, an existing computer code for structural analysis and optimization of longitudinally stiffened composite panels. PASCO combines a rigorous buckling analysis program with a nonlinear mathematical optimization routine to minimize panel mass. Macintosh PASCO accepts the same input as mainframe versions of PASCO. As output, Macintosh PASCO produces a text file and mode shape plots in the form of Apple Macintosh PICT files. Only the user interface for Macintosh is discussed here.

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

ERIC Educational Resources Information Center

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

2016-01-01

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

One-Year Integrated Mathematics and Mathematics Methods Course for Prospective Elementary School Teachers.

ERIC Educational Resources Information Center

Springer, George

This guide describes the content of a proposed mathematics course for prospective elementary school teachers. It is the result of a two-year study at Indiana University in which three existing courses were integrated and coordinated. For each unit of instruction, there are (1) remarks for motivation of study, (2) remarks on methods of teaching,…

A Lesson Based on the Use of Contexts: An Example of Effective Practice in Secondary School Mathematics

ERIC Educational Resources Information Center

Harvey, Roger; Averill, Robin

2012-01-01

The importance of using real-life contexts in teaching mathematics is emphasised in many policy and curriculum statements. The literature indicates using contexts to teach mathematics can be difficult and few detailed exemplars exist. This article describes the use of real-life contexts in one New Zealand Year 11 algebra lesson. Data included a…

Framing the structural role of mathematics in physics lectures: A case study on electromagnetism

NASA Astrophysics Data System (ADS)

Karam, Ricardo

2014-06-01

Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like) use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.

Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

NASA Astrophysics Data System (ADS)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

Existence and characterization of optimal control in mathematics model of diabetics population

NASA Astrophysics Data System (ADS)

Permatasari, A. H.; Tjahjana, R. H.; Udjiani, T.

2018-03-01

Diabetes is a chronic disease with a huge burden affecting individuals and the whole society. In this paper, we constructed the optimal control mathematical model by applying a strategy to control the development of diabetic population. The constructed mathematical model considers the dynamics of disabled people due to diabetes. Moreover, an optimal control approach is proposed in order to reduce the burden of pre-diabetes. Implementation of control is done by preventing the pre-diabetes develop into diabetics with and without complications. The existence of optimal control and characterization of optimal control is discussed in this paper. Optimal control is characterized by applying the Pontryagin minimum principle. The results indicate that there is an optimal control in optimization problem in mathematics model of diabetic population. The effect of the optimal control variable (prevention) is strongly affected by the number of healthy people.

Adding structure to the transition process to advanced mathematical activity

NASA Astrophysics Data System (ADS)

Engelbrecht, Johann

2010-03-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.

Mathematics Capital in the Educational Field: Bourdieu and Beyond

ERIC Educational Resources Information Center

Williams, Julian; Choudry, Sophina

2016-01-01

Mathematics education needs a better appreciation of the dominant power structures in the educational field: Bourdieu's theory of capital provides a good starting point. We argue from Bourdieu's perspective that school mathematics provides capital that is finely tuned to generationally reproduce the social structures that serve to keep the…

Secondary Mathematics Course Trajectories: Understanding Accumulated Disadvantages in Mathematics in Grades 9-12

ERIC Educational Resources Information Center

Schiller, Kathryn S.; Hunt, Donald J.

2011-01-01

Schools are institutions in which students' course taking creates series of linked learning opportunities continually shaped by not only curricular structures but demographic and academic backgrounds. In contrast to a seven-step normative course sequence reflecting the conventional hierarchical structure of mathematics, analysis of more than…

Structure of Primary Mathematics Teacher Education Programs in Spain

ERIC Educational Resources Information Center

Cañadas, María C.; Gómez, Pedro; Rico, Luis

2013-01-01

Spain was 1 of the 17 countries that participated in the International Association for the Evaluation of Educational Achievement's Teacher Education and Development Study in Mathematics (TEDS-M 2008). In this paper, we explore and describe the structure of Spanish primary mathematics teacher education programs. We analyzed the documents collected…

Mathematics anxiety affects counting but not subitizing during visual enumeration.

PubMed

Maloney, Erin A; Risko, Evan F; Ansari, Daniel; Fugelsang, Jonathan

2010-02-01

Individuals with mathematics anxiety have been found to differ from their non-anxious peers on measures of higher-level mathematical processes, but not simple arithmetic. The current paper examines differences between mathematics anxious and non-mathematics anxious individuals in more basic numerical processing using a visual enumeration task. This task allows for the assessment of two systems of basic number processing: subitizing and counting. Mathematics anxious individuals, relative to non-mathematics anxious individuals, showed a deficit in the counting but not in the subitizing range. Furthermore, working memory was found to mediate this group difference. These findings demonstrate that the problems associated with mathematics anxiety exist at a level more basic than would be predicted from the extant literature. Copyright 2009 Elsevier B.V. All rights reserved.

Computational modeling of the cell-autonomous mammalian circadian oscillator.

PubMed

Podkolodnaya, Olga A; Tverdokhleb, Natalya N; Podkolodnyy, Nikolay L

2017-02-24

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.

Integrated design of structures, controls, and materials

NASA Technical Reports Server (NTRS)

Blankenship, G. L.

1994-01-01

In this talk we shall discuss algorithms and CAD tools for the design and analysis of structures for high performance applications using advanced composite materials. An extensive mathematical theory for optimal structural (e.g., shape) design was developed over the past thirty years. Aspects of this theory have been used in the design of components for hypersonic vehicles and thermal diffusion systems based on homogeneous materials. Enhancement of the design methods to include optimization of the microstructure of the component is a significant innovation which can lead to major enhancements in component performance. Our work is focused on the adaptation of existing theories of optimal structural design (e.g., optimal shape design) to treat the design of structures using advanced composite materials (e.g., fiber reinforced, resin matrix materials). In this talk we shall discuss models and algorithms for the design of simple structures from composite materials, focussing on a problem in thermal management. We shall also discuss methods for the integration of active structural controls into the design process.

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

ERIC Educational Resources Information Center

Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

2016-01-01

Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

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

ERIC Educational Resources Information Center

Haciomeroglu, Guney

2014-01-01

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

Halo Nuclei

NASA Astrophysics Data System (ADS)

Al-Khalili, Jim

2017-10-01

While neutron halos were discovered 30 years ago, this is the first book written on the subject of this exotic form of nuclei that typically contain many more neutrons than stable isotopes of those elements. It provides an introductory description of the halo and outlines the discovery and evidence for its existence. It also discusses different theoretical models of the halo's structure as well as models and techniques in reaction theory that have allowed us to study the halo. This is written at the graduate student (starting at PhD) level. The author of the book, Jim Al-Khalili, is a theoretician who published some of the key papers on the structure of the halo in the mid and late 90s and was the first to determine its true size. This monograph is based on review articles he has written on the mathematical models used to determine the halo structure and the reactions used to model that structure.

Cognitive foundations for model-based sensor fusion

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.; Weijers, Bertus; Mutz, Chris W.

2003-08-01

Target detection, tracking, and sensor fusion are complicated problems, which usually are performed sequentially. First detecting targets, then tracking, then fusing multiple sensors reduces computations. This procedure however is inapplicable to difficult targets which cannot be reliably detected using individual sensors, on individual scans or frames. In such more complicated cases one has to perform functions of fusing, tracking, and detecting concurrently. This often has led to prohibitive combinatorial complexity and, as a consequence, to sub-optimal performance as compared to the information-theoretic content of all the available data. It is well appreciated that in this task the human mind is by far superior qualitatively to existing mathematical methods of sensor fusion, however, the human mind is limited in the amount of information and speed of computation it can cope with. Therefore, research efforts have been devoted toward incorporating "biological lessons" into smart algorithms, yet success has been limited. Why is this so, and how to overcome existing limitations? The fundamental reasons for current limitations are analyzed and a potentially breakthrough research and development effort is outlined. We utilize the way our mind combines emotions and concepts in the thinking process and present the mathematical approach to accomplishing this in the current technology computers. The presentation will summarize the difficulties encountered by intelligent systems over the last 50 years related to combinatorial complexity, analyze the fundamental limitations of existing algorithms and neural networks, and relate it to the type of logic underlying the computational structure: formal, multivalued, and fuzzy logic. A new concept of dynamic logic will be introduced along with algorithms capable of pulling together all the available information from multiple sources. This new mathematical technique, like our brain, combines conceptual understanding with emotional evaluation and overcomes the combinatorial complexity of concurrent fusion, tracking, and detection. The presentation will discuss examples of performance, where computational speedups of many orders of magnitude were attained leading to performance improvements of up to 10 dB (and better).

Numerosity as a topological invariant.

PubMed

Kluth, Tobias; Zetzsche, Christoph

2016-01-01

The ability to quickly recognize the number of objects in our environment is a fundamental cognitive function. However, it is far from clear which computations and which actual neural processing mechanisms are used to provide us with such a skill. Here we try to provide a detailed and comprehensive analysis of this issue, which comprises both the basic mathematical foundations and the peculiarities imposed by the structure of the visual system and by the neural computations provided by the visual cortex. We suggest that numerosity should be considered as a mathematical invariant. Making use of concepts from mathematical topology--like connectedness, Betti numbers, and the Gauss-Bonnet theorem--we derive the basic computations suited for the computation of this invariant. We show that the computation of numerosity is possible in a neurophysiologically plausible fashion using only computational elements which are known to exist in the visual cortex. We further show that a fundamental feature of numerosity perception, its Weber property, arises naturally, assuming noise in the basic neural operations. The model is tested on an extended data set (made publicly available). It is hoped that our results can provide a general framework for future research on the invariance properties of the numerosity system.

Examining Pre-Service Mathematics Teachers' Conceptual Structures about "Geometry"

ERIC Educational Resources Information Center

Erdogan, Ahmet

2017-01-01

The aim of this study is to examine pre-service mathematics teachers' conceptual structures about "geometry". Qualitative research methodology has been adopted in the study. The data of the study is obtained from mathematics teacher candidates who have been students at the faculties of education of an Anatolian university in the academic…

Measuring Developmental Students' Mathematics Anxiety

ERIC Educational Resources Information Center

Ding, Yanqing

2016-01-01

This study conducted an item-level analysis of mathematics anxiety and examined the dimensionality of mathematics anxiety in a sample of developmental mathematics students (N = 162) by Multi-dimensional Random Coefficients Multinominal Logit Model (MRCMLM). The results indicate a moderately correlated factor structure of mathematics anxiety (r =…

The Influence of Theoretical Mathematical Foundations on Teaching and Learning: A Case Study of Whole Numbers in Elementary School

ERIC Educational Resources Information Center

Chambris, Christine

2018-01-01

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

8th Grade Student's Skill of Connecting Mathematics to Real Life

ERIC Educational Resources Information Center

Altay, Mesture Kayhan; Yalvaç, Betül; Yeltekin, Emel

2017-01-01

The purpose of this study is to examine 8th grade students' skills of connecting mathematics to real life. This study uses survey design since it aims to determine existing situations regarding to students' skills of connecting mathematics to real life. The study sample consists of 176 students in total, who are studying at a state school in the…

Development of an Instrument to Assess and Deliberate on the Integration of Mathematics into Student-Centered Science Learning

ERIC Educational Resources Information Center

Judson, Eugene

2013-01-01

It has long been noted in research literature that there does not exist a shared definition of integration of science and mathematics. Classifying a particular set of integration practices by one of many labels has limited value. Moving past the definition debate, this study describes the development and testing of the Mathematics Integrated into…

Effects of Single-Gender Mathematics Classrooms on Self-Perception of Mathematical Ability and Post Secondary Engineering Paths: An Australian Case Study

ERIC Educational Resources Information Center

Tully, D.; Jacobs, B.

2010-01-01

This study focused on a population of female engineering students, probing the influences of their secondary school experience on their choice to pursue an engineering course of study at university. The motivating question is: Do unique opportunities exist in an all-female secondary school mathematics classroom, which impact a young woman's…

Unlocking the Structure of Positive

ERIC Educational Resources Information Center

Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.

2016-01-01

Recognizing and using mathematical structure are key components of mathematical reasoning. The authors believe that one productive way to support students' use of structure is by identifying opportunities to address structure in the context of what teachers are already doing, rather than developing additional tasks or new curriculum materials. The…

METSAT: Advanced Microwave Sounding Unit-A2 (AMSU-A2) structural mathematical model

NASA Technical Reports Server (NTRS)

Ely, Wayne

1995-01-01

This plan describes the Structural Mathematical Model of the METSAT AMSU-A2 instrument. The model is used to verify the structural adequacy of the AMSU-A2 instrument for the specified loading environments.

Force-induced bone growth and adaptation: A system theoretical approach to understanding bone mechanotransduction

NASA Astrophysics Data System (ADS)

Maldonado, Solvey; Findeisen, Rolf

2010-06-01

The modeling, analysis, and design of treatment therapies for bone disorders based on the paradigm of force-induced bone growth and adaptation is a challenging task. Mathematical models provide, in comparison to clinical, medical and biological approaches an structured alternative framework to understand the concurrent effects of the multiple factors involved in bone remodeling. By now, there are few mathematical models describing the appearing complex interactions. However, the resulting models are complex and difficult to analyze, due to the strong nonlinearities appearing in the equations, the wide range of variability of the states, and the uncertainties in parameters. In this work, we focus on analyzing the effects of changes in model structure and parameters/inputs variations on the overall steady state behavior using systems theoretical methods. Based on an briefly reviewed existing model that describes force-induced bone adaptation, the main objective of this work is to analyze the stationary behavior and to identify plausible treatment targets for remodeling related bone disorders. Identifying plausible targets can help in the development of optimal treatments combining both physical activity and drug-medication. Such treatments help to improve/maintain/restore bone strength, which deteriorates under bone disorder conditions, such as estrogen deficiency.

A mathematical description of the inclusive fitness theory.

PubMed

Wakano, Joe Yuichiro; Ohtsuki, Hisashi; Kobayashi, Yutaka

2013-03-01

Recent developments in the inclusive fitness theory have revealed that the direction of evolution can be analytically predicted in a wider class of models than previously thought, such as those models dealing with network structure. This paper aims to provide a mathematical description of the inclusive fitness theory. Specifically, we provide a general framework based on a Markov chain that can implement basic models of inclusive fitness. Our framework is based on the probability distribution of "offspring-to-parent map", from which the key concepts of the theory, such as fitness function, relatedness and inclusive fitness, are derived in a straightforward manner. We prove theorems showing that inclusive fitness always provides a correct prediction on which of two competing genes more frequently appears in the long run in the Markov chain. As an application of the theorems, we prove a general formula of the optimal dispersal rate in the Wright's island model with recurrent mutations. We also show the existence of the critical mutation rate, which does not depend on the number of islands and below which a positive dispersal rate evolves. Our framework can also be applied to lattice or network structured populations. Copyright © 2012 Elsevier Inc. All rights reserved.

A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

ONTIC: A Knowledge Representation System for Mathematics

DTIC Science & Technology

1987-01-01

rrrPrL rr.t - ~ jr V 1.2. O.NTIC ASA FORMAL LANGUAGE 11 (IS zr) :I. (EXISTS-SOME r) (EXISTS ((xI 71) (U2 T2 ) ... ) ( li . X2, -.) . (FORALL ((xl 71) (x2...language. Jonathan Rees spent j.. about a month defining various mathematical concepts in Ontic. Starting with onlv the fundamental notions described...novelty of the Ontic system lies in the way that the above four inference mechanisms are brought together. Ontic integrates constraint prop- agation

A mathematical model of a steady flow through the Kaplan turbine - The existence of a weak solution in the case of an arbitrarily large inflow

NASA Astrophysics Data System (ADS)

Neustupa, Tomáš

2017-07-01

The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called "artificial" or "natural" boundary condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.

The Search for Hidden Structure

ERIC Educational Resources Information Center

Matsuura, Ryota; Sword, Sarah; Finkelstein, Tatyana

2017-01-01

How does one look for mathematical structure? Finding structure is a challenging yet accessible activity for all students. This article describes a lesson in which seventh graders engaged with mathematical structure. The setting was a seventh-grade prealgebra classroom in a suburban school. The classroom teacher was co-author Tatyana Finkelstein.…

Understanding protein evolution: from protein physics to Darwinian selection.

PubMed

Zeldovich, Konstantin B; Shakhnovich, Eugene I

2008-01-01

Efforts in whole-genome sequencing and structural proteomics start to provide a global view of the protein universe, the set of existing protein structures and sequences. However, approaches based on the selection of individual sequences have not been entirely successful at the quantitative description of the distribution of structures and sequences in the protein universe because evolutionary pressure acts on the entire organism, rather than on a particular molecule. In parallel to this line of study, studies in population genetics and phenomenological molecular evolution established a mathematical framework to describe the changes in genome sequences in populations of organisms over time. Here, we review both microscopic (physics-based) and macroscopic (organism-level) models of protein-sequence evolution and demonstrate that bridging the two scales provides the most complete description of the protein universe starting from clearly defined, testable, and physiologically relevant assumptions.

Teaching Mathematical Word Problem Solving: The Quality of Evidence for Strategy Instruction Priming the Problem Structure

ERIC Educational Resources Information Center

Jitendra, Asha K.; Petersen-Brown, Shawna; Lein, Amy E.; Zaslofsky, Anne F.; Kunkel, Amy K.; Jung, Pyung-Gang; Egan, Andrea M.

2015-01-01

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et…

Abstraction and Concreteness in the Everyday Mathematics of Structural Engineers.

ERIC Educational Resources Information Center

Gainsburg, Julie

The everyday mathematics processes of structural engineers were studied and analyzed in terms of abstraction. A main purpose of the study was to explore the degree to which the notion of a gap between school and everyday mathematics holds when the scope of practices considered "everyday" is extended. J. Lave (1988) promoted a methodology…

Pre-Service Science Teachers' Cognitive Structures Regarding Science, Technology, Engineering, Mathematics (STEM) and Science Education

ERIC Educational Resources Information Center

Hacioglu, Yasemin; Yamak, Havva; Kavak, Nusret

2016-01-01

The aim of this study is to reveal pre-service science teachers' cognitive structures regarding Science, Technology, Engineering, Mathematics (STEM) and science education. The study group of the study consisted of 192 pre-service science teachers. A Free Word Association Test (WAT) consisting of science, technology, engineering, mathematics and…

Balancing Structure and Creativity in Culminating Projects for Liberal Arts Mathematics

ERIC Educational Resources Information Center

Kasman, Reva

2014-01-01

Liberal arts mathematics courses can provide non-majors the opportunity to connect mathematical topics with areas of personal interest. This article describes two end-of-unit writing assignments (on voting and graph theory) that have been structured so that each student is able to synthesize course material in a unique way, while ensuring a…

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…

Relations between Classroom Goal Structures and Students' Goal Orientations in Mathematics Classes: When Is a Mastery Goal Structure Adaptive?

ERIC Educational Resources Information Center

Skaalvik, Einar M.; Federici, Roger A.

2016-01-01

The purpose of this study was to test possible interactions between mastery and performance goal structures in mathematics classrooms when predicting students' goal orientations. More specifically, we tested if the degree of performance goal structure moderated the associations between mastery goal structure and students' goal orientations.…

The transition to formal thinking in mathematics

NASA Astrophysics Data System (ADS)

Tall, David

2008-09-01

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

The Spin-Orbit Resonances of the Solar System: A Mathematical Treatment Matching Physical Data

NASA Astrophysics Data System (ADS)

Antognini, Francesco; Biasco, Luca; Chierchia, Luigi

2014-06-01

In the mathematical framework of a restricted, slightly dissipative spin-orbit model, we prove the existence of periodic orbits for astronomical parameter values corresponding to all satellites of the Solar System observed in exact spin-orbit resonance.

Characteristics of manipulative in mathematics laboratory

NASA Astrophysics Data System (ADS)

Istiandaru, A.; Istihapsari, V.; Prahmana, R. C. I.; Setyawan, F.; Hendroanto, A.

2017-12-01

A manipulative is a teaching aid designed such that students could understand mathematical concepts by manipulating it. This article aims to provide an insight to the characteristics of manipulatives produced in the mathematics laboratory of Universitas Ahmad Dahlan, Indonesia. A case study was conducted to observe the existing manipulatives produced during the latest three years and classified the manipulatives based on the characteristics found. There are four kinds of manipulatives: constructivism manipulative, virtual manipulative, informative manipulative, and game-based manipulative. Each kinds of manipulative has different characteristics and impact towards the mathematics learning.

Mathematical methods for protein science

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

Hart, W.; Istrail, S.; Atkins, J.

1997-12-31

Understanding the structure and function of proteins is a fundamental endeavor in molecular biology. Currently, over 100,000 protein sequences have been determined by experimental methods. The three dimensional structure of the protein determines its function, but there are currently less than 4,000 structures known to atomic resolution. Accordingly, techniques to predict protein structure from sequence have an important role in aiding the understanding of the Genome and the effects of mutations in genetic disease. The authors describe current efforts at Sandia to better understand the structure of proteins through rigorous mathematical analyses of simple lattice models. The efforts have focusedmore » on two aspects of protein science: mathematical structure prediction, and inverse protein folding.« less

Failures and Reform in Mathematics Education: The Case of Engineering. National Institute Briefing Note No. 5.

ERIC Educational Resources Information Center

Wolf, Alison

The structure of education for 16- to 18-year-olds in Great Britain discourages them from making mathematics, science, and engineering serious options for future study. The emerging structure of the labor market, in which a large proportion of high-status jobs do not require higher mathematics, increases the numbers who decide not to commit…

Secondary School Students' Understanding of Mathematical Induction: Structural Characteristics and the Process of Proof Construction

ERIC Educational Resources Information Center

Palla, Marina; Potari, Despina; Spyrou, Panagiotis

2012-01-01

In this study, we investigate the meaning students attribute to the structure of mathematical induction (MI) and the process of proof construction using mathematical induction in the context of a geometric recursion problem. Two hundred and thirteen 17-year-old students of an upper secondary school in Greece participated in the study. Students'…

Structure and Maintenance of a Mathematical Creative Lesson as a Mean of Pupils' Meta-Subject Results Achievement

ERIC Educational Resources Information Center

Gorev, Pavel M.; Aydar M. Kalimullin

2017-01-01

The purpose of the research is to study and change the structure of a mathematical lesson to improve quality of pupils' mathematical training and design mechanisms of inclusion the systems of open type tasks in educational process considering specifics of pupils' creative personality development. The leading method is modeling of a mathematical…

The World According to Malthus and Volterra: The Mathematical Theory of the Struggle for Existence.

ERIC Educational Resources Information Center

Bogdanov, Constantine

1992-01-01

Discusses the mathematical model presented by Vito Volterra to describe the dynamics of population density. Discusses the predator prey relationship, presents an computer simulated model from marine life involving sharks and mackerels, and discusses ecological chaos. (MDH)

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

From empirical data to time-inhomogeneous continuous Markov processes.

PubMed

Lencastre, Pedro; Raischel, Frank; Rogers, Tim; Lind, Pedro G

2016-03-01

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60% of tested matrices, typically 80% to 90%, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.

A mathematical model captures the structure of subjective affect

PubMed Central

Mattek, Alison M.; Wolford, George; Whalen, Paul J.

2016-01-01

While it is possible to observe when another person is having an emotional moment, we also derive information about the affective states of others from what they tell us they are feeling. In an effort to distill the complexity of affective experience, psychologists routinely focus on a simplified subset of subjective rating scales (i.e., dimensions) that capture considerable variability in reported affect: reported valence (i.e., how good or bad?) and reported arousal (e.g., how strong is the emotion you are feeling?). Still, existing theoretical approaches address the basic organization and measurement of these affective dimensions differently. Some approaches organize affect around the dimensions of bipolar valence and arousal (e.g., the circumplex model; Russell, 1980), whereas alternative approaches organize affect around the dimensions of unipolar positivity and unipolar negativity (e.g., the bivariate evaluative model; Cacioppo & Berntson, 1994). In this report, we (1) replicate the data structure observed when collected according to the two approaches described above, and re-interpret these data to suggest that the relationship between each pair of affective dimensions is conditional on valence ambiguity; then (2) formalize this structure with a mathematical model depicting a valence ambiguity dimension that decreases in range as arousal decreases (a triangle). This model captures variability in affective ratings better than alternative approaches, increasing variance explained from ~60% to over 90% without adding parameters. PMID:28544868

Modeling the chemistry of complex petroleum mixtures.

PubMed Central

Quann, R J

1998-01-01

Determining the complete molecular composition of petroleum and its refined products is not feasible with current analytical techniques because of the astronomical number of molecular components. Modeling the composition and behavior of such complex mixtures in refinery processes has accordingly evolved along a simplifying concept called lumping. Lumping reduces the complexity of the problem to a manageable form by grouping the entire set of molecular components into a handful of lumps. This traditional approach does not have a molecular basis and therefore excludes important aspects of process chemistry and molecular property fundamentals from the model's formulation. A new approach called structure-oriented lumping has been developed to model the composition and chemistry of complex mixtures at a molecular level. The central concept is to represent an individual molecular or a set of closely related isomers as a mathematical construct of certain specific and repeating structural groups. A complex mixture such as petroleum can then be represented as thousands of distinct molecular components, each having a mathematical identity. This enables the automated construction of large complex reaction networks with tens of thousands of specific reactions for simulating the chemistry of complex mixtures. Further, the method provides a convenient framework for incorporating molecular physical property correlations, existing group contribution methods, molecular thermodynamic properties, and the structure--activity relationships of chemical kinetics in the development of models. PMID:9860903

Nontrivial paths and periodic orbits of the T-fractal billiard table

NASA Astrophysics Data System (ADS)

Lapidus, Michel L.; Miller, Robyn L.; Niemeyer, Robert G.

2016-07-01

We introduce and prove numerous new results about the orbits of the T-fractal billiard. Specifically, in section 3, we give a variety of sufficient conditions for the existence of a sequence of compatible periodic orbits. In section 4, we examine the limiting behavior of particular sequences of compatible periodic orbits. Additionally, sufficient conditions for the existence of particular nontrivial paths are given in section 4. The proofs of two results of Lapidus and Niemeyer (2013 The current state of fractal billiards Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II: Fractals in Applied Mathematics (Contemporary Mathematics vol 601) ed D Carfi et al (Providence, RI: American Mathematical Society) pp 251-88 (e-print: arXiv:math.DS.1210.0282v2, 2013) appear here for the first time, as well. In section 5, an orbit with an irrational initial direction reaches an elusive point in a way that yields a nontrivial path of finite length, yet, by our convention, constitutes a singular orbit of the fractal billiard table. The existence of such an orbit seems to indicate that the classification of orbits may not be so straightforward. A discussion of our results and directions for future research is then given in section 6.

Human sleep and circadian rhythms: a simple model based on two coupled oscillators.

PubMed

Strogatz, S H

1987-01-01

We propose a model of the human circadian system. The sleep-wake and body temperature rhythms are assumed to be driven by a pair of coupled nonlinear oscillators described by phase variables alone. The novel aspect of the model is that its equations may be solved analytically. Computer simulations are used to test the model against sleep-wake data pooled from 15 studies of subjects living for weeks in unscheduled, time-free environments. On these tests the model performs about as well as the existing models, although its mathematical structure is far simpler.

Cosmic strings: Gravitation without local curvature

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

Helliwell, T.M.; Konkowski, D.A.

1987-05-01

Cosmic strings are very long, thin structures which might stretch over vast reaches of the universe. If they exist, they would have been formed during phase transitions in the very early universe. The space-time surrounding a straight cosmic string is flat but nontrivial: A two-dimensional spatial section is a cone rather than a plane. This feature leads to unique gravitational effects. The flatness of the cone means that many of the gravitational effects can be understood with no mathematics beyond trigonometry. This includes the observational predictions of the double imaging of quasars and the truncation of the images of galaxies.

Science, technology, engineering, mathematics (STEM) as mathematics learning approach in 21st century

NASA Astrophysics Data System (ADS)

Milaturrahmah, Naila; Mardiyana, Pramudya, Ikrar

2017-08-01

This 21st century demands competent human resources in science, technology, engineering design and mathematics so that education is expected to integrate the four disciplines. This paper aims to describe the importance of STEM as mathematics learning approach in Indonesia in the 21st century. This paper uses a descriptive analysis research method, and the method reveals that STEM education growing in developed countries today can be a framework for innovation mathematics in Indonesia in the 21st century. STEM education integrate understanding of science, math skills, and the available technology with the ability to perform engineering design process. Implementation of mathematics learning with STEM approach makes graduates trained in using of mathematics knowledge that they have to create innovative products that are able to solve the problems that exist in society.

Evolutionary optimization of biopolymers and sequence structure maps

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

Reidys, C.M.; Kopp, S.; Schuster, P.

1996-06-01

Searching for biopolymers having a predefined function is a core problem of biotechnology, biochemistry and pharmacy. On the level of RNA sequences and their corresponding secondary structures we show that this problem can be analyzed mathematically. The strategy will be to study the properties of the RNA sequence to secondary structure mapping that is essential for the understanding of the search process. We show that to each secondary structure s there exists a neutral network consisting of all sequences folding into s. This network can be modeled as a random graph and has the following generic properties: it is densemore » and has a giant component within the graph of compatible sequences. The neutral network percolates sequence space and any two neutral nets come close in terms of Hamming distance. We investigate the distribution of the orders of neutral nets and show that above a certain threshold the topology of neutral nets allows to find practically all frequent secondary structures.« less

Exotic differentiable structures and general relativity

NASA Astrophysics Data System (ADS)

Brans, Carl H.; Randall, Duane

1993-02-01

We review recent developments in differential topology with special concern for their possible significance to physical theories, especially general relativity. In particular we are concerned here with the discovery of the existence of non-standard (“fake” or “exotic”) differentiable structures on topologically simple manifolds such asS 7, ℝ4 andS 3 X ℝ1. Because of the technical difficulties involved in the smooth case, we begin with an easily understood toy example looking at the role which the choice of complex structures plays in the formulation of two-dimensional vacuum electrostatics. We then briefly review the mathematical formalisms involved with differentiable structures on topological manifolds, diffeomorphisms and their significance for physics. We summarize the important work of Milnor, Freedman, Donaldson, and others in developing exotic differentiable structures on well known topological manifolds. Finally, we discuss some of the geometric implications of these results and propose some conjectures on possible physical implications of these new manifolds which have never before been considered as physical models.

Variation and Mathematics Pedagogy

ERIC Educational Resources Information Center

Leung, Allen

2012-01-01

This discussion paper put forwards variation as a theme to structure mathematical experience and mathematics pedagogy. Patterns of variation from Marton's Theory of Variation are understood and developed as types of variation interaction that enhance mathematical understanding. An idea of a discernment unit comprising mutually supporting variation…

Rethinking Mathematics.

ERIC Educational Resources Information Center

Abad, Ernesto A.

1994-01-01

Poses solutions for our failure to show students how well mathematics interlocks with the physical structures of the Universe. Some examples are provided to illustrate the natural integration of mathematics and science. (ZWH)

77 FR 70422 - Agency Information Collection Activities; Comment Request; Mathematics and Science Partnerships...

Federal Register 2010, 2011, 2012, 2013, 2014

2012-11-26

... DEPARTMENT OF EDUCATION [Docket No.: ED-2012-ICCD-0059] Agency Information Collection Activities; Comment Request; Mathematics and Science Partnerships Program: Annual Performance Report AGENCY: Office of... revision of an existing information collection. DATES: Interested persons are invited to submit comments on...

Documenting Collective Development in Online Settings

ERIC Educational Resources Information Center

Dean, Chrystal; Silverman, Jason

2015-01-01

In this paper the authors explored the question of collective understanding in online mathematics education settings and presented a brief overview of traditional methods for documenting norms and collective mathematical practices. A method for documenting collective development was proposed that builds on existing methods and frameworks yet is…

Differences between Experts' and Students' Conceptual Images of the Mathematical Structure of Taylor Series Convergence

ERIC Educational Resources Information Center

Martin, Jason

2013-01-01

Taylor series convergence is a complicated mathematical structure which incorporates multiple concepts. Therefore, it can be very difficult for students to initially comprehend. How might students make sense of this structure? How might experts make sense of this structure? To answer these questions, an exploratory study was conducted using…

Mathematics reflecting sensorimotor organization.

PubMed

McCollum, Gin

2003-02-01

This review combines short presentations of several mathematical approaches that conceptualize issues in sensorimotor neuroscience from different perspectives and levels of analysis. The intricate organization of neural structures and sensorimotor performance calls for characterization using a variety of mathematical approaches. This review points out the prospects for mathematical neuroscience: in addition to computational approaches, there is a wide variety of mathematical approaches that provide insight into the organization of neural systems. By starting from the perspective that provides the greatest clarity, a mathematical approach avoids specificity that is inaccurate in characterizing the inherent biological organization. Approaches presented include the mathematics of ordered structures, motion-phase space, subject-coincident coordinates, equivalence classes, topological biodynamics, rhythm space metric, and conditional dynamics. Issues considered in this paper include unification of levels of analysis, response equivalence, convergence, relationship of physics to motor control, support of rhythms, state transitions, and focussing on low-dimensional subspaces of a high-dimensional sensorimotor space.

The Implementation of an Interdisciplinary Co-planning Team Model Among Mathematics and Science Teachers

NASA Astrophysics Data System (ADS)

Brown, Michelle Cetner

In recent years, Science, Technology, Engineering, and Mathematics (STEM) education has become a significant focus of numerous theoretical and commentary articles as researchers have advocated for active and conceptually integrated learning in classrooms. Drawing connections between previously isolated subjects, especially mathematics and science, has been shown to increase student engagement, performance, and critical thinking skills. However, obstacles exist to the widespread implementation of integrated curricula in schools, such as teacher knowledge and school structure and culture. The Interdisciplinary Co-planning Team (ICT) model, in which teachers of different subjects come together regularly to discuss connections between content and to plan larger interdisciplinary activities and smaller examples and discussion points, offers a method for teachers to create sustainable interdisciplinary experiences for students within the bounds of the current school structure. The ICT model is designed to be an iterative, flexible model, providing teachers with both a regular time to come together as "experts" and "teach" each other important concepts from their separate disciplines, and then to bring their shared knowledge and language back to their own classrooms to implement with their students in ways that fit their individual classes. In this multiple-case study, which aims to describe the nature of the co-planning process, the nature of plans, and changes in teacher beliefs as a result of co-planning, three pairs of secondary mathematics and science teachers participated in a 10-week intervention with the ICT model. Each pair constituted one case. Data included observations, interviews, and artifact collection. All interviews, whole-group sessions, and co-planning sessions were transcribed and coded using both theory-based and data-based codes. Finally, a cross-case comparison was used to present similarities and differences across cases. Findings suggest that the ICT model can be implemented with pairs of mathematics and science teachers to create a sustainable way to share experience and expertise, and to create powerful interdisciplinary experiences for their students. In addition, there is evidence that participation with the ICT model positively influences teacher beliefs about the nature of mathematics and science, about teaching and learning, and about interdisciplinary connections. These findings seem to hold across grades, school type, and personal experience. Future implementation of the ICT model on a larger scale is recommended to continue to observe the effects on teachers and students.

Remembering the hindu festivities mathematically by the balinese using integer operations and least common multiple

NASA Astrophysics Data System (ADS)

Budi Darmayasa, Jero; Wahyudin; Mulyana, Tatang; Subali Noto, Muchamad

2018-04-01

Ethnomathematicsis considered as a new study in mathematic education. As a study, numerous regions in this world starts to explore through ethnomathematics, including Indonesia. As the intersection between mathematics and mathematical modelling and culture, ethnomathematics exists in various society’s cultural elements, including in the Balinese Hindus’ festivities. To find the mathematical concept used in determining the festivity days, the researcher(s) conducted ethnographic research in Bali Mula society in Kintamani District, Bali. Participation observation, in-depth interview, and literature and documentation were used in collecting the data. As the result, the researcher(s) revealed that the mathematical concept used is integer operations, least common multiple, mixed fraction, and number sequences. Since it contains mathematical concept used in junior high, thus ethnomathematics of “4-hindu’s festivities” may be used as context in mathematics learning. By using ethnomathematics as the context, the researcher(s) expect that it will help teachers in motivation their students to learn mathematics.

Mathematical Idea Analysis: What Embodied Cognitive Science Can Say about the Human Nature of Mathematics.

ERIC Educational Resources Information Center

Nunez, Rafael E.

This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive linguistics. It discusses Mathematical Idea Analysis, a set of techniques for studying implicit structures in mathematics. Particular attention is…

Investigation of Pre-School Teachers' Beliefs about Mathematics Education in Terms of Their Experience and Structure of Their Education

ERIC Educational Resources Information Center

Karatas, Ilhan; Guven, Bulent; Öztürk, Yasin; Arslan, Selahattin; Gürsöy, Kadir

2017-01-01

The aim of this study was to determine pre-school teachers' beliefs about teaching mathematics to young learners. In this context, we compared preschool teachers' beliefs with mathematical learning, talent-development-age appropriateness for mathematical learning, the nature of mathematics, the curriculum, teacher efficacy, and the teacher's role…

Toward an Analysis of Video Games for Mathematics Education

ERIC Educational Resources Information Center

Offenholley, Kathleen

2011-01-01

Video games have tremendous potential in mathematics education, yet there is a push to simply add mathematics to a video game without regard to whether the game structure suits the mathematics, and without regard to the level of mathematical thought being learned in the game. Are students practicing facts, or are they problem-solving? This paper…

A Conceptual and Procedural Research on the Hierarchical Structure of Mathematics Emerging in the Minds of University Students: An Example of Limit-Continuity-Integral-Derivative

ERIC Educational Resources Information Center

Dane, Arif; Çetin, Ömer Faruk; Bas, Fatih; Sagirli, Meryem Özturan

2016-01-01

In this present study, it was aimed to investigate whether the hierarchical structure of mathematics emerged in university students' minds or not, considering the concepts of limit, continuity derivative and integral from the perspective of students in the department of secondary school mathematics teacher training and the department of…

The Effects of Emphasizing Mathematical Structural Properties in Teaching and of Reflective Intelligence on Four Selected Criteria. Technical Report 275.

ERIC Educational Resources Information Center

Jurdak, Murad Eid

The purposes of this study were: (1) to compare the effectiveness of two teaching methods having two distinct levels of emphasis on mathematical structure in organizing and presenting the same mathematical content, and (2) to identify the effect of the cognitive ability of reflective intelligence on four cognitive levels of learning a second-order…

Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion

NASA Astrophysics Data System (ADS)

Choquet, C.; Diédhiou, M. M.; Rosier, C.

2015-10-01

We consider a new model mixing sharp and diffuse interface approaches for seawater intrusion phenomena in free aquifers. More precisely, a phase field model is introduced in the boundary conditions on the virtual sharp interfaces. We thus include in the model the existence of diffuse transition zones but we preserve the simplified structure allowing front tracking. The three-dimensional problem then reduces to a two-dimensional model involving a strongly coupled system of partial differential equations of parabolic type describing the evolution of the depths of the two free surfaces, that is the interface between salt- and freshwater and the water table. We prove the existence of a weak solution for the model completed with initial and boundary conditions. We also prove that the depths of the two interfaces satisfy a coupled maximum principle.

Students' Relationships with Mathematics: Affect and Identity

ERIC Educational Resources Information Center

Ingram, Naomi

2015-01-01

In this paper, an examination of students' relationships with mathematics is informed by affective research into internal mathematical structures and identity research into students' narratives. By analysing the perceptions of a class of 31 adolescents, five interacting elements emerged: students' views, feelings, mathematical knowledge,…

Is ``the Theory of Everything'' Merely the Ultimate Ensemble Theory?

NASA Astrophysics Data System (ADS)

Tegmark, Max

1998-11-01

We discuss some physical consequences of what might be called "the ultimate ensemble theory,", where not only worlds corresponding to say different sets of initial data or different physical constants are considered equally real, but also worlds ruled by altogether different equations. The only postulate in this theory is that all structures that exist mathematically exist also physically, by which we mean that in those complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically "real" world. We find that it is far from clear that this simple theory, which has no free parameters whatsoever, is observationally ruled out. The predictions of the theory take the form of probability distributions for the outcome of experiments, which makes it testable. In addition, it may be possible to rule it out by comparing its a priori predictions for the observable attributes of nature (the particle masses, the dimensionality of spacetime, etc.) with what is observed.

Building Knowledge Structures by Testing Helps Children With Mathematical Learning Difficulty.

PubMed

Zhang, Yiyun; Zhou, Xinlin

2016-01-01

Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by testing using a web-based curriculum learning system. A total of 142 children with MLD were recruited; half of the children were in the experimental group (using the system), and the other half were in the control group (not using the system). The children were encouraged to use the web-based learning system at home for at least a 15-min session, at least once a week, for one and a half months. The mean accumulated time of testing on the system for children in the experimental group was 56.2 min. Children in the experimental group had significantly higher scores on their final mathematical examination compared to the control group. The results suggest that web-based curriculum learning through testing that promotes the building of knowledge structures for a mathematical course was helpful for children with MLD. © Hammill Institute on Disabilities 2014.

Rate Kinetics and Molecular Dynamics of the Structural Transitions in Amyloidogenic Proteins

NASA Astrophysics Data System (ADS)

Steckmann, Timothy M.

Amyloid fibril aggregation is associated with several horrific diseases such as Alzheimer's, Creutzfeld-Jacob, diabetes, Parkinson's and others. The process of amyloid aggregation involves forming myriad different metastable intermediate aggregates. Amyloid fibrils are composed of proteins that originate in an innocuous alpha-helix or random-coil structure. The alpha-helices convert their structure to beta-strands that aggregate into beta-sheets, and then into protofibrils, and ultimately into fully formed amyloid fibrils. On the basis of experimental data, I have developed a mathematical model for the kinetics of the reaction pathways and determined rate parameters for peptide secondary structural conversion and aggregation during the entire fibrillogenesis process from random coil to fibrils, including the molecular species that accelerate the conversions. The specific steps of the model and the rate constants that are determined by fitting to experimental data provide insight on the molecular species involved in the fibril formation process. To better understand the molecular basis of the protein structural transitions and aggregation, I report on molecular dynamics (MD) computational studies on the formation of amyloid protofibrillar structures in the small model protein ccbeta, which undergoes many of the structural transitions of the larger, naturally occurring amyloid forming proteins. Two different structural transition processes involving hydrogen bonds are observed for aggregation into fibrils: the breaking of intrachain hydrogen bonds to allow beta-hairpin proteins to straighten, and the subsequent formation of interchain hydrogen bonds during aggregation into amyloid fibrils. For my MD simulations, I found that the temperature dependence of these two different structural transition processes results in the existence of a temperature window that the ccbeta protein experiences during the process of forming protofibrillar structures. Both the mathematical modeling of the kinetics and the MD simulations show that molecular structural heterogeneity is a major factor in the process. The MD simulations also show that intrachain and interchain hydrogen bonds breaking and forming is strongly correlated to the process of amyloid formation.

Education and Research in the SEENET-MTP Regional Framework for Higher Education in Physics

NASA Astrophysics Data System (ADS)

Constantinescu, R.; Djordjevic, G. S.

2010-01-01

Southeastern European countries undergo significant changes in the demand/supply ratio on the labour market and in the structure of professional competences that are necessary for undertaking a professional activity. In addition, brain-drain process and decrease of interest for a career in basic sciences put many challenges for our community. Consequently, based on the activity of the Southeastern European Network in Mathematical and Theoretical Physics (SEENET MTP Network) in connecting groups and persons working in mathematics and theoretical physics, we investigate specific qualifications recognized in these fields in all the countries from the region, and the related competences necessary for practising the respective occupations. A list of new possible occupations will be promoted for inclusion in the National Qualifications Register for Higher Education. Finally, we analyze the vision existing in this region on the higher education qualifications against the European vision and experience, in particular in training of Master students, PhD students, and senior teaching and research staff through the Network, i.e. multilateral and bilateral programs.

The formal Darwinism project: a mid-term report.

PubMed

Grafen, A

2007-07-01

For 8 years I have been pursuing in print an ambitious and at times highly technical programme of work, the 'Formal Darwinism Project', whose essence is to underpin and formalize the fitness optimization ideas used by behavioural ecologists, using a new kind of argument linking the mathematics of motion and the mathematics of optimization. The value of the project is to give stronger support to current practices, and at the same time sharpening theoretical ideas and suggesting principled resolutions of some untidy areas, for example, how to define fitness. The aim is also to unify existing free-standing theoretical structures, such as inclusive fitness theory, Evolutionary Stable Strategy (ESS) theory and bet-hedging theory. The 40-year-old misunderstanding over the meaning of fitness optimization between mathematicians and biologists is explained. Most of the elements required for a general theory have now been implemented, but not together in the same framework, and 'general time' remains to be developed and integrated with the other elements to produce a final unified theory of neo-Darwinian natural selection.

Cell-oriented modeling of angiogenesis.

PubMed

Guidolin, Diego; Rebuffat, Piera; Albertin, Giovanna

2011-01-01

Due to its significant involvement in various physiological and pathological conditions, angiogenesis (the development of new blood vessels from an existing vasculature) represents an important area of the actual biological research and a field in which mathematical modeling proved particularly useful in supporting the experimental work. In this paper, we focus on a specific modeling strategy, known as "cell-centered" approach. This type of mathematical models work at a "mesoscopic scale," assuming the cell as the natural level of abstraction for computational modeling of development. They treat cells phenomenologically, considering their essential behaviors to study how tissue structure and organization emerge from the collective dynamics of multiple cells. The main contributions of the cell-oriented approach to the study of the angiogenic process will be described. From one side, they have generated "basic science understanding" about the process of capillary assembly during development, growth, and pathology. On the other side, models were also developed supporting "applied biomedical research" for the purpose of identifying new therapeutic targets and clinically relevant approaches for either inhibiting or stimulating angiogenesis.

Novel method for edge detection of retinal vessels based on the model of the retinal vascular network and mathematical morphology

NASA Astrophysics Data System (ADS)

Xu, Lei; Zheng, Xiaoxiang; Zhang, Hengyi; Yu, Yajun

1998-09-01

Accurate edge detection of retinal vessels is a prerequisite for quantitative analysis of subtle morphological changes of retinal vessels under different pathological conditions. A novel method for edge detection of retinal vessels is presented in this paper. Methods: (1) Wavelet-based image preprocessing. (2) The signed edge detection algorithm and mathematical morphological operation are applied to get the approximate regions that contain retinal vessels. (3) By convolving the preprocessed image with a LoG operator only on the detected approximate regions of retinal vessels, followed by edges refining, clear edge maps of the retinal vessels are fast obtained. Results: A detailed performance evaluation together with the existing techniques is given to demonstrate the strong features of our method. Conclusions: True edge locations of retinal vessels can be fast detected with continuous structures of retinal vessels, less non- vessel segments left and insensitivity to noise. The method is also suitable for other application fields such as road edge detection.

The APU and the 1978 Mathematics Survey

ERIC Educational Resources Information Center

Bell, Alan

1977-01-01

A tentative structure for a survey concerned with assessing the whole range of outcomes of school mathematics education is outlined. The structure provides for surveying content categories, process categories, and attitudes, utilizing practical manipulative problems. (MN)

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, George J.

1990-01-01

The development of a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads is examined. In the mathematical model, geometric as well as material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.

1991-01-01

This report deals with the development of a general mathematical model and solution methodology for analyzing the structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads. In the mathematical model, geometric as well as the material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Structure and inference in annotated networks

PubMed Central

Newman, M. E. J.; Clauset, Aaron

2016-01-01

For many networks of scientific interest we know both the connections of the network and information about the network nodes, such as the age or gender of individuals in a social network. Here we demonstrate how this ‘metadata' can be used to improve our understanding of network structure. We focus in particular on the problem of community detection in networks and develop a mathematically principled approach that combines a network and its metadata to detect communities more accurately than can be done with either alone. Crucially, the method does not assume that the metadata are correlated with the communities we are trying to find. Instead, the method learns whether a correlation exists and correctly uses or ignores the metadata depending on whether they contain useful information. We demonstrate our method on synthetic networks with known structure and on real-world networks, large and small, drawn from social, biological and technological domains. PMID:27306566

Space structure vibration modes: How many exist? Which ones are important?

NASA Technical Reports Server (NTRS)

Hughes, P. C.

1984-01-01

This report attempts to shed some light on the two issues raised in the title, namely, how many vibration modes does a real structure have, and which of these modes are important? The surprise-free answers to these two questions are, respectively, an infinite number and the first several modes. The author argues that the absurd subspace (all but the first billion modes) is not a strength of continuum modeling, but, in fact, a weakness. Partial differential equations are not real structures, only mathematical models. This note also explains (1) that the PDE model and the finite element model are, in fact, the same model, the latter being a numerical method for dealing with the former, (2) that modes may be selected on dynamical grounds other than frequency alone, and (3) that long slender rods are useful as primitive cases but dangerous to extrapolate from.

Structure and inference in annotated networks

NASA Astrophysics Data System (ADS)

Newman, M. E. J.; Clauset, Aaron

2016-06-01

For many networks of scientific interest we know both the connections of the network and information about the network nodes, such as the age or gender of individuals in a social network. Here we demonstrate how this `metadata' can be used to improve our understanding of network structure. We focus in particular on the problem of community detection in networks and develop a mathematically principled approach that combines a network and its metadata to detect communities more accurately than can be done with either alone. Crucially, the method does not assume that the metadata are correlated with the communities we are trying to find. Instead, the method learns whether a correlation exists and correctly uses or ignores the metadata depending on whether they contain useful information. We demonstrate our method on synthetic networks with known structure and on real-world networks, large and small, drawn from social, biological and technological domains.

Differentiated Instruction in Developmental Mathematics Classes and Achievement of Ethnic Minority Students

ERIC Educational Resources Information Center

Hood, Otis D., Jr.

2012-01-01

National educational assessment organizations present statistical information that an achievement gap exists between White students and students of color. This achievement gap closely relates to students representing lower SES conditions. This study examined the lack of achievement for ethnic minorities in the field of mathematics using an…

Students' Preferences in Undergraduate Mathematics Assessment

ERIC Educational Resources Information Center

Iannone, P.; Simpson, A.

2015-01-01

Existing research into students' preferences for assessment methods has been developed from a restricted sample: in particular, the voice of students in the 'hard-pure sciences' has rarely been heard. We conducted a mixed method study to explore mathematics students' preferences of assessment methods. In contrast to the message from the general…

Math and Science Model Programs Manual.

ERIC Educational Resources Information Center

Sawyer, Donna, Comp.; And Others

This implementation manual has been developed to describe four model mathematics and science programs designed to increase African-American students' interest in mathematics and science. The manual will help affiliates of the Urban League to mobilize existing community resources to achieve the goals of the national education initiative. The four…

A Design To Improve Children's Competencies in Solving Mathematical Word Problems.

ERIC Educational Resources Information Center

Zimmerman, Helene

A discrepancy exists between children's ability to compute and their ability to solve mathematical word problems. The literature suggests a variety of methods that have been attempted to improve this skill with varying success. The utilization of manipulatives, visualization, illustration, and emphasis on improving listening skills all were…

Robotics: Assessing Its Role in Improving Mathematics Skills for Grades 4 to 5

ERIC Educational Resources Information Center

Laughlin, Sara Rose

2013-01-01

Inspiring and motivating students to pursue science, technology, engineering, and mathematics education continues to be an important educational focus in the United States. Robotics programs are one strategy developed to accomplish this goal. This causal comparative study focused on investigating whether a causal relationship exists between…

Development of an Intelligent Instruction System for Mathematical Computation

ERIC Educational Resources Information Center

Kim, Du Gyu; Lee, Jaemu

2013-01-01

In this paper, we propose the development of a web-based, intelligent instruction system to help elementary school students for mathematical computation. We concentrate on the intelligence facilities which support diagnosis and advice. The existing web-based instruction systems merely give information on whether the learners' replies are…

STEAM by Another Name: Transdisciplinary Practice in Art and Design Education

ERIC Educational Resources Information Center

Costantino, Tracie

2018-01-01

The recent movement to include art and design in Science, Technology, Engineering, and Mathematics (STEM) education has made Science, Technology, Engineering, Arts, and Mathematics (STEAM) an increasingly common acronym in the education lexicon. The STEAM movement builds on existing models of interdisciplinary curriculum, but what makes the union…

The Role of Culture in Rural Ugandan Mathematics Teaching and Learning

ERIC Educational Resources Information Center

Kaahwa, Janet

2011-01-01

Education systems are culturally embedded and, therefore, difficult to improve without understanding actions, beliefs, and attitudes related to education existing within the culture. This article discusses the role culture plays in the teaching and learning of mathematics. It specifically dwells on the ways culture could benefit learners from…

Evaluating Mathematics Teachers' Professional Development Motivations and Needs

ERIC Educational Resources Information Center

Caddle, Mary C.; Bautista, Alfredo; Brizuela, Bárbara M.; Sharpe, Sheree T.

2016-01-01

While there is widespread agreement that one-size-fits-all professional development (PD) initiatives have limited potential to foster teacher learning, much existing PD is still designed without attention to teachers' motivations and needs. This paper shows that the strengths and weaknesses of middle school mathematics teachers that engage in PD…

Learning Is Moving in New Ways: The Ecological Dynamics of Mathematics Education

ERIC Educational Resources Information Center

Abrahamson, Dor; Sánchez-García, Raúl

2016-01-01

Whereas emerging technologies, such as touchscreen tablets, are bringing sensorimotor interaction back into mathematics learning activities, existing educational theory is not geared to inform or analyze passages from action to concept. We present case studies of tutor-student behaviors in an embodied-interaction learning environment, the…

Preparation of the Future Teacher for Work with Gifted Children

ERIC Educational Resources Information Center

Bochkareva, Tatyana; Akhmetshin, Elvir; Osadchy, Eduard; Romanov, Petr; Konovalova, Elena

2018-01-01

The paper is devoted to the problem of creating a system of training of future teachers for work with gifted schoolchildren in mathematics. The authors analyze the existing curricula and basic professional educational programs for the preparation of Bachelors in the directions of training "Pedagogical Education" and "Mathematics and…

A Vector Representation for Thermodynamic Relationships

ERIC Educational Resources Information Center

Pogliani, Lionello

2006-01-01

The existing vector formalism method for thermodynamic relationship maintains tractability and uses accessible mathematics, which can be seen as a diverting and entertaining step into the mathematical formalism of thermodynamics and as an elementary application of matrix algebra. The method is based on ideas and operations apt to improve the…

A Preservice Mathematics Teacher's Beliefs about Teaching Mathematics with Technology

ERIC Educational Resources Information Center

Belbase, Shashidhar

2015-01-01

This paper analyzed a preservice mathematics teacher's beliefs about teaching mathematics with technology. The researcher used five semi-structured task-based interviews in the problematic contexts of teaching fraction multiplications with JavaBars, functions and limits, and geometric transformations with Geometer's Sketchpad, and statistical data…

Teachers' Perception of Social Justice in Mathematics Classrooms

ERIC Educational Resources Information Center

Panthi, Ram Krishna; Luitel, Bal Chandra; Belbase, Shashidhar

2017-01-01

The purpose of this study was to explore mathematics teachers' perception of social justice in mathematics classrooms. We applied interpretive qualitative method for data collection, analysis, and interpretation through iterative process. We administered in-depth semi-structured interviews to capture the perceptions of three mathematics teachers…

Mathematical Identity for a Sustainable Future: An Interpretative Phenomenological Analysis

ERIC Educational Resources Information Center

Pipere, Anita; Micule, Ilona

2014-01-01

Individual in-depth, semi-structured interviews with three mathematics teachers were conducted to investigate the dynamics of their life-long relationships with mathematics, synthesised as mathematical identity from different identity positions in the context of dialogical self. The qualitative data were scrutinised employing interpretive…

Teachers' Perception of Social Justice in Mathematics Classrooms

ERIC Educational Resources Information Center

Panthi, Ram Krishna; Luitel, Bal Chandra; Belbase, Shashidhar

2018-01-01

The purpose of this study was to explore mathematics teachers' perception of social justice in mathematics classrooms. We applied interpretive qualitative method for data collection, analysis, and interpretation through iterative process. We administered in-depth semi-structured interviews to capture the perceptions of three mathematics teachers…

Mathematical model of polyethylene pipe bending stress state

NASA Astrophysics Data System (ADS)

Serebrennikov, Anatoly; Serebrennikov, Daniil

2018-03-01

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

NASTRAN nonlinear vibration analysis of beam and frame structures

NASA Technical Reports Server (NTRS)

Mei, C.; Rogers, J. L., Jr.

1975-01-01

A capability for the nonlinear vibration analysis of beam and frame structures suitable for use with NASTRAN level 15.5 is described. The nonlinearity considered is due to the presence of axial loads induced by longitudinal end restraints and lateral displacements that are large compared to the beam height. A brief discussion is included of the mathematical analysis and the geometrical stiffness matrix for a prismatic beam (BAR) element. Also included are a brief discussion of the equivalent linearization iterative process used to determine the nonlinear frequency, the required modifications to subroutines DBAR and XMPLBD of the NASTRAN code, and the appropriate vibration capability, four example problems are presented. Comparisons with existing experimental and analytical results show that excellent accuracy is achieved with NASTRAN in all cases.

The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

NASA Astrophysics Data System (ADS)

Frey, Kimberly

The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum mathematics in a sense which parallels the foundational role of classical set theory in classical mathematics. One immediate application of the quantum set theory we develop is to provide a foundation on which to construct quantum natural numbers, which are the quantum analog of the classical counting numbers. It turns out that in a special class of models, there exists a 1-1 correspondence between the quantum natural numbers and bounded observables in quantum theory whose eigenvalues are (ordinary) natural numbers. This 1-1 correspondence is remarkably satisfying, and not only gives us great confidence in our quantum set theory, but indicates the naturalness of such models for quantum theory itself. We go on to develop a Peano-like arithmetic for these new "numbers," as well as consider some of its consequences. Finally, we conclude by summarizing our results, and discussing directions for future work.

Canadian Mathematics Education Study Group = Groupe Canadien d'etude en didactique des mathematiques. Proceedings of the Annual Meeting (22nd, Vancouver, British Columbia, Canada, May 29-June 2, 1998).

ERIC Educational Resources Information Center

Pothier, Yvonne M., Ed.

This proceedings includes the following papers: (1) "Structure of Attention in Teaching Mathematics" (John Mason); (2) "Communicating Mathematics or Mathematics Storytelling" (Kathy Heinrich); (3) "Assessing Mathematical Thinking" (Florence Glanfield and Pat Rogers); (4) "From Theory to Observational Data (and…

A Randomized Controlled Trial of the Impact of Schema-Based Instruction on Mathematical Outcomes for Third-Grade Students with Mathematics Difficulties

ERIC Educational Resources Information Center

Jitendra, Asha K.; Dupuis, Danielle N.; Rodriguez, Michael C.; Zaslofsky, Anne F.; Slater, Susan; Cozine-Corroy, Kelly; Church, Chris

2013-01-01

This study compared the effects of delivering a supplemental, small-group tutoring intervention on the mathematics outcomes of third-grade students at risk for mathematics difficulties (MD) who were randomly assigned to either a schema-based instruction (SBI) or control group. SBI emphasized the underlying mathematical structure of additive…

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2014-12-01

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

Physical Realization of von Neumann Lattices in Rotating Bose Gases with Dipole Interatomic Interactions.

PubMed

Cheng, Szu-Cheng; Jheng, Shih-Da

2016-08-22

This paper reports a novel type of vortex lattice, referred to as a bubble crystal, which was discovered in rapidly rotating Bose gases with long-range interactions. Bubble crystals differ from vortex lattices which possess a single quantum flux per unit cell, while atoms in bubble crystals are clustered periodically and surrounded by vortices. No existing model is able to describe the vortex structure of bubble crystals; however, we identified a mathematical lattice, which is a subset of coherent states and exists periodically in the physical space. This lattice is called a von Neumann lattice, and when it possesses a single vortex per unit cell, it presents the same geometrical structure as an Abrikosov lattice. In this report, we extend the von Neumann lattice to one with an integral number of flux quanta per unit cell and demonstrate that von Neumann lattices well reproduce the translational properties of bubble crystals. Numerical simulations confirm that, as a generalized vortex, a von Neumann lattice can be physically realized using vortex lattices in rapidly rotating Bose gases with dipole interatomic interactions.

On recursion.

PubMed

Watumull, Jeffrey; Hauser, Marc D; Roberts, Ian G; Hornstein, Norbert

2014-01-08

It is a truism that conceptual understanding of a hypothesis is required for its empirical investigation. However, the concept of recursion as articulated in the context of linguistic analysis has been perennially confused. Nowhere has this been more evident than in attempts to critique and extend Hauseretal's. (2002) articulation. These authors put forward the hypothesis that what is uniquely human and unique to the faculty of language-the faculty of language in the narrow sense (FLN)-is a recursive system that generates and maps syntactic objects to conceptual-intentional and sensory-motor systems. This thesis was based on the standard mathematical definition of recursion as understood by Gödel and Turing, and yet has commonly been interpreted in other ways, most notably and incorrectly as a thesis about the capacity for syntactic embedding. As we explain, the recursiveness of a function is defined independent of such output, whether infinite or finite, embedded or unembedded-existent or non-existent. And to the extent that embedding is a sufficient, though not necessary, diagnostic of recursion, it has not been established that the apparent restriction on embedding in some languages is of any theoretical import. Misunderstanding of these facts has generated research that is often irrelevant to the FLN thesis as well as to other theories of language competence that focus on its generative power of expression. This essay is an attempt to bring conceptual clarity to such discussions as well as to future empirical investigations by explaining three criterial properties of recursion: computability (i.e., rules in intension rather than lists in extension); definition by induction (i.e., rules strongly generative of structure); and mathematical induction (i.e., rules for the principled-and potentially unbounded-expansion of strongly generated structure). By these necessary and sufficient criteria, the grammars of all natural languages are recursive.

On recursion

PubMed Central

Watumull, Jeffrey; Hauser, Marc D.; Roberts, Ian G.; Hornstein, Norbert

2014-01-01

It is a truism that conceptual understanding of a hypothesis is required for its empirical investigation. However, the concept of recursion as articulated in the context of linguistic analysis has been perennially confused. Nowhere has this been more evident than in attempts to critique and extend Hauseretal's. (2002) articulation. These authors put forward the hypothesis that what is uniquely human and unique to the faculty of language—the faculty of language in the narrow sense (FLN)—is a recursive system that generates and maps syntactic objects to conceptual-intentional and sensory-motor systems. This thesis was based on the standard mathematical definition of recursion as understood by Gödel and Turing, and yet has commonly been interpreted in other ways, most notably and incorrectly as a thesis about the capacity for syntactic embedding. As we explain, the recursiveness of a function is defined independent of such output, whether infinite or finite, embedded or unembedded—existent or non-existent. And to the extent that embedding is a sufficient, though not necessary, diagnostic of recursion, it has not been established that the apparent restriction on embedding in some languages is of any theoretical import. Misunderstanding of these facts has generated research that is often irrelevant to the FLN thesis as well as to other theories of language competence that focus on its generative power of expression. This essay is an attempt to bring conceptual clarity to such discussions as well as to future empirical investigations by explaining three criterial properties of recursion: computability (i.e., rules in intension rather than lists in extension); definition by induction (i.e., rules strongly generative of structure); and mathematical induction (i.e., rules for the principled—and potentially unbounded—expansion of strongly generated structure). By these necessary and sufficient criteria, the grammars of all natural languages are recursive. PMID:24409164

The Psychophysics of Algebra Expertise: Mathematics Perceptual Learning Interventions Produce Durable Encoding Changes

ERIC Educational Resources Information Center

Bufford, Carolyn A.; Mettler, Everett; Geller, Emma H.; Kellman, Philip J.

2014-01-01

Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM)…

Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

ERIC Educational Resources Information Center

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-01-01

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…

Structurally Sound Statistics Instruction

ERIC Educational Resources Information Center

Casey, Stephanie A.; Bostic, Jonathan D.

2016-01-01

The Common Core's Standards for Mathematical Practice (SMP) call for all K-grade 12 students to develop expertise in the processes and proficiencies of doing mathematics. However, the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) as a whole addresses students' learning of not only mathematics but also statistics. This situation…

Factors That Explains Student Anxiety toward Mathematics

ERIC Educational Resources Information Center

García-Santillán, Arturo; Escalera-Chávez, Milka Elena; Moreno-García, Elena; Santana-Villegas, Josefina del Carmen

2016-01-01

The aim of this research is to test whether anxiety toward mathematics is made up of a five-factor structure: anxiety toward evaluation, anxiety toward temporality, anxiety toward understanding of mathematical problems, anxiety toward numbers and operations, and anxiety toward mathematical situations in real life. Our study sample was formed of…

Gender Differences in Mathematics: Does the Story Need to Be Rewritten?

ERIC Educational Resources Information Center

Brunner, Martin; Krauss, Stefan; Kunter, Mareike

2008-01-01

Empirical studies of high school mathematics typically report small gender differences in favor of boys. The present article challenges this established finding by comparing two competing structural conceptions of mathematical ability. The standard model assumes mathematical ability alone to account for the interindividual differences observed on…

Supporting Mathematics Teachers' Development through Higher Education

ERIC Educational Resources Information Center

Prendergast, Mark; Roche, Joseph

2017-01-01

Mathematics education, both nationally and internationally, is facing a number of challenges with significant on-going shifts in the structure, content, and core principles of mathematics curricula in countries around the world. For example, in Ireland there was an ambitious reform of the post-primary mathematics curricula in 2010 with further…

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

A Guided Reinvention of Ring, Integral Domain, and Field

ERIC Educational Resources Information Center

Cook, John Paul

2012-01-01

Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by exposing them to structures that form its foundation--it arguably approximates the actual practice of mathematics better than any…

Using Diagrams as Tools for the Solution of Non-Routine Mathematical Problems

ERIC Educational Resources Information Center

Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada

2009-01-01

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

Mathematics Curricula and Age Cohort Participation: A Six Nation Comparison.

ERIC Educational Resources Information Center

Natsoulas, Anthula

Secondary level mathematics programs of England, Finland, France, Israel, Japan and Swaziland are compared using data from the Second International Mathematics Study and United Nations sources. Within a clearly defined school structure, the number of mathematics course options, age cohort enrollments and male/female ratios are considered with an…

The Emergence of Mathematical Structures

ERIC Educational Resources Information Center

Hegedus, Stephen John; Moreno-Armella, Luis

2011-01-01

We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…

A structural equation modeling analysis of students' understanding in basic mathematics

NASA Astrophysics Data System (ADS)

Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus

2017-11-01

This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.

A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

NASA Astrophysics Data System (ADS)

Tuminaro, Jonathan

Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of mathematical use in the context physics, and (2) a detailed understanding, in terms of the proposed theoretical framework, of the errors that students make when using mathematics in the context of physics.

Approximation concepts for efficient structural synthesis

NASA Technical Reports Server (NTRS)

Schmit, L. A., Jr.; Miura, H.

1976-01-01

It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

Communication of Geometrical Structure and Its Relationship to Student Mathematical Achievement.

ERIC Educational Resources Information Center

Norrie, Alexander L.

The purpose of this study was to examine whether the mathematical structures inherent in grade 7 geometry curriculum objectives can be used to improve the communication of the objectives to students. Teacher inservice based upon geometrical properties and structures was combined with student teaching materials to try to improve student achievement…

Mathematics, Thermodynamics, and Modeling to Address Ten Common Misconceptions about Protein Structure, Folding, and Stability

ERIC Educational Resources Information Center

Robic, Srebrenka

2010-01-01

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative…

A Chinese Zodiac Mathematical Structure.

ERIC Educational Resources Information Center

Lamb, John F., Jr.

2000-01-01

Helps students identify the animal that corresponds to the year of their birth according to the Chinese zodiac. Defines the structure of the Chinese zodiac so that the subsets of compatibles and opposites form closed substructures with interesting mathematical properties. (ASK)

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

PubMed

Glaister, Karen

2007-05-01

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

Mathematical Approach to Identification of Load Structure at the Nodes of the Distribution Grids 6-10 kV and 0.4 kV

NASA Astrophysics Data System (ADS)

Nizamutdinova, T.; Mukhlynin, N.

2017-06-01

A significant increasing energy efficiency of the full cycle of production, transmission and distribution of electricity in grids should be based on the management of separate consumers of electricity. The existing energy supply systems based on the concept of «smart things» do not allow to identify the technical structure of the electricity consumption in the load nodes from the grid side. It makes solving the tasks of energy efficiency more difficult. To solve this problem, the use of Wavelet transform to create a mathematical tool for monitoring the load composition in the nodes of the distribution grids of 6-10 kV, 0.4 kV is proposed in this paper. The authors have created a unique wavelet based functions for some consumers, based on their current consumption graphs of these power consumers. Possibility of determination of the characteristics of individual consumers of electricity in total nodal charts of load is shown in the test case. In future, creation of a unified technical and informational model of load control will allow to solve the problem of increasing the economic efficiency of not only certain consumers, but also the entire power supply system as a whole.

Image-based modelling of skeletal muscle oxygenation

PubMed Central

Clough, G. F.

2017-01-01

The supply of oxygen in sufficient quantity is vital for the correct functioning of all organs in the human body, in particular for skeletal muscle during exercise. Disease is often associated with both an inhibition of the microvascular supply capability and is thought to relate to changes in the structure of blood vessel networks. Different methods exist to investigate the influence of the microvascular structure on tissue oxygenation, varying over a range of application areas, i.e. biological in vivo and in vitro experiments, imaging and mathematical modelling. Ideally, all of these methods should be combined within the same framework in order to fully understand the processes involved. This review discusses the mathematical models of skeletal muscle oxygenation currently available that are based upon images taken of the muscle microvasculature in vivo and ex vivo. Imaging systems suitable for capturing the blood vessel networks are discussed and respective contrasting methods presented. The review further informs the association between anatomical characteristics in health and disease. With this review we give the reader a tool to understand and establish the workflow of developing an image-based model of skeletal muscle oxygenation. Finally, we give an outlook for improvements needed for measurements and imaging techniques to adequately investigate the microvascular capability for oxygen exchange. PMID:28202595

An imaging-based stochastic model for simulation of tumour vasculature

NASA Astrophysics Data System (ADS)

Adhikarla, Vikram; Jeraj, Robert

2012-10-01

A mathematical model which reconstructs the structure of existing vasculature using patient-specific anatomical, functional and molecular imaging as input was developed. The vessel structure is modelled according to empirical vascular parameters, such as the mean vessel branching angle. The model is calibrated such that the resultant oxygen map modelled from the simulated microvasculature stochastically matches the input oxygen map to a high degree of accuracy (R2 ≈ 1). The calibrated model was successfully applied to preclinical imaging data. Starting from the anatomical vasculature image (obtained from contrast-enhanced computed tomography), a representative map of the complete vasculature was stochastically simulated as determined by the oxygen map (obtained from hypoxia [64Cu]Cu-ATSM positron emission tomography). The simulated microscopic vasculature and the calculated oxygenation map successfully represent the imaged hypoxia distribution (R2 = 0.94). The model elicits the parameters required to simulate vasculature consistent with imaging and provides a key mathematical relationship relating the vessel volume to the tissue oxygen tension. Apart from providing an excellent framework for visualizing the imaging gap between the microscopic and macroscopic imagings, the model has the potential to be extended as a tool to study the dynamics between the tumour and the vasculature in a patient-specific manner and has an application in the simulation of anti-angiogenic therapies.

Teaching undergraduate biomechanics with Just-in-Time Teaching.

PubMed

Riskowski, Jody L

2015-06-01

Biomechanics education is a vital component of kinesiology, sports medicine, and physical education, as well as for many biomedical engineering and bioengineering undergraduate programmes. Little research exists regarding effective teaching strategies for biomechanics. However, prior work suggests that student learning in undergraduate physics courses has been aided by using the Just-in-Time Teaching (JiTT). As physics understanding plays a role in biomechanics understanding, the purpose of study was to evaluate the use of a JiTT framework in an undergraduate biomechanics course. This two-year action-based research study evaluated three JiTT frameworks: (1) no JiTT; (2) mathematics-based JiTT; and (3) concept-based JiTT. A pre- and post-course assessment of student learning used the biomechanics concept inventory and a biomechanics concept map. A general linear model assessed differences between the course assessments by JiTT framework in order to evaluate learning and teaching effectiveness. The results indicated significantly higher learning gains and better conceptual understanding in a concept-based JiTT course, relative to a mathematics-based JiTT or no JiTT course structure. These results suggest that a course structure involving concept-based questions using a JiTT strategy may be an effective method for engaging undergraduate students and promoting learning in biomechanics courses.

The futility of utility: how market dynamics marginalize Adam Smith

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2000-10-01

Economic theorizing is based on the postulated, nonempiric notion of utility. Economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics I show the following. A utility function generally does not exist mathematically due to nonintegrable dynamics when production/investment are accounted for, resolving Mirowski's thesis. Price as a function of demand does not exist mathematically either. All equilibria are unstable. I then explain how deterministic chaos can be distinguished from random noise at short times. In the generalization to liquid markets and finance theory described by stochastic excess demand dynamics, I also show the following. Market price distributions cannot be rescaled to describe price movements as ‘equilibrium’ fluctuations about a systematic drift in price. Utility maximization does not describe equilibrium. Maximization of the Gibbs entropy of the observed price distribution of an asset would describe equilibrium, if equilibrium could be achieved, but equilibrium does not describe real, liquid markets (stocks, bonds, foreign exchange). There are three inconsistent definitions of equilibrium used in economics and finance, only one of which is correct. Prices in unregulated free markets are unstable against both noise and rising or falling expectations: Adam Smith's stabilizing invisible hand does not exist, either in mathematical models of liquid market data, or in real market data.

R A Fisher, design theory, and the Indian connection.

PubMed

Rau, A R P

2009-09-01

Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R A Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.

A Mathematical Model for the Middle Ear Ventilation

NASA Astrophysics Data System (ADS)

Molnárka, G.; Miletics, E. M.; Fücsek, M.

2008-09-01

The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([l]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation.

RNA Secondary Structure Prediction by Using Discrete Mathematics: An Interdisciplinary Research Experience for Undergraduate Students

PubMed Central

Ellington, Roni; Wachira, James

2010-01-01

The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses discrete mathematical techniques and identifies specified base pairs as parameters. The goal of the REU was to introduce upper-level undergraduate students to the principles and challenges of interdisciplinary research in molecular biology and discrete mathematics. At the beginning of the project, students from the biology and mathematics departments of a mid-sized university received instruction on the role of secondary structure in the function of eukaryotic RNAs and RNA viruses, RNA related to combinatorics, and the National Center for Biotechnology Information resources. The student research projects focused on RNA secondary structure prediction on a regulatory region of the yellow fever virus RNA genome and on an untranslated region of an mRNA of a gene associated with the neurological disorder epilepsy. At the end of the project, the REU students gave poster and oral presentations, and they submitted written final project reports to the program director. The outcome of the REU was that the students gained transferable knowledge and skills in bioinformatics and an awareness of the applications of discrete mathematics to biological research problems. PMID:20810968

RNA secondary structure prediction by using discrete mathematics: an interdisciplinary research experience for undergraduate students.

PubMed

Ellington, Roni; Wachira, James; Nkwanta, Asamoah

2010-01-01

The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses discrete mathematical techniques and identifies specified base pairs as parameters. The goal of the REU was to introduce upper-level undergraduate students to the principles and challenges of interdisciplinary research in molecular biology and discrete mathematics. At the beginning of the project, students from the biology and mathematics departments of a mid-sized university received instruction on the role of secondary structure in the function of eukaryotic RNAs and RNA viruses, RNA related to combinatorics, and the National Center for Biotechnology Information resources. The student research projects focused on RNA secondary structure prediction on a regulatory region of the yellow fever virus RNA genome and on an untranslated region of an mRNA of a gene associated with the neurological disorder epilepsy. At the end of the project, the REU students gave poster and oral presentations, and they submitted written final project reports to the program director. The outcome of the REU was that the students gained transferable knowledge and skills in bioinformatics and an awareness of the applications of discrete mathematics to biological research problems.

A Critical Evaluation of Mathematics Courses in Architectural Education and Practice

ERIC Educational Resources Information Center

Cikis, Seniz

2010-01-01

Mathematics courses are integral part of architectural education. The content and objectives of these courses were determined in the Age of Enlightenment. Although conditions have changed since then, they still exist without being subjected to a radical revision. This study aims to introduce the necessary information for upgrading the content of…

Improving First Year Mathematics Teaching through Making Connections: An Action Research Approach

ERIC Educational Resources Information Center

Balatti, Jo; Belward, Shaun

2012-01-01

Four university lecturers at an Australian university have been undertaking an action research project for almost two years to improve first year mathematics teaching. The project is analysed here through the single idea of "connection". Making new connections or changing the nature of existing connections with colleagues and especially…

High Level Technology in a Low Level Mathematics Course.

ERIC Educational Resources Information Center

Schultz, James E.; Noguera, Norma

2000-01-01

Describes a teaching experiment in which spreadsheets and computer algebra systems were used to teach a low-level college consumer mathematics course. Students were successful in using different types of functions to solve a variety of problems drawn from real-world situations. Provides an existence proof that computer algebra systems can assist…

Adapting the Academic Motivation Scale for Use in Pre-Tertiary Mathematics Classrooms

ERIC Educational Resources Information Center

Lim, Siew Yee; Chapman, Elaine

2015-01-01

The Academic Motivation Scale (AMS) is a comprehensive and widely used instrument for assessing motivation based on the self-determination theory. Currently, no such comprehensive instrument exists to assess the different domains of motivation (stipulated by the self-determination theory) in mathematics education at the pre-tertiary level (grades…

A Voyage of Mathematical and Cultural Awareness for Students of Upper Secondary School

ERIC Educational Resources Information Center

Panagiotou, Evangelos N.

2014-01-01

Many papers have emphasized the need for and importance of particular examples and the underlying rationale for introducing a historical dimension in mathematics education. This article presents the development and implementation of a project, based on original sources, in a situation where the existing curriculum does not include history. The…

Statistics and Style. Mathematical Linguistics and Automatic Language Processing No. 6.

ERIC Educational Resources Information Center

Dolezel, Lubomir, Ed.; Bailey, Richard W., Ed.

This collection of 17 articles concerning the application of mathematical models and techniques to the study of literary style is an attempt to overcome the communication barriers that exist between scholars in the various fields that find their meeting ground in statistical stylistics. The articles selected were chosen to represent the best…

A Mathematical model to investigate quorum sensing regulation and its heterogenecity in pseudomonas syringae on leaves

USDA-ARS?s Scientific Manuscript database

The bacterium Pseudomonas syringae is a plant-pathogen, which through quorum sensing (QS), controls virulence. In this paper, by means of mathematical modeling, we investigate QS of this bacterium when living on leaf surfaces. We extend an existing stochastic model for the formation of Pseudomonas s...

National Survey of STEM High Schools' Curricular and Instructional Strategies and Practices

ERIC Educational Resources Information Center

Forman, Jennifer; Gubbins, Elizabeth Jean; Villanueva, Merzili; Massicotte, Cindy; Callahan, Carolyn; Tofel-Grehl, Colby

2015-01-01

A limited number of highly selective high schools specializing in science, technology, engineering and mathematics (STEM) education have existed for many decades, encouraging youth with identified STEM talent to pursue careers as STEM leaders and innovators. As members of the National Consortium for Specialized Secondary Schools of Mathematics,…

Mathematics Content Standards Benchmarks and Performance Standards

ERIC Educational Resources Information Center

New Mexico Public Education Department, 2008

2008-01-01

New Mexico Mathematics Content Standards, Benchmarks, and Performance Standards identify what students should know and be able to do across all grade levels, forming a spiraling framework in the sense that many skills, once introduced, develop over time. While the Performance Standards are set forth at grade-specific levels, they do not exist as…

Leadership for School Numeracy: How School Leaders' Knowledge and Attitudes Impact Student Mathematics Achievement

ERIC Educational Resources Information Center

Walker-Glenn, Michelle Lynn

2010-01-01

Although most high schools espouse school-wide literacy initiatives, few schools place equal emphasis on numeracy, or quantitative literacy. This lack of attention to quantitative skills is ironic in light of documented deficiencies in student mathematics achievement. While significant research exists regarding best practices for mathematics…

Synchronous Chat and Electronic Ink for Distance Support in Mathematics

ERIC Educational Resources Information Center

Loch, Birgit; McDonald, Christine

2007-01-01

For online mathematics instructors, synchronous communication can be a challenge due to the need for specialized symbols, graphics, or notations to explain key concepts. While software tools exist to support such communication, they can often be cumbersome and time-consuming for users to adopt in online exchanges. As one way of addressing this…

Vibration isolation by exploring bio-inspired structural nonlinearity.

PubMed

Wu, Zhijing; Jing, Xingjian; Bian, Jing; Li, Fengming; Allen, Robert

2015-10-08

Inspired by the limb structures of animals/insects in motion vibration control, a bio-inspired limb-like structure (LLS) is systematically studied for understanding and exploring its advantageous nonlinear function in passive vibration isolation. The bio-inspired system consists of asymmetric articulations (of different rod lengths) with inside vertical and horizontal springs (as animal muscle) of different linear stiffness. Mathematical modeling and analysis of the proposed LLS reveal that, (a) the system has very beneficial nonlinear stiffness which can provide flexible quasi-zero, zero and/or negative stiffness, and these nonlinear stiffness properties are adjustable or designable with structure parameters; (b) the asymmetric rod-length ratio and spring-stiffness ratio present very beneficial factors for tuning system equivalent stiffness; (c) the system loading capacity is also adjustable with the structure parameters which presents another flexible benefit in application. Experiments and comparisons with existing quasi-zero-stiffness isolators validate the advantageous features above, and some discussions are also given about how to select structural parameters for practical applications. The results would provide an innovative bio-inspired solution to passive vibration control in various engineering practice.

Application of geologic-mathematical 3D modeling for complex structure deposits by the example of Lower- Cretaceous period depositions in Western Ust - Balykh oil field (Khanty-Mansiysk Autonomous District)

NASA Astrophysics Data System (ADS)

Perevertailo, T.; Nedolivko, N.; Prisyazhnyuk, O.; Dolgaya, T.

2015-11-01

The complex structure of the Lower-Cretaceous formation by the example of the reservoir BC101 in Western Ust - Balykh Oil Field (Khanty-Mansiysk Autonomous District) has been studied. Reservoir range relationships have been identified. 3D geologic- mathematical modeling technique considering the heterogeneity and variability of a natural reservoir structure has been suggested. To improve the deposit geological structure integrity methods of mathematical statistics were applied, which, in its turn, made it possible to obtain equal probability models with similar input data and to consider the formation conditions of reservoir rocks and cap rocks.

Third Graders' Mathematical Thinking of Place Value through the Use of Concrete and Virtual Manipulatives

ERIC Educational Resources Information Center

Burris, Justin T.

2010-01-01

As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with…

A Structural Equation Model Explaining 8th Grade Students' Mathematics Achievements

ERIC Educational Resources Information Center

Yurt, Eyüp; Sünbül, Ali Murat

2014-01-01

The purpose of this study is to investigate, via a model, the explanatory and predictive relationships among the following variables: Mathematical Problem Solving and Reasoning Skills, Sources of Mathematics Self-Efficacy, Spatial Ability, and Mathematics Achievements of Secondary School 8th Grade Students. The sample group of the study, itself…

The Characteristics of a Good Mathematics Teacher in Terms of Students, Mathematics Teachers, and School Administrators

ERIC Educational Resources Information Center

Yesildere-Imre, Sibel

2017-01-01

This qualitative research aims to examine the opinions of school administrators, teachers, and middle school students about what makes a good mathematics teacher. Interviews were conducted with thirty-five participants: ten school administrators, ten mathematics teachers, and fifteen middle school students. A semi-structured interview form…

Adding Structure to the Transition Process to Advanced Mathematical Activity

ERIC Educational Resources Information Center

Engelbrecht, Johann

2010-01-01

The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…

Parent-Child Mathematical Interactions: Examining Self-Report and Direct Observation

ERIC Educational Resources Information Center

Missall, Kristen N.; Hojnoski, Robin L.; Moreano, Ginna

2017-01-01

Variability in children's early-learning home environments points to the need to better understand specific mechanisms of early mathematical development. We used a sample of 66 parent-preschool child dyads to describe parent-reported mathematical activities in the home and observed parent-child mathematical activities in a semi-structured play…

Identifying Systems of Interaction in Mathematical Engagement

ERIC Educational Resources Information Center

Brown, Bruce J. L.

2014-01-01

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

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

ERIC Educational Resources Information Center

Tutak, Tayfun; Güder, Yunus

2013-01-01

The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…

Traffic Flow Density Distribution Based on FEM

NASA Astrophysics Data System (ADS)

Ma, Jing; Cui, Jianming

In analysis of normal traffic flow, it usually uses the static or dynamic model to numerical analyze based on fluid mechanics. However, in such handling process, the problem of massive modeling and data handling exist, and the accuracy is not high. Finite Element Method (FEM) is a production which is developed from the combination of a modern mathematics, mathematics and computer technology, and it has been widely applied in various domain such as engineering. Based on existing theory of traffic flow, ITS and the development of FEM, a simulation theory of the FEM that solves the problems existing in traffic flow is put forward. Based on this theory, using the existing Finite Element Analysis (FEA) software, the traffic flow is simulated analyzed with fluid mechanics and the dynamics. Massive data processing problem of manually modeling and numerical analysis is solved, and the authenticity of simulation is enhanced.

Mathematical theory of exchange-driven growth

NASA Astrophysics Data System (ADS)

Esenturk, Emre

2018-07-01

Exchange-driven growth is a process in which pairs of clusters interact by exchanging single unit of mass at a time. The rate of exchange is given by an interaction kernel which depends on the masses of the two interacting clusters. In this paper we establish the fundamental mathematical properties of the mean field rate equations of this process for the first time. We find two different classes of behavior depending on whether is symmetric or not. For the non-symmetric case, we prove global existence and uniqueness of solutions for kernels satisfying . This result is optimal in the sense that we show for a large class of initial conditions and kernels satisfying the solutions cannot exist. On the other hand, for symmetric kernels, we prove global existence of solutions for ( while existence is lost for ( In the intermediate regime we can only show local existence. We conjecture that the intermediate regime exhibits finite-time gelation in accordance with the heuristic results obtained for particular kernels.

Rescheduling nursing shifts: scoping the challenge and examining the potential of mathematical model based tools.

PubMed

Clark, Alistair; Moule, Pam; Topping, Annie; Serpell, Martin

2015-05-01

To review research in the literature on nursing shift scheduling / rescheduling, and to report key issues identified in a consultation exercise with managers in four English National Health Service trusts to inform the development of mathematical tools for rescheduling decision-making. Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives from scheduling. Poor rescheduling decisions can have quality, cost and morale implications. A systematic critical literature review identified rescheduling issues and existing mathematic modelling tools. A consultation exercise with nursing managers examined the complex challenges associated with rescheduling. Minimal research exists on rescheduling compared with scheduling. Poor rescheduling can result in greater disruption to planned nursing shifts and may impact negatively on the quality and cost of patient care, and nurse morale and retention. Very little research examines management challenges or mathematical modelling for rescheduling. Shift rescheduling is a complex and frequent management activity that is more challenging than scheduling. Mathematical modelling may have potential as a tool to support managers to minimise rescheduling disruption. The lack of specific methodological support for rescheduling that takes into account its complexity, increases the likelihood of harm for patients and stress for nursing staff and managers. © 2013 John Wiley & Sons Ltd.

A Unified Mathematical Definition of Classical Information Retrieval.

ERIC Educational Resources Information Center

Dominich, Sandor

2000-01-01

Presents a unified mathematical definition for the classical models of information retrieval and identifies a mathematical structure behind relevance feedback. Highlights include vector information retrieval; probabilistic information retrieval; and similarity information retrieval. (Contains 118 references.) (Author/LRW)

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief

PubMed Central

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H.; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors “Mathematical Test Anxiety” (MTA) and “Numerical Anxiety” (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established. PMID:26924996

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief.

PubMed

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors "Mathematical Test Anxiety" (MTA) and "Numerical Anxiety" (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established.

The mysterious connection between mathematics and physics.

PubMed

Kauffman, Louis H; Ul-Haq, Rukhsan

2015-12-01

The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of "It from Bit" as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed. Copyright © 2015. Published by Elsevier Ltd.

Structural, Linguistic and Topic Variables in Verbal and Computational Problems in Elementary Mathematics.

ERIC Educational Resources Information Center

Beardslee, Edward C.; Jerman, Max E.

Five structural, four linguistic and twelve topic variables are used in regression analyses on results of a 50-item achievement test. The test items are related to 12 topics from the third-grade mathematics curriculum. The items reflect one of two cases of the structural variable, cognitive level; the two levels are characterized, inductive…

Students' Perceptions of Mathematics Classroom Goal Structures: Implications for Perceived Task Values and Study Behavior

ERIC Educational Resources Information Center

Skaalvik, Einar M.; Federici, Roger A.; Wigfield, Allan; Tangen, Truls N.

2017-01-01

Relations between 8th and 10th grade students' perceptions of classroom goal structures, task values, anxiety, help-seeking behavior, and effort in mathematics classes were examined. The authors investigated whether the associations between perceived goal structures and anxiety, help-seeking behavior, and effort are mediated through students'…

Evidence-based development of a diagnosis-dependent therapy planning system and its implementation in modern diagnostic software.

PubMed

Ahlers, M O; Jakstat, H A

2005-07-01

The prerequisite for structured individual therapy of craniomandibular dysfunctions is differential diagnostics. Suggestions for the structured recording of findings and their structured evaluation beyond the global diagnosis of "craniomandibular disorders" have been published. Only this structured approach enables computerization of the diagnostic process. The respective software is available for use in practice (CMDcheck for CMD screening, CMDfact for the differential diagnostics). Based on this structured diagnostics, knowledge-based therapy planning is also conceivable. The prerequisite for this would be a model of achieving consensus on the indicated forms of therapy related to the diagnosis. Therefore, a procedure for evidence-based achievement of consensus on suitable forms of therapy in CMD was developed first in multicentric cooperation, and then implemented in corresponding software. The clinical knowledge of experienced specialists was included consciously for the consensus achievement process. At the same time, anonymized mathematical statistical evaluations were used for control and objectification. Different examiners form different departments of several universities working independently of one another assigned the theoretically conceiveable therapeutic alternatives to the already published diagnostic scheme. After anonymization, the correlation of these assignments was then calculated mathematically. For achieving consensus in those cases for which no agreement initally existed, agreement was subsequently arrived at in the course of a consensus conference on the basis of literature evaluations and the discussion of clinical case examples. This consensus in turn finally served as the basis of a therapy planner implemented in the above-mentioned diagnostic software CMDfact. Contributing to quality assurance, the principles of programming this assistant as well as the interface for linking into the diagnostic software are documented and also published here.

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

Best packing of identical helices

NASA Astrophysics Data System (ADS)

Huh, Youngsik; Hong, Kyungpyo; Kim, Hyoungjun; No, Sungjong; Oh, Seungsang

2016-10-01

In this paper we prove the unique existence of a ropelength-minimizing conformation of the θ-spun double helix in a mathematically rigorous way, and find the minimal ropelength {{{Rop}}}* (θ )=-\\tfrac{8π }{t} where t is the unique solution in [-θ ,0] of the equation 2-2\\cos (t+θ )={t}2. Using this result, the pitch angles of the standard, triple and quadruple helices are around 39.3771^\\circ , 42.8354^\\circ and 43.8351^\\circ , respectively, which are almost identical with the approximated pitch angles of the zero-twist structures previously known by Olsen and Bohr. We also find the ropelength of the standard N-helix.

Coherent delocalization: views of entanglement in different scenarios

NASA Astrophysics Data System (ADS)

León-Montiel, R. de J.; Vallés, A.; Moya-Cessa, H. M.; Torres, J. P.

2015-08-01

The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar correlations can be observed when considering different degrees of freedom of a single system, even a classical one. Surprisingly, it has also been suggested that entanglement might be playing a relevant role in certain biological processes, such as the functioning of pigment-proteins that constitute light-harvesting complexes of photosynthetic bacteria. The aim of this work is to show that the presence of entanglement in all of these different scenarios should not be unexpected, once it is realized that the very same mathematical structure can describe all of them. We show this by considering three different, realistic cases in which the only condition for entanglement to exist is that a single excitation is coherently delocalized between the different subsystems that compose the system of interest.

Do Vampires Exist? Using Spreadsheets To Investigate a Common Folktale.

ERIC Educational Resources Information Center

Drier, Hollylynne Stohl

1999-01-01

Describes the use of spreadsheets in a third grade class to teach basic mathematical concepts by investigating the existence of vampires. Incorporates addition and multiplication skills, patterning, variables, formulas, exponential growth, and proof by contradiction. (LRW)

A Literature Review: The Effect of Implementing Technology in a High School Mathematics Classroom

ERIC Educational Resources Information Center

Murphy, Daniel

2016-01-01

This study is a literature review to investigate the effects of implementing technology into a high school mathematics classroom. Mathematics has a hierarchical structure in learning and it is essential that students get a firm understanding of mathematics early in education. Some students that miss beginning concepts may continue to struggle with…

The Vector Space as a Unifying Concept in School Mathematics.

ERIC Educational Resources Information Center

Riggle, Timothy Andrew

The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

Mathematics and Culture in Micronesia: The Structure and Function of a Capacity Building Project

ERIC Educational Resources Information Center

Dawson, A. J. Sandy

2013-01-01

The first goal of this Project is the development of elementary school mathematics curricula sensitive to indigenous mathematical thought and experience. A necessary prerequisite for the achievement of this goal is to recapture and honor the mathematics developed and practiced in the Micronesian communities. This is the Project's second goal. The…

Separate but correlated: The latent structure of space and mathematics across development.

PubMed

Mix, Kelly S; Levine, Susan C; Cheng, Yi-Ling; Young, Chris; Hambrick, D Zachary; Ping, Raedy; Konstantopoulos, Spyros

2016-09-01

The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the within domain analyses, all of the measures formed single factors at each age, suggesting consistent, unitary structures across this age range. Yet, as in previous work, the 2 domains were highly correlated, both in terms of overall composite score and pairwise comparisons of individual tasks. When both spatial and mathematics scores were submitted to the same factor analysis, the 2 domain specific factors again emerged, but there also were significant cross-domain factor loadings that varied with age. Multivariate regressions replicated the factor analysis and further revealed that mental rotation was the best predictor of mathematical performance in kindergarten, and visual-spatial working memory was the best predictor of mathematical performance in sixth grade. The mathematical tasks that predicted the most variance in spatial skill were place value (K, 3rd, 6th), word problems (3rd, 6th), calculation (K), fraction concepts (3rd), and algebra (6th). Thus, although spatial skill and mathematics each have strong internal structures, they also share significant overlap, and have particularly strong cross-domain relations for certain tasks. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

A complex-network perspective on Alexander's wholeness

NASA Astrophysics Data System (ADS)

Jiang, Bin

2016-12-01

The wholeness, conceived and developed by Christopher Alexander, is what exists to some degree or other in space and matter, and can be described by precise mathematical language. However, it remains somehow mysterious and elusive, and therefore hard to grasp. This paper develops a complex network perspective on the wholeness to better understand the nature of order or beauty for sustainable design. I bring together a set of complexity-science subjects such as complex networks, fractal geometry, and in particular underlying scaling hierarchy derived by head/tail breaks - a classification scheme and a visualization tool for data with a heavy-tailed distribution, in order to make Alexander's profound thoughts more accessible to design practitioners and complexity-science researchers. Through several case studies (some of which Alexander studied), I demonstrate that the complex-network perspective helps reduce the mystery of wholeness and brings new insights to Alexander's thoughts on the concept of wholeness or objective beauty that exists in fine and deep structure. The complex-network perspective enables us to see things in their wholeness, and to better understand how the kind of structural beauty emerges from local actions guided by the 15 fundamental properties, and in particular by differentiation and adaptation processes. The wholeness goes beyond current complex network theory towards design or creation of living structures.

Top-down causation and emergence: some comments on mechanisms

PubMed Central

Ellis, George F. R.

2012-01-01

Both bottom-up and top-down causation occur in the hierarchy of structure and causation. A key feature is multiple realizability of higher level functions, and consequent existence of equivalence classes of lower level variables that correspond to the same higher level state. Five essentially different classes of top-down influence can be identified, and their existence demonstrated by many real-world examples. They are: algorithmic top-down causation; top-down causation via non-adaptive information control, top-down causation via adaptive selection, top-down causation via adaptive information control and intelligent top-down causation (the effect of the human mind on the physical world). Through the mind, abstract entities such as mathematical structures have causal power. The causal slack enabling top-down action to take place lies in the structuring of the system so as to attain higher level functions; in the way the nature of lower level elements is changed by context, and in micro-indeterminism combined with adaptive selection. Understanding top-down causation can have important effects on society. Two cases will be mentioned: medical/healthcare issues, and education—in particular, teaching reading and writing. In both cases, an ongoing battle between bottom-up and top-down approaches has important consequences for society. PMID:23386967

Individual Differences in Inhibitory Control, Not Non-Verbal Number Acuity, Correlate with Mathematics Achievement

PubMed Central

Gilmore, Camilla; Attridge, Nina; Clayton, Sarah; Cragg, Lucy; Johnson, Samantha; Marlow, Neil; Simms, Victoria; Inglis, Matthew

2013-01-01

Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task) is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate. PMID:23785521

Characteristic behaviors of students with LD who have teacher-identified math weaknesses.

PubMed

Bryant, D P; Bryant, B R; Hammill, D D

2000-01-01

Mathematics learning disabilities (LD) have gained increased attention over the last decade from both researchers and practitioners. A large percentage of students receiving learning disability services experience difficulties with mathematics, but little research has examined the specific mathematics behaviors of students with LD who have teacher-identified math weaknesses. This study examines the literature on mathematics LD and identifies specific behaviors from that body of research for the purpose of determining the extent to which those behaviors are observed in students with LD. Data are presented from observations of 391 special education professionals on 1724 students with LD, 870 of whom had identified math weaknesses and 854 of whom did not. Our results validate the existing literature and provide implications for teachers, researchers, and others interested in studying mathematics LD.

The Effect of Emphasizing Mathematical Structure in the Acquisition of Whole Number Computation Skills (Addition and Subtraction) By Seven- and Eight-Year Olds: A Clinical Investigation.

ERIC Educational Resources Information Center

Uprichard, A. Edward; Collura, Carolyn

This investigation sought to determine the effect of emphasizing mathematical structure in the acquisition of computational skills by seven- and eight-year-olds. The meaningful development-of-structure approach emphasized closure, commutativity, associativity, and the identity element of addition; the inverse relationship between addition and…

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Practical Math Skills: Situations--Strategies--Solutions. Intermediate Level. Grades 4-5-6.

ERIC Educational Resources Information Center

Duncan, Jim

This material is a supplement to existing mathematics programs for young learners. The activities presented are based on assumptions about the young problem solver which are difficult to address in standard mathematics texts. In these pages it is assumed that each learner brings to the problem-solving effort a very personal experience base and a…

The Effects of Glossary and Read-Aloud Accommodations on English Language Learners' Performance on a Mathematics Assessment

ERIC Educational Resources Information Center

Wolf, Mikyung Kim; Kim, Jinok; Kao, Jenny

2012-01-01

Glossary and reading aloud test items are commonly allowed in many states' accommodation policies for English language learner (ELL) students for large-scale mathematics assessments. However, little research is available regarding the effects of these accommodations on ELL students' performance. Further, no research exists that examines how…

Teaching Mathematics Problem Solving to Students with Limited English Proficiency through Nested Spiral Approach.

ERIC Educational Resources Information Center

Chyu, Chi-Oy W.

The Nested Spiral Approach (NSA) is an integrated instructional approach used to promote the motivated learning of mathematics problem solving in limited-English-proficient (LEP) students. The NSA is described and a trial use is discussed. The approach extends, elaborates, and supplements existing education and instruction theories to help LEP…

Accelerated Instruction and Parent Involvement: The Impact on 3rd and 5th Grade Mathematics Performance

ERIC Educational Resources Information Center

Kramb, Amy D.

2014-01-01

The public school system in the United States is facing severe criticism. There exists today, a constant stream of negative messages through media coverage, news articles and charter school marketing campaigns claiming the failing of the public school system specifically in the content area of mathematics. Current research exposes alarming…

A Study of the Relationship between Physical Skills and Achievement in Listening Comprehension, Mathematics, and Reading.

ERIC Educational Resources Information Center

Templeton, Josey; Jones, Robbie

To determine if a relationship existed between physical skills and achievement in reading, mathematics, and listening comprehension of fifth-grade students, a study evaluated 334 fifth-graders in Starkville, Mississippi, on 20 physical fitness, motor fitness, and sports skills, as well as the Stanford Achievement Tests. The physical skills test…

Please Sir, I Want Some More!

ERIC Educational Resources Information Center

Stansfield, Jayne

2008-01-01

To make the Mathematics Enhancement Course (MEC) students realize that mathematics exist in a wider range of forms and environments than most will have encountered before, they are sent out on several trips and visits during the six-month course. This year one of the trips was to spend a day at the ATM conference. Afterwards the students had to…

The Effects of Schema-Based Instruction on the Mathematical Problem Solving of Students with Emotional and Behavioral Disorders

ERIC Educational Resources Information Center

Peltier, Corey; Vannest, Kimberly J.

2018-01-01

The current study examines the effects of schema instruction on the problem-solving performance of four second-grade students with emotional and behavioral disorders. The existence of a functional relationship between the schema instruction intervention and problem-solving accuracy in mathematics is examined through a single case experiment using…

A Systematic Review of the Literature on Mathematics Manipulatives to Support Students with Disabilities

ERIC Educational Resources Information Center

Bouck, Emily C.; Park, Jiyoon

2018-01-01

Manipulatives are considered a common tool for mathematics teaching and learning, for both students with and without disabilities. Yet, a systematic review of the current state of research regarding manipulatives for students with disabilities did not exist prior to this article. This manuscript presents a systematic review of the literature…

The Relationship among Self-Concept, Self-Efficacy, and Performance in Mathematics during Secondary School.

ERIC Educational Resources Information Center

Pietsch, James; Walker, Richard; Chapman, Elaine

2003-01-01

Examines the relationship among self-concept, self-efficacy, and performance in mathematics among 416 high school students. Confirmatory factor analyses supported the existence of two self-concept components--a competency component and an affective component. Self-efficacy items and the competency items of self-concept also loaded on a single…

I See What You Are Doing: Student Views on Lecturer Use of Tablet PCs in the Engineering Mathematics Classroom

ERIC Educational Resources Information Center

Maclaren, Peter; Wilson, David; Klymchuk, Sergiy

2017-01-01

Mathematically intensive engineering subjects at a tertiary level have traditionally been taught in classroom environments using whiteboards or blackboards. This paper reports on student views of the effectiveness of board and alternative technologies used within existing classroom contexts. Students in this study revealed a strong preference for…

Investigating the Differences between Girls and Boys Regarding the Factors of Frustration, Boredom and Insecurity They Experience during Science Lessons

ERIC Educational Resources Information Center

Wegner, Claas; Strehlke, Friederike; Weber, Phillip

2014-01-01

Science, technology, engineering and mathematics (STEM) are subjects comprising knowledge whose schooling is essential for every country striving after long-term economic success. Despite the already existing shortage of skilled labour within the mathematic-technical-scientific professional field, men still dominate the respective subjects and…

Leveraging Quiz-Based Multiple-Prize Web Tournaments for Reinforcing Routine Mathematical Skills

ERIC Educational Resources Information Center

Gonzalez-Tablas, Ana I.; de Fuentes, Jose M.; Hernandez-Ardieta, Jorge L.; Ramos, Benjamin

2013-01-01

In Higher Education Engineering studies, there exists the need of engaging students in performing drill and practice activities with the goal of reinforcing routine mathematical skills. The usual optionality of these tasks entails the risk of students not fulfilling them in an effective way. Although competitive approaches are not a trend in…

The Impact of Higher Expectations in Math on the Perception of Achievement of High School Students with Disabilities

ERIC Educational Resources Information Center

Przybylinski, Vincent S., Jr.

2016-01-01

There exists a dearth of research on strategies that will help students with disabilities gain greater access to standards-based mathematics and close the mathematics achievement gap between general education students and students with disabilities (Browder et al., 2012; Jitendra, 2013; van Garderen, Scheuermann, Jackson, & Hampton, 2009).…

A Meta-Analysis of the Effects of Computer Technology on School Students' Mathematics Learning

ERIC Educational Resources Information Center

Li, Qing; Ma, Xin

2010-01-01

This study examines the impact of computer technology (CT) on mathematics education in K-12 classrooms through a systematic review of existing literature. A meta-analysis of 85 independent effect sizes extracted from 46 primary studies involving a total of 36,793 learners indicated statistically significant positive effects of CT on mathematics…

An Algebraic-Habits-of-Mind Perspective on Elementary School

ERIC Educational Resources Information Center

Goldenberg, E. Paul; Mark, June; Cuoco, Al

2010-01-01

More important than infusing courses and curricula with modern content is to give students the tools to use and understand mathematics--including some that does not yet exist. A curriculum organized around habits of mind tries to close the gap between what users and makers of mathematics do and what they say. These cross-journal articles are…

Gender Differences in Participation in Elective Mathematics of Senior Secondary School Students in Ghana

ERIC Educational Resources Information Center

Baah-Korang, Kwame; Gyan, Emmanuel; McCarthy, Paul; McCarthy, Peter

2015-01-01

This paper aims at contributing to the body of knowledge that exists in the area of differences in participation in elective mathematics, between boys and girls in Secondary Schools in Ghana. A sample of 738 respondents from five Secondary Schools was purposively selected using purposive sampling technique. All the respondents were final year…

About a mathematical model of market

NASA Astrophysics Data System (ADS)

Kulikov, D. A.

2017-01-01

In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.

Experiences Situating Mathematical Problem Solving at the Core of Early Childhood Classrooms

ERIC Educational Resources Information Center

Lopes, Celi Espasandin; Grando, Regina Célia; D'Ambrosio, Beatriz Silva

2017-01-01

Our goal in this article is to discuss the importance of problems in early childhood education for the child's development and engagement with the mathematics existing in childhood culture. Our assumption is that an important task for young children's education is to create a democratic and critical environment, in which multiplicity of…

A Study on the Relationship between Six-Year-Old Children's Creativity and Mathematical Ability

ERIC Educational Resources Information Center

Baran, Gülen; Erdogan, Serap; Çakmak, Aygen

2011-01-01

Creativity is defined as a totality of processes and a way of attitude and behavior which exists in every child to a different extent. Every child is creative owing to their nature and their perspective on life. Offering children creative environments, especially during early childhood education, affects their mathematical abilities and supports…

Comparing the Effectiveness of Virtual and Concrete Manipulatives to Teach Algebra to Secondary Students with Learning Disabilities

ERIC Educational Resources Information Center

Satsangi, Rajiv; Bouck, Emily C.; Taber-Doughty, Teresa; Bofferding, Laura; Roberts, Carly A.

2016-01-01

A sizable body of literature exists studying various technologies and pedagogical practices for teaching secondary mathematics curriculum to students with a learning disability in mathematics. However, with the growing footprint of computer-based technologies in today's classrooms, some areas of study, such as the use of virtual manipulatives,…

An Analysis of Mathematics Teacher Candidates' Critical Thinking Dispositions and Their Logical Thinking Skills

ERIC Educational Resources Information Center

Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri

2013-01-01

This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…

Researching Race in Mathematics Education

ERIC Educational Resources Information Center

Martin, Danny Bernard

2009-01-01

Background: Within mathematics education research, policy, and practice, race remains undertheorized in relation to mathematics learning and participation. Although race is characterized in the sociological and critical theory literatures as socially and politically constructed with structural expressions, most studies of differential outcomes in…

Mathematics Classrooms in Japan, Taiwan, and the United States.

ERIC Educational Resources Information Center

Stigler, James W.; And Others

1987-01-01

Studies were conducted in Chinese, Japanese, and American classrooms during mathematics classes. Large cross-cultural differences were found in variables related to classroom structure and management. These paralleled differences in mathematics achievement among China, Japan, and the United States. (PCB)

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

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

Khots, Boris, E-mail: bkhots@cccglobal.com; Khots, Dmitriy, E-mail: dkhots@imathconsulting.com

2014-12-10

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We considermore » the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.« less

Stability of nonlinear waves and patterns and related topics

NASA Astrophysics Data System (ADS)

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-01

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Molecular Architecture of the Retroviral Capsid.

PubMed

Perilla, Juan R; Gronenborn, Angela M

2016-05-01

Retroviral capsid cores are proteinaceous containers that self-assemble to encase the viral genome and a handful of proteins that promote infection. Their function is to protect and aid in the delivery of viral genes to the nucleus of the host, and, in many cases, infection pathways are influenced by capsid-cellular interactions. From a mathematical perspective, capsid cores are polyhedral cages and, as such, follow well-defined geometric rules. However, marked morphological differences in shapes exist, depending on virus type. Given the specific roles of capsid in the viral life cycle, the availability of detailed molecular structures, particularly at assembly interfaces, opens novel avenues for targeted drug development against these pathogens. Here, we summarize recent advances in the structure and understanding of retroviral capsid, with particular emphasis on assemblies and the capsid cores. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Multifaceted Mathematical Approach for Complex Systems

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

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

2012-03-07

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

Development Mathematic Assessment to Increase Mathematical Prerequisite Ability on The Student with Learning Disabilities in Inclusive Elementary School

NASA Astrophysics Data System (ADS)

Robiansyah, S. T. U.; Nanang, F.; Hidayat

2018-01-01

The purpose of this study was to introduce about mathematic assessment is a process of obtaining data or information about the mastery of a student's mathematical skills as an ingredient in preparing a learning program. With this mathematics assessment can be known obstacles, difficulties and needs of students especially in the field of mathematic, so that the learning program will be in accordance with the potential students because it is tailored to what is required of students. This research study was conducted at elementary school of inclusive precisely at SDN Sukagalih I Bandung City based learning in setting of inclusive education. This research study is motivated by the existence of a first-grade student who has disabilities learning in mathematics, the ability of the mathematical prerequisite mastery of the classification of objects by color. The results of the research can provide a profile picture of student data information, the data obtained from the results of the development of systematic and formal mathematical assessment. After doing the development of mathematics assessment then the teacher gets important related information: 1. process the analysis of students’ learning needs, especially in the field of mathematics, 2. preparing the learning program planning according to student learning needs, 3. Designing procedural of method remedial program.

Actuality of transcendental æsthetics for modern physics

NASA Astrophysics Data System (ADS)

Petitot, Jean

1. The more mathematics and physics unify themselves in the physico-mathematical modern theories, the more an objective epistemology becomes necessary. Only such a transcendental epistemology is able to thematize correctly the status of the mathematical determination of physical reality. 2. There exists a transcendental history of the synthetic a priori and of the construction of physical categories. 3. The transcendental approach allows to supersed Wittgenstein's and Carnap's antiplatonist thesis according to which pure mathematics are physically applicable only if they lack any descriptive, cognitive or objective, content and reduce to mere prescriptive and normative devices. In fact, pure mathematics are prescriptive-normative in physics because: (i) the categories of physical objectivity are prescriptive-normative, and (ii) their categorial content is mathematically “constructed” through a Transcendental Aesthetics. Only a transcendental approach make compatible, in the one hand, a grammatical conventionalism of Wittgensteinian or Carnapian type and, on the other hand, a platonist realism of Gödelian type. Mathematics are not a grammar of the world but a mathematical hermeneutics of the intuitive forms and of the categorial grammar of the world.

Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry

ERIC Educational Resources Information Center

Kennedy, Nadia Stoyanova

2009-01-01

This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…

Mathematics Education: Student Terminal Goals, Program Goals, and Behavioral Objectives.

ERIC Educational Resources Information Center

Mesa Public Schools, AZ.

Behavioral objectives are listed for the primary, intermediate and junior high mathematics curriculum in the Mesa Public Schools (Arizona). Lists of specific objectives are given by level for sets, symbol recognition, number operations, mathematical structures, measurement and problem solving skills. (JP)

Mapping Mathematics in Classroom Discourse

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth A.; Otten, Samuel

2011-01-01

This article offers a particular analytic method from systemic functional linguistics, "thematic analysis," which reveals the mathematical meaning potentials construed in discourse. Addressing concerns that discourse analysis is too often content-free, thematic analysis provides a way to represent semantic structures of mathematical content,…

The "Verbification" of Mathematics: Using the Grammatical Structures of Mi'kmaq to Support Student Learning

ERIC Educational Resources Information Center

Borden, Lisa Lunney

2011-01-01

As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw…

On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

NASA Astrophysics Data System (ADS)

Boulanouar, Mohamed

2013-04-01

In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.

Framing the Structural Role of Mathematics in Physics Lectures: A Case Study on Electromagnetism

ERIC Educational Resources Information Center

Karam, Ricardo

2014-01-01

Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction.…

Students' Emotions in the High School Mathematical Class: Appraisals in Terms of a Structure of Goals

ERIC Educational Resources Information Center

Martínez-Sierra, Gustavo; García-González, María del Socorro

2017-01-01

Little research in the field of Mathematics Education is directed towards emotions of students beyond their emotions in problem-solving. In particular, the daily emotions of students in a mathematics class have been sparsely studied in the field of mathematics education. In order to fill this gap, this qualitative research aims to identify high…

The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

Mathematical Skills and Motor Life Skills in Toddlers: Do Differences in Mathematical Skills Reflect Differences in Motor Skills?

ERIC Educational Resources Information Center

Reikerås, Elin; Moser, Thomas; Tønnessen, Finn Egil

2017-01-01

This study examines possible relations between early mathematical skills and motor life skills in 450 toddlers aged two years and nine months. The study employs baseline data from the longitudinal Stavanger Project--The Learning Child. The children's mathematical skills and motor life skills were assessed by structured observation in the natural…

An overview of the formulation, existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction

NASA Astrophysics Data System (ADS)

Ballard, Patrick; Charles, Alexandre

2018-03-01

In the end of the seventies, Schatzman and Moreau undertook to revisit the venerable dynamics of rigid bodies with contact and dry friction in the light of more recent mathematics. One claimed objective was to reach, for the first time, a mathematically consistent formulation of an initial value problem associated with the dynamics. The purpose of this article is to make a review of the today state-of-art concerning not only the formulation, but also the issues of existence and uniqueness of solution. xml:lang="fr"

Teaching mathematical word problem solving: the quality of evidence for strategy instruction priming the problem structure.

PubMed

Jitendra, Asha K; Petersen-Brown, Shawna; Lein, Amy E; Zaslofsky, Anne F; Kunkel, Amy K; Jung, Pyung-Gang; Egan, Andrea M

2015-01-01

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et al. and 10 single case design (SCD) research studies using criteria suggested by Horner et al. and the What Works Clearinghouse. Results indicated that 14 group design studies met the criteria for high-quality or acceptable research, whereas SCD studies did not meet the standards for an evidence-based practice. Based on these findings, strategy instruction priming the mathematics problem structure is considered an evidence-based practice using only group design methodological criteria. Implications for future research and for practice are discussed. © Hammill Institute on Disabilities 2013.

Physical Concepts and Mathematical Symbols

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

2007-12-01

According to traditional empiricist philosophy of science, concepts and meaning grow out of sense experience, and the mathematical structure of a physical theory is nothing but a formalisation of a given meaning-content. This view seems to work well in classical mechanics. But it breaks down in quantum physics, where we have a self-supported mathematical structure which resists any conceptual or pictorial interpretation in the traditional sense. Thus, traditional empiricism is flawed. Quantum physics teaches us that mathematics is a language in itself which extends beyond ordinary language. To understand the meaning of this extended language, we have to explore how new concepts and intuitions grow out of mathematics, not the other way around. The symbolic structure is prior to its meaning. This point of view is called linguistic empiricism, to stress that the connection with experience is still crucial. As cases, I compare the concept of stiffness in classical mechanics and the concept of electron density in quantum mechanics. The last case demonstrates that the wave function has a richer interpretation than the probabilistic one concerning measurement of position.

The College Mathematics Experience and Changes in Majors: A Structural Model Analysis.

ERIC Educational Resources Information Center

Whiteley, Meredith A.; Fenske, Robert H.

1990-01-01

Testing of a structural equation model with college mathematics experience as the focal variable in 745 students' final decisions concerning major or dropping out over 4 years of college yielded separate model estimates for 3 fields: scientific/technical, quantitative business, and business management majors. (Author/MSE)

How Does Lesson Structure Shape Teacher Perceptions of Teaching with Challenging Tasks?

ERIC Educational Resources Information Center

Russo, James; Hopkins, Sarah

2017-01-01

Despite reforms in mathematics education, many teachers remain reluctant to incorporate challenging (i.e., more cognitively demanding) tasks into their mathematics instruction. The current study examines how lesson structure shapes teacher perceptions of teaching with challenging tasks. Participants included three Year 1/2 classroom teachers who…

Allium To Zircon: Mathematics and Nature.

ERIC Educational Resources Information Center

Harrell, Marvin E.; Fosnaugh, Linda S.

1997-01-01

Discusses how nature can illustrate mathematical structures and concepts in the classroom. For example, the upper surface of a typical leaf structure illustrates the notion of tessellating with polygons. Also lists classroom applications and hands-on activities such as growing crystals to investigate the natural forms of polyhedra and measuring…

Caring teaching practices in multiethnic mathematics classrooms: attending to health and well-being

NASA Astrophysics Data System (ADS)

Averill, Robin

2012-06-01

Factors that contribute to strong teacher-student relationships are vital to understand because of the influence these relationships have on achievement and motivation, particularly for minority group students. This article draws from a substantial quantity of empirical data, grounded in a wide theoretical and cultural base, regarding aspects of caring teacher practice to discuss mathematics teacher behaviours in relation to an existing model of health and well-being that encompasses cognitive, social, spiritual, and physical dimensions. Drawing from 100 Year 10 mathematics lesson observations involving six teachers and their classes across three urban schools, evidence emerged that for many indigenous (Māori), New Zealand Pacific, and New Zealand European students, caring teacher behaviours important for student engagement and achievement both include, and range beyond, traditional teaching practices. Examples include capitalising on student reactions and shared endeavours within the context of mathematics learning, expecting mathematical progress, showing respect for students and for their mathematics learning, being explicit about practice and expectations, incorporating one-to-one interactions, making opportunities within mathematics learning for sharing personal identities, and incorporating movement. This research illustrates how mathematics educators can attend to the specific and holistic mathematical learning needs of their students, including those often marginalised.

Mathematical Interaction Shaped by Communication, Epistemological Constraints and Enactivism

ERIC Educational Resources Information Center

Steinbring, Heinz

2015-01-01

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

Supporting All Learners in Productive Struggle

ERIC Educational Resources Information Center

Townsend, Cynthia; Slavit, David; McDuffie, Amy Roth

2018-01-01

In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…

Measuring and modeling polymer concentration profiles near spindle boundaries argues that spindle microtubules regulate their own nucleation

NASA Astrophysics Data System (ADS)

Kaye, Bryan; Stiehl, Olivia; Foster, Peter J.; Shelley, Michael J.; Needleman, Daniel J.; Fürthauer, Sebastian

2018-05-01

Spindles are self-organized microtubule-based structures that segregate chromosomes during cell division. The mass of the spindle is controlled by the balance between microtubule turnover and nucleation. The mechanisms that control the spatial regulation of microtubule nucleation remain poorly understood. While previous work found that microtubule nucleators bind to pre-existing microtubules in the spindle, it is still unclear whether this binding regulates the activity of those nucleators. Here we use a combination of experiments and mathematical modeling to investigate this issue. We measured the concentration of microtubules and soluble tubulin in and around the spindle. We found a very sharp decay in the concentration of microtubules at the spindle interface. This is inconsistent with a model in which the activity of nucleators is independent of their association with microtubules but consistent with a model in which microtubule nucleators are only active when bound to pre-existing microtubules. This argues that the activity of microtubule nucleators is greatly enhanced when bound to pre-existing microtubules. Thus, microtubule nucleators are both localized and activated by the microtubules they generate.

Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness

NASA Astrophysics Data System (ADS)

Jiang, Qi-Jie; Jin, Mao-Zhu; Ren, Pei-Yu

2017-04-01

How to optimize agro-product supply chain to promote its operating efficiency so as to enhance the competitiveness of regional agricultural products has posed a problem to academic circles, business circles and governments of various levels. One way to solve this problem is to introduce an information platform into the supply chain, which this essay focuses on. Firstly, a review of existing research findings concerning the agro-product competitiveness, agro-product supply chain (ASC) and information platform was given. Secondly, we constructed a mathematical model to analyze the impact of information platform on the bullwhip effect in ASC. Thirdly, another mathematical model was constructed to help compare and analyze the impact of information platform on information acquisition of members in ASC. The research results show that the implantation of information platform can mitigate the bullwhip effect in ASC, and members can determine order amount or production more close to the actual market demand. And also the information platform can reduce the time for members in ASC to get information from other members. Besides, information platform can help ASC to alleviate information asymmetry among upstream and downstream members. Furthermore, researches about the operating mechanism and pattern, technical feature and running structure of the information platform, along with their impacts on agro-product supply chain and the competitiveness of agricultural products need to be advanced.

Practical Math Skills: Situations--Strategies--Solutions. Junior High Level. Grades 7-8-9.

ERIC Educational Resources Information Center

Duncan, Jim

This material is a supplement to existing mathematics programs for young learners. The activities presented are based on assumptions about the young problem solver which are difficult to address in standard mathematics texts. In these pages it is assumed that each learner brings to the problem-solving effort a very personal experience base and a…

The Effects of Single-Gender Classrooms on the Mathematics Achievement of 9th Grade, African American Male Students

ERIC Educational Resources Information Center

Newbold, Anthony J.

2014-01-01

An achievement gap exists in mathematics between low-income African American male students and their European American counterparts. Although this problem has been approached using different interventions with minimal results, the impact of homogenous grouping is not well understood in spite of its use. As a result, this study was conducted to…

Identifying Students' Mathematical Skills from a Multiple-Choice Diagnostic Test Using an Iterative Technique to Minimise False Positives

ERIC Educational Resources Information Center

Manning, S.; Dix, A.

2008-01-01

There is anecdotal evidence that a significant number of students studying computing related courses at degree level have difficulty with sub-GCE mathematics. Testing of students' skills is often performed using diagnostic tests and a number of computer-based diagnostic tests exist, which work, essentially, by testing one specific diagnostic skill…

Instructional Strategies and Best Practices for Improving the Achievement Gap in Mathematics: An Exploratory Case Study

ERIC Educational Resources Information Center

Lord, Joey

2017-01-01

This qualitative exploratory case study focused on the achievement gap in mathematics that exists in one urban North Carolina middle school and the strategies used by school personnel to narrow this gap. The goal of this research was to determine effective instructional strategies and best practices used to engage students in learning that will…

Visual Working Memory and Number Sense: Testing the Double Deficit Hypothesis in Mathematics

ERIC Educational Resources Information Center

Toll, Sylke W. M.; Kroesbergen, Evelyn H.; Van Luit, Johannes E. H.

2016-01-01

Background: Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis. Aims: The aim of this study was to test the DD…

Big Challenges and Big Opportunities: The Power of "Big Ideas" to Change Curriculum and the Culture of Teacher Planning

ERIC Educational Resources Information Center

Hurst, Chris

2014-01-01

Mathematical knowledge of pre-service teachers is currently "under the microscope" and the subject of research. This paper proposes a different approach to teacher content knowledge based on the "big ideas" of mathematics and the connections that exist within and between them. It is suggested that these "big ideas"…

Using Incremental Rehearsal to Increase Fluency of Single-Digit Multiplication Facts with Children Identified as Learning Disabled in Mathematics Computation

ERIC Educational Resources Information Center

Burns, Matthew K.

2005-01-01

Previous research suggested that Incremental Rehearsal (IR; Tucker, 1989) led to better retention than other drill practices models. However, little research exists in the literature regarding drill models for mathematics and no studies were found that used IR to practice multiplication facts. Therefore, the current study used IR as an…

Mathematics from High School to Community College: Using Existing Tools to Increase College-Readiness Now. Policy Brief 14-1

ERIC Educational Resources Information Center

Jaffe, Louise

2014-01-01

The adoption and implementation of the Common Core State Standards and Smarter Balanced assessments in mathematics are intended to provide all students in California with the knowledge and skills required to transition from high school to college-level coursework. This implementation will take time. Concurrent with these efforts, policymakers and…

A Study of Single-Gender Grouping for Sixth Grade Math as a Strategy for Improving Student Achievement

ERIC Educational Resources Information Center

Van Zyl, Douglas G.

2011-01-01

Purpose of the study. The purpose of this study was to examine single-gender groupings for sixth grade mathematics classes as a strategy to improve student achievement. The method of research was quantitative, with MAP mathematics test data being used to determine if any relationship exists between the strategy and student achievement. Findings.…

Instructional Strategies and Best Practices to Narrow the Mathematics Achievement Gaps between African American, Hispanic, and European American Students

ERIC Educational Resources Information Center

Bolden, Felicia Mickles

2012-01-01

A persistent mathematics achievement gap between African American, Hispanic, and European American students at one elementary school was the focus of this investigation. The research questions of this single site case study involved understanding why an achievement gap exists, and to identify the instructional strategies and best practices used to…

Development of an Instrument to Assess Attitudes toward Science, Technology, Engineering, and Mathematics (STEM)

ERIC Educational Resources Information Center

Guzey, S. Selcen; Harwell, Michael; Moore, Tamara

2014-01-01

There is a need for more students to be interested in science, technology, engineering, and mathematics (STEM) careers to advance U.S. competitiveness and economic growth. A consensus exists that improving STEM education is necessary for motivating more students to pursue STEM careers. In this study, a survey to measure student (grades 4-6)…

A Phenomenological Study of the Lived Experiences of Non-Traditional Students in Higher Level Mathematics at a Midwest University

ERIC Educational Resources Information Center

Wood, Brian B.

2017-01-01

The current literature suggests that the use of Husserl's and Heidegger's approaches to phenomenology is still practiced. However, a clear gap exists on how these approaches are viewed in the context of constructivism, particularly with non-traditional female students' study of mathematics. The dissertation attempts to clarify the constructivist…

Mapping the Relationships among Basic Facts, Concepts and Application, and Common Core Curriculum-Based Mathematics Measures

ERIC Educational Resources Information Center

Codding, Robin S.; Mercer, Sterett; Connell, James; Fiorello, Catherine; Kleinert, Whitney

2016-01-01

There is a paucity of evidence supporting the use of curriculum-based mathematics measures (M-CBMs) at the middle school level, which makes data-based decisions challenging for school professionals. The purpose of this study was to examine the relationships among three existing M-CBM indices: (a) basic facts, (b) concepts/application, and (c)…

Winning the Popularity Contest: Researcher Preference When Selecting Resources for Civil Engineering, Computer Science, Mathematics and Physics Dissertations

ERIC Educational Resources Information Center

Dotson, Daniel S.; Franks, Tina P.

2015-01-01

More than 53,000 citations from 609 dissertations published at The Ohio State University between 1998-2012 representing four science disciplines--civil engineering, computer science, mathematics and physics--were examined to determine what, if any, preferences or trends exist. This case study seeks to identify whether or not researcher preferences…

Affordances of the Cultural Inquiry Process in Building Secondary Mathematics Teachers' Capacity for Cultural Responsiveness

ERIC Educational Resources Information Center

Parker, Frieda; Bartell, Tonya; Novak, Jodie D.

2017-01-01

Over the last couple of decades, there has been a growing call for teachers to become more responsive to the increasing cultural diversity of students as a means of improving students' experiences in school and their learning outcomes. Challenges exist in working with secondary mathematics teachers due to the common belief that math is…

Adaptation and Extension of the Framework of Reducing Abstraction in the Case of Differential Equations

ERIC Educational Resources Information Center

Raychaudhuri, Debasree

2014-01-01

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

University course timetabling and the requirements: Survey in several universities in the east-coast of Malaysia

NASA Astrophysics Data System (ADS)

Aziz, Nurul Liyana Abdul; Aizam, Nur Aidya Hanum

2017-08-01

Course timetabling problem receives the highlight at the beginning of every semester. The problem is mainly on assigning courses to timeslot, rooms and lecturers which involving a set of rules and policies constraints. Generally, researchers present different features to signify their own universities' timetable according to the structure and behavior of their institution. However, the gap between theory and real-world applications that can be seen in the resulted timetable is the lacking of acknowledging human preferences. As to overcome this, it is very important to consider all the demands and preferences from timetabling community. This research therefore tries to accommodate the problem by investigating through surveys to several universities in the east coast of Malaysia the demands and preferences of individuals involved directly. Results from the questionnaires will be analyzed by using SPSS and all current issues regarding the demands will be included into our existing general university course timetabling mathematical model. The new university course timetabling mathematical model could best represent universities and be useful, especially in universities in Malaysia.

[Computer simulation of thyroid regulatory mechanisms in health and malignancy].

PubMed

Abduvaliev, A A; Gil'dieva, M S; Khidirov, B N; Saĭdalieva, M; Saatov, T S

2010-07-01

The paper describes a computer model for regulation of the number of thyroid follicular cells in health and malignancy. The authors'computer program for mathematical simulation of the regulatory mechanisms of a thyroid follicular cellular community cannot be now referred to as good commercial products. For commercialization of this product, it is necessary to draw up a direct relation of the introduced corrected values from the actually existing normal values, such as the peripheral blood concentrations of thyroid hormones or the mean values of endocrine tissue mitotic activity. However, the described computer program has been also used in researches by our scientific group in the study of thyroid cancer. The available biological experimental data and theoretical provisions on thyroid structural and functional organization at the cellular level allow one to construct mathematical models for quantitative analysis of the regulation of the size of a cellular community of a thyroid follicle in health and abnormalities, by using the method for simulation of the regulatory mechanisms of living systems and the equations of cellular community regulatory communities.

Skeptical notes on a physics of passage.

PubMed

Huggett, Nick

2014-10-01

This paper investigates the mathematical representation of time in physics. In existing theories, time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question of the paper is whether the existing representation of time is adequate, or whether it can or should be supplemented: especially, do we need a physics incorporating some kind of "dynamical passage" of time? The paper argues that the existing mathematical framework is resistant to such changes, and might have to be rejected by anyone seeking a physics of passage. Then it rebuts two common arguments for incorporating passage into physics, especially the claim that it is an element of experience. Finally, the paper investigates whether, as has been claimed, causal set theory provides a physics of passage. © 2014 New York Academy of Sciences.

General existence principles for Stieltjes differential equations with applications to mathematical biology

NASA Astrophysics Data System (ADS)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

Attitudes to teaching mathematics: Further development of a measurement instrument

NASA Astrophysics Data System (ADS)

Relich, Joe; Way, Jenni; Martin, Andrew

1994-07-01

The evidence that a relationship exists between attitudes to teaching mathematics and the formation of positive attitudes to mathematics among pupils is somewhat tenuous. Nevertheless, there is a strong belief among pre-service teacher educators that positive attitudes need to be fostered in teacher education students, particularly for prospective primary school teachers. Unfortunately, the research evidence suggests that high proportions of pre-service teachers hold negative attitudes towards mathematics. Although many instruments measuring affect in areas such as self-concept, anxiety, etc. have appeared in the literature over the years, no comprehensive instrument on attitudes is available to help teacher educators monitor attitudinal changes among their pre-service student teachers to the teaching of mathematics. This research re-examines an earlier attempt to develop such an instrument in Australia (Nisbet, 1991) and posits an alternative and refined version.

The link between middle school mathematics course placement and achievement.

PubMed

Domina, Thurston

2014-01-01

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. © 2014 The Author. Child Development © 2014 Society for Research in Child Development, Inc.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

NASA Astrophysics Data System (ADS)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

The Influence of Building Block Play on Mathematics Achievement and Logical and Divergent Thinking in Italian Primary School Mathematics Classes

ERIC Educational Resources Information Center

Pirrone, Concetta; Tienken, Christopher H.; Pagano, Tatiana; Di Nuovo, Santo

2018-01-01

In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thinking, nonverbal reasoning, and mental imagery, students in the experimental group scored significantly higher (p = 0.05) in mathematics achievement and…

Structural Exclusion through School Mathematics: Using Bourdieu to Understand Mathematics as a Social Practice

ERIC Educational Resources Information Center

Jorgensen, Robyn; Gates, Peter; Roper, Vanessa

2014-01-01

In this paper, we explore a sociological approach to mathematics education and offer a theoretical lens through which we can come to understand mathematics education as part of a wider set of social practices. Many studies of children's experiences in school show that a child's academic success is a product of many factors, some of which…

Towards methodical modelling: Differences between the structure and output dynamics of multiple conceptual models

NASA Astrophysics Data System (ADS)

Knoben, Wouter; Woods, Ross; Freer, Jim

2016-04-01

Conceptual hydrologic models consist of a certain arrangement of spatial and temporal dynamics consisting of stores, fluxes and transformation functions, depending on the modeller's choices and intended use. They have the advantages of being computationally efficient, being relatively easy model structures to reconfigure and having relatively low input data demands. This makes them well-suited for large-scale and large-sample hydrology, where appropriately representing the dominant hydrologic functions of a catchment is a main concern. Given these requirements, the number of parameters in the model cannot be too high, to avoid equifinality and identifiability issues. This limits the number and level of complexity of dominant hydrologic processes the model can represent. Specific purposes and places thus require a specific model and this has led to an abundance of conceptual hydrologic models. No structured overview of these models exists and there is no clear method to select appropriate model structures for different catchments. This study is a first step towards creating an overview of the elements that make up conceptual models, which may later assist a modeller in finding an appropriate model structure for a given catchment. To this end, this study brings together over 30 past and present conceptual models. The reviewed model structures are simply different configurations of three basic model elements (stores, fluxes and transformation functions), depending on the hydrologic processes the models are intended to represent. Differences also exist in the inner workings of the stores, fluxes and transformations, i.e. the mathematical formulations that describe each model element's intended behaviour. We investigate the hypothesis that different model structures can produce similar behavioural simulations. This can clarify the overview of model elements by grouping elements which are similar, which can improve model structure selection.

Structure and structure-preserving algorithms for plasma physics

NASA Astrophysics Data System (ADS)

Morrison, P. J.

2016-10-01

Conventional simulation studies of plasma physics are based on numerically solving the underpinning differential (or integro-differential) equations. Usual algorithms in general do not preserve known geometric structure of the physical systems, such as the local energy-momentum conservation law, Casimir invariants, and the symplectic structure (Poincaré invariants). As a consequence, numerical errors may accumulate coherently with time and long-term simulation results may be unreliable. Recently, a series of geometric algorithms that preserve the geometric structures resulting from the Hamiltonian and action principle (HAP) form of theoretical models in plasma physics have been developed by several authors. The superiority of these geometric algorithms has been demonstrated with many test cases. For example, symplectic integrators for guiding-center dynamics have been constructed to preserve the noncanonical symplectic structures and bound the energy-momentum errors for all simulation time-steps; variational and symplectic algorithms have been discovered and successfully applied to the Vlasov-Maxwell system, MHD, and other magnetofluid equations as well. Hamiltonian truncations of the full Vlasov-Maxwell system have opened the field of discrete gyrokinetics and led to the GEMPIC algorithm. The vision that future numerical capabilities in plasma physics should be based on structure-preserving geometric algorithms will be presented. It will be argued that the geometric consequences of HAP form and resulting geometric algorithms suitable for plasma physics studies cannot be adapted from existing mathematical literature but, rather, need to be discovered and worked out by theoretical plasma physicists. The talk will review existing HAP structures of plasma physics for a variety of models, and how they have been adapted for numerical implementation. Supported by DOE DE-FG02-04ER-54742.

21st Century Mathematics

ERIC Educational Resources Information Center

Seeley, Cathy

2004-01-01

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

Leveling the Playing Field: Graphical Aids on Mathematics Tests

ERIC Educational Resources Information Center

Jiménez, Albert M.; Nixon, Casey B.; Zepeda, Sally J.

2017-01-01

This research suggests that structural accommodation can be implemented during the construction phase of standardized mathematics examinations. Data from a racially diverse district in the United States are used to compare student performance on questions with and without graphical aids. Findings suggest that mathematics questions possessing…

A Semiotic Perspective of Mathematical Activity: The Case of Number

ERIC Educational Resources Information Center

Ernest, Paul

2006-01-01

A semiotic perspective on mathematical activity provides a way of conceptualizing the teaching and learning of mathematics that transcends and encompasses both psychological perspectives focussing exclusively on mental structures and functions, and performance-focussed perspectives concerned only with student's behaviours. Instead it considers the…

Mathematics and Computer Science: Exploring a Symbiotic Relationship

ERIC Educational Resources Information Center

Bravaco, Ralph; Simonson, Shai

2004-01-01

This paper describes a "learning community" designed for sophomore computer science majors who are simultaneously studying discrete mathematics. The learning community consists of three courses: Discrete Mathematics, Data Structures and an Integrative Seminar/Lab. The seminar functions as a link that integrates the two disciplines. Participation…

Brazilian Peasant Mathematics, School Mathematics and Adult Education

ERIC Educational Resources Information Center

Knijnik, Gelsa

2007-01-01

The paper analyzes adult mathematics education from a cultural perspective. Specifically, its purpose is to broaden our comprehension about this field of knowledge using as a theoretical tool-box an Ethnomathematics perspective founded on post-modern thought, post-structuralism theorizations and Wittgenstein's work developed in his book…

Recent literature on structural modeling, identification, and analysis

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1990-01-01

The literature on the mathematical modeling of large space structures is first reviewed, with attention given to continuum models, model order reduction, substructuring, and computational techniques. System identification and mode verification are then discussed with reference to the verification of mathematical models of large space structures. In connection with analysis, the paper surveys recent research on eigensolvers and dynamic response solvers for large-order finite-element-based models.

Game Theory, Conditional Preferences, and Social Influence

PubMed Central

Stirling, Wynn C.; Felin, Teppo

2013-01-01

Neoclassical noncooperative game theory is based on a simple, yet powerful synthesis of mathematical and logical concepts: unconditional and immutable preference orderings and individual rationality. Although this structure has proven useful for characterizing competitive multi-player behavior, its applicability to scenarios involving complex social relationships is problematic. In this paper we directly address this limitation by the introduction of a conditional preference structure that permits players to modulate their preference orderings as functions of the preferences of other players. Embedding this expanded preference structure in a formal and graphical framework provides a systematic approach for characterizing a complex society. The result is an influence network that allows conditional preferences to propagate through the community, resulting in an emergent social model which characterizes all of the social relationships that exist and which leads to solution concepts that account for both group and individual interests. The Ultimatum game is presented as an example of how social influence can be modeled with conditional preferences. PMID:23451078

Game theory, conditional preferences, and social influence.

PubMed

Stirling, Wynn C; Felin, Teppo

2013-01-01

Neoclassical noncooperative game theory is based on a simple, yet powerful synthesis of mathematical and logical concepts: unconditional and immutable preference orderings and individual rationality. Although this structure has proven useful for characterizing competitive multi-player behavior, its applicability to scenarios involving complex social relationships is problematic. In this paper we directly address this limitation by the introduction of a conditional preference structure that permits players to modulate their preference orderings as functions of the preferences of other players. Embedding this expanded preference structure in a formal and graphical framework provides a systematic approach for characterizing a complex society. The result is an influence network that allows conditional preferences to propagate through the community, resulting in an emergent social model which characterizes all of the social relationships that exist and which leads to solution concepts that account for both group and individual interests. The Ultimatum game is presented as an example of how social influence can be modeled with conditional preferences.

MIST: An Open Source Environmental Modelling Programming Language Incorporating Easy to Use Data Parallelism.

NASA Astrophysics Data System (ADS)

Bellerby, Tim

2014-05-01

Model Integration System (MIST) is open-source environmental modelling programming language that directly incorporates data parallelism. The language is designed to enable straightforward programming structures, such as nested loops and conditional statements to be directly translated into sequences of whole-array (or more generally whole data-structure) operations. MIST thus enables the programmer to use well-understood constructs, directly relating to the mathematical structure of the model, without having to explicitly vectorize code or worry about details of parallelization. A range of common modelling operations are supported by dedicated language structures operating on cell neighbourhoods rather than individual cells (e.g.: the 3x3 local neighbourhood needed to implement an averaging image filter can be simply accessed from within a simple loop traversing all image pixels). This facility hides details of inter-process communication behind more mathematically relevant descriptions of model dynamics. The MIST automatic vectorization/parallelization process serves both to distribute work among available nodes and separately to control storage requirements for intermediate expressions - enabling operations on very large domains for which memory availability may be an issue. MIST is designed to facilitate efficient interpreter based implementations. A prototype open source interpreter is available, coded in standard FORTRAN 95, with tools to rapidly integrate existing FORTRAN 77 or 95 code libraries. The language is formally specified and thus not limited to FORTRAN implementation or to an interpreter-based approach. A MIST to FORTRAN compiler is under development and volunteers are sought to create an ANSI-C implementation. Parallel processing is currently implemented using OpenMP. However, parallelization code is fully modularised and could be replaced with implementations using other libraries. GPU implementation is potentially possible.

Compression-bending of multi-component semi-rigid columns in response to axial loads and conjugate reciprocal extension-prediction of mechanical behaviours and implications for structural design.

PubMed

Lau, Ernest W

2013-01-01

The mathematical modelling of column buckling or beam bending under an axial or transverse load is well established. However, the existent models generally assume a high degree of symmetry in the structure of the column and minor longitudinal and transverse displacements. The situation when the column is made of several components with different mechanical properties asymmetrically distributed in the transverse section, semi-rigid, and subjected to multiple axial loads with significant longitudinal and transverse displacements through compression and bending has not been well characterised. A more comprehensive theoretical model allowing for these possibilities and assuming a circular arc contour for the bend is developed, and used to establish the bending axes, balance between compression and bending, and equivalent stiffness of the column. In certain situations, such as with pull cable catheters commonly used for minimally invasive surgical procedures, the compression loads are applied via cables running through channels inside a semi-rigid column. The model predicts the mathematical relationships between the radius of curvature of the bend and the tension in and normal force exerted by such cables. Conjugate extension with reciprocal compression-bending is a special structural arrangement for a semi-rigid column such that extension of one segment is linked to compression-bending of another by inextensible cables running between them. Leads are cords containing insulated electrical conductor coil and cables between the heart muscle and cardiac implantable electronic devices. Leads can behave like pull cable catheters through differential component pulling, providing a possible mechanism for inside-out abrasion and conductor cable externalisation. Certain design features may predispose to this mode of structural failure. Copyright © 2012 Elsevier Ltd. All rights reserved.

Shared Teaching Culture in Different Forms: A Comparison of Expert and Novice Teachers' Practices

ERIC Educational Resources Information Center

Arani, Mohammad Reza Sarkar

2017-01-01

This study aims to reveal the teaching script and structure of lesson practice of two seventh-grade Japanese mathematics teachers--a "novice" and "expert"--through comparative analysis of mathematics lessons. Specifically, it aims to clarify how the teachers' views of teaching as tacit knowledge determine lesson structure and…

¡Enséname! Teaching Each Other to Reason through Math in the Second Grade

ERIC Educational Resources Information Center

Schmitz, Lindsey

2016-01-01

This action research sought to evaluate the effect of peer teaching structures across subgroups of students differentiated by language and mathematical skill ability. These structures were implemented in an effort to maintain mathematical rigor while building my students' academic language capacity. More specifically, the study investigated peer…

Does Inquiry Based Learning Affect Students' Beliefs and Attitudes towards Mathematics?

ERIC Educational Resources Information Center

McGregor, Darren

2014-01-01

Ill-structured tasks presented in an inquiry learning environment have the potential to affect students' beliefs and attitudes towards mathematics. This empirical research followed a Design Experiment approach to explore how aspects of using ill-structured tasks may have affected students' beliefs and attitudes. Results showed this task type and…

Developing a Structural Model on the Relationship among Motivational Beliefs, Self-Regulated Learning Strategies, and Achievement in Mathematics

ERIC Educational Resources Information Center

Fadlelmula, Fatma Kayan; Cakiroglu, Erdinc; Sungur, Semra

2015-01-01

This study examines the interrelationships among students' motivational beliefs (i.e. achievement goal orientations, perception of classroom goal structure, and self-efficacy), use of self-regulated learning strategies (i.e. elaboration, organization, and metacognitive self-regulation strategies), and achievement in mathematics, by proposing and…

The Semiotic Structure of Geometry Diagrams: How Textbook Diagrams Convey Meaning

ERIC Educational Resources Information Center

Dimmel, Justin K.; Herbst, Patricio G.

2015-01-01

Geometry diagrams use the visual features of specific drawn objects to convey meaning about generic mathematical entities. We examine the semiotic structure of these visual features in two parts. One, we conduct a semiotic inquiry to conceptualize geometry diagrams as mathematical texts that comprise choices from different semiotic systems. Two,…

Post-Structuralism and Ethical Practical Action: Issues of Identity and Power

ERIC Educational Resources Information Center

Walshaw, Margaret

2013-01-01

In an era when familiar categories of identity are breaking down, an argument is made for using post-structuralist vocabulary to talk about ethical practical action in mathematics education. Using aspects of Foucault's post-structuralism, an explanation is offered of how mathematical identifications are tied to the social organization of power. An…

The Role of Visual Representations for Structuring Classroom Mathematical Activity

ERIC Educational Resources Information Center

David, Maria Manuela; Tomaz, Vanessa Sena

2012-01-01

It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching…

Microteaching Lesson Study: Mentor Interaction Structure and Its Relation to Elementary Preservice Mathematics Teacher Knowledge Development

ERIC Educational Resources Information Center

Molina, Roxanne V.

2012-01-01

This study investigated Microteaching Lesson Study (MLS) and three possible MLS mentor interaction structures during the debriefing sessions in relation to elementary preservice teacher development of knowledge for teaching. One hundred three elementary preservice teachers enrolled in five different sections of a mathematics methods course at a…

Mathematical marriages: intercourse between mathematics and Semiotic choice.

PubMed

Wagner, Roy

2009-04-01

This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

Effective Moment Feature Vectors for Protein Domain Structures

PubMed Central

Shi, Jian-Yu; Yiu, Siu-Ming; Zhang, Yan-Ning; Chin, Francis Yuk-Lun

2013-01-01

Imaging processing techniques have been shown to be useful in studying protein domain structures. The idea is to represent the pairwise distances of any two residues of the structure in a 2D distance matrix (DM). Features and/or submatrices are extracted from this DM to represent a domain. Existing approaches, however, may involve a large number of features (100–400) or complicated mathematical operations. Finding fewer but more effective features is always desirable. In this paper, based on some key observations on DMs, we are able to decompose a DM image into four basic binary images, each representing the structural characteristics of a fundamental secondary structure element (SSE) or a motif in the domain. Using the concept of moments in image processing, we further derive 45 structural features based on the four binary images. Together with 4 features extracted from the basic images, we represent the structure of a domain using 49 features. We show that our feature vectors can represent domain structures effectively in terms of the following. (1) We show a higher accuracy for domain classification. (2) We show a clear and consistent distribution of domains using our proposed structural vector space. (3) We are able to cluster the domains according to our moment features and demonstrate a relationship between structural variation and functional diversity. PMID:24391828

A historical survey of algorithms and hardware architectures for neural-inspired and neuromorphic computing applications

DOE PAGES

James, Conrad D.; Aimone, James B.; Miner, Nadine E.; ...

2017-01-04

In this study, biological neural networks continue to inspire new developments in algorithms and microelectronic hardware to solve challenging data processing and classification problems. Here in this research, we survey the history of neural-inspired and neuromorphic computing in order to examine the complex and intertwined trajectories of the mathematical theory and hardware developed in this field. Early research focused on adapting existing hardware to emulate the pattern recognition capabilities of living organisms. Contributions from psychologists, mathematicians, engineers, neuroscientists, and other professions were crucial to maturing the field from narrowly-tailored demonstrations to more generalizable systems capable of addressing difficult problem classesmore » such as object detection and speech recognition. Algorithms that leverage fundamental principles found in neuroscience such as hierarchical structure, temporal integration, and robustness to error have been developed, and some of these approaches are achieving world-leading performance on particular data classification tasks. Additionally, novel microelectronic hardware is being developed to perform logic and to serve as memory in neuromorphic computing systems with optimized system integration and improved energy efficiency. Key to such advancements was the incorporation of new discoveries in neuroscience research, the transition away from strict structural replication and towards the functional replication of neural systems, and the use of mathematical theory frameworks to guide algorithm and hardware developments.« less

A historical survey of algorithms and hardware architectures for neural-inspired and neuromorphic computing applications

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

James, Conrad D.; Aimone, James B.; Miner, Nadine E.

In this study, biological neural networks continue to inspire new developments in algorithms and microelectronic hardware to solve challenging data processing and classification problems. Here in this research, we survey the history of neural-inspired and neuromorphic computing in order to examine the complex and intertwined trajectories of the mathematical theory and hardware developed in this field. Early research focused on adapting existing hardware to emulate the pattern recognition capabilities of living organisms. Contributions from psychologists, mathematicians, engineers, neuroscientists, and other professions were crucial to maturing the field from narrowly-tailored demonstrations to more generalizable systems capable of addressing difficult problem classesmore » such as object detection and speech recognition. Algorithms that leverage fundamental principles found in neuroscience such as hierarchical structure, temporal integration, and robustness to error have been developed, and some of these approaches are achieving world-leading performance on particular data classification tasks. Additionally, novel microelectronic hardware is being developed to perform logic and to serve as memory in neuromorphic computing systems with optimized system integration and improved energy efficiency. Key to such advancements was the incorporation of new discoveries in neuroscience research, the transition away from strict structural replication and towards the functional replication of neural systems, and the use of mathematical theory frameworks to guide algorithm and hardware developments.« less

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

ERIC Educational Resources Information Center

Harper, Frances Kay

2017-01-01

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

Achieving Standards in a Fiber Optic Mathematics Classroom.

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Foletta, Gina M.

1995-01-01

In response to standards set by the National Council of Teachers of Mathematics, K-12 teachers were interviewed to investigate issues related to implementing standards in K-12 fiber optic mathematics classes. Issues include: achieving student-centered classrooms; incorporating technology into distance education; and structuring assessment so more…

Effects of Background and School Factors on the Mathematics Achievement.

ERIC Educational Resources Information Center

Papanastasiou, Constantinos

2002-01-01

Using a structural equation model, this study investigated the mathematics achievement of eighth graders in Cyprus enrolled in the year 1994-1995. The model considered two exogenous constructs related to student background and five endogenous constructs. Although attitudes, teaching, and beliefs had direct effect on mathematics outcomes, these…

The Concrete-Representational-Abstract Sequence of Instruction in Mathematics Classrooms

ERIC Educational Resources Information Center

Mudaly, Vimolan; Naidoo, Jayaluxmi

2015-01-01

The purpose of this paper is to explore how master mathematics teachers use the concrete-representational-abstract (CRA) sequence of instruction in mathematics classrooms. Data was collected from a convenience sample of six master teachers by observations, video recordings of their teaching, and semi-structured interviews. Data collection also…

Structural and Conceptual Interweaving of Mathematics Methods Coursework and Field Practica

ERIC Educational Resources Information Center

Bahr, Damon L.; Monroe, Eula Ewing; Eggett, Dennis

2014-01-01

This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the…

Structure Sense: A Precursor to Competency in Undergraduate Mathematics

ERIC Educational Resources Information Center

Vincent, Jill; Pierce, Robyn; Bardini, Caroline

2017-01-01

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

Elementary Administrators' Mathematics Supervision and Self-Efficacy Development

ERIC Educational Resources Information Center

Johnson, Kelly M. Gomez

2017-01-01

Mathematics curriculum reform is changing the content and resources in today's elementary classrooms as well as the culture of mathematics teaching and learning. Administrators face the challenge of leading large-scale curricular change efforts with limited prior knowledge or experiences with reform curricula structures. Administrators, as the…

Effects of General and Broad Cognitive Abilities on Mathematics Achievement

ERIC Educational Resources Information Center

Taub, Gordon E.; Keith, Timothy Z.; Floyd, Randy G.; Mcgrew, Kevin S.

2008-01-01

This study investigated the direct and indirect effects of general intelligence and 7 broad cognitive abilities on mathematics achievement. Structural equation modeling was used to investigate the simultaneous effects of both general and broad cognitive abilities on students' mathematics achievement. A hierarchical model of intelligence derived…

Beliefs and Achievement in Seventh-Grade Mathematics.

ERIC Educational Resources Information Center

Kloosterman, Peter

1991-01-01

This study highlights the correlation between seventh grade students' (n=429) beliefs about how mathematics is learned and their achievement in mathematics. Results from structural relation modeling indicate that, when beliefs are considered as a single construct, the relationship between beliefs and achievement is much stronger than when beliefs…

Cognitive, Educational and Psychological Determinants of Prospective Preschool Teachers' Beliefs

ERIC Educational Resources Information Center

Blömeke, Sigrid; Dunekacke, Simone; Jenßen, Lars

2017-01-01

This study examined the level, structure and cognitive, educational and psychological determinants of beliefs about the relevance and nature of mathematics, about gender-stereotypes with respect to mathematics abilities and about enjoyment of mathematics. Prospective preschool teachers from programs at vocational schools and higher education…

Practise What You Preach: The Interactive Whiteboard in Preschool Mathematics Education

ERIC Educational Resources Information Center

Bourbour, Maryam; Masoumi, Davoud

2017-01-01

The Interactive Whiteboard (IWB) is now a common technological artefact in Swedish preschools and schools. This study examines preschool teachers' thinking behind the embedding of IWB in the early years' mathematics classroom and how preschool teachers structure their mathematical activities when using IWB. Two complementary empirical studies,…

Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

NASA Astrophysics Data System (ADS)

Hitt, Fernando

2011-09-01

Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.

CelOWS: an ontology based framework for the provision of semantic web services related to biological models.

PubMed

Matos, Ely Edison; Campos, Fernanda; Braga, Regina; Palazzi, Daniele

2010-02-01

The amount of information generated by biological research has lead to an intensive use of models. Mathematical and computational modeling needs accurate description to share, reuse and simulate models as formulated by original authors. In this paper, we introduce the Cell Component Ontology (CelO), expressed in OWL-DL. This ontology captures both the structure of a cell model and the properties of functional components. We use this ontology in a Web project (CelOWS) to describe, query and compose CellML models, using semantic web services. It aims to improve reuse and composition of existent components and allow semantic validation of new models.

Boundary crossing and brokering between disciplines in pre-service mathematics teacher education

NASA Astrophysics Data System (ADS)

Goos, Merrilyn; Bennison, Anne

2017-12-01

In many countries, pre-service teacher education programs are structured so that mathematics content is taught in the university's mathematics department and mathematics pedagogy in the education department. Such program structures make it difficult to authentically interweave content with pedagogy in ways that acknowledge the roles of both mathematicians and mathematics educators in preparing future teachers. This article reports on a project that deliberately fostered collaboration between mathematicians and mathematics educators in six Australian universities in order to investigate the potential for learning at the boundaries between the two disciplinary communities. Data sources included two rounds of interviews with mathematicians and mathematics educators and annual reports prepared by each participating university over the three years of the project. The study identified interdisciplinary boundary practices that led to integration of content and pedagogy through new courses co-developed and co-taught by mathematicians and mathematics educators, and new approaches to building communities of pre-service teachers. It also developed an evidence-based classification of conditions that enable or hinder sustained collaboration across disciplinary boundaries, together with an empirical grounding for Akkerman and Bakker's conceptualisation of transformation as a mechanism for learning at the boundary between communities. The study additionally highlighted the ambiguous nature of boundaries and implications for brokers who work there to connect disciplinary paradigms.

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school.

PubMed

Cerda, Gamal; Pérez, Carlos; Navarro, José I; Aguilar, Manuel; Casas, José A; Aragón, Estíbaliz

2015-01-01

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students' level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 and 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

Capturing the Large Scale Behavior of Many Particle Systems Through Coarse-Graining

NASA Astrophysics Data System (ADS)

Punshon-Smith, Samuel

This dissertation is concerned with two areas of investigation: the first is understanding the mathematical structures behind the emergence of macroscopic laws and the effects of small scales fluctuations, the second involves the rigorous mathematical study of such laws and related questions of well-posedness. To address these areas of investigation the dissertation involves two parts: Part I concerns the theory of coarse-graining of many particle systems. We first investigate the mathematical structure behind the Mori-Zwanzig (projection operator) formalism by introducing two perturbative approaches to coarse-graining of systems that have an explicit scale separation. One concerns systems with little dissipation, while the other concerns systems with strong dissipation. In both settings we obtain an asymptotic series of `corrections' to the limiting description which are small with respect to the scaling parameter, these corrections represent the effects of small scales. We determine that only certain approximations give rise to dissipative effects in the resulting evolution. Next we apply this framework to the problem of coarse-graining the locally conserved quantities of a classical Hamiltonian system. By lumping conserved quantities into a collection of mesoscopic cells, we obtain, through a series of approximations, a stochastic particle system that resembles a discretization of the non-linear equations of fluctuating hydrodynamics. We study this system in the case that the transport coefficients are constant and prove well-posedness of the stochastic dynamics. Part II concerns the mathematical description of models where the underlying characteristics are stochastic. Such equations can model, for instance, the dynamics of a passive scalar in a random (turbulent) velocity field or the statistical behavior of a collection of particles subject to random environmental forces. First, we study general well-posedness properties of stochastic transport equation with rough diffusion coefficients. Our main result is strong existence and uniqueness under certain regularity conditions on the coefficients, and uses the theory of renormalized solutions of transport equations adapted to the stochastic setting. Next, in a work undertaken with collaborator Scott-Smith we study the Boltzmann equation with a stochastic forcing. The noise describing the forcing is white in time and colored in space and describes the effects of random environmental forces on a rarefied gas undergoing instantaneous, binary collisions. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. Tightness of the appropriate quantities is proved by an extension of the Skorohod theorem to non-metric spaces.

Advancement of understanding in physical science and reduction of mathematical anxiety through the use of supplemental mathematics material

NASA Astrophysics Data System (ADS)

Roberson, James Chadwick

The purpose of this study was to determine if supplementary mathematics materials (created to be complementary to a physical science course) could provide a significant change in the attitudes and performance of the students involved. The supplementary text was provided in the form of a booklet. Participants were students in a physical science class. Students were given surveys to evaluate existing knowledge of physical science, mathematics skill, and mathematics anxiety in the context of a science class. Students were divided into control and experimental groups by lab section, with the experimental group receiving a supplemental booklet. At the end of the semester, another anxiety survey was given. The anxiety surveys and test grades were compared between groups. Anxiety scores were compared between the beginning and end of the semester within each group. Too few students reported using the booklets for a reliable statistical comparison (of grades) to be made. A statistically significant difference in mathematics anxiety levels was found between the groups.

Gender differences in prospective teachers’ mathematical literacy: problem solving of occupational context on shipping company

NASA Astrophysics Data System (ADS)

Lestari, N. D. S.; Juniati, D.; Suwarsono, St.

2018-04-01

The purpose of this paper is to describe to what extent the prospective teachers can be considered as mathematically literate and how they communicate their reasoning in solving the problem based on the sex differences. Data were collected through mathematics literacy test on occupational context by 157 of prospective teachers from three universities in East Java, Indonesia. Their written responses were collected, organized based on the sex differences, analyzed and categorized to one of three levels of mathematical literacy. The examples of interesting students’ response altogether with the scoring are discussed to describe their characteristic on mathematical literacy and their communication. The result showed that in general the mathematical literacy of female prospective teachers tend to be better than male prospective math teachers. Female prospective teachers are more capable of logical reasoning, using concepts, facts and procedures and algebraic operations to draw conclusions; make an interpretations and evaluations. This study has an implication that gender differences in mathematical literacy of prospective math teachers do exist, therefore this issue should be given a serious concern from the development programs of the faculty.

Information transfer in community structured multiplex networks

NASA Astrophysics Data System (ADS)

Solé Ribalta, Albert; Granell, Clara; Gómez, Sergio; Arenas, Alex

2015-08-01

The study of complex networks that account for different types of interactions has become a subject of interest in the last few years, specially because its representational power in the description of users interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.). The mathematical description of these interacting networks has been coined under the name of multilayer networks, where each layer accounts for a type of interaction. It has been shown that diffusive processes on top of these networks present a phenomenology that cannot be explained by the naive superposition of single layer diffusive phenomena but require the whole structure of interconnected layers. Nevertheless, the description of diffusive phenomena on multilayer networks has obviated the fact that social networks have strong mesoscopic structure represented by different communities of individuals driven by common interests, or any other social aspect. In this work, we study the transfer of information in multilayer networks with community structure. The final goal is to understand and quantify, if the existence of well-defined community structure at the level of individual layers, together with the multilayer structure of the whole network, enhances or deteriorates the diffusion of packets of information.

Proportioning Cats and Rats

ERIC Educational Resources Information Center

Markworth, Kimberly A.

2012-01-01

Students may be able to set up a relevant proportion and solve through cross multiplication. However, this ability may not reflect the desired mathematical understanding of the covarying relationship that exists between two variables or the equivalent relationship that exists between two ratios. Students who lack this understanding are likely to…

Light, temperature, and leaf nitrogen distribution in the tropical rain forest of Biosphere 2 and their importance in the mathematical models for global environmental changes

NASA Technical Reports Server (NTRS)

Tohda, Motofumi

1997-01-01

As the environmental changes occur throughout the world in rapid rate, we need to have further understandings for our planet. Since the ecosystems are so complex, it is almost impossible for us to integrate every factor. However, mathematical models are powerful tools which can be used to simulate those ecosystems with limited data. In this project, I collected light intensity, canopy leaf temperature and Air Handler (AHU) temperature, and nitrogen concentration in the leaves for different profiles in the rainforest mesocosm. These data will later be put into mathematical models such as "big-leaf" and "sun/shade" models to determine how these factors will affect CO2 exchange in the rainforest. As rainforests are diminishing from our planet and their existence is very important for all living things on earth, it is necessary for us to learn more about the unique system of rainforests and how we can co-exist rather than destroy.

Zoonotic Transmission of Waterborne Disease: A Mathematical Model.

PubMed

Waters, Edward K; Hamilton, Andrew J; Sidhu, Harvinder S; Sidhu, Leesa A; Dunbar, Michelle

2016-01-01

Waterborne parasites that infect both humans and animals are common causes of diarrhoeal illness, but the relative importance of transmission between humans and animals and vice versa remains poorly understood. Transmission of infection from animals to humans via environmental reservoirs, such as water sources, has attracted attention as a potential source of endemic and epidemic infections, but existing mathematical models of waterborne disease transmission have limitations for studying this phenomenon, as they only consider contamination of environmental reservoirs by humans. This paper develops a mathematical model that represents the transmission of waterborne parasites within and between both animal and human populations. It also improves upon existing models by including animal contamination of water sources explicitly. Linear stability analysis and simulation results, using realistic parameter values to describe Giardia transmission in rural Australia, show that endemic infection of an animal host with zoonotic protozoa can result in endemic infection in human hosts, even in the absence of person-to-person transmission. These results imply that zoonotic transmission via environmental reservoirs is important.

Hearing shapes of drums: Mathematical and physical aspects of isospectrality

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

Giraud, Olivier; Thas, Koen; LPT

2010-07-15

In a celebrated paper ''Can one hear the shape of a drum?'' M. Kac [Am. Math. Monthly 73, 1 (1966)] asked his famous question about the existence of nonisometric billiards having the same spectrum of the Laplacian. This question was eventually answered positively in 1992 by the construction of noncongruent planar isospectral pairs. This review highlights mathematical and physical aspects of isospectrality.

Using Bayesian Networks to Understand Relationships among Math Anxiety, Genders, Personality Types, and Study Habits at a University in Jordan

ERIC Educational Resources Information Center

Smail, Linda

2017-01-01

Mathematics is the foundation of all sciences, but most students have problems learning math. Although students' success in life related to their success in learning, many would not take a math course unless it is their university's core requirements. Multiple reasons exist for students' poor performance in mathematics, but one prevalent variable…

A Comparison of Students in Single-Sex Classes and Coeducational Classes in High Poverty Public Elementary Schools in Mathematics and Reading Achievement

ERIC Educational Resources Information Center

Aldridge, Ashley Elizabeth

2009-01-01

The purpose of this study was to investigate whether any statistically significant differences in mathematics and reading academic achievement and academic gains of male and female students taught in single-sex classes existed when compared to male and female students taught in coeducational classes. This study reported findings from mathematics…

Not just a theory--the utility of mathematical models in evolutionary biology.

PubMed

Servedio, Maria R; Brandvain, Yaniv; Dhole, Sumit; Fitzpatrick, Courtney L; Goldberg, Emma E; Stern, Caitlin A; Van Cleve, Jeremy; Yeh, D Justin

2014-12-01

Progress in science often begins with verbal hypotheses meant to explain why certain biological phenomena exist. An important purpose of mathematical models in evolutionary research, as in many other fields, is to act as “proof-of-concept” tests of the logic in verbal explanations, paralleling the way in which empirical data are used to test hypotheses. Because not all subfields of biology use mathematics for this purpose, misunderstandings of the function of proof-of-concept modeling are common. In the hope of facilitating communication, we discuss the role of proof-of-concept modeling in evolutionary biology.

Genetic Code Analysis Toolkit: A novel tool to explore the coding properties of the genetic code and DNA sequences

NASA Astrophysics Data System (ADS)

Kraljić, K.; Strüngmann, L.; Fimmel, E.; Gumbel, M.

2018-01-01

The genetic code is degenerated and it is assumed that redundancy provides error detection and correction mechanisms in the translation process. However, the biological meaning of the code's structure is still under current research. This paper presents a Genetic Code Analysis Toolkit (GCAT) which provides workflows and algorithms for the analysis of the structure of nucleotide sequences. In particular, sets or sequences of codons can be transformed and tested for circularity, comma-freeness, dichotomic partitions and others. GCAT comes with a fertile editor custom-built to work with the genetic code and a batch mode for multi-sequence processing. With the ability to read FASTA files or load sequences from GenBank, the tool can be used for the mathematical and statistical analysis of existing sequence data. GCAT is Java-based and provides a plug-in concept for extensibility. Availability: Open source Homepage:http://www.gcat.bio/

Mathematical model of susceptibility, resistance, and resilience in the within-host dynamics between a Plasmodium parasite and the immune system.

PubMed

Yan, Yi; Adam, Brian; Galinski, Mary; C Kissinger, Jessica; Moreno, Alberto; Gutierrez, Juan B

2015-12-01

We developed a coupled age-structured partial differential equation model to capture the disease dynamics during blood-stage malaria. The addition of age structure for the parasite population, with respect to previous models, allows us to better characterize the interaction between the malaria parasite and red blood cells during infection. Here we prove that the system we propose is well-posed and there exist at least two global states. We further demonstrate that the numerical simulation of the system coincides with clinically observed outcomes of primary and secondary malaria infection. The well-posedness of this system guarantees that the behavior of the model remains smooth, bounded, and continuously dependent on initial conditions; calibration with clinical data will constrain domains of parameters and variables to physiological ranges. Copyright © 2015 Elsevier Inc. All rights reserved.

Stability of nonlinear waves and patterns and related topics.

PubMed

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-13

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties.This article is part of the theme issue 'Stability of nonlinear waves and patterns and related topics'. © 2018 The Author(s).

Evaluation of the Thermodynamic Consistency of Closure Approximations in Several Models Proposed for the Description of Liquid Crystalline Dynamics

NASA Astrophysics Data System (ADS)

Edwards, Brian J.

2002-05-01

Given the premise that a set of dynamical equations must possess a definite, underlying mathematical structure to ensure local and global thermodynamic stability, as has been well documented, several different models for describing liquid crystalline dynamics are examined with respect to said structure. These models, each derived during the past several years using a specific closure approximation for the fourth moment of the distribution function in Doi's rigid rod theory, are all shown to be inconsistent with this basic mathematical structure. The source of this inconsistency lies in Doi's expressions for the extra stress tensor and temporal evolution of the order parameter, which are rederived herein using a transformation that allows for internal compatibility with the underlying mathematical structure that is present on the distribution function level of description.

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

PubMed

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Bio-inspired structural bistability employing elastomeric origami for morphing applications

NASA Astrophysics Data System (ADS)

Daynes, Stephen; Trask, Richard S.; Weaver, Paul M.

2014-12-01

A structural concept based upon the principles of adaptive morphing cells is presented whereby controlled bistability from a flat configuration into a textured arrangement is shown. The material consists of multiple cells made from silicone rubber with locally reinforced regions based upon kirigami principles. On pneumatic actuation these cells fold or unfold based on the fold lines created by the interaction of the geometry with the reinforced regions. Each cell is able to maintain its shape in either a retracted or deployed state, without the aid of mechanisms or sustained actuation, due to the existence of structural bistability. Mathematical quantification of the surface texture is introduced, based on out-of-plane deviations of a deployed structure compared to a reference plane. Additionally, finite element analysis is employed to characterize the geometry and stability of an individual cell during actuation and retraction. This investigation highlights the critical role that angular rotation, at the center of each cell, plays on the deployment angle as it transitions through the elastically deployed configuration. The analysis of this novel concept is presented and a pneumatically actuated proof-of-concept demonstrator is fabricated.

Non-patchy strategy for inter-atomic distances from Extended X-ray Absorption Fine Structure

PubMed Central

Xu, Gu; Li, Guifang; LI, Xianya; Liang, Yi; Feng, Zhechuan

2017-01-01

Extended X-ray Absorption Fine Structure (EXAFS) has been one of the few structural probes available for crystalline, non-crystalline and even highly disordered specimens. However, the data analysis involves a patchy and tinkering process, including back-and-forth fitting and filtering, leading to ambiguous answers sometimes. Here we try to resolve this long standing problem, to extract the inter-atomic distances from the experimental data by a single step minimization, in order to replace the tedious and tinkering process. The new strategy is built firmly by the mathematical logic, and made straightforward and undeniable. The finding demonstrates that it is possible to break off from the traditional patchy model fitting, and to remove the logical confusion of a priori prediction of the structure to be matched with experimental data, making it a much more powerful technique than the existing methods. The new method is expected to benefit EXAFS users covering all disciplines. Also, it is anticipated that the current work to be the motivation and inspiration to the further efforts. PMID:28181529

Analysis of shell type structures subjected to time dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1985-01-01

A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is considered. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratchetting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model.

A Self-paced Course in Pharmaceutical Mathematics Using Web-based Databases

PubMed Central

Bourne, David W.A.; Davison, A. Machelle

2006-01-01

Objective To transform a pharmaceutical mathematics course to a self-paced instructional format using Web-accessed databases for student practice and examination preparation. Design The existing pharmaceutical mathematics course was modified from a lecture style with midsemester and final examinations to a self-paced format in which students had multiple opportunities to complete online, nongraded self-assessments as well as in-class module examinations. Assessment Grades and course evaluations were compared between students taking the class in lecture format with midsemester and final examinations and students taking the class in the self-paced instructional format. The number of times it took students to pass examinations was also analyzed. Conclusions Based on instructor assessment and student feedback, the course succeeded in giving students who were proficient in pharmaceutical mathematics a chance to progress quickly and students who were less skillful the opportunity to receive instruction at their own pace and develop mathematical competence. PMID:17149445

A self-paced course in pharmaceutical mathematics using web-based databases.

PubMed

Bourne, David W A; Davison, A Machelle

2006-10-15

To transform a pharmaceutical mathematics course to a self-paced instructional format using Web-accessed databases for student practice and examination preparation. The existing pharmaceutical mathematics course was modified from a lecture style with midsemester and final examinations to a self-paced format in which students had multiple opportunities to complete online, nongraded self-assessments as well as in-class module examinations. Grades and course evaluations were compared between students taking the class in lecture format with midsemester and final examinations and students taking the class in the self-paced instructional format. The number of times it took students to pass examinations was also analyzed. Based on instructor assessment and student feedback, the course succeeded in giving students who were proficient in pharmaceutical mathematics a chance to progress quickly and students who were less skillful the opportunity to receive instruction at their own pace and develop mathematical competence.

Integration of bioinformatics into an undergraduate biology curriculum and the impact on development of mathematical skills.

PubMed

Wightman, Bruce; Hark, Amy T

2012-01-01

The development of fields such as bioinformatics and genomics has created new challenges and opportunities for undergraduate biology curricula. Students preparing for careers in science, technology, and medicine need more intensive study of bioinformatics and more sophisticated training in the mathematics on which this field is based. In this study, we deliberately integrated bioinformatics instruction at multiple course levels into an existing biology curriculum. Students in an introductory biology course, intermediate lab courses, and advanced project-oriented courses all participated in new course components designed to sequentially introduce bioinformatics skills and knowledge, as well as computational approaches that are common to many bioinformatics applications. In each course, bioinformatics learning was embedded in an existing disciplinary instructional sequence, as opposed to having a single course where all bioinformatics learning occurs. We designed direct and indirect assessment tools to follow student progress through the course sequence. Our data show significant gains in both student confidence and ability in bioinformatics during individual courses and as course level increases. Despite evidence of substantial student learning in both bioinformatics and mathematics, students were skeptical about the link between learning bioinformatics and learning mathematics. While our approach resulted in substantial learning gains, student "buy-in" and engagement might be better in longer project-based activities that demand application of skills to research problems. Nevertheless, in situations where a concentrated focus on project-oriented bioinformatics is not possible or desirable, our approach of integrating multiple smaller components into an existing curriculum provides an alternative. Copyright © 2012 Wiley Periodicals, Inc.

Structural analysis of online handwritten mathematical symbols based on support vector machines

NASA Astrophysics Data System (ADS)

Simistira, Foteini; Papavassiliou, Vassilis; Katsouros, Vassilis; Carayannis, George

2013-01-01

Mathematical expression recognition is still a very challenging task for the research community mainly because of the two-dimensional (2d) structure of mathematical expressions (MEs). In this paper, we present a novel approach for the structural analysis between two on-line handwritten mathematical symbols of a ME, based on spatial features of the symbols. We introduce six features to represent the spatial affinity of the symbols and compare two multi-class classification methods that employ support vector machines (SVMs): one based on the "one-against-one" technique and one based on the "one-against-all", in identifying the relation between a pair of symbols (i.e. subscript, numerator, etc). A dataset containing 1906 spatial relations derived from the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2012 training dataset is constructed to evaluate the classifiers and compare them with the rule-based classifier of the ILSP-1 system participated in the contest. The experimental results give an overall mean error rate of 2.61% for the "one-against-one" SVM approach, 6.57% for the "one-against-all" SVM technique and 12.31% error rate for the ILSP-1 classifier.

Structuring students’ analogical reasoning in solving algebra problem

NASA Astrophysics Data System (ADS)

Lailiyah, S.; Nusantara, T.; Sa'dijah, C.; Irawan, E. B.; Kusaeri; Asyhar, A. H.

2018-01-01

The average achievement of Indonesian students’ mathematics skills according to Benchmark International Trends in Mathematics and Science Study (TIMSS) is ranked at the 38th out of 42 countries and according to the survey result in Program for International Student Assessment (PISA) is ranked at the 64th out of 65 countries. The low mathematics skill of Indonesian student has become an important reason to research more deeply about reasoning and algebra in mathematics. Analogical reasoning is a very important component in mathematics because it is the key to creativity and it can make the learning process in the classroom become effective. The major part of the analogical reasoning is about structuring including the processes of inferencing and decision-making happens. Those processes involve base domain and target domain. Methodologically, the subjects of this research were 42 students from class XII. The sources of data were derived from the results of thinks aloud, the transcribed interviews, and the videos taken while the subject working on the instruments and interviews. The collected data were analyzed using qualitative techniques. The result of this study described the structuring characteristics of students’ analogical reasoning in solving algebra problems from all the research subjects.

Teaching where there are no schools.

PubMed

Helwig, J F; Friend, J

1985-01-01

An experimental project designed to investigate the feasibility of using radio as a medium of instruction in the teaching of elementary school mathematics, the Radio Mathematics Project, which was located in Nicaragua from mid-1974 to early 1979, developed mathematics lessons for the first 4 years of elementary school. These lessons -- daily radio broadcasts plus postbroadcast activities conducted by the classroom teachers -- proved to be successful in improving the students' mathematics achievement. The cost of widescale implementation of the materials was estimated to be well within Nicaragua's budget. The success of the project can be attributed largely to the innovative style of the broadcast lessons, a style characterized as "interactive" in recognition of its mimicry of a conversation between students and teacher. The interactive lesson style is easily adapted to the teaching of many other subjects and has been used, with minor modifications, to teach English as a 2nd language and initial reading. In all these settings, the lessons provide daily instruction and are intended to replace rather than supplement existing instruction in the subject matter. Each lesson consists of a broadcast portion of the lesson carries the major burden of instruction. The interactive radio lessons are designed to provide direct instruction to the students. The radio teachers explain concepts, provide examples, and guide the students in the completion of exercises. The students listening to the radio lessons are expected to participate actively. After every student response, the radio gives the correct response so that the children can immediately compare their own responses with the correct one. Segmented structure is characteristic of the radio lessons used in all 3 projects mentioned. Radio Math's lessons are reinforced by rigorous research to validate their teaching effectiveness.

A study of students' learning styles and mathematics anxiety amongst form four students in Kerian Perak

NASA Astrophysics Data System (ADS)

Esa, Suraya; Mohamed, Nurul Akmal

2017-05-01

This study aims to identify the relationship between students' learning styles and mathematics anxiety amongst Form Four students in Kerian, Perak. The study involves 175 Form Four students as respondents. The instrument which is used to assess the students' learning styles and mathematic anxiety is adapted from the Grasha's Learning Styles Inventory and the Mathematics Anxiety Scale (MAS) respectively. The types of learning styles used are independent, avoidant, collaborative, dependent, competitive and participant. The collected data is processed by SPSS (Statistical Packages for Social Sciences 16.0). The data is analysed by using descriptive statistics and inferential statistics that include t-test and Pearson correlation. The results show that majority of the students adopt collaborative learning style and the students have moderate level of mathematics anxiety. Moreover, it is found that there is significant difference between learning style avoidant, collaborative, dependent and participant based on gender. Amongst all students' learning style, there exists a weak but significant correlation between avoidant, independent and participant learning style and mathematics anxiety. It is very important for the teachers need to be concerned about the effects of learning styles on mathematics anxiety. Therefore, the teachers should understand mathematics anxiety and implement suitable learning strategies in order for the students to overcome their mathematics anxiety.

Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring

ERIC Educational Resources Information Center

Simpson, Adrian; Stehlikova, Nada

2006-01-01

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

Identification of Prospective Science Teachers' Mathematical-Logical Structures in Reference to Magnetism

ERIC Educational Resources Information Center

Yilmaz, Ismail

2014-01-01

This paper is a qualitative case study designed to identify prospective science teachers' mathematical-logical structures on the basis of their knowledge and achievement levels in magnetism. The study also made an attempt to reveal the effects of knowledge-level variables and procedural variables, which were considered to be potential…

Semiotic Structure and Meaning Making: The Performance of English Language Learners on Mathematics Tests

ERIC Educational Resources Information Center

Solano-Flores, Guillermo; Barnett-Clarke, Carne; Kachchaf, Rachel R.

2013-01-01

We examined the performance of English language learners (ELLs) and non-ELLs on Grade 4 and Grade 5 mathematics content knowledge (CK) and academic language (AL) tests. CK and AL items had different semiotic loads (numbers of different types of semiotic features) and different semiotic structures (relative frequencies of different semiotic…

Perceptual Learning in Early Mathematics: Interacting with Problem Structure Improves Mapping, Solving and Fluency

ERIC Educational Resources Information Center

Thai, Khanh-Phuong; Son, Ji Y.; Hoffman, Jessica; Devers, Christopher; Kellman, Philip J.

2014-01-01

Mathematics is the study of structure but students think of math as solving problems according to rules. Students can learn procedures, but they often have trouble knowing when to apply learned procedures, especially to problems unlike those they trained with. In this study, the authors rely on the psychological mechanism of perceptual learning…