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

NASA Technical Reports Server (NTRS)

Simitses, G. J.

1989-01-01

The objective is to develop 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. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and racheting. 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. Furthermore, this must also be accommodated in the solution procedures.

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

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Riff, R.

1988-01-01

The objective of this research is to develop 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. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and racheting. 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. Furthermore, this must also be accommodated in the solution procedures.

Mathematical modeling of shell configurations made of homogeneous and composite materials experiencing intensive short actions and large displacements

NASA Astrophysics Data System (ADS)

Khairnasov, K. Z.

2018-04-01

The paper presents a mathematical model for solving the problem of behavior of shell configurations under the action of static and dynamic impacts. The problem is solved in geometrically nonlinear statement with regard to the finite element method. The composite structures with different material layers are considered. The obtained equations are used to study the behavior of shell configurations under the action of dynamic loads. The results agree well with the experimental data.

Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.

PubMed

Millat, Thomas; Winzer, Klaus

2017-03-01

Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.

Zig-Zagging in Geometrical Reasoning in Technological Collaborative Environments: A Mathematical Working Space-Framed Study Concerning Cognition and Affect

ERIC Educational Resources Information Center

Gómez-Chacón, Inés Ma.; Romero Albaladejo, Isabel Ma.; del Mar García López, Ma.

2016-01-01

This study highlights the importance of cognition-affect interaction pathways in the construction of mathematical knowledge. Scientific output demands further research on the conceptual structure underlying such interaction aimed at coping with the high complexity of its interpretation. The paper discusses the effectiveness of using a dynamic…

Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading

NASA Technical Reports Server (NTRS)

Simitses, George J.; Carlson, Robert L.; Riff, Richard

1991-01-01

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Mathematical investigation of IP3-dependent calcium dynamics in astrocytes.

PubMed

Handy, Gregory; Taheri, Marsa; White, John A; Borisyuk, Alla

2017-06-01

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.

Mathematical model for adaptive control system of ASEA robot at Kennedy Space Center

NASA Technical Reports Server (NTRS)

Zia, Omar

1989-01-01

The dynamic properties and the mathematical model for the adaptive control of the robotic system presently under investigation at Robotic Application and Development Laboratory at Kennedy Space Center are discussed. NASA is currently investigating the use of robotic manipulators for mating and demating of fuel lines to the Space Shuttle Vehicle prior to launch. The Robotic system used as a testbed for this purpose is an ASEA IRB-90 industrial robot with adaptive control capabilities. The system was tested and it's performance with respect to stability was improved by using an analogue force controller. The objective of this research project is to determine the mathematical model of the system operating under force feedback control with varying dynamic internal perturbation in order to provide continuous stable operation under variable load conditions. A series of lumped parameter models are developed. The models include some effects of robot structural dynamics, sensor compliance, and workpiece dynamics.

In accordance with a "more majestic order". The new math and the nature of mathematics at midcentury.

PubMed

Phillips, Christopher J

2014-09-01

The "new math" curriculum, one version of which was developed in the 1950s and 1960s by the School Mathematics Study Group under the auspices of the National Science Foundation, occasioned a great deal of controversy among mathematicians. Well before its rejection by parents and teachers, some mathematicians were vocal critics, decrying the new curriculum because of the way it described the practice and history of the discipline. The nature of mathematics, despite the field's triumphs in helping to win World War II and its midcentury promotion as the key to a modern technological society, was surprisingly contested in this period. Supporters of the School Mathematics Study Group, like its director, Edward Begle, emphasized the importance of portraying mathematics as a system of abstract structures, while opponents like Morris Kline argued that math was essentially a tool for understanding the natural world. The debate about the curriculum--and the role of mathematicians in its design--was also a debate about the underlying identity of the subject itself.

An Analysis of Teacher Education Context, Structure, and Quality-Assurance Arrangements in TEDS-M Countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M)

ERIC Educational Resources Information Center

Ingvarson, Lawrence; Schwille, John; Tatto, Maria Teresa; Rowley, Glenn; Peck, Ray; Senk, Sharon L.

2013-01-01

The Teacher Education and Development Study (TEDS-M) is the first crossnational study to examine the mathematics preparation of future teachers for both primary and secondary school levels. The study, conducted under the auspices of the International Association for the Evaluation of Educational Achievement (IEA), collected data from…

If It's Resonance, What is Resonating?

ERIC Educational Resources Information Center

Kerber, Robert C.

2006-01-01

The phenomenon under the name "resonance," which, is based on the mathematical analogy between mechanical resonance and the behavior of wave functions in quantum mechanical exchange phenomena was described. The resonating system does not have a structure intermediate between those involved in the resonance, but instead a structure which is further…

Surface growth kinematics via local curve evolution.

PubMed

Moulton, Derek E; Goriely, Alain

2014-01-01

A mathematical framework is developed to model the kinematics of surface growth for objects that can be generated by evolving a curve in space, such as seashells and horns. Growth is dictated by a growth velocity vector field defined at every point on a generating curve. A local orthonormal basis is attached to each point of the generating curve and the velocity field is given in terms of the local coordinate directions, leading to a fully local and elegant mathematical structure. Several examples of increasing complexity are provided, and we demonstrate how biologically relevant structures such as logarithmic shells and horns emerge as analytical solutions of the kinematics equations with a small number of parameters that can be linked to the underlying growth process. Direct access to cell tracks and local orientation enables for connections to be made to the underlying growth process.

Mathematical model of the heat transfer process taking into account the consequences of nonlocality in structurally sensitive materials

NASA Astrophysics Data System (ADS)

Kuvyrkin, G. N.; Savelyeva, I. Y.; Kuvshynnikova, D. A.

2018-04-01

Creation of new materials based on nanotechnology is an important direction of modern materials science development. Materials obtained using nanotechnology can possess unique physical-mechanical and thermophysical properties, allowing their effective use in structures exposed to high-intensity thermomechanical effects. An important step in creation and use of new materials is the construction of mathematical models to describe the behavior of these materials in a wide range of changes under external effects. The model of heat conduction of structural-sensitive materials is considered with regard to the medium nonlocality effects. The relations of the mathematical model include an integral term describing the spatial nonlocality of the medium. A difference scheme, which makes it possible to obtain a numerical solution of the problem of nonstationary heat conduction with regard to the influence of the medium nonlocality on space, has been developed. The influence of the model parameters on the temperature distributions is analyzed.

Statics and buckling problems of aircraft structurally-anisotropic composite panels with the influence of production technology

NASA Astrophysics Data System (ADS)

Gavva, L. M.; Endogur, A. I.

2018-02-01

The mathematical model relations for stress-strain state and for buckling investigation of structurally-anisotropic panels made of composite materials are presented. The mathematical model of stiffening rib being torsioned under one-side contact with the skin is refined. One takes into account the influence of panel production technology: residual thermal stresses and reinforcing fibers preliminary tension. The resolved eight order equation and natural boundary conditions are obtained with variation Lagrange procedure. Exact analytical solutions for edge problems are considered. Computer program package is developed using operating MATLAB environment. The influence of the structure parameters on the level of stresses, displacements, of critical buckling forces for bending and for torsion modes has analyzed.

A finite element program for postbuckling calculations (PSTBKL)

NASA Technical Reports Server (NTRS)

Simitses, G. T.; Carlson, R. L.; Riff, R.

1991-01-01

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermochemical loads. This report describes the computer program resulting from the research. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) have been anticipated and are considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strains is clearly demonstrated, through the chosen applications.

Topological Classification of Crystalline Insulators through Band Structure Combinatorics

NASA Astrophysics Data System (ADS)

Kruthoff, Jorrit; de Boer, Jan; van Wezel, Jasper; Kane, Charles L.; Slager, Robert-Jan

2017-10-01

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented match the mathematical structure underlying the topological classification of these crystals in terms of K -theory and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify all allowed topological phases of spinless particles in crystals in class A . Employing this classification, we study transitions between topological phases within class A that are driven by band inversions at high-symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure and to identify whether or not they give rise to intermediate Weyl semimetallic phases.

Simulation-Visualization and Self-Assessment Modules' Capabilities in Structural Analysis Course Including Survey Analysis Results

ERIC Educational Resources Information Center

Kadiam, Subhash Chandra Bose S. V.; Mohammed, Ahmed Ali; Nguyen, Duc T.

2010-01-01

In this paper, we describe an approach to analyze 2D truss/Frame/Beam structures under Flash-based environment. Stiffness Matrix Method (SMM) module was developed as part of ongoing projects on a broad topic "Students' Learning Improvements in Science, Technology, Engineering and Mathematics (STEM) Related Areas" at Old Dominion…

Effect of hybrid layer on stress distribution in a premolar tooth restored with composite or ceramic inlay: an FEM study.

PubMed

Belli, Sema; Eskitaşcioglu, Gürcan; Eraslan, Oguz; Senawongse, Pisol; Tagami, Junji

2005-08-01

The aim of this finite elemental stress analysis study was to evaluate the effect of hybrid layer on distribution and amount of stress formed under occlusal loading in a premolar tooth restored with composite or ceramic inlay. The mandibular premolar tooth was selected as the model based on the anatomical measurements suggested by Wheeler. The analysis is performed by using a Pentium II IBM compatible computer with the SAP 2000 structural analysis program. Four different mathematical models including the following structures were evaluated: 1) composite inlay, adhesive resin, and tooth structure; 2) composite inlay, adhesive resin, hybrid layer, and tooth structure; 3) ceramic inlay, adhesive resin, and tooth structure; 4) ceramic inlay, adhesive resin, hybrid layer, and tooth structure. Loading was applied from the occlusal surface of the restoration, and shear stresses under loading were evaluated. The findings were drawn by the Saplot program, and the results were analyzed by graphical comparison method. The output indicated that the hybrid layer acts as a stress absorber in models 2 and 4. The hybrid layer has also changed mathematical values of stress on cavity floors in both restoration types. Ceramic inlay collected the stress inside the body of the material, but the composite inlay directly transferred the stress through dental tissues. As a result, it was concluded that the hybrid layer has an effect on stress distribution under loading in a premolar tooth model restored with composite or ceramic inlay. Copyright 2005 Wiley Periodicals, Inc.

Non-isothermal buckling behavior of viscoplastic shell structures

NASA Technical Reports Server (NTRS)

Riff, Richard; Simitses, G. J.

1988-01-01

Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.

Experimental and theoretical investigation of deformation and fracture of subcutaneous fat under compression

NASA Astrophysics Data System (ADS)

Sapozhnikov, S. B.; Ignatova, A. V.

2013-01-01

The subcutaneous fat is considered as a structural material undergoing large inelastic deformations and failure under uniform compression. In calculation, the fat is replaced with a set of cells operating in parallel and suffering failure independently of one another. An elementary cell is considered as a closed thin-wall cylindrical shell filled with an incompressible liquid. All cells in the model are of the same size, and their material is hyperelastic, whose stiffness grows in tension. By comparing experimental data with the mathematical shell model, three parameters are determined to describe the hyperelastic behavior of the cells in transverse compression. A mathematical model with seven constants is presented for describing the deformation of subcutaneous fat under compression. The results obtained are used in a model of human thorax subjected to a local pulse action corresponding to the loading of human body under the impact of a bullet on an armor vest.

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.

Neural Mechanisms Underlying the Computation of Hierarchical Tree Structures in Mathematics

PubMed Central

Nakai, Tomoya; Sakai, Kuniyoshi L.

2014-01-01

Whether mathematical and linguistic processes share the same neural mechanisms has been a matter of controversy. By examining various sentence structures, we recently demonstrated that activations in the left inferior frontal gyrus (L. IFG) and left supramarginal gyrus (L. SMG) were modulated by the Degree of Merger (DoM), a measure for the complexity of tree structures. In the present study, we hypothesize that the DoM is also critical in mathematical calculations, and clarify whether the DoM in the hierarchical tree structures modulates activations in these regions. We tested an arithmetic task that involved linear and quadratic sequences with recursive computation. Using functional magnetic resonance imaging, we found significant activation in the L. IFG, L. SMG, bilateral intraparietal sulcus (IPS), and precuneus selectively among the tested conditions. We also confirmed that activations in the L. IFG and L. SMG were free from memory-related factors, and that activations in the bilateral IPS and precuneus were independent from other possible factors. Moreover, by fitting parametric models of eight factors, we found that the model of DoM in the hierarchical tree structures was the best to explain the modulation of activations in these five regions. Using dynamic causal modeling, we showed that the model with a modulatory effect for the connection from the L. IPS to the L. IFG, and with driving inputs into the L. IFG, was highly probable. The intrinsic, i.e., task-independent, connection from the L. IFG to the L. IPS, as well as that from the L. IPS to the R. IPS, would provide a feedforward signal, together with negative feedback connections. We indicate that mathematics and language share the network of the L. IFG and L. IPS/SMG for the computation of hierarchical tree structures, and that mathematics recruits the additional network of the L. IPS and R. IPS. PMID:25379713

Application of Lanczos vectors to control design of flexible structures, part 2

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.; Su, Tzu-Jeng

1992-01-01

This report covers the period of the grant from January 1991 until its expiration in June 1992. Together with an Interim Report (Ref. 9), it summarizes the research conducted under NASA Grant NAG9-357 on the topic 'Application of Lanczos Vectors to Control Design of Flexible Structures.' The research concerns various ways to obtain reduced-order mathematical models of complex structures for use in dynamics analysis and in the design of control systems for these structures. This report summarizes the research.

Structure Shapes Dynamics and Directionality in Diverse Brain Networks: Mathematical Principles and Empirical Confirmation in Three Species

NASA Astrophysics Data System (ADS)

Moon, Joon-Young; Kim, Junhyeok; Ko, Tae-Wook; Kim, Minkyung; Iturria-Medina, Yasser; Choi, Jee-Hyun; Lee, Joseph; Mashour, George A.; Lee, Uncheol

2017-04-01

Identifying how spatially distributed information becomes integrated in the brain is essential to understanding higher cognitive functions. Previous computational and empirical studies suggest a significant influence of brain network structure on brain network function. However, there have been few analytical approaches to explain the role of network structure in shaping regional activities and directionality patterns. In this study, analytical methods are applied to a coupled oscillator model implemented in inhomogeneous networks. We first derive a mathematical principle that explains the emergence of directionality from the underlying brain network structure. We then apply the analytical methods to the anatomical brain networks of human, macaque, and mouse, successfully predicting simulation and empirical electroencephalographic data. The results demonstrate that the global directionality patterns in resting state brain networks can be predicted solely by their unique network structures. This study forms a foundation for a more comprehensive understanding of how neural information is directed and integrated in complex brain networks.

Putting the "th" in Tenths: Providing Place-Value Labels Helps Reveal the Structure of Our Base-10 Numeral System

ERIC Educational Resources Information Center

Loehr, Abbey M.; Rittle-Johnson, Bethany

2017-01-01

Research has demonstrated that providing labels helps children notice key features of examples. Much less is known about how different labels impact children's ability to make inferences about the structure underlying mathematical notation. We tested the impact of labeling decimals such as 0.34 using formal place-value labels ("3 tenths and 4…

[For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden].

PubMed

Koreuber, Mechthild

2015-09-01

,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.

Mathematics, anxiety, and the brain.

PubMed

Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

2017-05-24

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

Structural optimization of framed structures using generalized optimality criteria

NASA Technical Reports Server (NTRS)

Kolonay, R. M.; Venkayya, Vipperla B.; Tischler, V. A.; Canfield, R. A.

1989-01-01

The application of a generalized optimality criteria to framed structures is presented. The optimality conditions, Lagrangian multipliers, resizing algorithm, and scaling procedures are all represented as a function of the objective and constraint functions along with their respective gradients. The optimization of two plane frames under multiple loading conditions subject to stress, displacement, generalized stiffness, and side constraints is presented. These results are compared to those found by optimizing the frames using a nonlinear mathematical programming technique.

Identity: a complex structure for researching students' academic behavior in science and mathematics

NASA Astrophysics Data System (ADS)

Aydeniz, Mehmet; Hodge, Lynn Liao

2011-06-01

This article is a response to Pike and Dunne's research. The focus of their analysis is on reflections of studying science post-16. Pike and Dunne draw attention to under enrollments in science, technology, engineering, and mathematics (STEM) fields, in particular, in the field of physics, chemistry and biology in the United Kingdom. We provide an analysis of how the authors conceptualize the problem of scientific career choices, the theoretical framework through which they study the problem, and the methodology they use to collect and analyze data. In addition, we examine the perspective they provide in light of new developments in the field of students' attitudes towards science and mathematics. More precisely, we draw attention to and explicate the authors' use of identity from the perspective of emerging theories that explore the relationships between the learner and culture in the context of science and mathematics.

Mathematical Logic in the Human Brain: Semantics

PubMed Central

Friedrich, Roland M.; Friederici, Angela D.

2013-01-01

As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge. PMID:23301101

Mathematical logic in the human brain: semantics.

PubMed

Friedrich, Roland M; Friederici, Angela D

2013-01-01

As a higher cognitive function in humans, mathematics is supported by parietal and prefrontal brain regions. Here, we give an integrative account of the role of the different brain systems in processing the semantics of mathematical logic from the perspective of macroscopic polysynaptic networks. By comparing algebraic and arithmetic expressions of identical underlying structure, we show how the different subparts of a fronto-parietal network are modulated by the semantic domain, over which the mathematical formulae are interpreted. Within this network, the prefrontal cortex represents a system that hosts three major components, namely, control, arithmetic-logic, and short-term memory. This prefrontal system operates on data fed to it by two other systems: a premotor-parietal top-down system that updates and transforms (external) data into an internal format, and a hippocampal bottom-up system that either detects novel information or serves as an access device to memory for previously acquired knowledge.

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…

The structural identifiability and parameter estimation of a multispecies model for the transmission of mastitis in dairy cows with postmilking teat disinfection.

PubMed

White, L J; Evans, N D; Lam, T J G M; Schukken, Y H; Medley, G F; Godfrey, K R; Chappell, M J

2002-01-01

A mathematical model for the transmission of two interacting classes of mastitis causing bacterial pathogens in a herd of dairy cows is presented and applied to a specific data set. The data were derived from a field trial of a specific measure used in the control of these pathogens, where half the individuals were subjected to the control and in the others the treatment was discontinued. The resultant mathematical model (eight non-linear simultaneous ordinary differential equations) therefore incorporates heterogeneity in the host as well as the infectious agent and consequently the effects of control are intrinsic in the model structure. A structural identifiability analysis of the model is presented demonstrating that the scope of the novel method used allows application to high order non-linear systems. The results of a simultaneous estimation of six unknown system parameters are presented. Previous work has only estimated a subset of these either simultaneously or individually. Therefore not only are new estimates provided for the parameters relating to the transmission and control of the classes of pathogens under study, but also information about the relationships between them. We exploit the close link between mathematical modelling, structural identifiability analysis, and parameter estimation to obtain biological insights into the system modelled.

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…

Concepts and tools for predictive modeling of microbial dynamics.

PubMed

Bernaerts, Kristel; Dens, Els; Vereecken, Karen; Geeraerd, Annemie H; Standaert, Arnout R; Devlieghere, Frank; Debevere, Johan; Van Impe, Jan F

2004-09-01

Description of microbial cell (population) behavior as influenced by dynamically changing environmental conditions intrinsically needs dynamic mathematical models. In the past, major effort has been put into the modeling of microbial growth and inactivation within a constant environment (static models). In the early 1990s, differential equation models (dynamic models) were introduced in the field of predictive microbiology. Here, we present a general dynamic model-building concept describing microbial evolution under dynamic conditions. Starting from an elementary model building block, the model structure can be gradually complexified to incorporate increasing numbers of influencing factors. Based on two case studies, the fundamentals of both macroscopic (population) and microscopic (individual) modeling approaches are revisited. These illustrations deal with the modeling of (i) microbial lag under variable temperature conditions and (ii) interspecies microbial interactions mediated by lactic acid production (product inhibition). Current and future research trends should address the need for (i) more specific measurements at the cell and/or population level, (ii) measurements under dynamic conditions, and (iii) more comprehensive (mechanistically inspired) model structures. In the context of quantitative microbial risk assessment, complexity of the mathematical model must be kept under control. An important challenge for the future is determination of a satisfactory trade-off between predictive power and manageability of predictive microbiology models.

Electrohydrodynamic fibrillation governed enhanced thermal transport in dielectric colloids under a field stimulus.

PubMed

Dhar, Purbarun; Maganti, Lakshmi Sirisha; Harikrishnan, A R

2018-05-30

Electrorheological (ER) fluids are known to exhibit enhanced viscous effects under an electric field stimulus. The present article reports the hitherto unreported phenomenon of greatly enhanced thermal conductivity in such electro-active colloidal dispersions in the presence of an externally applied electric field. Typical ER fluids are synthesized employing dielectric fluids and nanoparticles and experiments are performed employing an in-house designed setup. Greatly augmented thermal conductivity under a field's influence was observed. Enhanced thermal conduction along the fibril structures under the field effect is theorized as the crux of the mechanism. The formation of fibril structures has also been experimentally verified employing microscopy. Based on classical models for ER fluids, a mathematical formalism has been developed to predict the propensity of chain formation and statistically feasible chain dynamics at given Mason numbers. Further, a thermal resistance network model is employed to computationally predict the enhanced thermal conduction across the fibrillary colloid microstructure. Good agreement between the mathematical model and the experimental observations is achieved. The domineering role of thermal conductivity over relative permittivity has been shown by proposing a modified Hashin-Shtrikman (HS) formalism. The findings have implications towards better physical understanding and design of ER fluids from both 'smart' viscoelastic as well as thermally active materials points of view.

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…

Impact of the rate of the additive process of forming a heavy structure deforming in creep on the development of its technological stresses

NASA Astrophysics Data System (ADS)

Parshin, Dmitry A.

2018-05-01

The additive process of forming a semicircular arched structure by means of layer-by-layer addition of material to its inner surface is simulated. The impact of this process running mode on the development of the technological stresses fields in the structure being formed under the action of gravity under properties of the material creep and aging is examined. In the framework of the linear mechanics of accreted solids a mathematical model of the process under study is offered and numerical experiments are conducted. It is shown that the stress-strain state of the additively formed heavy objects decisively depends on their formation mode. Various practically important trends and features of this dependence are studied.

Modeling Spatial and Temporal Aspects of Visual Backward Masking

ERIC Educational Resources Information Center

Hermens, Frouke; Luksys, Gediminas; Gerstner, Wulfram; Herzog, Michael H.; Ernst, Udo

2008-01-01

Visual backward masking is a versatile tool for understanding principles and limitations of visual information processing in the human brain. However, the mechanisms underlying masking are still poorly understood. In the current contribution, the authors show that a structurally simple mathematical model can explain many spatial and temporal…

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

PubMed

Miskovic, Ljubisa; Hatzimanikatis, Vassily

2010-08-01

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

Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation

NASA Astrophysics Data System (ADS)

Maslovskaya, A. G.; Barabash, T. K.

2018-03-01

The paper presents the results of the fractal and multifractal analysis of polarization switching current in ferroelectrics under electron irradiation, which allows statistical memory effects to be estimated at dynamics of domain structure. The mathematical model of formation of electron beam-induced polarization current in ferroelectrics was suggested taking into account the fractal nature of domain structure dynamics. In order to realize the model the computational scheme was constructed using the numerical solution approximation of fractional differential equation. Evidences of electron beam-induced polarization switching process in ferroelectrics were specified at a variation of control model parameters.

CORRECTING FOR MEASUREMENT ERROR IN LATENT VARIABLES USED AS PREDICTORS*

PubMed Central

Schofield, Lynne Steuerle

2015-01-01

This paper represents a methodological-substantive synergy. A new model, the Mixed Effects Structural Equations (MESE) model which combines structural equations modeling and item response theory is introduced to attend to measurement error bias when using several latent variables as predictors in generalized linear models. The paper investigates racial and gender disparities in STEM retention in higher education. Using the MESE model with 1997 National Longitudinal Survey of Youth data, I find prior mathematics proficiency and personality have been previously underestimated in the STEM retention literature. Pre-college mathematics proficiency and personality explain large portions of the racial and gender gaps. The findings have implications for those who design interventions aimed at increasing the rates of STEM persistence among women and under-represented minorities. PMID:26977218

Embedding Number-Combinations Practice Within Word-Problem Tutoring

PubMed Central

Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas

2012-01-01

Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems. PMID:22661880

Embedding Number-Combinations Practice Within Word-Problem Tutoring.

PubMed

Powell, Sarah R; Fuchs, Lynn S; Fuchs, Douglas

2010-09-01

Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems.

Application of attachment modes in the control of large space structures

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.

1989-01-01

Various ways are examined to obtain reduced order mathematical models of structures for use in dynamic response analyses and in controller design studies. Attachment modes are deflection shapes of a structure subjected to specified unit load distributions. Attachment modes are frequently employed to supplement free-interface normal modes to improve the modeling of components (structures) employed in component mode synthesis analyses. Deflection shapes of structures subjected to generalized loads of some specified distribution and of unit magnitude can also be considered to be attachment modes. Several papers which were written under this contract are summarized herein.

Mathematic simulation of soil-vegetation condition and land use structure applying basin approach

NASA Astrophysics Data System (ADS)

Mishchenko, Natalia; Shirkin, Leonid; Krasnoshchekov, Alexey

2016-04-01

Ecosystems anthropogenic transformation is basically connected to the changes of land use structure and human impact on soil fertility. The Research objective is to simulate the stationary state of river basins ecosystems. Materials and Methods. Basin approach has been applied in the research. Small rivers basins of the Klyazma river have been chosen as our research objects. They are situated in the central part of the Russian plain. The analysis is carried out applying integrated characteristics of ecosystems functioning and mathematic simulation methods. To design mathematic simulator functional simulation methods and principles on the basis of regression, correlation and factor analysis have been applied in the research. Results. Mathematic simulation resulted in defining possible permanent conditions of "phytocenosis-soil" system in coordinates of phytomass, phytoproductivity, humus percentage in soil. Ecosystem productivity is determined not only by vegetation photosynthesis activity but also by the area ratio of forest and meadow phytocenosis. Local maximums attached to certain phytomass areas and humus content in soil have been defined on the basin phytoproductivity distribution diagram. We explain the local maximum by synergetic effect. It appears with the definite ratio of forest and meadow phytocenosis. In this case, utmost values of phytomass for the whole area are higher than just a sum of utmost values of phytomass for the forest and meadow phytocenosis. Efficient correlation of natural forest and meadow phytocenosis has been defined for the Klyazma river. Conclusion. Mathematic simulation methods assist in forecasting the ecosystem conditions under various changes of land use structure. Nowadays overgrowing of the abandoned agricultural lands is very actual for the Russian Federation. Simulation results demonstrate that natural ratio of forest and meadow phytocenosis for the area will restore during agricultural overgrowing.

The enhancement of students' mathematical self-efficacy through teaching with metacognitive scaffolding approach

NASA Astrophysics Data System (ADS)

Prabawanto, S.

2018-05-01

This research aims to investigate the enhancement of students’ mathematical self- efficacy through teaching with metacognitive scaffolding approach. This research used a quasi- experimental design with pre-post respon control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 students who acquire teaching mathematics under metacognitive approach, while the control group consists of 58 students who acquire teaching mathematics under direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical self-efficacy instruments. By using mean difference test, two conclusions of the research: (1) there is a significant difference in the enhancement of mathematical self-efficacy between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and (2) there is no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students’ mathematical self-efficacy.

Vocational Assessment of Students with Disadvantages: Their Peculiar Needs.

ERIC Educational Resources Information Center

Nolte, Deborah

A study examined the underlying factor structure of the aptitude tests and work samples being completed by students with educational disadvantages (limited reading and mathematics skills) who were assessed with the current assessment model in the Akron (Ohio) Public Schools. The amount of variance accounted for by the factors was also…

Effects of a Research-Based Intervention to Improve Seventh-Grade Students' Proportional Problem Solving: A Cluster Randomized Trial

ERIC Educational Resources Information Center

Jitendra, Asha K.; Harwell, Michael R.; Dupuis, Danielle N.; Karl, Stacy R.; Lein, Amy E.; Simonson, Gregory; Slater, Susan C.

2015-01-01

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem-solving and metacognitive…

Effects of a Research-Based Intervention to Improve Seventh-Grade Students' Proportional Problem Solving: A Cluster Randomized Trial

ERIC Educational Resources Information Center

Jitendra, Asha K.; Harwell, Michael R.; Dupuis, Danielle N.; Karl, Stacy R.; Lein, Amy E.; Simonson, Gregory; Slater, Susan C.

2015-01-01

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem solving and metacognitive…

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,…

Catastrophe modelling in the biological sciences.

PubMed

Deakin, M A

1990-03-01

Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional "physical" way, it could also be applied in a new "metaphysical" way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology. Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said to have been fully realised. This paper will document and classify the work that has been done. It will be argued that, like other applied Mathematics, applied Catastrophe Theory works best where the underlying laws are securely known and precisely quantified, requiring those same guarantees as does any other branch of Mathematics when it confronts a real-life situation.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

PubMed Central

Cantone, Martina; Santos, Guido; Wentker, Pia; Lai, Xin; Vera, Julio

2017-01-01

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung. PMID:28912729

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection.

PubMed

Cantone, Martina; Santos, Guido; Wentker, Pia; Lai, Xin; Vera, Julio

2017-01-01

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

Wide-range simulation of elastoplastic wave fronts and failure of solids under high-speed loading

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

Saveleva, Natalia, E-mail: saveleva@icmm.ru; Bayandin, Yuriy, E-mail: buv@icmm.ru; Naimark, Oleg, E-mail: naimark@icmm.ru

2015-10-27

The aim of this paper is numerical study of deformation processes and failure of vanadium under shock-wave loading. According developed statistical theory of solid with mesoscopic defects the constitutive equations were proposed in terms of two structural variables characterizing behavior of defects ensembles: defect density tensor and structural scaling parameter. On the basis of wide-range constitutive equations the mathematical model of deformation behavior and failure of vanadium was developed taking into account the bond relaxation mechanisms, multistage of fracture and nonlinearity kinetic of defects. Results of numerical simulation allow the description of the major effects of shock wave propagation (elasticmore » precursor decay, grow of spall strength under grow strain rate)« less

A review of failure models for unidirectional ceramic matrix composites under monotonic loads

NASA Technical Reports Server (NTRS)

Tripp, David E.; Hemann, John H.; Gyekenyesi, John P.

1989-01-01

Ceramic matrix composites offer significant potential for improving the performance of turbine engines. In order to achieve their potential, however, improvements in design methodology are needed. In the past most components using structural ceramic matrix composites were designed by trial and error since the emphasis of feasibility demonstration minimized the development of mathematical models. To understand the key parameters controlling response and the mechanics of failure, the development of structural failure models is required. A review of short term failure models with potential for ceramic matrix composite laminates under monotonic loads is presented. Phenomenological, semi-empirical, shear-lag, fracture mechanics, damage mechanics, and statistical models for the fast fracture analysis of continuous fiber unidirectional ceramic matrix composites under monotonic loads are surveyed.

Self-reports of mathematics self-concept and educational outcomes: the roles of ego-dimensions and self-consciousness.

PubMed

Martin, A J; Debus, R L

1998-12-01

There is a need for research to (a) explore more fully the academic outcomes that follow from under-/over-rating of self-concept and (b) identify factors that predict the nature of self-reports of self-concept as well as under- and over-rating of this self-concept. The study examines the link between students' self-appraisals of both mathematics self-concept and under-/over-rating of this self-concept and educational outcomes in mathematics such as achievement and motivation (future plans for mathematics). Ego-dimensions (ego-orientation and competence-valuation) and public self-consciousness were examined as two factors that might contribute to predicting these self-appraisals. Findings are drawn from a sample of 382 male and female high school students ranging in age from 14 to 16 years. Students responded to a questionnaire (at Time 1) that assessed self-concept, motivation orientation, competence-valuation, self-consciousness, and mathematics motivation. Teachers rated each student using a brief mathematics self-concept scale. Higher mathematics self-concept and over-rating of this self-concept were predictive of higher levels of mathematics motivation and later mathematics achievement (Time 2). Findings also indicate that ego-orientation and competence-valuation are positively associated with mathematics self-concept and over-rating, whilst public self-consciousness negatively predicts mathematics self-concept and is also associated with a tendency to under-rate oneself in this domain.

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…

A mathematical problem and a Spacecraft Control Laboratory Experiment (SCOLE) used to evaluate control laws for flexible spacecraft. NASA/IEEE design challenge

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Balakrishnan, A. V.

1988-01-01

The problen of controlling large, flexible space systems has been evaluated using computer simulation. In several cases, ground experiments have also been used to validate system performance under more realistic conditions. There remains a need, however, to test additional control laws for flexible spacecraft and to directly compare competing design techniques. A program is discussed which has been initiated to make direct comparisons of control laws for, first, a mathematical problem, then and experimental test article being assembled under the cognizance of the Spacecraft Control Branch at the NASA Langley Research Center with the advice and counsel of the IEEE Subcommittee on Large Space Structures. The physical apparatus will consist of a softly supported dynamic model of an antenna attached to the Shuttle by a flexible beam. The control objective will include the task of directing the line-of-sight of the Shuttle antenna configuration toward a fixed target, under conditions of noisy data, control authority and random disturbances.

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.

Dynamic behaviour of thin composite plates for different boundary conditions

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

Sprintu, Iuliana, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com; Rotaru, Constantin, E-mail: sprintui@yahoo.com, E-mail: rotaruconstantin@yahoo.com

2014-12-10

In the context of composite materials technology, which is increasingly present in industry, this article covers a topic of great interest and theoretical and practical importance. Given the complex design of fiber-reinforced materials and their heterogeneous nature, mathematical modeling of the mechanical response under different external stresses is very difficult to address in the absence of simplifying assumptions. In most structural applications, composite structures can be idealized as beams, plates, or shells. The analysis is reduced from a three-dimensional elasticity problem to a oneor two-dimensional problem, based on certain simplifying assumptions that can be made because the structure is thin.more » This paper aims to validate a mathematical model illustrating how thin rectangular orthotropic plates respond to the actual load. Thus, from the theory of thin plates, new analytical solutions are proposed corresponding to orthotropic rectangular plates having different boundary conditions. The proposed analytical solutions are considered both for solving equation orthotropic rectangular plates and for modal analysis.« less

Dynamic Creep Buckling: Analysis of Shell 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

The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.

Language Policy, Teacher Beliefs, and Practice: Implications for English Language Learners in Mathematics

ERIC Educational Resources Information Center

Llamas-Flores, Silvia

2013-01-01

In 2007, Arizona voters passed House Bill (HB) 2064, a law that fundamentally restructured the Structured English Immersion (SEI) program, putting into place a 4-hour English language development (ELD) block for educating English language learners (ELLs). Under this new language policy, ELL students are segregated from their English-speaking peers…

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…

A New View of Mathematics Will Help Mathematics Teachers

ERIC Educational Resources Information Center

Maasz, Juergen

2005-01-01

For many people mathematics is something like a very huge and impressive building. It has a given structure with lots of levels and rooms. For many people this structure and therefore mathematics itself is independent from society, culture and history. It exists and mathematicians try to recover (not: to construct!) new parts of it. From this…

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

2015-09-01

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Theoretical foundations of spatially-variant mathematical morphology part ii: gray-level images.

PubMed

Bouaynaya, Nidhal; Schonfeld, Dan

2008-05-01

In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the Euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (i.e., SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV graylevel morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper-semi-continuous V-systems. This representation unifies a large class of spatially-variant linear and non-linear systems under the same mathematical framework. Finally, simulation results show the potential power of the general theory of gray-level spatially-variant mathematical morphology in several image analysis and computer vision applications.

Preliminary design procedure for insulated structures subjected to transient heating

NASA Technical Reports Server (NTRS)

Adelman, H. M.

1979-01-01

Minimum-mass designs were obtained for insulated structural panels loaded by a general set of inplane forces and a time dependent temperature. Temperature and stress histories in the structure are given by closed-form solutions, and optimization of the insulation and structural thicknesses is performed by nonlinear mathematical programming techniques. Design calculations are described to evaluate the structural efficiency of eight materials under combined heating and mechanical loads: graphite/polyimide, graphite/epoxy, boron/aluminum, titanium, aluminum, Rene 41, carbon/carbon, and Lockalloy. The effect on design mass of intensity and duration of heating were assessed. Results indicate that an optimum structure may have a temperature response well below the recommended allowable temperature for the material.

Performance evaluation of functioning of natural-industrial system of mining-processing complex with help of analytical and mathematical models

NASA Astrophysics Data System (ADS)

Bosikov, I. I.; Klyuev, R. V.; Revazov, V. Ch; Pilieva, D. E.

2018-03-01

The article describes research and analysis of hazardous processes occurring in the natural-industrial system and effectiveness assessment of its functioning using mathematical models. Studies of the functioning regularities of the natural and industrial system are becoming increasingly relevant in connection with the formulation of the task of modernizing production and the economy of Russia as a whole. In connection with a significant amount of poorly structured data, it is complicated by regulations for the effective functioning of production processes, social and natural complexes, under which a sustainable development of the natural-industrial system of the mining and processing complex would be ensured. Therefore, the scientific and applied problems, the solution of which allows one to formalize the hidden structural functioning patterns of the natural-industrial system and to make managerial decisions of organizational and technological nature to improve the efficiency of the system, are very relevant.

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…

Modelling the social and structural determinants of tuberculosis: opportunities and challenges

PubMed Central

Boccia, D.; Dodd, P. J.; Lönnroth, K.; Dowdy, D. W.; Siroka, A.; Kimerling, M. E.; White, R. G.; Houben, R. M. G. J.

2017-01-01

INTRODUCTION: Despite the close link between tuberculosis (TB) and poverty, most mathematical models of TB have not addressed underlying social and structural determinants. OBJECTIVE: To review studies employing mathematical modelling to evaluate the epidemiological impact of the structural determinants of TB. METHODS: We systematically searched PubMed and personal libraries to identify eligible articles. We extracted data on the modelling techniques employed, research question, types of structural determinants modelled and setting. RESULTS: From 232 records identified, we included eight articles published between 2008 and 2015; six employed population-based dynamic TB transmission models and two non-dynamic analytic models. Seven studies focused on proximal TB determinants (four on nutritional status, one on wealth, one on indoor air pollution, and one examined overcrowding, socioeconomic and nutritional status), and one focused on macro-economic influences. CONCLUSIONS: Few modelling studies have attempted to evaluate structural determinants of TB, resulting in key knowledge gaps. Despite the challenges of modelling such a complex system, models must broaden their scope to remain useful for policy making. Given the intersectoral nature of the interrelations between structural determinants and TB outcomes, this work will require multidisciplinary collaborations. A useful starting point would be to focus on developing relatively simple models that can strengthen our knowledge regarding the potential effect of the structural determinants on TB outcomes. PMID:28826444

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.…

A general modeling framework for describing spatially structured population dynamics

USGS Publications Warehouse

Sample, Christine; Fryxell, John; Bieri, Joanna; Federico, Paula; Earl, Julia; Wiederholt, Ruscena; Mattsson, Brady; Flockhart, Tyler; Nicol, Sam; Diffendorfer, James E.; Thogmartin, Wayne E.; Erickson, Richard A.; Norris, D. Ryan

2017-01-01

Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network-based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life-history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network-based population is modeled with discrete time steps. Using both theoretical and real-world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network-based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles

Application of Lanczos vectors to control design of flexible structures

NASA Technical Reports Server (NTRS)

Craig, Roy R., Jr.; Su, Tzu-Jeng

1990-01-01

This report covers research conducted during the first year of the two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to obtain reduced-order mathematical models for use in dynamic response analyses and in control design studies. This report summarizes research described in several reports and papers that were written under this contract. Extended abstracts are presented for technical papers covering the following topics: controller reduction by preserving impulse response energy; substructuring decomposition and controller synthesis; model reduction methods for structural control design; and recent literature on structural modeling, identification, and analysis.

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields.

PubMed

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge-in particular in mathematics domains-influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of their ability, in particular in response to the potentially inhibiting influence of stereotype threat on their pathways to scientific degrees.

Perceived mathematical ability under challenge: a longitudinal perspective on sex segregation among STEM degree fields

PubMed Central

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge—in particular in mathematics domains—influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of their ability, in particular in response to the potentially inhibiting influence of stereotype threat on their pathways to scientific degrees. PMID:26113823

Design of dry sand soil stratified sampler

NASA Astrophysics Data System (ADS)

Li, Erkang; Chen, Wei; Feng, Xiao; Liao, Hongbo; Liang, Xiaodong

2018-04-01

This paper presents a design of a stratified sampler for dry sand soil, which can be used for stratified sampling of loose sand under certain conditions. Our group designed the mechanical structure of a portable, single - person, dry sandy soil stratified sampler. We have set up a mathematical model for the sampler. It lays the foundation for further development of design research.

Does Early Mathematics Intervention Change the Processes Underlying Children’s Learning?

PubMed Central

Watts, Tyler W.; Clements, Douglas H.; Sarama, Julie; Wolfe, Christopher B.; Spitler, Mary Elaine; Bailey, Drew H.

2017-01-01

Early educational intervention effects typically fade in the years following treatment, and few studies have investigated why achievement impacts diminish over time. The current study tested the effects of a preschool mathematics intervention on two aspects of children’s mathematical development. We tested for separate effects of the intervention on “state” (occasion-specific) and “trait” (relatively stable) variability in mathematics achievement. Results indicated that, although the treatment had a large impact on state mathematics, the treatment had no effect on trait mathematics, or the aspect of mathematics achievement that influences stable individual differences in mathematics achievement over time. Results did suggest, however, that the intervention could affect the underlying processes in children’s mathematical development by inducing more transfer of knowledge immediately following the intervention for students in the treated group. PMID:29399243

Some Implications of a Behavioral Analysis of Verbal Behavior for Logic and Mathematics

PubMed Central

2013-01-01

The evident power and utility of the formal models of logic and mathematics pose a puzzle: Although such models are instances of verbal behavior, they are also essentialistic. But behavioral terms, and indeed all products of selection contingencies, are intrinsically variable and in this respect appear to be incommensurate with essentialism. A distinctive feature of verbal contingencies resolves this puzzle: The control of behavior by the nonverbal environment is often mediated by the verbal behavior of others, and behavior under control of verbal stimuli is blind to the intrinsic variability of the stimulating environment. Thus, words and sentences serve as filters of variability and thereby facilitate essentialistic model building and the formal structures of logic, mathematics, and science. Autoclitic frames, verbal chains interrupted by interchangeable variable terms, are ubiquitous in verbal behavior. Variable terms can be substituted in such frames almost without limit, a feature fundamental to formal models. Consequently, our fluency with autoclitic frames fosters generalization to formal models, which in turn permit deduction and other kinds of logical and mathematical inference. PMID:28018038

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.

Essays on symmetry

NASA Astrophysics Data System (ADS)

Ismael, Jenann Tareq

1997-04-01

Structures of many different sorts arise in physics, e.g., the concrete structures of material bodies, the structure exemplified by the spatiotemporal configuration of a set of bodies, the structures of more abstract objects like states, state-spaces, laws, and so on. To each structure of any of these types there corresponds a set of transformations which map it onto itself. These are its symmetries. Increasingly ubiquitous in theoretical discussions in physics, the notion of symmetry is also at the root of some time-worn philosophical debates. This dissertation consists of a set of essays on topics drawn from places where the two fields overlap. The first essay is an informal introduction to the mathematical study of symmetry. The second essay defends a famous principle of Pierre Curie which states that the symmetries of a cause are always symmetries of its effect. The third essay takes up the case of reflection in space in the context of a controversy stemming from one of Kant's early arguments for the substantivality of space. The fourth essay is a discussion of the general conditions under which an asymmetry in a phenomenon suggests an asymmetry in the laws which govern it. The case of reflection in time-specifically, the theoretical strategy used in statistical mechanics to subsume the time-asymmetric phenomena of Thermodynamics under the time-symmetric classical dynamical laws-is used to illustrate the general points. The philosophical heart of the thesis lies in its fifth essay. Here a somewhat novel way of conceiving scientific theorizing is articulated, one suggested by the abstract mathematical perspective of symmetry.

Quantitative Analysis of Cellular Metabolic Dissipative, Self-Organized Structures

PubMed Central

de la Fuente, Ildefonso Martínez

2010-01-01

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life. PMID:20957111

A general population-genetic model for the production by population structure of spurious genotype-phenotype associations in discrete, admixed or spatially distributed populations.

PubMed

Rosenberg, Noah A; Nordborg, Magnus

2006-07-01

In linkage disequilibrium mapping of genetic variants causally associated with phenotypes, spurious associations can potentially be generated by any of a variety of types of population structure. However, mathematical theory of the production of spurious associations has largely been restricted to population structure models that involve the sampling of individuals from a collection of discrete subpopulations. Here, we introduce a general model of spurious association in structured populations, appropriate whether the population structure involves discrete groups, admixture among such groups, or continuous variation across space. Under the assumptions of the model, we find that a single common principle--applicable to both the discrete and admixed settings as well as to spatial populations--gives a necessary and sufficient condition for the occurrence of spurious associations. Using a mathematical connection between the discrete and admixed cases, we show that in admixed populations, spurious associations are less severe than in corresponding mixtures of discrete subpopulations, especially when the variance of admixture across individuals is small. This observation, together with the results of simulations that examine the relative influences of various model parameters, has important implications for the design and analysis of genetic association studies in structured populations.

Super: a web server to rapidly screen superposable oligopeptide fragments from the protein data bank.

PubMed

Collier, James H; Lesk, Arthur M; Garcia de la Banda, Maria; Konagurthu, Arun S

2012-07-01

Searching for well-fitting 3D oligopeptide fragments within a large collection of protein structures is an important task central to many analyses involving protein structures. This article reports a new web server, Super, dedicated to the task of rapidly screening the protein data bank (PDB) to identify all fragments that superpose with a query under a prespecified threshold of root-mean-square deviation (RMSD). Super relies on efficiently computing a mathematical bound on the commonly used structural similarity measure, RMSD of superposition. This allows the server to filter out a large proportion of fragments that are unrelated to the query; >99% of the total number of fragments in some cases. For a typical query, Super scans the current PDB containing over 80,500 structures (with ∼40 million potential oligopeptide fragments to match) in under a minute. Super web server is freely accessible from: http://lcb.infotech.monash.edu.au/super.

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.

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…

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.

Theoretical Mathematics

NASA Astrophysics Data System (ADS)

Stöltzner, Michael

Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

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…

Photoresponsive polymer design for solar concentrator self-steering heliostats

NASA Astrophysics Data System (ADS)

Barker, Jessica; Basnet, Amod; Bhaduri, Moinak; Burch, Caroline; Chow, Amenda; Li, Xue; Oates, William S.; Massad, Jordan E.; Smith, Ralph

2014-03-01

Concentrating solar energy and transforming it into electricity is clean, economical and renewable. One design of solar power plants consists of an array of heliostats which redirects sunlight to a fixed receiver tower and the generated heat is converted into electricity. Currently, the angles of elevation of heliostats are controlled by motors and drives that are costly and require diverting power that can otherwise be used for producing electricity. We consider replacing the motor and drive system of the heliostat with a photosensitive polymer design that can tilt the mirror using the ability of the polymer to deform when subjected to light. The light causes the underlying molecular structure to change and subsequently, the polymer deforms. The deformation of the polymer is quantified in terms of photostrictive constitutive relations. A mathematical model is derived governing the behaviour of the angle of elevation as the photostrain varies. Photostrain depends on the composition of the polymer, intensity and temperature of light and angle of light polarization. Preliminary findings show a photomechanical rod structural design can provide 60° elevation for temperatures of about 40°C. A photomechanical beam structural design can generate more tilt at lower temperatures. The mathematical analysis illustrates that photostrains on the order of 1% to 10% are desired for both rod and beam designs to produce sufficient tilt under most heliostat field conditions.

Adolescent-perceived parent and teacher overestimation of mathematics ability: Developmental implications for students' mathematics task values.

PubMed

Gniewosz, Burkhard; Watt, Helen M G

2017-07-01

This study examines whether and how student-perceived parents' and teachers' overestimation of students' own perceived mathematical ability can explain trajectories for adolescents' mathematical task values (intrinsic and utility) controlling for measured achievement, following expectancy-value and self-determination theories. Longitudinal data come from a 3-cohort (mean ages 13.25, 12.36, and 14.41 years; Grades 7-10), 4-wave data set of 1,271 Australian secondary school students. Longitudinal structural equation models revealed positive effects of student-perceived overestimation of math ability by parents and teachers on students' intrinsic and utility math task values development. Perceived parental overestimations predicted intrinsic task value changes between all measurement occasions, whereas utility task value changes only were predicted between Grades 9 and 10. Parental influences were stronger for intrinsic than utility task values. Teacher influences were similar for both forms of task values and commenced after the curricular school transition in Grade 8. Results support the assumptions that the perceived encouragement conveyed by student-perceived mathematical ability beliefs of parents and teachers, promote positive mathematics task values development. Moreover, results point to different mechanisms underlying parents' and teachers' support. Finally, the longitudinal changes indicate transition-related increases in the effects of student-perceived overestimations and stronger effects for intrinsic than utility values. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

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.…

Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

PubMed

Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

2013-01-01

Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.

Modeling and validating the grabbing forces of hydraulic log grapples used in forest operations

Treesearch

Jingxin Wang; Chris B. LeDoux; Lihai Wang

2003-01-01

The grabbing forces of log grapples were modeled and analyzed mathematically under operating conditions when grabbing logs from compact log piles and from bunch-like log piles. The grabbing forces are closely related to the structural parameters of the grapple, the weight of the grapple, and the weight of the log grabbed. An operational model grapple was designed and...

Thermal loading in the laser holography nondestructive testing of a composite structure

NASA Technical Reports Server (NTRS)

Liu, H. K.; Kurtz, R. L.

1975-01-01

A laser holographic interferometry method that has variable sensitivity to surface deformation was applied to the investigation of composite test samples under thermal loading. A successful attempt was made to detect debonds in a fiberglass-epoxy-ceramic plate. Experimental results are presented along with the mathematical analysis of the physical model of the thermal loading and current conduction in the composite material.

Automated design optimization of supersonic airplane wing structures under dynamic constraints

NASA Technical Reports Server (NTRS)

Fox, R. L.; Miura, H.; Rao, S. S.

1972-01-01

The problems of the preliminary and first level detail design of supersonic aircraft wings are stated as mathematical programs and solved using automated optimum design techniques. The problem is approached in two phases: the first is a simplified equivalent plate model in which the envelope, planform and structural parameters are varied to produce a design, the second is a finite element model with fixed configuration in which the material distribution is varied. Constraints include flutter, aeroelastically computed stresses and deflections, natural frequency and a variety of geometric limitations.

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 =…

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.

Modeling Flow in Porous Media with Double Porosity/Permeability.

NASA Astrophysics Data System (ADS)

Seyed Joodat, S. H.; Nakshatrala, K. B.; Ballarini, R.

2016-12-01

Although several continuum models are available to study the flow of fluids in porous media with two pore-networks [1], they lack a firm theoretical basis. In this poster presentation, we will present a mathematical model with firm thermodynamic basis and a robust computational framework for studying flow in porous media that exhibit double porosity/permeability. The mathematical model will be derived by appealing to the maximization of rate of dissipation hypothesis, which ensures that the model is in accord with the second law of thermodynamics. We will also present important properties that the solutions under the model satisfy, along with an analytical solution procedure based on the Green's function method. On the computational front, a stabilized mixed finite element formulation will be derived based on the variational multi-scale formalism. The equal-order interpolation, which is computationally the most convenient, is stable under this formulation. The performance of this formulation will be demonstrated using patch tests, numerical convergence study, and representative problems. It will be shown that the pressure and velocity profiles under the double porosity/permeability model are qualitatively and quantitatively different from the corresponding ones under the classical Darcy equations. Finally, it will be illustrated that the surface pore-structure is not sufficient in characterizing the flow through a complex porous medium, which pitches a case for using advanced characterization tools like micro-CT. References [1] G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, "Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]," Journal of Applied Mathematics and Mechanics, vol. 24, pp. 1286-1303, 1960.

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…

The Effects of Constructivist Learning Environment on Prospective Mathematics Teachers' Opinions

ERIC Educational Resources Information Center

Narli, Serkan; Baser, Nes'e

2010-01-01

To explore the effects of constructivist learning environment on prospective teachers' opinions about "mathematics, department of mathematics, discrete mathematics, countable and uncountable infinity" taught under the subject of Cantorian Set Theory in discrete mathematics class, 60 first-year students in the Division of Mathematics…

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.

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…

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…

Long-Term Structural Health Monitoring System for a High-Speed Railway Bridge Structure.

PubMed

Ding, You-Liang; Wang, Gao-Xin; Sun, Peng; Wu, Lai-Yi; Yue, Qing

2015-01-01

Nanjing Dashengguan Bridge, which serves as the shared corridor crossing Yangtze River for both Beijing-Shanghai high-speed railway and Shanghai-Wuhan-Chengdu railway, is the first 6-track high-speed railway bridge with the longest span throughout the world. In order to ensure safety and detect the performance deterioration during the long-time service of the bridge, a Structural Health Monitoring (SHM) system has been implemented on this bridge by the application of modern techniques in sensing, testing, computing, and network communication. The SHM system includes various sensors as well as corresponding data acquisition and transmission equipment for automatic data collection. Furthermore, an evaluation system of structural safety has been developed for the real-time condition assessment of this bridge. The mathematical correlation models describing the overall structural behavior of the bridge can be obtained with the support of the health monitoring system, which includes cross-correlation models for accelerations, correlation models between temperature and static strains of steel truss arch, and correlation models between temperature and longitudinal displacements of piers. Some evaluation results using the mean value control chart based on mathematical correlation models are presented in this paper to show the effectiveness of this SHM system in detecting the bridge's abnormal behaviors under the varying environmental conditions such as high-speed trains and environmental temperature.

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.…

Effect of Directed Study of Mathematics Vocabulary on Standardized Mathematics Assessment Questions

ERIC Educational Resources Information Center

Waite, Adel Marlane

2017-01-01

The problems under investigation included (a) Did a directed study of mathematics vocabulary significantly affect student performance levels on standardized mathematical questions? and (b) Did the strategies used in this study significantly affect student performance levels on standardized mathematical questions? The population consisted of…

Teaching Undergraduate Mathematics Using CAS Technology: Issues and Prospects

ERIC Educational Resources Information Center

Tobin, Patrick C.; Weiss, Vida

2016-01-01

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

Communicational Perspectives on Learning and Teaching Mathematics: Prologue

ERIC Educational Resources Information Center

Tabach, Michal; Nachlieli, Talli

2016-01-01

This special issue comprises five studies which vary in their focus and mathematical content, yet they all share an underlying communicational theoretical framework--commognition. Within this framework, learning mathematics is defined as a change in one's mathematical discourse, that is, in the form of communication known as mathematical. Teaching…

Unitals and ovals of symmetric block designs in LDPC and space-time coding

NASA Astrophysics Data System (ADS)

Andriamanalimanana, Bruno R.

2004-08-01

An approach to the design of LDPC (low density parity check) error-correction and space-time modulation codes involves starting with known mathematical and combinatorial structures, and deriving code properties from structure properties. This paper reports on an investigation of unital and oval configurations within generic symmetric combinatorial designs, not just classical projective planes, as the underlying structure for classes of space-time LDPC outer codes. Of particular interest are the encoding and iterative (sum-product) decoding gains that these codes may provide. Various small-length cases have been numerically implemented in Java and Matlab for a number of channel models.

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.…

Modeling of composite coupling technology for oil-gas pipeline section resource-saving repair

NASA Astrophysics Data System (ADS)

Donkova, Irina; Yakubovskiy, Yuriy; Kruglov, Mikhail

2017-10-01

The article presents a variant of modeling and calculation of a main pipeline repair section with a composite coupling installation. This section is presented in a shape of a composite cylindrical shell. The aim of this work is mathematical modeling and study of main pipeline reconstruction section stress-strain state (SSS). There has been given a description of a structure deformation mathematical model. Based on physical relations of elasticity, integral characteristics of rigidity for each layer of a two-layer pipe section have been obtained. With the help of the systems of forces and moments which affect the layers differential equations for the first and second layer (pipeline and coupling) have been obtained. The study of the SSS has been conducted using the statements and hypotheses of the composite structures deformation theory with consideration of interlayer joint stresses. The relations to describe the work of the joint have been stated. Boundary conditions for each layer have been formulated. To describe the deformation of the composite coupling with consideration of the composite cylindrical shells theory a mathematical model in the form of a system of differential equations in displacements and boundary conditions has been obtained. Calculation of a two-layer cylindrical shell under the action of an axisymmetric load has been accomplished.

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.

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

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

Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.

Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can bemore » potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.« less

Inconclusive quantum measurements and decisions under uncertainty

NASA Astrophysics Data System (ADS)

Yukalov, Vyacheslav; Sornette, Didier

2016-04-01

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

Promoting students’ mathematical problem-solving skills through 7e learning cycle and hypnoteaching model

NASA Astrophysics Data System (ADS)

Saleh, H.; Suryadi, D.; Dahlan, J. A.

2018-01-01

The aim of this research was to find out whether 7E learning cycle under hypnoteaching model can enhance students’ mathematical problem-solving skill. This research was quasi-experimental study. The design of this study was pretest-posttest control group design. There were two groups of sample used in the study. The experimental group was given 7E learning cycle under hypnoteaching model, while the control group was given conventional model. The population of this study was the student of mathematics education program at one university in Tangerang. The statistical analysis used to test the hypothesis of this study were t-test and Mann-Whitney U. The result of this study show that: (1) The students’ achievement of mathematical problem solving skill who obtained 7E learning cycle under hypnoteaching model are higher than the students who obtained conventional model; (2) There are differences in the students’ enhancement of mathematical problem-solving skill based on students’ prior mathematical knowledge (PMK) category (high, middle, and low).

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

Mathematical structure of unit systems

NASA Astrophysics Data System (ADS)

Kitano, Masao

2013-05-01

We investigate the mathematical structure of unit systems and the relations between them. Looking over the entire set of unit systems, we can find a mathematical structure that is called preorder (or quasi-order). For some pair of unit systems, there exists a relation of preorder such that one unit system is transferable to the other unit system. The transfer (or conversion) is possible only when all of the quantities distinguishable in the latter system are always distinguishable in the former system. By utilizing this structure, we can systematically compare the representations in different unit systems. Especially, the equivalence class of unit systems (EUS) plays an important role because the representations of physical quantities and equations are of the same form in unit systems belonging to an EUS. The dimension of quantities is uniquely defined in each EUS. The EUS's form a partially ordered set. Using these mathematical structures, unit systems and EUS's are systematically classified and organized as a hierarchical tree.

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

Conditioning and Robustness of RNA Boltzmann Sampling under Thermodynamic Parameter Perturbations.

PubMed

Rogers, Emily; Murrugarra, David; Heitsch, Christine

2017-07-25

Understanding how RNA secondary structure prediction methods depend on the underlying nearest-neighbor thermodynamic model remains a fundamental challenge in the field. Minimum free energy (MFE) predictions are known to be "ill conditioned" in that small changes to the thermodynamic model can result in significantly different optimal structures. Hence, the best practice is now to sample from the Boltzmann distribution, which generates a set of suboptimal structures. Although the structural signal of this Boltzmann sample is known to be robust to stochastic noise, the conditioning and robustness under thermodynamic perturbations have yet to be addressed. We present here a mathematically rigorous model for conditioning inspired by numerical analysis, and also a biologically inspired definition for robustness under thermodynamic perturbation. We demonstrate the strong correlation between conditioning and robustness and use its tight relationship to define quantitative thresholds for well versus ill conditioning. These resulting thresholds demonstrate that the majority of the sequences are at least sample robust, which verifies the assumption of sampling's improved conditioning over the MFE prediction. Furthermore, because we find no correlation between conditioning and MFE accuracy, the presence of both well- and ill-conditioned sequences indicates the continued need for both thermodynamic model refinements and alternate RNA structure prediction methods beyond the physics-based ones. Copyright © 2017. Published by Elsevier Inc.

A Mathematical Model for the Hippocampus: Towards the Understanding of Episodic Memory and Imagination

NASA Astrophysics Data System (ADS)

Tsuda, I.; Yamaguti, Y.; Kuroda, S.; Fukushima, Y.; Tsukada, M.

How does the brain encode episode? Based on the fact that the hippocampus is responsible for the formation of episodic memory, we have proposed a mathematical model for the hippocampus. Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ an association of memories. David Marr correctly pointed out in his theory of archecortex for a simple memory that the hippocampal CA3 is responsible for the formation of associative memories. However, a conventional mathematical model of associative memory simply guarantees a single association of memory unless a rule for an order of successive association of memories is given. The recent clinical studies in Maguire's group for the patients with the hippocampal lesion show that the patients cannot make a new story, because of the lack of ability of imagining new things. Both episodic memory and imagining things include various common characteristics: imagery, the sense of now, retrieval of semantic information, and narrative structures. Taking into account these findings, we propose a mathematical model of the hippocampus in order to understand the common mechanism of episodic memory and imagination.

Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models?

PubMed

Ledzewicz, Urszula; Schättler, Heinz

2017-08-10

Metronomic chemotherapy refers to the frequent administration of chemotherapy at relatively low, minimally toxic doses without prolonged treatment interruptions. Different from conventional or maximum-tolerated-dose chemotherapy which aims at an eradication of all malignant cells, in a metronomic dosing the goal often lies in the long-term management of the disease when eradication proves elusive. Mathematical modeling and subsequent analysis (theoretical as well as numerical) have become an increasingly more valuable tool (in silico) both for determining conditions under which specific treatment strategies should be preferred and for numerically optimizing treatment regimens. While elaborate, computationally-driven patient specific schemes that would optimize the timing and drug dose levels are still a part of the future, such procedures may become instrumental in making chemotherapy effective in situations where it currently fails. Ideally, mathematical modeling and analysis will develop into an additional decision making tool in the complicated process that is the determination of efficient chemotherapy regimens. In this article, we review some of the results that have been obtained about metronomic chemotherapy from mathematical models and what they infer about the structure of optimal treatment regimens. Copyright © 2017 Elsevier B.V. All rights reserved.

Features of control systems analysis with discrete control devices using mathematical packages

NASA Astrophysics Data System (ADS)

Yakovleva, E. M.; Faerman, V. A.

2017-02-01

The article contains presentation of basic provisions of the theory of automatic pulse control systems as well as methods of analysis of such systems using the mathematical software widespread in the academic environment. The pulse systems under research are considered as analogues systems interacting among themselves, including sensors, amplifiers, controlled objects, and discrete parts. To describe such systems, one uses a mathematical apparatus of difference equations as well as discrete transfer functions. To obtain a transfer function of the open-loop system, being important from the point of view of the analysis of control systems, one uses mathematical packages Mathcad and Matlab. Despite identity of the obtained result, the way of its achievement from the point of view of user’s action is various for the specified means. In particular, Matlab uses a structural model of the control system while Mathcad allows only execution of a chain of operator transforms. It is worth noting that distinctions taking place allow considering transformation of signals during interaction of the linear and continuous parts of the control system from different sides. The latter can be used in an educational process for the best assimilation of the course of the control system theory by students.

Functionality, Complexity, and Approaches to Assessment of Resilience Under Constrained Energy and Information

DTIC Science & Technology

2015-03-26

albeit powerful , method available for exploring CAS. As discussed above, there are many useful mathematical tools appropriate for CAS modeling. Agent-based...cells, tele- phone calls, and sexual contacts approach power -law distributions. [48] Networks in general are robust against random failures, but...targeted failures can have powerful effects – provided the targeter has a good understanding of the network structure. Some argue (convincingly) that all

Space, time, and host evolution facilitate coexistence of competing bacteriophages: theory and experiment.

PubMed

Coberly, L Caitlin; Wei, Wei; Sampson, Koffi Y; Millstein, Jack; Wichman, Holly A; Krone, Stephen M

2009-04-01

We present a joint experimental/theoretical investigation into the roles of spatial structure and time in the competition between two pathogens for a single host. We suggest a natural mechanism by which competing pathogens can coexist when host evolution and competitive dynamics occur on similar timescales. Our experimental system consisted of a single bacterial host species and two competing bacteriophage strains grown on agar plates, with a serial transfer of samples of the bacteriophage population to fresh host populations after each incubation cycle. The experiments included two incubation times and two transfer protocols that either maintained or disrupted the spatial structure of the viruses at each transfer. The same bacteriophage acted as the dominant competitor under both transfer protocols. A striking difference between the treatments is that the weak competitor was able to persist in the long-incubation experiments but not in the short-incubation experiments. Mathematical and experimental evidence suggest that coexistence is due to the appearance of resistant mutant host cells that provide a transient "spatiotemporal refuge" for the weaker competitor. Our mathematical model is individual based, captures the stochastic spatial dynamics down to the level of individual cells, and helps to explain the differences in behavior under the various experimental conditions.

Mathematical modelling of convective processes in a weld pool under electric arc surfacing

NASA Astrophysics Data System (ADS)

Sarychev, V. D.; Granovskii, A. Yu; Nevskii, S. A.; Konovalov, S. V.

2017-01-01

The authors develop the mathematical model of convective processes in a molten pool under electric arc surfacing with flux-cored wire. The model is based on the ideas of how convective flows appear due to temperature gradient and action of electromagnetic forces. Influence of alloying elements in the molten metal was modeled as a non-linear dependence of surface tension upon temperature. Surface tension and its temperature coefficient were calculated according to the electron density functional method with consideration to asymmetric electron distribution at the interface “molten metal / shielding gas”. Simultaneous solution of Navier-Stokes and Maxwell equations according to finite elements method with consideration to the moving heat source at the interface showed that there is a multi-vortex structure in the molten metal. This structure gives rise to a downward heat flux which, at the stage of heating, moves from the centre of the pool and stirs it full width. At the cooling stage this flux moves towards the centre of the pool and a single vortex is formed near the symmetry centre. This flux penetration is ∼ 10 mm. Formation of the downward heat flux is determined by sign reversal of the temperature coefficient of surface tension due to the presence of alloying elements.

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…

Mathematics anxiety and mathematics achievement

NASA Astrophysics Data System (ADS)

Sherman, Brian F.; Wither (Post.), David P.

2003-09-01

This paper is a distillation of the major result from the 1998 Ph.D. thesis of the late David Wither. It details a longitudinal study over five years of the relationship between mathematics anxiety and mathematics achievement. It starts from the already well documented negative correlation between the two, and seeks to establish one of the three hypotheses—that mathematics anxiety causes an impairment of mathematics achievement; that lack of mathematics achievement causes mathematics anxiety; or that there is a third underlying cause of the two.

Modelling fungal growth in heterogeneous soil: analyses of the effect of soil physical structure on fungal community dynamics

NASA Astrophysics Data System (ADS)

Falconer, R.; Radoslow, P.; Grinev, D.; Otten, W.

2009-04-01

Fungi play a pivital role in soil ecosystems contributing to plant productivity. The underlying soil physical and biological processes responsible for community dynamics are interrelated and, at present, poorly understood. If these complex processes can be understood then this knowledge can be managed with an aim to providing more sustainable agriculture. Our understanding of microbial dynamics in soil has long been hampered by a lack of a theoretical framework and difficulties in observation and quantification. We will demonstrate how the spatial and temporal dynamics of fungi in soil can be understood by linking mathematical modelling with novel techniques that visualise the complex structure of the soil. The combination of these techniques and mathematical models opens up new possibilities to understand how the physical structure of soil affects fungal colony dynamics and also how fungal dynamics affect soil structure. We will quantify, using X ray tomography, soil structure for a range of artificially prepared microcosms. We characterise the soil structures using soil metrics such as porosity, fractal dimension, and the connectivity of the pore volume. Furthermore we will use the individual based fungal colony growth model of Falconer et al. 2005, which is based on the physiological processes of fungi, to assess the effect of soil structure on microbial dynamics by qualifying biomass abundances and distributions. We demonstrate how soil structure can critically affect fungal species interactions with consequences for biological control and fungal biodiversity.

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)

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.

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…

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,…

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.

Mathematical models in simulation process in rehabilitation of persons with disabilities

NASA Astrophysics Data System (ADS)

Gorie, Nina; Dolga, Valer; Mondoc, Alina

2012-11-01

The problems of people with disability are varied. A disability may be physical, cognitive, mental, sensory, emotional, developmental or some combination of these. The major disabilities which can appear in people's lives are: the blindness, the deafness, the limb-girdle muscular dystrophy, the orthopedic impairment, the visual impairment. A disability is an umbrella term, covering impairments, activity limitations and participation restrictions. A disability may occur during a person's lifetime or may be present from birth. The authors conclude that some of these disabilities like physical, cognitive, mental, sensory, emotional, developmental can be rehabilitated. Starting from this state of affairs the authors present briefly the possibility of using certain mechatronic systems for rehabilitation of persons with different disabilities. The authors focus their presentation on alternative calling the Stewart platform in order to achieve the proposed goal. The authors present a mathematical model of systems theory approach under the parallel system and described its contents can. The authors analyze in a meaningful mathematical model describing the procedure of rehabilitation process. From the affected function biomechanics and taking into account medical recommendations the authors illustrate the mathematical models of rehabilitation work. The authors assemble a whole mathematical model of parallel structure and the rehabilitation process and making simulation and highlighting the results estimated. The authors present in the end work the results envisaged in the end analysis work, conclusions and steps for future work program..

Super: a web server to rapidly screen superposable oligopeptide fragments from the protein data bank

PubMed Central

Collier, James H.; Lesk, Arthur M.; Garcia de la Banda, Maria; Konagurthu, Arun S.

2012-01-01

Searching for well-fitting 3D oligopeptide fragments within a large collection of protein structures is an important task central to many analyses involving protein structures. This article reports a new web server, Super, dedicated to the task of rapidly screening the protein data bank (PDB) to identify all fragments that superpose with a query under a prespecified threshold of root-mean-square deviation (RMSD). Super relies on efficiently computing a mathematical bound on the commonly used structural similarity measure, RMSD of superposition. This allows the server to filter out a large proportion of fragments that are unrelated to the query; >99% of the total number of fragments in some cases. For a typical query, Super scans the current PDB containing over 80 500 structures (with ∼40 million potential oligopeptide fragments to match) in under a minute. Super web server is freely accessible from: http://lcb.infotech.monash.edu.au/super. PMID:22638586

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)

Flawed Mathematical Conceptualizations: Marlon's Dilemma

ERIC Educational Resources Information Center

Garrett, Lauretta

2013-01-01

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

Variational Integrators for Interconnected Lagrange-Dirac Systems

NASA Astrophysics Data System (ADS)

Parks, Helen; Leok, Melvin

2017-10-01

Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interconnection of simpler subsystems. Lagrange-Dirac mechanical systems provide a broad category of mathematical models that are closed under interconnection, and in this paper, we develop a framework for the interconnection of discrete Lagrange-Dirac mechanical systems, with a view toward constructing geometric structure-preserving discretizations of interconnected systems. This work builds on previous work on the interconnection of continuous Lagrange-Dirac systems (Jacobs and Yoshimura in J Geom Mech 6(1):67-98, 2014) and discrete Dirac variational integrators (Leok and Ohsawa in Found Comput Math 11(5), 529-562, 2011). We test our results by simulating some of the continuous examples given in Jacobs and Yoshimura (2014).

Shakedown Analysis of Composite Steel-Concrete Frame Systems with Plastic and Brittle Elements Under Seismic Action

NASA Astrophysics Data System (ADS)

Alawdin, Piotr; Bulanov, George

2017-06-01

In this paper the earthquake analysis of composite steel-concrete frames is performed by finding solution of the optimization problem of shakedown analysis, which takes into account the nonlinear properties of materials. The constructions are equipped with systems bearing structures of various elastic-plastic and brittle elements absorbing energy of seismic actions. A mathematical model of this problem is presented on the base of limit analysis theory with partial redistribution of self-stressed internal forces. It is assumed that the load varies randomly within the specified limits. These limits are determined by the possible direction and magnitude of seismic loads. The illustrative example of such analysis of system is introduced. Some attention has been paid to the practical application of the proposed mathematical model.

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 physics: Glitches in time [Glitches in time: Capturing the underlying dynamics of data with flawed timing

DOE PAGES

Haley, Charlotte A. L.

2016-04-27

Here, a mathematical technique has now been developed that reveals the underlying dynamics of time-dependent data collected with extreme temporal uncertainty, without using additional, costly instrumentation.

A general panel sizing computer code and its application to composite structural panels

NASA Technical Reports Server (NTRS)

Anderson, M. S.; Stroud, W. J.

1978-01-01

A computer code for obtaining the dimensions of optimum (least mass) stiffened composite structural panels is described. The procedure, which is based on nonlinear mathematical programming and a rigorous buckling analysis, is applicable to general cross sections under general loading conditions causing buckling. A simplified method of accounting for bow-type imperfections is also included. Design studies in the form of structural efficiency charts for axial compression loading are made with the code for blade and hat stiffened panels. The effects on panel mass of imperfections, material strength limitations, and panel stiffness requirements are also examined. Comparisons with previously published experimental data show that accounting for imperfections improves correlation between theory and experiment.

Noise elimination algorithm for modal analysis

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

Bao, X. X., E-mail: baoxingxian@upc.edu.cn; Li, C. L.; Xiong, C. B.

2015-07-27

Modal analysis is an ongoing interdisciplinary physical issue. Modal parameters estimation is applied to determine the dynamic characteristics of structures under vibration excitation. Modal analysis is more challenging for the measured vibration response signals are contaminated with noise. This study develops a mathematical algorithm of structured low rank approximation combined with the complex exponential method to estimate the modal parameters. Physical experiments using a steel cantilever beam with ten accelerometers mounted, excited by an impulse load, demonstrate that this method can significantly eliminate noise from measured signals and accurately identify the modal frequencies and damping ratios. This study provides amore » fundamental mechanism of noise elimination using structured low rank approximation in physical fields.« less

On the stability of lung parenchymal lesions with applications to early pneumothorax diagnosis.

PubMed

Bhandarkar, Archis R; Banerjee, Rohan; Seshaiyer, Padmanabhan

2013-01-01

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

NASA Astrophysics Data System (ADS)

Klewicki, J. C.; Chini, G. P.; Gibson, J. F.

2017-03-01

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted.

A quasi-QSPR modelling for the photocatalytic decolourization rate constants and cellular viability (CV%) of nanoparticles by CORAL.

PubMed

Toropova, A P; Toropov, A A; Benfenati, E

2015-01-01

Most quantitative structure-property/activity relationships (QSPRs/QSARs) predict various endpoints related to organic compounds. Gradually, the variety of organic compounds has been extended to inorganic, organometallic compounds and polymers. However, the so-called molecular descriptors cannot be defined for super-complex substances such as different nanomaterials and peptides, since there is no simple and clear representation of their molecular structure. Some possible ways to define approaches for a predictive model in the case of super-complex substances are discussed. The basic idea of the approach is to change the traditionally used paradigm 'the endpoint is a mathematical function of the molecular structure' with another paradigm 'the endpoint is a mathematical function of available eclectic information'. The eclectic data can be (i) conditions of a synthesis, (ii) technological attributes, (iii) size of nanoparticles, (iv) concentration, (v) attributes related to cell membranes, and so on. Two examples of quasi-QSPR/QSAR analyses are presented and discussed. These are (i) photocatalytic decolourization rate constants (DRC) (10(-5)/s) of different nanopowders; and (ii) the cellular viability under the effect of nano-SiO(2).

Application of Mathematical Modeling in Potentially Survivable Blast Threats in Military Vehicles

DTIC Science & Technology

2008-12-01

elastic – compression and tension of body under loading if elastic tolerances are exceeded, (b) viscous – when fluid matter is involved in the...lumbar spine biomechanical response. The model is a simple spring and damper system and its equation of motion is represented as: 2...dynamic motion. The seat structural management system was represented using Kelvin spring damper element provided in MADYMO. In the actual seat system

The Study of Crew Coordination and Performance in Hierarchical Team Decision Making

DTIC Science & Technology

1992-11-01

Technical Report 92-01 3 decision making (Carley, 1991; Levis, 1984; Miao , Luh, Kleinman, & Castanon, 1991). This type of approach uses mathematical 5...Boston: Allyn and Bacon. Bieth, B. H . (1987). Subjective workload under individual and team performance conditions. Proceedings of the Human Factors...B. B., Jr. (1992, June). H •ri•oiLal_ and vertical structures in small teams: Team performance and communication Datteins. Paper presented at the 1991

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…

Mathematics in Early Years Education. 3rd Edition

ERIC Educational Resources Information Center

Montague-Smith, Ann; Price, Alison

2012-01-01

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

From Parental Involvement to Children's Mathematical Performance: The Role of Mathematics Anxiety

ERIC Educational Resources Information Center

Vukovic, Rose K.; Roberts, Steven O.; Green Wright, Linnie

2013-01-01

This study examined whether children's mathematics anxiety serves as an underlying pathway between parental involvement and children's mathematics achievement. Participants included 78 low-income, ethnic minority parents and their children residing in a large urban center in the northeastern United States. Parents completed a short survey tapping…

Ethical Dimensions of Mathematics Education

ERIC Educational Resources Information Center

Boylan, Mark

2016-01-01

The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…

A Guide to Curriculum Planning in Mathematics. Bulletin No. 6284.

ERIC Educational Resources Information Center

Chambers, Donald L.; And Others

This guide was written under the basic assumptions that the mathematics curriculum must continuously change and that mathematics is most effectively learned through a spiral approach. Further, it is assumed that the audience will be members of district mathematics curriculum committees. Instructional objectives have been organized to reveal the…

Re-"Conceptualizing" Procedural Knowledge in Mathematics.

ERIC Educational Resources Information Center

Star, Jon R.

Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is…

Reflective Awareness in Mathematics Teachers' Learning and Teaching

ERIC Educational Resources Information Center

Chapman, Olive

2015-01-01

The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

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…

Topological framework for local structure analysis in condensed matter

PubMed Central

Lazar, Emanuel A.; Han, Jian; Srolovitz, David J.

2015-01-01

Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent particles, understanding that structure is a primary objective of condensed matter research. Although perfect crystals are fully described by a set of translation and basis vectors, real-world materials are never perfect, as thermal vibrations and defects introduce significant deviation from ideal order. Meanwhile, liquids and glasses present yet more complexity. A complete understanding of structure thus remains a central, open problem. Here we propose a unified mathematical framework, based on the topology of the Voronoi cell of a particle, for classifying local structure in ordered and disordered systems that is powerful and practical. We explain the underlying reason why this topological description of local structure is better suited for structural analysis than continuous descriptions. We demonstrate the connection of this approach to the behavior of physical systems and explore how crystalline structure is compromised at elevated temperatures. We also illustrate potential applications to identifying defects in plastically deformed polycrystals at high temperatures, automating analysis of complex structures, and characterizing general disordered systems. PMID:26460045

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.

Long-Term Structural Health Monitoring System for a High-Speed Railway Bridge Structure

PubMed Central

Wu, Lai-Yi

2015-01-01

Nanjing Dashengguan Bridge, which serves as the shared corridor crossing Yangtze River for both Beijing-Shanghai high-speed railway and Shanghai-Wuhan-Chengdu railway, is the first 6-track high-speed railway bridge with the longest span throughout the world. In order to ensure safety and detect the performance deterioration during the long-time service of the bridge, a Structural Health Monitoring (SHM) system has been implemented on this bridge by the application of modern techniques in sensing, testing, computing, and network communication. The SHM system includes various sensors as well as corresponding data acquisition and transmission equipment for automatic data collection. Furthermore, an evaluation system of structural safety has been developed for the real-time condition assessment of this bridge. The mathematical correlation models describing the overall structural behavior of the bridge can be obtained with the support of the health monitoring system, which includes cross-correlation models for accelerations, correlation models between temperature and static strains of steel truss arch, and correlation models between temperature and longitudinal displacements of piers. Some evaluation results using the mean value control chart based on mathematical correlation models are presented in this paper to show the effectiveness of this SHM system in detecting the bridge's abnormal behaviors under the varying environmental conditions such as high-speed trains and environmental temperature. PMID:26451387

A bioinspired study on the compressive resistance of helicoidal fibre structures

NASA Astrophysics Data System (ADS)

Tan, Ting; Ribbans, Brian

2017-10-01

Helicoidal fibre structures are widely observed in natural materials. In this paper, an integrated experimental and analytical approach was used to investigate the compressive resistance of helicoidal fibre structures. First, helicoidal fibre-reinforced composites were created using three-dimensionally printed helicoids and polymeric matrices, including plain, ring-reinforced and helix-reinforced helicoids. Then, load-displacement curves under monotonic compression tests were collected to measure the compressive strengths of helicoidal fibre composites. Fractographic characterization was performed using an X-ray microtomographer and scanning electron microscope, through which crack propagations in helicoidal structures were illustrated. Finally, mathematical modelling was performed to reveal the essential fibre architectures in the compressive resistance of helicoidal fibre structures. This work reveals that fibre-matrix ratios, helix pitch angles and interlayer rotary angles are critical to the compressive resistance of helicoidal structures.

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)

Enhancing students’ mathematical representation and selfefficacy through situation-based learning assisted by geometer’s sketchpad program

NASA Astrophysics Data System (ADS)

Sowanto; Kusumah, Y. S.

2018-05-01

This research was conducted based on the problem of a lack of students’ mathematical representation ability as well as self-efficacy in accomplishing mathematical tasks. To overcome this problem, this research used situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP). This research investigated students’ improvement of mathematical representation ability who were taught under situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP) and regular method that viewed from the whole students’ prior knowledge (high, average, and low level). In addition, this research investigated the difference of students’ self-efficacy after learning was given. This research belongs to quasi experiment research using non-equivalent control group design with purposive sampling. The result of this research showed that students’ enhancement in their mathematical representation ability taught under SBL assisted by GSP was better than the regular method. Also, there was no interaction between learning methods and students prior knowledge in student’ enhancement of mathematical representation ability. There was significant difference of students’ enhancement of mathematical representation ability taught under SBL assisted by GSP viewed from students’ prior knowledge. Furthermore, there was no significant difference in terms of self-efficacy between those who were taught by SBL assisted by GSP with the regular method.

Quantitative analysis of transverse bacterial migration induced by chemotaxis in a packed column with structured physical heterogeneity.

PubMed

Wang, Meng; Ford, Roseanne M

2010-01-15

A two-dimensional mathematical model was developed to simulate transport phenomena of chemotactic bacteria in a sand-packed column designed with structured physical heterogeneity in the presence of a localized chemical source. In contrast to mathematical models in previous research work, in which bacteria were typically treated as immobile colloids, this model incorporated a convective-like chemotaxis term to represent chemotactic migration. Consistency between experimental observation and model prediction supported the assertions that (1) dispersion-induced microbial transfer between adjacent conductive zones occurred at the interface and had little influence on bacterial transport in the bulk flow of the permeable layers and (2) the enhanced transverse bacterial migration in chemotactic experiments relative to nonchemotactic controls was mainly due to directed migration toward the chemical source zone. On the basis of parameter sensitivity analysis, chemotactic parameters determined in bulk aqueous fluid were adequate to predict the microbial transport in our intermediate-scale porous media system. Additionally, the analysis of adsorption coefficient values supported the observation of a previous study that microbial deposition to the surface of porous media might be decreased under the effect of chemoattractant gradients. By quantitatively describing bacterial transport and distribution in a heterogeneous system, this mathematical model serves to advance our understanding of chemotaxis and motility effects in granular media systems and provides insights for modeling microbial transport in in situ microbial processes.

Integrated Modeling of Complex Optomechanical Systems

NASA Astrophysics Data System (ADS)

Andersen, Torben; Enmark, Anita

2011-09-01

Mathematical modeling and performance simulation are playing an increasing role in large, high-technology projects. There are two reasons; first, projects are now larger than they were before, and the high cost calls for detailed performance prediction before construction. Second, in particular for space-related designs, it is often difficult to test systems under realistic conditions beforehand, and mathematical modeling is then needed to verify in advance that a system will work as planned. Computers have become much more powerful, permitting calculations that were not possible before. At the same time mathematical tools have been further developed and found acceptance in the community. Particular progress has been made in the fields of structural mechanics, optics and control engineering, where new methods have gained importance over the last few decades. Also, methods for combining optical, structural and control system models into global models have found widespread use. Such combined models are usually called integrated models and were the subject of this symposium. The objective was to bring together people working in the fields of groundbased optical telescopes, ground-based radio telescopes, and space telescopes. We succeeded in doing so and had 39 interesting presentations and many fruitful discussions during coffee and lunch breaks and social arrangements. We are grateful that so many top ranked specialists found their way to Kiruna and we believe that these proceedings will prove valuable during much future work.

An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching. Part 1: Notation and Mathematics.

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

Introduces and develops mathematical notation to assist undergraduate students in overcoming conceptual difficulties involving the underlying mathematics of state functions, which tend to be different from functions encountered by students in previous mathematical courses, because of the need to manipulate special types of partial derivatives and…

Mathematics Enrichment for All--Noticing and Enhancing Mathematical Potentials of Underprivileged Students as an Issue of Equity

ERIC Educational Resources Information Center

Schnell, Susanne; Prediger, Susanne

2017-01-01

Whereas equity issues are mainly discussed with respect to students at risk, this article focuses on mathematical potentials of under-privileged students and therefore elaborates a wide, dynamic and participatory conceptualization of (sometimes still hidden) mathematical potentials. An extended research review theoretically and empirically grounds…

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.

Reasoning and mathematical skills contribute to normatively superior decision making under risk: evidence from the game of dice task.

PubMed

Pertl, Marie-Theres; Zamarian, Laura; Delazer, Margarete

2017-08-01

In this study, we assessed to what extent reasoning improves performance in decision making under risk in a laboratory gambling task (Game of Dice Task-Double, GDT-D). We also investigated to what degree individuals with above average mathematical competence decide better than those with average mathematical competence. Eighty-five participants performed the GDT-D and several numerical tasks. Forty-two individuals were asked to calculate the probabilities and the outcomes associated with the different options of the GDT-D before performing it. The other 43 individuals performed the GDT-D at the beginning of the test session. Both reasoning and mathematical competence had a positive effect on decision making. Different measures of mathematical competence correlated with advantageous performance in decision making. Results suggest that decision making under explicit risk conditions improves when individuals are encouraged to reflect about the contingencies of a decision situation. Interventions based on numerical reasoning may also be useful for patients with difficulties in decision making.

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.

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…

An Algorithm for Protein Helix Assignment Using Helix Geometry

PubMed Central

Cao, Chen; Xu, Shutan; Wang, Lincong

2015-01-01

Helices are one of the most common and were among the earliest recognized secondary structure elements in proteins. The assignment of helices in a protein underlies the analysis of its structure and function. Though the mathematical expression for a helical curve is simple, no previous assignment programs have used a genuine helical curve as a model for helix assignment. In this paper we present a two-step assignment algorithm. The first step searches for a series of bona fide helical curves each one best fits the coordinates of four successive backbone Cα atoms. The second step uses the best fit helical curves as input to make helix assignment. The application to the protein structures in the PDB (protein data bank) proves that the algorithm is able to assign accurately not only regular α-helix but also 310 and π helices as well as their left-handed versions. One salient feature of the algorithm is that the assigned helices are structurally more uniform than those by the previous programs. The structural uniformity should be useful for protein structure classification and prediction while the accurate assignment of a helix to a particular type underlies structure-function relationship in proteins. PMID:26132394

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'…

78 FR 34671 - Invitation for Membership on Advisory Committee

Federal Register 2010, 2011, 2012, 2013, 2014

2013-06-10

... by successful completion of Joint Board examinations in basic actuarial mathematics and methodology and in actuarial mathematics and methodology relating to pension plans qualifying under ERISA. The... (ERISA), is responsible for the enrollment of individuals who wish to perform actuarial services under...

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

NASA Astrophysics Data System (ADS)

Borhan, Noziati; Zakaria, Effandi

2017-05-01

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

Basic research planning in mathematical pattern recognition and image analysis

NASA Technical Reports Server (NTRS)

Bryant, J.; Guseman, L. F., Jr.

1981-01-01

Fundamental problems encountered while attempting to develop automated techniques for applications of remote sensing are discussed under the following categories: (1) geometric and radiometric preprocessing; (2) spatial, spectral, temporal, syntactic, and ancillary digital image representation; (3) image partitioning, proportion estimation, and error models in object scene interference; (4) parallel processing and image data structures; and (5) continuing studies in polarization; computer architectures and parallel processing; and the applicability of "expert systems" to interactive analysis.

The Potential Effects of the Defense Business Board Military Compensation Task Group’s 2011 Recommendations on Active-Duty Service Member Retirement

DTIC Science & Technology

2012-12-01

system be implemented. In this study, we created a mathematical model to simulate accumulated savings under the proposed defined...retirement system be implemented. In this study, we created a mathematical model to simulate accumulated savings under the proposed defined...lumbering recovery, it has reemerged as a potential austerity measure within the U.S. government. B. METHODOLOGY We created a mathematical model of

Simulation of Patterned Glass Film Formation in the Evaporating Colloidal Liquid under IR Heating

NASA Astrophysics Data System (ADS)

Kolegov, K. S.

2018-02-01

The paper theoretically studies the method of evaporative lithography in combination with external infrared heating. This method makes it possible to form solid microstructures of the required relief shape as a result of evaporation of the liquid film of the colloidal solution under the mask. The heated particles are sintered easier, so there are no cracks in the obtained structure, unlike the structure obtained employing the standard method of evaporative lithography. The paper puts forward a modification of the mathematical model which allows to describe not only heat and mass transfer at the initial stage of the process, but also the phase transition of colloidal solution into glass. Aqueous latex is taken as an example. The resulting final form of solid film is in good agreement with the experimental data of other authors.

Dynamic analysis of elastic rubber tired car wheel breaking under variable normal load

NASA Astrophysics Data System (ADS)

Fedotov, A. I.; Zedgenizov, V. G.; Ovchinnikova, N. I.

2017-10-01

The purpose of the paper is to analyze the dynamics of the braking of the wheel under normal load variations. The paper uses a mathematical simulation method according to which the calculation model of an object as a mechanical system is associated with a dynamically equivalent schematic structure of the automatic control. Transfer function tool analyzing structural and technical characteristics of an object as well as force disturbances were used. It was proved that the analysis of dynamic characteristics of the wheel subjected to external force disturbances has to take into account amplitude and phase-frequency characteristics. Normal load variations impact car wheel braking subjected to disturbances. The closer slip to the critical point is, the higher the impact is. In the super-critical area, load variations cause fast wheel blocking.

Representations of spacetime: Formalism and ontological commitment

NASA Astrophysics Data System (ADS)

Bain, Jonathan Stanley

This dissertation consists of two parts. The first is on the relation between formalism and ontological commitment in the context of theories of spacetime, and the second is on scientific realism. The first part begins with a look at how the substantivalist/relationist debate over the ontological status of spacetime has been influenced by a particular mathematical formalism, that of tensor analysis on differential manifolds (TADM). This formalism has motivated the substantivalist position known as manifold substantivalism. Chapter 1 focuses on the hole argument which maintains that manifold substantivalism is incompatible with determinism. I claim that the realist motivations underlying manifold substantivalism can be upheld, and the hole argument avoided, by adopting structural realism with respect to spacetime. In this context, this is the claim that it is the structure that spacetime points enter into that warrants belief and not the points themselves. In Chapter 2, an elimination principle is defined by means of which a distinction can be made between surplus structure and essential structure with respect to formulations of a theory in two distinct mathematical formulations and some prior ontological commitments. This principle is then used to demonstrate that manifold points may be considered surplus structure in the formulation of field theories. This suggests that, if we are disposed to read field theories literally, then, at most, it should be the essential structure common to all alternative formulations of such theories that should be taken literally. I also investigate how the adoption of alternative formalisms informs other issues in the philosophy of spacetime. Chapter 3 offers a realist position which takes a semantic moral from the preceding investigation and an epistemic moral from work done on reliability. The semantic moral advises us to read only the essential structure of our theories literally. The epistemic moral shows us that such structure is robust under theory change, given an adequate reliabilist notion of epistemic warrant. I call the realist position that subscribes to these morals structural realism and attempt to demonstrate that it is immune to the semantic and epistemic versions of the underdetermination argument posed by the anti-realist.

Recent advances in the analysis of behavioural organization and interpretation as indicators of animal welfare

PubMed Central

Asher, Lucy; Collins, Lisa M.; Ortiz-Pelaez, Angel; Drewe, Julian A.; Nicol, Christine J.; Pfeiffer, Dirk U.

2009-01-01

While the incorporation of mathematical and engineering methods has greatly advanced in other areas of the life sciences, they have been under-utilized in the field of animal welfare. Exceptions are beginning to emerge and share a common motivation to quantify ‘hidden’ aspects in the structure of the behaviour of an individual, or group of animals. Such analyses have the potential to quantify behavioural markers of pain and stress and quantify abnormal behaviour objectively. This review seeks to explore the scope of such analytical methods as behavioural indicators of welfare. We outline four classes of analyses that can be used to quantify aspects of behavioural organization. The underlying principles, possible applications and limitations are described for: fractal analysis, temporal methods, social network analysis, and agent-based modelling and simulation. We hope to encourage further application of analyses of behavioural organization by highlighting potential applications in the assessment of animal welfare, and increasing awareness of the scope for the development of new mathematical methods in this area. PMID:19740922

Mathematical modeling and design of a novel 2-DOF micro attraction actuator for a micro optical switch

NASA Astrophysics Data System (ADS)

Kamiya, Daiki; Bagheri, Saeed; Horie, Mikio

2004-08-01

Many studies on optical switches have been performed in an attempt to develop optical information networks to speed information technology. In reality, however, mirror manipulators cannot be applied to multiple input and output systems due to both insufficient output displacements by the mirror parts inside the manipulator, and the difficulty of designing structures and mechanisms suitable for multi-dimensional manipulation. The principal reasons for insufficient displacement are the high rigidity of the elastic parts compared to the available driving forces and the pull-in effect. Therefore, in order to develop optical switches capable of multiple input and output switching, we suggest a novel 2-DOF(degree of freedom) electrostatic microactuator. The actuator is composed of one mirror with four beams laid about it in a corkscrew pattern, with four corkscrew electrodes on the substrate below and one mirror support pyramid situated under the mirror. Using electrostatic force, one or more of the beams are attracted from their outer ends toward the substrate. The mirror is then tilted by an angle proportional to the attracted length along the beam. The inclination and direction of the mirror are determined by the combined attracted length of the four beams. In this work we derive the mathematical model for the corkscrew beam microactuator for optical switches and show that this mathematical model accurately simulates the device by comparison with finite element analysis results. We use this mathematical model for design of the microactuator. Further we show that the designed optical switch microactuator is capable of rotating the mirror from +32 to -32 degrees about two axes with a maximum operating voltage of 163 volts. Finally, stress analysis of the actuator shows that the generated stress in the structure is at most 369 MPa.

Mathematics Education in Rural Communities in Light of Current Trends in Mathematics Education. Working Paper.

ERIC Educational Resources Information Center

Schultz, James E.

Despite the considerable efforts now under way to improve our nation's mathematics education for all students, students in rural settings do not receive their share of attention. This paper considers school mathematics in rural communities in the larger context of current reform from a number of perspectives, including curricular materials,…

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.

Mathematical models of carbon-carbon composite deformation

NASA Astrophysics Data System (ADS)

Golovin, N. N.; Kuvyrkin, G. N.

2016-09-01

Mathematical models of carbon-carbon composites (CCC) intended for describing the processes of deformation of structures produced by using CCC under high-temperature loading are considered. A phenomenological theory of CCC inelastic deformation is proposed, where such materials are considered as homogeneous ones with effective characteristics and where their high anisotropy of mechanical characteristics and different ways of resistance to extension and compression are taken into account. Micromechanical models are proposed for spatially reinforced CCC, where the difference between mechanical characteristics of components and the reinforcement scheme are taken into account. Themodel parameters are determined from the results of experiments of composite macrospecimens in the directions typical of the material. A version of endochronictype theory with several internal times "launched" for each composite component and related to some damage accumulation mechanisms is proposed for describing the inelastic deformation. Some practical examples are considered.

Implications of the method of capital cost payment on the weighted average cost of capital.

PubMed Central

Boles, K E

1986-01-01

The author develops a theoretical and mathematical model, based on published financial management literature, to describe the cost of capital structure for health care delivery entities. This model is then used to generate the implications of changing the capital cost reimbursement mechanism from a cost basis to a prospective basis. The implications are that the cost of capital is increased substantially, the use of debt must be restricted, interest rates for borrowed funds will increase, and, initially, firms utilizing debt efficiently under cost-basis reimbursement will be restricted to the generation of funds from equity only under a prospective system. PMID:3525468

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…

Connective stability of nonlinear matrix systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.

1974-01-01

Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.

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).

Effects of mass variation on structures of differentially rotating polytropic stars

NASA Astrophysics Data System (ADS)

Kumar, Sunil; Saini, Seema; Singh, Kamal Krishan

2018-07-01

A method is proposed for determining equilibrium structures and various physical parameters of differentially rotating polytropic models of stars, taking into account the effect of mass variation inside the star and on its equipotential surfaces. The law of differential rotation has been assumed to be the form of ω2(s) =b1 +b2s2 +b3s4 . The proposed method utilizes the averaging approach of Kippenhahn and Thomas and concepts of Roche-equipotential to incorporate the effects of differential rotation on the equilibrium structures of polytropic stellar models. Mathematical expressions of determining the equipotential surfaces, volume, surface area and other physical parameters are also obtained under the effects of mass variation inside the stars. Some significant conclusions are also drawn.

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.

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.

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)

Structured Matrix Completion with Applications to Genomic Data Integration.

PubMed

Cai, Tianxi; Cai, T Tony; Zhang, Anru

2016-01-01

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

Integrating Mathematical Learning during Caregiving Routines: A Study of Toddlers in Swedish Preschools

ERIC Educational Resources Information Center

Palmér, Hanna; Henriksson, Jenny; Hussein, Rania

2016-01-01

In recent years the interest in preschool mathematics has increased. However, studies seldom focus on children under the age of three and research is scarce on the early use of mathematics observed in natural settings. This article reports a study of mathematical possibilities during diaper changing in a preschool setting. A diaper change can be a…

How Does a Co-Learner Delivery Model in Professional Development Affect Teachers' Self-Efficacy in Teaching Mathematics and Specialized Mathematics Knowledge for Teaching?

ERIC Educational Resources Information Center

Ribeiro, John J.

2009-01-01

The National Mathematics Advisory Panel, established under the Bush Administration, was created to improve teaching and learning of mathematics in the United States. One component of the study was focused on teachers and professional development opportunities. They found that the majority of professional development studies available were mostly…

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

ERIC Educational Resources Information Center

Gafoor, Kunnathodi Abdul; Sarabi, M. K.

2015-01-01

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

The enhancement of students' mathematical problem solving ability through teaching with metacognitive scaffolding approach

NASA Astrophysics Data System (ADS)

Prabawanto, Sufyani

2017-05-01

This research aims to investigate the enhancement of students' mathematical problem solving through teaching with metacognitive scaffolding approach. This research used a quasi-experimental design with pretest-posttest control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 studentswho acquire teaching mathematicsunder metacognitive scaffolding approach, while the control group consists of 58 studentswho acquire teaching mathematicsunder direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical problem solving test instruments. By usingmean difference test, two conclusions of the research:(1) there is a significant difference in the enhancement of mathematical problem solving between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and(2) thereis no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students' mathematical problem solving.

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…

Geometry in the Secondary School, A Compendium of Papers Presented in Houston, Texas, January 29, 1967, at a Joint Session of The Mathematical Association of America and The National Council of Teachers of Mathematics.

ERIC Educational Resources Information Center

McNabb, W. K.

This booklet is a collection of the papers presented at a joint session of the Mathematical Association of America and the National Council of Teachers of Mathematics during the fiftieth annual meeting of the MAA. These papers were presented under the headings of "Geometry and School Mathematics,""High School Geometry," and…

A Practitioner Implementation of a Tier 2 First-Grade Mathematics Intervention

ERIC Educational Resources Information Center

Strand Cary, Mari G.; Clarke, Ben; Doabler, Christian T.; Smolkowski, Keith; Fien, Hank; Baker, Scott K.

2017-01-01

We report on a practitioner implementation of Fusion, a first-grade mathematics intervention. Studies such as this evaluation of a loose implementation under realistic conditions are important to curriculum developers' understanding of how evidence-based programs and tools work under a variety of implementation scenarios. In this…

Parameters of Models of Structural Transformations in Alloy Steel Under Welding Thermal Cycle

NASA Astrophysics Data System (ADS)

Kurkin, A. S.; Makarov, E. L.; Kurkin, A. B.; Rubtsov, D. E.; Rubtsov, M. E.

2017-05-01

A mathematical model of structural transformations in an alloy steel under the thermal cycle of multipass welding is suggested for computer implementation. The minimum necessary set of parameters for describing the transformations under heating and cooling is determined. Ferritic-pearlitic, bainitic and martensitic transformations under cooling of a steel are considered. A method for deriving the necessary temperature and time parameters of the model from the chemical composition of the steel is described. Published data are used to derive regression models of the temperature ranges and parameters of transformation kinetics in alloy steels. It is shown that the disadvantages of the active visual methods of analysis of the final phase composition of steels are responsible for inaccuracy and mismatch of published data. The hardness of a specimen, which correlates with some other mechanical properties of the material, is chosen as the most objective and reproducible criterion of the final phase composition. The models developed are checked by a comparative analysis of computational results and experimental data on the hardness of 140 alloy steels after cooling at various rates.

Hierarchical thinking in network biology: the unbiased modularization of biochemical networks.

PubMed

Papin, Jason A; Reed, Jennifer L; Palsson, Bernhard O

2004-12-01

As reconstructed biochemical reaction networks continue to grow in size and scope, there is a growing need to describe the functional modules within them. Such modules facilitate the study of biological processes by deconstructing complex biological networks into conceptually simple entities. The definition of network modules is often based on intuitive reasoning. As an alternative, methods are being developed for defining biochemical network modules in an unbiased fashion. These unbiased network modules are mathematically derived from the structure of the whole network under consideration.

Modeling microbial diversity in anaerobic digestion through an extended ADM1 model.

PubMed

Ramirez, Ivan; Volcke, Eveline I P; Rajinikanth, Rajagopal; Steyer, Jean-Philippe

2009-06-01

The anaerobic digestion process comprises a whole network of sequential and parallel reactions, of both biochemical and physicochemical nature. Mathematical models, aiming at understanding and optimization of the anaerobic digestion process, describe these reactions in a structured way, the IWA Anaerobic Digestion Model No. 1 (ADM1) being the most well established example. While these models distinguish between different microorganisms involved in different reactions, to our knowledge they all neglect species diversity between organisms with the same function, i.e. performing the same reaction. Nevertheless, available experimental evidence suggests that the structure and properties of a microbial community may be influenced by process operation and on their turn also determine the reactor functioning. In order to adequately describe these phenomena, mathematical models need to consider the underlying microbial diversity. This is demonstrated in this contribution by extending the ADM1 to describe microbial diversity between organisms of the same functional group. The resulting model has been compared with the traditional ADM1 in describing experimental data of a pilot-scale hybrid Upflow Anaerobic Sludge Filter Bed (UASFB) reactor, as well as in a more detailed simulation study. The presented model is further shown useful in assessing the relationship between reactor performance and microbial community structure in mesophilic CSTRs seeded with slaughterhouse wastewater when facing increasing levels of ammonia.

Two's company, three (or more) is a simplex : Algebraic-topological tools for understanding higher-order structure in neural data.

PubMed

Giusti, Chad; Ghrist, Robert; Bassett, Danielle S

2016-08-01

The language of graph theory, or network science, has proven to be an exceptional tool for addressing myriad problems in neuroscience. Yet, the use of networks is predicated on a critical simplifying assumption: that the quintessential unit of interest in a brain is a dyad - two nodes (neurons or brain regions) connected by an edge. While rarely mentioned, this fundamental assumption inherently limits the types of neural structure and function that graphs can be used to model. Here, we describe a generalization of graphs that overcomes these limitations, thereby offering a broad range of new possibilities in terms of modeling and measuring neural phenomena. Specifically, we explore the use of simplicial complexes: a structure developed in the field of mathematics known as algebraic topology, of increasing applicability to real data due to a rapidly growing computational toolset. We review the underlying mathematical formalism as well as the budding literature applying simplicial complexes to neural data, from electrophysiological recordings in animal models to hemodynamic fluctuations in humans. Based on the exceptional flexibility of the tools and recent ground-breaking insights into neural function, we posit that this framework has the potential to eclipse graph theory in unraveling the fundamental mysteries of cognition.

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…

The reasonable effectiveness of mathematics in the natural sciences

NASA Astrophysics Data System (ADS)

Harvey, Alex

2011-12-01

Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.

Mathematical modeling of chemical composition modification and etching of polymers under the atomic oxygen influence

NASA Astrophysics Data System (ADS)

Chirskaia, Natalia; Novikov, Lev; Voronina, Ekaterina

2016-07-01

Atomic oxygen (AO) of the upper atmosphere is one of the most important space factors that can cause degradation of spacecraft surface. In our previous mathematical model the Monte Carlo method and the "large particles" approximation were used for simulating processes of polymer etching under the influence of AO [1]. The interaction of enlarged AO particles with the polymer was described in terms of probabilities of reactions such as etching of polymer and specular and diffuse scattering of the AO particles on polymer. The effects of atomic oxygen on protected polymers and microfiller containing composites were simulated. The simulation results were in quite good agreement with the results of laboratory experiments on magnetoplasmadynamic accelerator of the oxygen plasma of SINP MSU [2]. In this paper we present a new model that describes the reactions of AO interactions with polymeric materials in more detail. Reactions of formation and further emission of chemical compounds such as CO, CO _{2}, H _{2}O, etc. cause the modification of the chemical composition of the polymer and change the probabilities of its consequent interaction with the AO. The simulation results are compared with the results of previous simulation and with the results of laboratory experiments. The reasons for the differences between the results of natural experiments on spacecraft, laboratory experiments and simulations are discussed. N. Chirskaya, M. Samokhina, Computer modeling of polymer structures degradation under the atomic oxygen exposure, WDS'12 Proceedings of Contributed Papers: Part III - Physics, Matfyzpress Prague, 2012, pp. 30-35. E. Voronina, L. Novikov, V. Chernik, N. Chirskaya, K. Vernigorov, G. Bondarenko, and A. Gaidar, Mathematical and experimental simulation of impact of atomic oxygen of the earth's upper atmosphere on nanostructures and polymer composites, Inorganic Materials: Applied Research, 2012, vol. 3, no. 2, pp. 95-101.

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)…

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

The Teacher Education and Development Study in Mathematics (TEDS-M): Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 Countries. Technical Report

ERIC Educational Resources Information Center

Tatto, Maria Teresa, Ed.

2013-01-01

The Teacher Education and Development Study in Mathematics (TEDS-M), conducted under the aegis of the International Association for the Evaluation of Educational Achievement (IEA), was designed to inform policy and practice in mathematics teacher education. For educational policymakers, TEDS-M contributes data on institutional arrangements that…

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…

Parameter Estimation in Atmospheric Data Sets

NASA Technical Reports Server (NTRS)

Wenig, Mark; Colarco, Peter

2004-01-01

In this study the structure tensor technique is used to estimate dynamical parameters in atmospheric data sets. The structure tensor is a common tool for estimating motion in image sequences. This technique can be extended to estimate other dynamical parameters such as diffusion constants or exponential decay rates. A general mathematical framework was developed for the direct estimation of the physical parameters that govern the underlying processes from image sequences. This estimation technique can be adapted to the specific physical problem under investigation, so it can be used in a variety of applications in trace gas, aerosol, and cloud remote sensing. As a test scenario this technique will be applied to modeled dust data. In this case vertically integrated dust concentrations were used to derive wind information. Those results can be compared to the wind vector fields which served as input to the model. Based on this analysis, a method to compute atmospheric data parameter fields will be presented. .

DAISY: a new software tool to test global identifiability of biological and physiological systems.

PubMed

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D'Angiò, Leontina

2007-10-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.

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…

Deriving and Analyzing Analytical Structures of a Class of Typical Interval Type-2 TS Fuzzy Controllers.

PubMed

Zhou, Haibo; Ying, Hao

2017-09-01

A conventional controller's explicit input-output mathematical relationship, also known as its analytical structure, is always available for analysis and design of a control system. In contrast, virtually all type-2 (T2) fuzzy controllers are treated as black-box controllers in the literature in that their analytical structures are unknown, which inhibits precise and comprehensive understanding and analysis. In this regard, a long-standing fundamental issue remains unresolved: how a T2 fuzzy set's footprint of uncertainty, a key element differentiating a T2 controller from a type-1 (T1) controller, affects a controller's analytical structure. In this paper, we describe an innovative technique for deriving analytical structures of a class of typical interval T2 (IT2) TS fuzzy controllers. This technique makes it possible to analyze the analytical structures of the controllers to reveal the role of footprints of uncertainty in shaping the structures. Specifically, we have mathematically proven that under certain conditions, the larger the footprints, the more the IT2 controllers resemble linear or piecewise linear controllers. When the footprints are at their maximum, the IT2 controllers actually become linear or piecewise linear controllers. That is to say the smaller the footprints, the more nonlinear the controllers. The most nonlinear IT2 controllers are attained at zero footprints, at which point they become T1 controllers. This finding implies that sometimes if strong nonlinearity is most important and desired, one should consider using a smaller footprint or even just a T1 fuzzy controller. This paper exemplifies the importance and value of the analytical structure approach for comprehensive analysis of T2 fuzzy controllers.

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.

Secondary Schools Curriculum Guide, Mathematics, Grades 10-12, Levels 87-112.

ERIC Educational Resources Information Center

Rogers, Arnold R., Ed.; And Others

Behavioral objectives for geometry, algebra, computer mathematics, trigonometry, analytic geometry, calculus, and probability are specified for grades 10 through 12. General objectives are stated for major areas under each topic and are followed by a list of specific objectives for that area. This work was prepared under an ESEA Title III…

Academic Mathematicians' Dispositions toward Software Use in Mathematics Instruction: What Are the Underlying Reasons?

ERIC Educational Resources Information Center

Khoshaim, Heba Bakr

2012-01-01

Academic mathematicians' opinions are divided regarding software use in undergraduate mathematics instruction. This study explored these opinions through interviews and a subsequent survey of mathematicians at PhD-granting institutions in the United States regarding their dispositions and the underlying attitudes. Most prior related work had…

Spatial structure and nutrients promote invasion of IncP-1 plasmids in bacterial populations

PubMed Central

Fox, Randal E; Zhong, Xue; Krone, Stephen M; Top, Eva M

2008-01-01

In spite of the importance of plasmids in bacterial adaptation, we have a poor understanding of their dynamics. It is not known if or how plasmids persist in and spread through (invade) a bacterial population when there is no selection for plasmid-encoded traits. Moreover, the differences in dynamics between spatially structured and mixed populations are poorly understood. Through a joint experimental/theoretical approach, we tested the hypothesis that self-transmissible IncP-1 plasmids can invade a bacterial population in the absence of selection when initially very rare, but only in spatially structured habitats and when nutrients are regularly replenished. Using protocols that differed in the degree of spatial structure and nutrient levels, the invasiveness of plasmid pB10 in Escherichia coli was monitored during at least 15 days, with an initial fraction of plasmid-bearing (p+) cells as low as 10−7. To further explore the mechanisms underlying plasmid dynamics, we developed a spatially explicit mathematical model. When cells were grown on filters and transferred to fresh medium daily, the p+ fraction increased to 13%, whereas almost complete invasion occurred when the population structure was disturbed daily. The plasmid was unable to invade in liquid. When carbon source levels were lower or not replenished, plasmid invasion was hampered. Simulations of the mathematical model closely matched the experimental results and produced estimates of the effects of alternative experimental parameters. This allowed us to isolate the likely mechanisms most responsible for the observations. In conclusion, spatial structure and nutrient availability can be key determinants in the invasiveness of plasmids. PMID:18528415

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.

System/observer/controller identification toolbox

NASA Technical Reports Server (NTRS)

Juang, Jer-Nan; Horta, Lucas G.; Phan, Minh

1992-01-01

System Identification is the process of constructing a mathematical model from input and output data for a system under testing, and characterizing the system uncertainties and measurement noises. The mathematical model structure can take various forms depending upon the intended use. The SYSTEM/OBSERVER/CONTROLLER IDENTIFICATION TOOLBOX (SOCIT) is a collection of functions, written in MATLAB language and expressed in M-files, that implements a variety of modern system identification techniques. For an open loop system, the central features of the SOCIT are functions for identification of a system model and its corresponding forward and backward observers directly from input and output data. The system and observers are represented by a discrete model. The identified model and observers may be used for controller design of linear systems as well as identification of modal parameters such as dampings, frequencies, and mode shapes. For a closed-loop system, an observer and its corresponding controller gain directly from input and output data.

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

PubMed

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

2013-08-01

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

Investigating Stratification, Language Diversity and Mathematics Classroom Interaction

ERIC Educational Resources Information Center

Barwell, Richard

2016-01-01

Research on the socio-political dimensions of language diversity in mathematics classrooms is under-theorised and largely focuses on language choice. These dimensions are, however, likely to influence mathematics classroom interaction in many other ways than participants' choice of language. To investigate these influences, I propose that the…

Pupils' View of Mathematics: Initial Report for an International Comparison Project. Research Report 152.

ERIC Educational Resources Information Center

Pehkonen, Erkki

This report describes the theoretical background of an international comparison project on pupils' mathematical beliefs and outlines its realization. The first chapter briefly discusses problems with the underlying concepts of "belief" and "conception." The central concept, view of mathematics, is introduced in the second…

Perceived Mathematical Ability under Challenge: A Longitudinal Perspective on Sex Segregation among STEM Degree Fields

ERIC Educational Resources Information Center

Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby

2015-01-01

Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite…

Supporting Mathematical Discussions: The Roles of Comparison and Cognitive Load

ERIC Educational Resources Information Center

Richland, Lindsey E.; Begolli, Kreshnik Nasi; Simms, Nina; Frausel, Rebecca R.; Lyons, Emily A.

2016-01-01

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

Supporting Mathematical Discussions: The Roles of Comparison and Cognitive Load

ERIC Educational Resources Information Center

Richland, Lindsey E.; Begolli, Kreshnik Nasi; Simms, Nina; Frausel, Rebecca R.; Lyons, Emily A.

2017-01-01

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

Strategies Students with and without Mathematics Disabilities Use When Estimating Fractions on Number Lines

ERIC Educational Resources Information Center

Zhang, Dake; Stecker, Pamela; Beqiri, Klesti

2017-01-01

We examined faulty strategies with possible underlying misconceptions, as well as execution mistakes, among middle schoolers with and without mathematics disabilities when estimating fractions on number lines. Fifty-one middle schoolers participated in this study, including 27 students with mathematics disabilities. Participants were asked to…

Chaos and insect ecology

Treesearch

Jesse A. Logan; Fred P. Hain

1990-01-01

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

Mathematics, Engineering Science Achievement (MESA). Washington's Community and Technical Colleges

ERIC Educational Resources Information Center

Washington State Board for Community and Technical Colleges, 2014

2014-01-01

Growing Science, Technology, Education, and Mathematics (STEM) talent Washington MESA--Mathematics Engineering Science Achievement--helps under-represented community college students excel in school and ultimately earn STEM bachelor's degrees. MESA has two key programs: one for K-12 students, and the other for community and technical college…

Modularizing Remedial Mathematics

ERIC Educational Resources Information Center

Wong, Aaron

2013-01-01

As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…

Mathematical Literacy of School Leaving Pupils in South Africa

ERIC Educational Resources Information Center

Howie, S.; Plomp, T.

2002-01-01

This paper discusses some results of South African (SA) grade 12 pupils on an international test of mathematical literacy, administered in the framework of the Third International Mathematics and Science Study (TIMSS) under the auspices of the International Association for the Evaluation of Educational Achievement (IEA). Three questions are…

Under Threes' Mathematical Learning

ERIC Educational Resources Information Center

Franzén, Karin

2015-01-01

The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…

Why? Why? Why?: Future Teachers Discover Mathematical Depth

ERIC Educational Resources Information Center

Myers, Perla

2007-01-01

In mathematics, it is not just the "how," the procedures for solving problems, that is important, but the "why," the underlying concepts, Perla Myers explains. A good mathematical foundation is becoming crucial for a large number of careers in science, engineering, medicine, technology, and even business. However, the applications of mathematics…

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…

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

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.

Age- and bite-structured models for vector-borne diseases.

PubMed

Rock, K S; Wood, D A; Keeling, M J

2015-09-01

The biology and behaviour of biting insects is a vitally important aspect in the spread of vector-borne diseases. This paper aims to determine, through the use of mathematical models, what effect incorporating vector senescence and realistic feeding patterns has on disease. A novel model is developed to enable the effects of age- and bite-structure to be examined in detail. This original PDE framework extends previous age-structured models into a further dimension to give a new insight into the role of vector biting and its interaction with vector mortality and spread of disease. Through the PDE model, the roles of the vector death and bite rates are examined in a way which is impossible under the traditional ODE formulation. It is demonstrated that incorporating more realistic functions for vector biting and mortality in a model may give rise to different dynamics than those seen under a more simple ODE formulation. The numerical results indicate that the efficacy of control methods that increase vector mortality may not be as great as predicted under a standard host-vector model, whereas other controls including treatment of humans may be more effective than previously thought. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

An Investigation into the Affective Profiles of Girls from Single-Sex and Co-Educational Schools, as They Relate to the Learning of Mathematics.

ERIC Educational Resources Information Center

Walter, Howard Maurice

Central to this dissertation is an attempt to investigate whether or not a single-sex environment has a positive impact upon girls' attitudes and beliefs, as they pertain to the learning of mathematics. All learners of mathematics are enveloped by the social practices pertaining to both mathematics and society at large. Underlying these social…

Reshaping Assessment Practices: Mathematics Assessment under Challenge. Proceedings from the National Conference on Assessment in the Mathematical Sciences (1st, Geelong, Victoria, Australia November 20-24, 1991).

ERIC Educational Resources Information Center

Stephens, Max, Ed.; Izard, John, Ed.

The purpose of the Australian conference on mathematical assessment was to address the challenges to traditional methods of assessment that have resulted as part of the call for reform in the mathematics curriculum. The 28 papers presented were: "Who Assesses Whom and To What Purpose?" (Leone Burton; "Assessment of the Learned…

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,…

The flow of plasma in the solar terrestrial environment

NASA Technical Reports Server (NTRS)

Schunk, R. W.

1992-01-01

The overall goal of our NASA Theory Program is to study the coupling, time delays, and feedback mechanisms between the various regions of the solar-terrestrial system in a self-consistent, quantitative manner. To accomplish this goal, it will eventually be necessary to have time-dependent macroscopic models of the different regions of the solar-terrestrial system and we are continually working toward this goal. However, our immediate emphasis is on the near-earth plasma environment, including the ionosphere, the plasmasphere, and the polar wind. In this area, we have developed unique global models that allow us to study the coupling between the different regions. Another important aspect of our NASA Theory Program concerns the effect that localized structure has on the macroscopic flow in the ionosphere, plasmasphere, thermosphere, and polar wind. The localized structure can be created by structured magnetospheric inputs (i.e., structured plasma convection, particle precipitation or Birkeland current patterns) or time variations in these inputs due to storms and substorms. Also, some of the plasma flows that we predict with our macroscopic models may be unstable, and another one of our goals is to examine the stability of our predicted flows. Because time-dependent, three-dimensional numerical models of the solar-terrestrial environment generally require extensive computer resources, they are usually based on relatively simple mathematical formulations (i.e., simple MHD or hydrodynamic formulation). Therefore, another long-range goal of our NASA Theory Program is to study the conditions under which various mathematical formulations can be applied to specific solar-terrestrial regions. This may involve a detailed comparison of kinetic, semikinetic, and hydrodynamic predictions for a given polar wind scenario or it may involve the comparison of a small-scale particle-in-cell (PIC) simulation of a plasma expansion event with a similar macroscopic expansion event. The different mathematical formulations have different strengths and weaknesses and a careful comparison of model predictions for similar geophysical situations will provide insight into when the various models can be used with confidence.

P-polarized reflectance spectroscopy: A high sensitive real-time monitoring technique to study surface kinetics under steady state epitaxial deposition conditions

NASA Technical Reports Server (NTRS)

Dietz, Nikolaus; Bachmann, Klaus J.

1995-01-01

This paper describes the results of real-time optical monitoring of epitaxial growth processes by p-polarized reflectance spectroscopy (PRS) using a single wavelength application under pulsed chemical beam epitaxy (PCBE) condition. The high surface sensitivity of PRS allows the monitoring of submonolayer precursors coverage on the surface as shown for GaP homoepitaxy and GaP on Si heteroepitaxy as examples. In the case of heteroepitaxy, the growth rate and optical properties are revealed by PRS using interference oscillations as they occur during growth. Super-imposed on these interference oscillations, the PRS signal exhibits a fine structure caused by the periodic alteration of the surface chemistry by the pulsed supply of chemical precursors. This fine structure is modeled under conditions where the surface chemistry cycles between phosphorus supersaturated and phosphorus depleted surfaces. The mathematical model describes the fine structure using a surface layer that increases during the tertiarybutyl phosphine (TBP) supply and decreases during and after the triethylgallium (TEG) pulse, which increases the growing GaP film thickness. The imaginary part of the dielectric function of the surface layer is revealed from the turning points in the fine structure, where the optical response to the first precursor pulse in the cycle sequence changes sign. The amplitude of the fine structure is determined by the surface layer thickness and the complex dielectric functions for the surface layer with the underlying bulk film. Surface kinetic data can be obtained by analyzing the rise and decay transients of the fine structure.

Architectures for wrist-worn energy harvesting

NASA Astrophysics Data System (ADS)

Rantz, R.; Halim, M. A.; Xue, T.; Zhang, Q.; Gu, L.; Yang, K.; Roundy, S.

2018-04-01

This paper reports the simulation-based analysis of six dynamical structures with respect to their wrist-worn vibration energy harvesting capability. This work approaches the problem of maximizing energy harvesting potential at the wrist by considering multiple mechanical substructures; rotational and linear motion-based architectures are examined. Mathematical models are developed and experimentally corroborated. An optimization routine is applied to the proposed architectures to maximize average power output and allow for comparison. The addition of a linear spring element to the structures has the potential to improve power output; for example, in the case of rotational structures, a 211% improvement in power output was estimated under real walking excitation. The analysis concludes that a sprung rotational harvester architecture outperforms a sprung linear architecture by 66% when real walking data is used as input to the simulations.

Oriented matroids—combinatorial structures underlying loop quantum gravity

NASA Astrophysics Data System (ADS)

Brunnemann, Johannes; Rideout, David

2010-10-01

We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator (Ashtekar A and Lewandowski J 1998 Adv. Theor. Math. Phys. 1 388) in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in three-dimensional Riemannian space and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid (Ziegler G M 1998 Electron. J. Comb.; Björner A et al 1999 Oriented Matroids (Cambridge: Cambridge University Press)). Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence, the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of Brunnemann and Rideout (2008 Class. Quantum Grav. 25 065001 and 065002), and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3 (Ziegler G M 1998 Electron. J. Comb.; Björner A et al 1999 Oriented Matroids (Cambridge: Cambridge University Press)), and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.

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.

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.

Time Analysis of Building Dynamic Response Under Seismic Action. Part 1: Theoretical Propositions

NASA Astrophysics Data System (ADS)

Ufimtcev, E. M.

2017-11-01

The first part of the article presents the main provisions of the analytical approach - the time analysis method (TAM) developed for the calculation of the elastic dynamic response of rod structures as discrete dissipative systems (DDS) and based on the investigation of the characteristic matrix quadratic equation. The assumptions adopted in the construction of the mathematical model of structural oscillations as well as the features of seismic forces’ calculating and recording based on the data of earthquake accelerograms are given. A system to resolve equations is given to determine the nodal (kinematic and force) response parameters as well as the stress-strain state (SSS) parameters of the system’s rods.

A mathematical model for mesenchymal and chemosensitive cell dynamics.

PubMed

Häcker, Anita

2012-01-01

The structure of an underlying tissue network has a strong impact on cell dynamics. If, in addition, cells alter the network by mechanical and chemical interactions, their movement is called mesenchymal. Important examples for mesenchymal movement include fibroblasts in wound healing and metastatic tumour cells. This paper is focused on the latter. Based on the anisotropic biphasic theory of Barocas and Tranquillo, which models a fibre network and interstitial solution as two-component fluid, a mathematical model for the interactions of cells with a fibre network is developed. A new description for fibre reorientation is given and orientation-dependent proteolysis is added to the model. With respect to cell dynamics, the equation, based on anisotropic diffusion, is extended by haptotaxis and chemotaxis. The chemoattractants are the solute network fragments, emerging from proteolysis, and the epidermal growth factor which may guide the cells to a blood vessel. Moreover the cell migration is impeded at either high or low network density. This new model enables us to study chemotactic cell migration in a complex fibre network and the consequential network deformation. Numerical simulations for the cell migration and network deformation are carried out in two space dimensions. Simulations of cell migration in underlying tissue networks visualise the impact of the network structure on cell dynamics. In a scenario for fibre reorientation between cell clusters good qualitative agreement with experimental results is achieved. The invasion speeds of cells in an aligned and an isotropic fibre network are compared. © Springer-Verlag 2011

Comparison of university students' understanding of graphs in different contexts

NASA Astrophysics Data System (ADS)

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-12-01

This study investigates university students’ understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was administered to 385 first year students at University of Zagreb who were either prospective physics or mathematics teachers or prospective physicists or mathematicians. Rasch analysis of data was conducted and linear measures for item difficulties were obtained. Average difficulties of items in three domains (mathematics, physics, and other contexts) and over two concepts (graph slope, area under the graph) were computed and compared. Analysis suggests that the variation of average difficulty among the three domains is much smaller for the concept of graph slope than for the concept of area under the graph. Most of the slope items are very close in difficulty, suggesting that students who have developed sufficient understanding of graph slope in mathematics are generally able to transfer it almost equally successfully to other contexts. A large difference was found between the difficulty of the concept of area under the graph in physics and other contexts on one side and mathematics on the other side. Comparison of average difficulty of the three domains suggests that mathematics without context is the easiest domain for students. Adding either physics or other context to mathematical items generally seems to increase item difficulty. No significant difference was found between the average item difficulty in physics and contexts other than physics, suggesting that physics (kinematics) remains a difficult context for most students despite the received instruction on kinematics in high school.

The birth of the blues: how physics underlies music

NASA Astrophysics Data System (ADS)

Gibson, J. M.

2009-07-01

Art and science have intimate connections, although these are often underappreciated. Western music provides compelling examples. The sensation of harmony and related melodic development are rooted in physical principles that can be understood with simple mathematics. The focus of this review is not the better known acoustics of instruments, but the structure of music itself. The physical basis of the evolution of Western music in the last half millennium is discussed, culminating with the development of the 'blues'. The paper refers to a number of works which expand the connections, and introduces material specific to the development of the 'blues'. Several conclusions are made: (1) that music is axiomatic like mathematics and that to appreciate music fully listeners must learn the axioms; (2) that this learning does not require specific conscious study but relies on a linkage between the creative and quantitative brain and (3) that a key element of the musical 'blues' comes from recreating missing notes on the modern equal temperament scale. The latter is an example of 'art built on artifacts'. Finally, brief reference is made to the value of music as a tool for teaching physics, mathematics and engineering to non-scientists.

The Principle of General Tovariance

NASA Astrophysics Data System (ADS)

Heunen, C.; Landsman, N. P.; Spitters, B.

2008-06-01

We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our principle of general tovariance states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our equivalence principle states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos.

The birth of the blues : how physics underlies music.

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

Gibson, J. M.

Art and science have intimate connections, although these are often underappreciated. Western music provides compelling examples. The sensation of harmony and related melodic development are rooted in physical principles that can be understood with simple mathematics. The focus of this review is not the better known acoustics of instruments, but the structure of music itself. The physical basis of the evolution of Western music in the last half millennium is discussed, culminating with the development of the 'blues'. The paper refers to a number of works which expand the connections, and introduces material specific to the development of the 'blues'.more » Several conclusions are made: (1) that music is axiomatic like mathematics and that to appreciate music fully listeners must learn the axioms; (2) that this learning does not require specific conscious study but relies on a linkage between the creative and quantitative brain and (3) that a key element of the musical 'blues' comes from recreating missing notes on the modern equal temperament scale. The latter is an example of 'art built on artifacts'. Finally, brief reference is made to the value of music as a tool for teaching physics, mathematics and engineering to non-scientists.« less

Women's Leadership in Science, Technology, Engineering and Mathematics: Barriers to Participation

ERIC Educational Resources Information Center

McCullough, Laura

2011-01-01

Despite gains overall, women are still under-represented in leadership positions in science, technology, engineering, and mathematics (STEM) fields. Data in the US suggest around one-quarter of deans and department heads are women; in science this drops to nearly 1 in 20. Part of this problem of under-representation stems from the population pool:…

Classroom Motivational Environment Influences on Emotional and Cognitive Dimensions of Student Interest in Mathematics

ERIC Educational Resources Information Center

Carmichael, Colin; Callingham, Rosemary; Watt, Helen M. G.

2017-01-01

Interest has long been regarded as an important motivational construct in the learning of mathematics. It has been contended that the development of interest is directed by two control systems: an emotional and a cognitive. Under the former, students are attracted to activities that are enjoyable, whereas under the latter they consciously engage…

Differential Psychological Processes Underlying the Skill-Development Model and Self-Enhancement Model across Mathematics and Science in 28 Countries

ERIC Educational Resources Information Center

Chiu, Mei-Shiu

2012-01-01

The skill-development model contends that achievements have an effect on academic self-confidences, while the self-enhancement model contends that self-confidences have an effect on achievements. Differential psychological processes underlying the 2 models across the domains of mathematics and science were posited and examined with structural…

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.

Cognitive Mechanisms Underlying Achievement Deficits in Children with Mathematical Learning Disability

ERIC Educational Resources Information Center

Geary, David C.; Hoard, Mary K.; Byrd-Craven, Jennifer; Nugent, Lara; Numtee, Chattavee

2007-01-01

Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n = 15) and low achieving (LA, n = 44) were identified. These groups and a group of typically achieving (TA, n = 46) children were administered a battery of mathematical cognition, working…

REASON: A Self-Instruction Strategy for Twice-Exceptional Learners Struggling With Common Core Mathematics

ERIC Educational Resources Information Center

Van Boxtel, Joanne M.

2016-01-01

Educators across the nation are now well under way in implementing the Common Core State Standards (CCSS; National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA & CCSSO], 2010) for mathematics. The emerging literature regarding CCSS mathematics instruction for students with disabilities urges…

The I Hate Mathematics! Book. A Brown Paper School Book.

ERIC Educational Resources Information Center

Burns, Marilyn

This 1975 book is written for children who do not like mathematics and presents activities which may help them to begin understanding mathematics. Activities are organized under the following headings: "Street Math"; "Maybe Grownups Aren't as Smart as You Think"; "Things to Do When You Have the Flu"; "A…

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…

1970-71 Basic Mathematics Improvement Component. Final Report.

ERIC Educational Resources Information Center

Rodosky, Robert

The Basic Mathematics Improvement Component, funded under Title I of the 1965 Elementary Secondary Education Act, served nearly 800 pupils in grades four through nine in 20 high priority inner-city schools. The philosophy behind the program was that high achievement in mathematics correlates highly with the high achievement in other areas, and a…

34 CFR 200.20 - Making adequate yearly progress.

Code of Federal Regulations, 2010 CFR

2010-07-01

... paragraph (a) or (b) of this section separately in reading/language arts and in mathematics. (a)(1) A school... reading/language arts and mathematics in grades 3 through 8 and once in grades 10 through 12 required... the reading/language arts and mathematics assessments in the three grade spans required under § 200.5...

Circles and the Lines That Intersect Them

ERIC Educational Resources Information Center

Clay, Ellen L.; Rhee, Katherine L.

2014-01-01

In this article, Clay and Rhee use the mathematics topic of circles and the lines that intersect them to introduce the idea of looking at the single mathematical idea of relationships--in this case, between angles and arcs--across a group of problems. They introduce the mathematics that underlies these relationships, beginning with the questions…

76 FR 21715 - Notice of Submission for OMB Review

Federal Register 2010, 2011, 2012, 2013, 2014

2011-04-18

...: Revision. Title of Collection: Hispanic-Serving Institutions Science Technology Engineering, Mathematics... Technology Engineering, Mathematics and Articulation Program, authorized under section 371 of Part F of the...

The Training of Teachers of Mathematics for the Secondary Schools of the Countries Represented in the International Commission on the Teaching of Mathematics. Bulletin, 1917, No. 27

ERIC Educational Resources Information Center

Archibald, Raymond Clare

1918-01-01

This bulletin is based upon reports to the International Commission on the Teaching of Mathematics concerning the development of the teacher of mathematics in the better secondary schools of different countries. For the most part, only those schools which are under the immediate direction of the Government have been considered. And even here…

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…

Similarities and Dissimilarities in Coauthorship Networks: Gestalt Theory as Explanation for Well-Ordered Collaboration Structures and Production of Scientific Literature.

ERIC Educational Resources Information Center

Kretschmer, Hildrun

2002-01-01

Based on Gestalt theory, the author assumes the existence of a field-force equilibrium to explain how, according to the conciseness principle, mathematically precise gestalts could exist in coauthorship networks. Develops a mathematical function to describe these gestalts in scientific literature and discusses structural characteristics of…

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…

Pre-service teachers' experiences teaching secondary mathematics in English-medium schools in Tanzania

NASA Astrophysics Data System (ADS)

Kasmer, Lisa

2013-09-01

In order to promote mathematical understanding among English Language Learners (ELLs), it is necessary to modify instructional strategies to effectively communicate mathematical content. This paper discusses the instructional strategies used by four pre-service teachers to teach mathematics to secondary students in English-medium schools in Arusha, Tanzania as a result of the tensions they faced and reflections on their teaching. Strategies such as code switching, attending to sentence structure, non-linguistic representations, and placing the content within a familiar context proved to be beneficial strategies for conveying mathematical ideas.

Toward Model Building for Visual Aesthetic Perception

PubMed Central

Lughofer, Edwin; Zeng, Xianyi

2017-01-01

Several models of visual aesthetic perception have been proposed in recent years. Such models have drawn on investigations into the neural underpinnings of visual aesthetics, utilizing neurophysiological techniques and brain imaging techniques including functional magnetic resonance imaging, magnetoencephalography, and electroencephalography. The neural mechanisms underlying the aesthetic perception of the visual arts have been explained from the perspectives of neuropsychology, brain and cognitive science, informatics, and statistics. Although corresponding models have been constructed, the majority of these models contain elements that are difficult to be simulated or quantified using simple mathematical functions. In this review, we discuss the hypotheses, conceptions, and structures of six typical models for human aesthetic appreciation in the visual domain: the neuropsychological, information processing, mirror, quartet, and two hierarchical feed-forward layered models. Additionally, the neural foundation of aesthetic perception, appreciation, or judgement for each model is summarized. The development of a unified framework for the neurobiological mechanisms underlying the aesthetic perception of visual art and the validation of this framework via mathematical simulation is an interesting challenge in neuroaesthetics research. This review aims to provide information regarding the most promising proposals for bridging the gap between visual information processing and brain activity involved in aesthetic appreciation. PMID:29270194

Physics and Mathematics as Interwoven Disciplines in Science Education

NASA Astrophysics Data System (ADS)

Galili, Igal

2018-03-01

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

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.

Modelling nutritional mutualisms: challenges and opportunities for data integration.

PubMed

Clark, Teresa J; Friel, Colleen A; Grman, Emily; Shachar-Hill, Yair; Friesen, Maren L

2017-09-01

Nutritional mutualisms are ancient, widespread, and profoundly influential in biological communities and ecosystems. Although much is known about these interactions, comprehensive answers to fundamental questions, such as how resource availability and structured interactions influence mutualism persistence, are still lacking. Mathematical modelling of nutritional mutualisms has great potential to facilitate the search for comprehensive answers to these and other fundamental questions by connecting the physiological and genomic underpinnings of mutualisms with ecological and evolutionary processes. In particular, when integrated with empirical data, models enable understanding of underlying mechanisms and generalisation of principles beyond the particulars of a given system. Here, we demonstrate how mathematical models can be integrated with data to address questions of mutualism persistence at four biological scales: cell, individual, population, and community. We highlight select studies where data has been or could be integrated with models to either inform model structure or test model predictions. We also point out opportunities to increase model rigour through tighter integration with data, and describe areas in which data is urgently needed. We focus on plant-microbe systems, for which a wealth of empirical data is available, but the principles and approaches can be generally applied to any nutritional mutualism. © 2017 John Wiley & Sons Ltd/CNRS.

Plotting Intersections along the Political Axis: The Interior Voice of Dissenting Mathematics Teachers

ERIC Educational Resources Information Center

de Freitas, Elizabeth

2004-01-01

The supposed apolitical nature of mathematics is an institutional frame that functions to sustain specific power structures within schools. This paper disrupts the common assumption that mathematics (as a body of knowledge constructed in situated historical moments) is free from entrenched ideological motives. Using narrative inquiry, the paper…

Does an Ability to Pattern Indicate That Our Thinking Is Mathematical?

ERIC Educational Resources Information Center

McCluskey, Catherine; Mitchelmore, Michael; Mulligan, Joanne

2013-01-01

Research affirms that pattern and structure underlie the development of a broad range of mathematical concepts. However, the concept of pattern also occurs in other fields. This theoretical paper explores pattern recognition, a neurological construct based on the world of Goldberg (2005), and pattern as defined in the field of mathematics to…

Mathematics and Structural Learning. Final Report.

ERIC Educational Resources Information Center

Scandura, Joseph M.

This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…

And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

ERIC Educational Resources Information Center

Street, Garrett M.; Laubach, Timothy A.

2013-01-01

We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

Mathematics: A Practical View. Volume I, Teacher Edition. Applied Basic Curriculum Series.

ERIC Educational Resources Information Center

Evaluation, Dissemination and Assessment Center, Dallas.

The activities in this volume of practical mathematics are intended for the intermediate grades. The manual contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate…

Parental Mathematics Homework Involvement of Low-Income Families with Middle School Students

ERIC Educational Resources Information Center

O'Sullivan, Robyn Hackford; Chen, Yung-Chi; Fish, Marian C.

2014-01-01

This study explores the relationships between methods of parental assistance (i.e., provision of structure, direct assistance, and autonomy support) with mathematics homework for high-achieving and low-achieving students and children's achievement in mathematics in low-income families and examines the impact of parental efficacy on these…

Identifying Core Elements of Argument-Based Inquiry in Primary Mathematics Learning

ERIC Educational Resources Information Center

Fielding-Wells, Jill

2015-01-01

Having students address mathematical inquiry problems that are ill-structured and ambiguous offers potential for them to develop a focus on mathematical evidence and reasoning. However, students may not necessarily focus on these aspects when responding to such problems. Argument-Based Inquiry is one way to guide students in this direction. This…

Mathematics Lectures as Narratives: Insights from Network Graph Methodology

ERIC Educational Resources Information Center

Weinberg, Aaron; Wiesner, Emilie; Fukawa-Connelly, Tim

2016-01-01

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the general structure of lectures. In this paper, we adapt ideas from narrative analysis and apply them to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture…

Student Perception of the Impact of Mathematics Support in Higher Education

ERIC Educational Resources Information Center

Ní Fhloinn, E.; Fitzmaurice, O.; Mac an Bhaird, C.; O'Sullivan, C.

2014-01-01

Mathematics support in higher education has become increasingly widespread over the past two decades, particularly in the UK, Ireland and Australia. Despite this, reliable evaluation of mathematics support continues to present challenges for those working in this area. One reason is because ideally, properly structured support should function as…

Turkish High School Teachers' Conceptions of Creativity in Mathematics

ERIC Educational Resources Information Center

Aktas, Meral Cansiz

2016-01-01

The aim of this research is to explore Turkish high school teachers' conceptions of creativity in mathematics. The research was carried out using qualitative research methods. The sample consisted of seven mathematics teachers, and semi-structured interviews were used as a data collection tool. Analysis of the responses indicated that mathematics…

Cognitive Activities in Solving Mathematical Tasks: The Role of a Cognitive Obstacle

ERIC Educational Resources Information Center

Antonijevic, Radovan

2016-01-01

In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…

On the Importance of Set-Based Meanings for Categories and Connectives in Mathematical Logic

ERIC Educational Resources Information Center

Dawkins, Paul Christian

2017-01-01

Based on data from a series of teaching experiments on standard tools of mathematical logic, this paper characterizes a range of student meanings for mathematical properties and logical connectives. Some observed meanings inhibited students' adoption of logical structure, while others greatly facilitated it. "Reasoning with predicates"…

Using Plot Twists to Engage Learners

ERIC Educational Resources Information Center

Ryan, Laura E.; Dietiker, Leslie

2018-01-01

One way to recognize how mathematical lessons can be stimulating for children is to interpret them as stories. If mathematical lessons follow a structure similar to that of a story, they can build anticipation, create surprise, and even generate intrigue (Egan 1988). To support the design of mathematical lessons with these types of aesthetic…

Mathematical form models of tree trunks

Treesearch

Rudolfs Ozolins

2000-01-01

Assortment structure analysis of tree trunks is a characteristic and proper problem that can be solved by using mathematical modeling and standard computer programs. Mathematical form model of tree trunks consists of tapering curve equations and their parameters. Parameters for nine species were obtained by processing measurements of 2,794 model trees and studying the...

Modeling Achievement in Mathematics: The Role of Learner and Learning Environment Characteristics

ERIC Educational Resources Information Center

Nasser-Abu Alhija, Fadia; Amasha, Marcel

2012-01-01

This study examined a structural model of mathematics achievement among Druze 8th graders in Israel. The model integrates 2 psychosocial theories: goal theory and social learning theory. Variables in the model included gender, father's and mother's education, classroom mastery and performance goal orientation, mathematics self-efficacy and…

Neutral model analysis of landscape patterns from mathematical morphology

Treesearch

Kurt H. Riitters; Peter Vogt; Pierre Soille; Jacek Kozak; Christine Estreguil

2007-01-01

Mathematical morphology encompasses methods for characterizing land-cover patterns in ecological research and biodiversity assessments. This paper reports a neutral model analysis of patterns in the absence of a structuring ecological process, to help set standards for comparing and interpreting patterns identified by mathematical morphology on real land-cover maps. We...

Teaching Multidigit Multiplication: Combining Multiple Frameworks to Analyse a Class Episode

ERIC Educational Resources Information Center

Clivaz, Stéphane

2017-01-01

This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher's mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and…

The system-resonance approach in modeling genetic structures.

PubMed

Petoukhov, Sergey V

2016-01-01

The founder of the theory of resonance in structural chemistry Linus Pauling established the importance of resonance patterns in organization of living systems. Any living organism is a great chorus of coordinated oscillatory processes. From the formal point of view, biological organism is an oscillatory system with a great number of degrees of freedom. Such systems are studied in the theory of oscillations using matrix mathematics of their resonance characteristics. This study is devoted to a new approach for modeling genetically inherited structures and processes in living organisms using mathematical tools of the theory of resonances. This approach reveals hidden relationships in a number of genetic phenomena and gives rise to a new class of bio-mathematical models, which contribute to a convergence of biology with physics and informatics. In addition some relationships of molecular-genetic ensembles with mathematics of noise-immunity coding of information in modern communications technology are shown. Perspectives of applications of the phenomena of vibrational mechanics for modeling in biology are discussed. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Automation of reliability evaluation procedures through CARE - The computer-aided reliability estimation program.

NASA Technical Reports Server (NTRS)

Mathur, F. P.

1972-01-01

Description of an on-line interactive computer program called CARE (Computer-Aided Reliability Estimation) which can model self-repair and fault-tolerant organizations and perform certain other functions. Essentially CARE consists of a repository of mathematical equations defining the various basic redundancy schemes. These equations, under program control, are then interrelated to generate the desired mathematical model to fit the architecture of the system under evaluation. The mathematical model is then supplied with ground instances of its variables and is then evaluated to generate values for the reliability-theoretic functions applied to the model.

Lightweight structure design for supporting plate of primary mirror

NASA Astrophysics Data System (ADS)

Wang, Xiao; Wang, Wei; Liu, Bei; Qu, Yan Jun; Li, Xu Peng

2017-10-01

A topological optimization design for the lightweight technology of supporting plate of the primary mirror is presented in this paper. The supporting plate of the primary mirror is topologically optimized under the condition of determined shape, loads and environment. And the optimal structure is obtained. The diameter of the primary mirror in this paper is 450mm, and the material is SiC1 . It is better to select SiC/Al as the supporting material. Six points of axial relative displacement can be used as constraints in optimization2 . Establishing the supporting plate model and setting up the model parameters. After analyzing the force of the main mirror on the supporting plate, the model is applied with force and constraints. Modal analysis and static analysis of supporting plates are calculated. The continuum structure topological optimization mathematical model is created with the variable-density method. The maximum deformation of the surface of supporting plate under the gravity of the mirror and the first model frequency are assigned to response variable, and the entire volume of supporting structure is converted to object function. The structures before and after optimization are analyzed using the finite element method. Results show that the optimized fundamental frequency increases 29.85Hz and has a less displacement compared with the traditional structure.

Metaphorical motion in mathematical reasoning: further evidence for pre-motor implementation of structure mapping in abstract domains.

PubMed

Fields, Chris

2013-08-01

The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.

[Reparative and neoplastic spheroid cellular structures and their mathematical model].

PubMed

Kogan, E A; Namiot, V A; Demura, T A; Faĭzullina, N M; Sukhikh, G T

2014-01-01

Spheroid cell structures in the cell cultures have been described and are used for studying cell-cell and cell- matrix interactions. At the same time, spheroid cell structure participation in the repair and development of cancer in vivo remains unexplored. The aim of this study was to investigate the cellular composition of spherical structures and their functional significance in the repair of squamous epithelium in human papilloma virus-associated cervical pathology--chronic cervicitis and cervical intraepithelial neoplasia 1-3 degree, and also construct a mathematical model to explain the development and behavior of such spheroid cell structure.

Fun with maths: exploring implications of mathematical models for malaria eradication.

PubMed

Eckhoff, Philip A; Bever, Caitlin A; Gerardin, Jaline; Wenger, Edward A

2014-12-11

Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.

Turing mechanism underlying a branching model for lung morphogenesis.

PubMed

Xu, Hui; Sun, Mingzhu; Zhao, Xin

2017-01-01

The mammalian lung develops through branching morphogenesis. Two primary forms of branching, which occur in order, in the lung have been identified: tip bifurcation and side branching. However, the mechanisms of lung branching morphogenesis remain to be explored. In our previous study, a biological mechanism was presented for lung branching pattern formation through a branching model. Here, we provide a mathematical mechanism underlying the branching patterns. By decoupling the branching model, we demonstrated the existence of Turing instability. We performed Turing instability analysis to reveal the mathematical mechanism of the branching patterns. Our simulation results show that the Turing patterns underlying the branching patterns are spot patterns that exhibit high local morphogen concentration. The high local morphogen concentration induces the growth of branching. Furthermore, we found that the sparse spot patterns underlie the tip bifurcation patterns, while the dense spot patterns underlies the side branching patterns. The dispersion relation analysis shows that the Turing wavelength affects the branching structure. As the wavelength decreases, the spot patterns change from sparse to dense, the rate of tip bifurcation decreases and side branching eventually occurs instead. In the process of transformation, there may exists hybrid branching that mixes tip bifurcation and side branching. Since experimental studies have reported that branching mode switching from side branching to tip bifurcation in the lung is under genetic control, our simulation results suggest that genes control the switch of the branching mode by regulating the Turing wavelength. Our results provide a novel insight into and understanding of the formation of branching patterns in the lung and other biological systems.

Using Structured e-Forum to Support the Legislation Formation Process

NASA Astrophysics Data System (ADS)

Xenakis, Alexandros; Loukis, Euripides

Many public policy problems are 'wicked', being characterised by high complexity, many heterogeneous views and conflicts among various stakeholders, and also lack of mathematically 'optimal' solutions and predefined algorithms for calculating them. The best approach for addressing such problems is through consultation and argumentation among stakeholders. The e-participation research has investigated and suggested several ICT tools for this purpose, such as e-forum, e-petition and e-community tools. This paper investigates the use of an advanced ICT tool, the structured e-forum, for addressing such wicked problems associated with the legislation formation. For this purpose we designed, implemented and evaluated two pilot e-consultations on legislation under formation in the Parliaments of Austria and Greece using a structured e-forum tool based on the Issue Based Information Systems (IBIS) framework. The conclusions drawn reveal the advantages offered by the structured e-forum, but also its difficulties as well.

Fuzzy Edge Connectivity of Graphical Fuzzy State Space Model in Multi-connected System

NASA Astrophysics Data System (ADS)

Harish, Noor Ainy; Ismail, Razidah; Ahmad, Tahir

2010-11-01

Structured networks of interacting components illustrate complex structure in a direct or intuitive way. Graph theory provides a mathematical modeling for studying interconnection among elements in natural and man-made systems. On the other hand, directed graph is useful to define and interpret the interconnection structure underlying the dynamics of the interacting subsystem. Fuzzy theory provides important tools in dealing various aspects of complexity, imprecision and fuzziness of the network structure of a multi-connected system. Initial development for systems of Fuzzy State Space Model (FSSM) and a fuzzy algorithm approach were introduced with the purpose of solving the inverse problems in multivariable system. In this paper, fuzzy algorithm is adapted in order to determine the fuzzy edge connectivity between subsystems, in particular interconnected system of Graphical Representation of FSSM. This new approach will simplify the schematic diagram of interconnection of subsystems in a multi-connected system.

Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization

PubMed Central

Bueno-Orovio, Alfonso; Kay, David; Grau, Vicente; Rodriguez, Blanca; Burrage, Kevin

2014-01-01

Impulse propagation in biological tissues is known to be modulated by structural heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity influences electrical spread is key to advancing our interpretation of dispersion of repolarization. We propose fractional diffusion models as a novel mathematical description of structurally heterogeneous excitable media, as a means of representing the modulation of the total electric field by the secondary electrical sources associated with tissue inhomogeneities. Our results, analysed against in vivo human recordings and experimental data of different animal species, indicate that structural heterogeneity underlies relevant characteristics of cardiac electrical propagation at tissue level. These include conduction effects on action potential (AP) morphology, the shortening of AP duration along the activation pathway and the progressive modulation by premature beats of spatial patterns of dispersion of repolarization. The proposed approach may also have important implications in other research fields involving excitable complex media. PMID:24920109

34 CFR 200.11 - Participation in NAEP.

Code of Federal Regulations, 2013 CFR

2013-07-01

... academic assessments of fourth and eighth grade reading and mathematics under the State National Assessment... academic achievement results in grades four and eight on the State's NAEP reading and mathematics...

34 CFR 200.11 - Participation in NAEP.

Code of Federal Regulations, 2014 CFR

2014-07-01

... academic assessments of fourth and eighth grade reading and mathematics under the State National Assessment... academic achievement results in grades four and eight on the State's NAEP reading and mathematics...

34 CFR 200.11 - Participation in NAEP.

Code of Federal Regulations, 2012 CFR

2012-07-01

... academic assessments of fourth and eighth grade reading and mathematics under the State National Assessment... academic achievement results in grades four and eight on the State's NAEP reading and mathematics...

34 CFR 200.11 - Participation in NAEP.

Code of Federal Regulations, 2011 CFR

2011-07-01

... academic assessments of fourth and eighth grade reading and mathematics under the State National Assessment... academic achievement results in grades four and eight on the State's NAEP reading and mathematics...

34 CFR 200.11 - Participation in NAEP.

Code of Federal Regulations, 2010 CFR

2010-07-01

... academic assessments of fourth and eighth grade reading and mathematics under the State National Assessment... academic achievement results in grades four and eight on the State's NAEP reading and mathematics...

Self-similar seismogenic structure of the crust: A review of the problem and a mathematical model

NASA Astrophysics Data System (ADS)

Stakhovsky, I. R.

2007-12-01

The paper presents a brief review of studies of the structural organization of a seismogenic medium showing that the crust of seismically active regions possesses a fractal structure. A new mathematical model of the self-similar seismogenic structure (SSS) of the crust generalizing the reviewed publications is proposed on the basis of the scaling correspondence between the fault, seismic, and seismic energy multifractal fields of the crust. Multifractal fields of other physical origin can also be incorporated in the SSS model.

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

PubMed

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

2014-11-01

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

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

PubMed Central

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

2015-01-01

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

Choking under Pressure: When an Additional Positive Stereotype Affects Performance for Domain Identified Male Mathematics Students

ERIC Educational Resources Information Center

Rosenthal, Harriet E. S.; Crisp, Richard J.

2007-01-01

This research aimed to establish if the presentation of two positive stereotypes would result in choking under pressure for identified male mathematics students. Seventy-five 16 year old men, who had just commenced their AS-level study, were either made aware of their gender group membership (single positive stereotype), their school group…

Bridging CAGD knowledge into CAD/CG applications: Mathematical theories as stepping stones of innovations

NASA Astrophysics Data System (ADS)

Gobithaasan, R. U.; Miura, Kenjiro T.; Hassan, Mohamad Nor

2014-07-01

Computer Aided Geometric Design (CAGD) which surpasses the underlying theories of Computer Aided Design (CAD) and Computer Graphics (CG) has been taught in a number of Malaysian universities under the umbrella of Mathematical Sciences' faculty/department. On the other hand, CAD/CG is taught either under the Engineering or Computer Science Faculty. Even though CAGD researchers/educators/students (denoted as contributors) have been enriching this field of study by means of article/journal publication, many fail to convert the idea into constructive innovation due to the gap that occurs between CAGD contributors and practitioners (engineers/product/designers/architects/artists). This paper addresses this issue by advocating a number of technologies that can be used to transform CAGD contributors into innovators where immediate impact in terms of practical application can be experienced by the CAD/CG practitioners. The underlying principle of solving this issue is twofold. First would be to expose the CAGD contributors on ways to turn mathematical ideas into plug-ins and second is to impart relevant CAGD theories to CAD/CG to practitioners. Both cases are discussed in detail and the final section shows examples to illustrate the importance of turning mathematical knowledge into innovations.

Pre-service mathematics teachers' attitudes towards learning English: A case study in Yogyakarta

NASA Astrophysics Data System (ADS)

Setyaningrum, Wahyu

2017-08-01

This study investigated attitudes of pre-service mathematics teachers towards English as one of the subject at the university. It is a qualitative study in which questionnaire and face-to-face interview were employed to collect the data. The participants of this study were sixty students of mathematics education department at one of the university in Yogyakarta. The main research question was concern with how pre-service mathematics teachers perceive the importance of learning English. This study found that most of the participants perceive English as an important language that should be acquired by mathematics teachers. Their beliefs about the importance of English were mostly due to instrumental orientation rather than integrative orientation, such as getting a good job, getting a scholarship and understanding learning sources that are written in English. The data also revealed some obstacles faced by pre-service mathematics teachers in learning English as an additional language for them. The main obstacles were related to the differences between English for mathematics and English in daily life including its vocabulary and structure. Most of the participants argued that several mathematics vocabularies had precise meaning and different from daily English. In addition, they found difficult to understand some sentences used in the paper journal due to its structure. This study therefore, provided an insight into the pre-service mathematics teachers' perception and obstacles when learning English that could be use in improving pre-service teachers' education.

Mathematical modeling of vortex induced vibrations of an elastic rod under air flow influence

NASA Astrophysics Data System (ADS)

Pogudalina, S. V.; Fedorova, N. N.

2018-03-01

The results of simulations of the oscillations of an elastic rod placed normally to the external air flow and rigidly fixed on a substrate are presented. The computations were carried out in ANSYS using the technology of two-way fluid-structure interaction (2FSI). Calculations of the problem were performed for various flow velocities, geometric parameters and properties of the rod material. The frequencies, amplitudes and shapes of vortex induced vibration were studied including those that are close to the lock-in mode.

Research reports: 1990 NASA/ASEE Summer Faculty Fellowship Program

NASA Technical Reports Server (NTRS)

Freeman, L. Michael (Editor); Chappell, Charles R. (Editor); Six, Frank (Editor); Karr, Gerald R. (Editor)

1990-01-01

Reports on the research projects performed under the NASA/ASEE Summer Faculty Fellowship Program are presented. The program was conducted by The University of Alabama and MSFC during the period from June 4, 1990 through August 10, 1990. Some of the topics covered include: (1) Space Shuttles; (2) Space Station Freedom; (3) information systems; (4) materials and processes; (4) Space Shuttle main engine; (5) aerospace sciences; (6) mathematical models; (7) mission operations; (8) systems analysis and integration; (9) systems control; (10) structures and dynamics; (11) aerospace safety; and (12) remote sensing

Supporting Middle Grades Mathematics Teachers and Students: A Curricular Activity System Used in an Urban School District

ERIC Educational Resources Information Center

Roy, George J.; Fueyo, Vivian; Vahey, Philip

2017-01-01

The exploration of proportional relationships is foundational to the mathematics studied in the middle grades and beyond. Research has shown that an early emphasis on procedures often leaves students with a shallow understanding of the important underlying mathematical concepts of proportional relationships. One approach that addresses the needs…

Inhibiting Factors in Generating Examples by Mathematics Teachers and Student Teachers: The Case of Binary Operation.

ERIC Educational Resources Information Center

Zaslavsky, Orit; Peled, Irit

1996-01-01

Inservice (n=36) and preservice (n=67) mathematics teachers were asked for a commutative, nonassociative binary operation. Responses were analyzed for correctness, productiveness, mathematical content, and underlying difficulties. Both groups exhibited a weak concept by failing to produce an example and using a limited content search space.…

Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land

ERIC Educational Resources Information Center

Pei, Christina; Weintrop, David; Wilensky, Uri

2018-01-01

There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…

A Hybrid Model of Mathematics Support for Science Students Emphasizing Basic Skills and Discipline Relevance

ERIC Educational Resources Information Center

Jackson, Deborah C.; Johnson, Elizabeth D.

2013-01-01

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support…

What Works: Building Natural Science Communities. A Plan for Strengthening Undergraduate Science and Mathematics. Volume One.

ERIC Educational Resources Information Center

Narum, Jeanne L., Ed.

In an era when the U.S. educational enterprise, particularly in mathematics, physical sciences, and engineering, has been found to be seriously flawed and has come under criticism from many different sectors, it is essential for science and mathematics educators from the nation's predominantly undergraduate institutions to take the lead in…

Investigating Pre-Service Mathematics Teachers' Innovation Awareness and Views Regarding Intelligent Tutoring Systems

ERIC Educational Resources Information Center

Erdemir, Mustafa; Ingeç, Sebnem Kandil

2016-01-01

The purpose of this study is to identify pre-service primary mathematics teachers' views regarding on Web-based Intelligent Tutoring Systems (WBITS) in relation to its usability and influence on teaching. A survey method was used. The study was conducted with 43 students attending the mathematics teaching program under the department of elementary…

Gender-Related Effects of Group Learning on Mathematics Achievement among the Rural Secondary Students

ERIC Educational Resources Information Center

Hossain, Md. Anowar; Tarmizi, Rohani Ahmad

2012-01-01

Problem Statement: Gender differences in the effects of group learning play a contested role in mathematics education. Several researchers concluded that male students perform better on mathematics than female students. Whilst on the other hand, others reported that female students perform best under the group learning setting whereas the male…

Analysis of the Mathematical Proof Skills of Students of Science Teaching

ERIC Educational Resources Information Center

Gökkt, Burçin; Soylu, Yasin; Sahin, Ömer

2014-01-01

Mathematics and proof are two closely related concepts. Mathematics not only shows what is right or wrong, but it also teaches that it is not enough to know the latest formulas and results should be explained with causality. In this context, students learn the underlying meaning behind what mathematicians do by way of proofs. Accordingly, this…

Effective Strategies for Teaching Mathematics to African American Students

ERIC Educational Resources Information Center

White, La Donna

2012-01-01

As of 2001 with the mandates issued under No Child Left Behind, the National Council of Teachers of Mathematics (NCTM) revised its standards to ensure that all students receive a quality mathematics education (NCTM, 2008). The 2009 report from U.S. Department of Education revealed that there is an increase in the number of minority students…

Mathematics and Science Teachers' Use of and Confidence in Empirical Reasoning: Implications for STEM Teacher Preparation

ERIC Educational Resources Information Center

Wasserman, Nicholas H.; Rossi, Dara

2015-01-01

The recent trend to unite mathematically related disciplines (science, technology, engineering, and mathematics) under the broader umbrella of STEM education has advantages. In this new educational context of integration, however, STEM teachers need to be able to distinguish between sufficient proof and reasoning across different disciplines,…

The Effect of Cultures in Eighth Grade Mathematics Classroom: A Case Study of a LEP Student.

ERIC Educational Resources Information Center

Duncan, Aki

The fastest-growing sector of the American school population is the limited English proficient (LEP) students, those students whose native language is not English. When mainstreamed they are usually enrolled in physical education, art, and music classes first. The students then enter mathematics classes under the assumption that mathematics is…

Mathematical Knowledge of Technology and Design Student Teachers: Diagnosis and Remediation

ERIC Educational Resources Information Center

Bell, Irene Teresa; Gibson, Ken

2009-01-01

This research examines how e-assessment and e-resources were used to assess and support the mathematics of Technology and Design students undertaking a B.Ed. (post-primary) teacher education course. The students participated in two similar tests in order to ascertain if their mathematical difficulties were in the underlying concepts of the…

Proof and Rhetoric: The Structure and Origin of Proof--From Ancient Greece to Abraham Lincoln's Speech in Defence of the Union and Paul Keating's Mabo Speech

ERIC Educational Resources Information Center

Padula, Janice

2016-01-01

According to the latest news about declining standards in mathematics learning in Australia, boys, and girls, in particular, need to be more engaged in mathematics learning. Only 30% of mathematics students at university level in Australia are female. Proofs are made up of words and mathematical symbols. One can assume the words would assist…

Responsiveness to mathematical problem-solving instruction: comparing students at risk of mathematics disability with and without risk of reading disability.

PubMed

Fuchs, Lynn S; Fuchs, Douglas; Prentice, Karin

2004-01-01

This study assessed responsiveness to a 16-week mathematical problem-solving treatment as a function of students' risk for disability. Among 301 third graders, TerraNova scores were used to categorize students as at risk for both reading and mathematics disability (MDR/RDR; 20 control and 12 experimental), at risk for mathematics disability only (MDR-only; 5 and 8), at risk for reading disability only (RDR-only; 12 and 15), or not at risk (NDR; 60 and 69). Interactions among at-risk status, treatment, and time showed that as a function of treatment, MDR/RDR, MDR-only, and RDR-only students improved less than NDR students on computation and labeling, and MDR/RDR students improved less than all other groups on conceptual underpinnings. Exploratory regressions suggested that MDR/RDR students' math deficits or their underlying mechanisms explained a greater proportion of variance in responsiveness to problem-solving treatment than reading deficits or their underlying mechanisms.

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school

PubMed Central

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. PMID:26441739

The development of executive functions and early mathematics: a dynamic relationship.

PubMed

Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Boom, Jan; Leseman, Paul P M

2012-03-01

The relationship between executive functions and mathematical skills has been studied extensively, but results are inconclusive, and how this relationship evolves longitudinally is largely unknown. The aim was to investigate the factor structure of executive functions in inhibition, shifting, and updating; the longitudinal development of executive functions and mathematics; and the relation between them. A total of 211 children in grade 2 (7-8 years old) from 10 schools in the Netherlands. Children were followed in grade 1 and 2 of primary education. Executive functions and mathematics were measured four times. The test battery contained multiple tasks for each executive function: Animal stroop, local global, and Simon task for inhibition; Animal Shifting, Trail Making Test in Colours, and Sorting Task for shifting; and Digit Span Backwards, Odd One Out, and Keep Track for updating. The factor structure of executive functions was assessed and relations with mathematics were investigated using growth modelling. Confirmatory factor analysis (CFA) showed that inhibition and shifting could not be distinguished from each other. Updating was a separate factor, and its development was strongly related to mathematical development while inhibition and shifting did not predict mathematics in the presence of the updating factor. The strong relationship between updating and mathematics suggest that updating skills play a key role in the maths learning process. This makes updating a promising target for future intervention studies. ©2011 The British Psychological Society.

The Latent Structure of Spatial Skills and Mathematics: A Replication of the Two-Factor Model

ERIC Educational Resources Information Center

Mix, Kelly S.; Levine, Susan C.; Cheng, Yi-Lang; Young, Christopher J.; Hambrick, David Z.; Konstantopoulos, Spyros

2017-01-01

In a previous study, Mix et al. (2016) reported that spatial skill and mathematics were composed of 2 highly correlated, domain-specific factors, with a few cross-domain loadings. The overall structure was consistent across grade (kindergarten, 3rd grade, 6th grade), but the cross-domain loadings varied with age. The present study sought to…

The Growing Awareness Inventory: Building Capacity for Culturally Responsive Science and Mathematics with a Structured Observation Protocol

ERIC Educational Resources Information Center

Brown, Julie C.; Crippen, Kent J.

2016-01-01

This study represents a first iteration in the design process of the Growing Awareness Inventory (GAIn), a structured observation protocol for building the awareness of preservice teachers (PSTs) for resources in mathematics and science classrooms that can be used for culturally responsive pedagogy (CRP). The GAIn is designed to develop awareness…

Students' Views on Mathematics in Single-Sex and Coed Classrooms in Ghana

ERIC Educational Resources Information Center

Bofah, Emmanuel Adu-tutu; Hannula, Markku S.

2016-01-01

In this study, we investigated students' views on themselves as learners of mathematics as a function of school-by-sex (N = 2034, MAge = 18.49, SDAge = 1.25; 12th-grade; 58.2% girls). Using latent variable Structural Equation Modeling (SEM), the measurement and structural equivalence as well as the equality of latent means of scores across…

Discrete structures in continuum descriptions of defective crystals

PubMed Central

2016-01-01

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of ‘plastic strain variables’, which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification. PMID:27002070

Developing Algebra Structure Module and Model of Cooperative Learning Helping Concept Map Media for Improving Proofing Ability

ERIC Educational Resources Information Center

Syafari

2017-01-01

This research was purposed to develop module and learning model and instrument of proofing ability in algebra structure through cooperative learning with helping map concept media for students of mathematic major and mathematics education in State University and Private University in North Sumatra province. The subject of this research was the…

Discrete mathematics in deaf education: a survey of teachers' knowledge and use.

PubMed

Pagliaro, Claudia M; Kritzer, Karen L

The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.

Mathematics is always invisible, Professor Dowling

NASA Astrophysics Data System (ADS)

Cable, John

2015-09-01

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

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

Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com; Plastino, A., E-mail: plastino@fisica.unlp.edu.ar

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS linkmore » and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.« less

Electro thermal analysis of rotary type micro thermal actuator

NASA Astrophysics Data System (ADS)

Anwar, M. Arefin; Packirisamy, Muthukumaran; Ahmed, A. K. Waiz

2005-09-01

In micro domain, thermal actuators are favored because it provides higher force and deflection than others. This paper presents a new type of micro thermal actuator that provides rotary motion of the circular disc shaped cold arm, which can be used in various optical applications, such as, switching, attenuation, diffraction, etc. The device has been fabricated in MUMPS technology. In this new design, the hot arms are arranged with the cold disc in such a way that thermal expansion of the hot arms due to Joule heating, will make the cold disc to rotate and the rotation is unidirectional on loading. The dominant heat transfer modes in the operating temperature zone are through the anchor and the air between the structure and the substrate because of the very low gap provided by MUMPS. A mathematical model was used for predicting steady state temperature profile along the actuator length and rotational behavior of the cold disc under different applied voltages. A 3-D coupled field finite element analysis (FEM) for the device is also presented. A FEM analysis was done by defining an air volume around the structure and substrate below the structure. Results obtained from the mathematical model, was compared with that of the finite element analysis. The presented results confirm the applicability of this novel rotary type thermal actuator for many optical MEMS applications.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number

PubMed Central

Klewicki, J. C.; Chini, G. P.; Gibson, J. F.

2017-01-01

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier–Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167585

Molecular mechanics and dynamics characterization of an in silico mutated protein: a stand-alone lab module or support activity for in vivo and in vitro analyses of targeted proteins.

PubMed

Chiang, Harry; Robinson, Lucy C; Brame, Cynthia J; Messina, Troy C

2013-01-01

Over the past 20 years, the biological sciences have increasingly incorporated chemistry, physics, computer science, and mathematics to aid in the development and use of mathematical models. Such combined approaches have been used to address problems from protein structure-function relationships to the workings of complex biological systems. Computer simulations of molecular events can now be accomplished quickly and with standard computer technology. Also, simulation software is freely available for most computing platforms, and online support for the novice user is ample. We have therefore created a molecular dynamics laboratory module to enhance undergraduate student understanding of molecular events underlying organismal phenotype. This module builds on a previously described project in which students use site-directed mutagenesis to investigate functions of conserved sequence features in members of a eukaryotic protein kinase family. In this report, we detail the laboratory activities of a MD module that provide a complement to phenotypic outcomes by providing a hypothesis-driven and quantifiable measure of predicted structural changes caused by targeted mutations. We also present examples of analyses students may perform. These laboratory activities can be integrated with genetics or biochemistry experiments as described, but could also be used independently in any course that would benefit from a quantitative approach to protein structure-function relationships. Copyright © 2013 Wiley Periodicals, Inc.

Prospectus: towards the development of high-fidelity models of wall turbulence at large Reynolds number.

PubMed

Klewicki, J C; Chini, G P; Gibson, J F

2017-03-13

Recent and on-going advances in mathematical methods and analysis techniques, coupled with the experimental and computational capacity to capture detailed flow structure at increasingly large Reynolds numbers, afford an unprecedented opportunity to develop realistic models of high Reynolds number turbulent wall-flow dynamics. A distinctive attribute of this new generation of models is their grounding in the Navier-Stokes equations. By adhering to this challenging constraint, high-fidelity models ultimately can be developed that not only predict flow properties at high Reynolds numbers, but that possess a mathematical structure that faithfully captures the underlying flow physics. These first-principles models are needed, for example, to reliably manipulate flow behaviours at extreme Reynolds numbers. This theme issue of Philosophical Transactions of the Royal Society A provides a selection of contributions from the community of researchers who are working towards the development of such models. Broadly speaking, the research topics represented herein report on dynamical structure, mechanisms and transport; scale interactions and self-similarity; model reductions that restrict nonlinear interactions; and modern asymptotic theories. In this prospectus, the challenges associated with modelling turbulent wall-flows at large Reynolds numbers are briefly outlined, and the connections between the contributing papers are highlighted.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Chronic ethanol feeding causes depression of mitochondrial elongation factor Tu in the rat liver: implications for the mitochondrial ribosome.

PubMed

Weiser, Brian; Gonye, Gregory; Sykora, Peter; Crumm, Sara; Cahill, Alan

2011-05-01

Chronic ethanol feeding is known to negatively impact hepatic energy metabolism. Previous studies have indicated that the underlying lesion responsible for this may lie at the level of the mitoribosome. The aim of this study was to characterize the structure of the hepatic mitoribosome in alcoholic male rats and their isocalorically paired controls. Our experiments revealed that chronic ethanol feeding resulted in a significant depletion of both structural (death-associated protein 3) and functional [elongation factor thermo unstable (EF-Tu)] mitoribosomal proteins. In addition, significant increases were found in nucleotide elongation factor thermo stable (EF-Ts) and structural mitochondrial ribosomal protein L12 (MRPL12). The increase in MRPL12 was found to correlate with an increase in the levels of the 39S large mitoribosomal subunit. These changes were accompanied by decreased levels of nuclear- and mitochondrially encoded respiratory subunits, decreased amounts of intact respiratory complexes, decreased hepatic ATP levels, and depressed mitochondrial translation. Mathematical modeling of ethanol-mediated changes in EF-Tu and EF-Ts using prederived kinetic data predicted that the ethanol-mediated decrease in EF-Tu levels could completely account for the impaired mitochondrial protein synthesis. In conclusion, chronic ethanol feeding results in a depletion of mitochondrial EF-Tu levels within the liver that is mathematically predicted to be responsible for the impaired mitochondrial protein synthesis seen in alcoholic animals.

Numerical Flexural Strength Analysis of Thermally Stressed Delaminated Composite Structure under Sinusoidal Loading

NASA Astrophysics Data System (ADS)

Hirwani, C. K.; Biswash, S.; Mehar, K.; Panda, S. K.

2018-03-01

In this article, we investigate the thermomechanical deflection characteristics of the debonded composite plate structure using an isoparametric type of higher-order finite element model. The current formulation is derived using higher-order kinematic theory and the displacement variables described as constant along the thickness direction whereas varying nonlinearly for the in-plane directions. The present mid-plane kinematic model mainly obsoletes the use of shear correction factor as in the other lower-order theories. The separation between the adjacent layers is modeled via the sub-laminate technique and the intermittent continuity conditions imposed to avoid the mathematical ill conditions. The governing equation of equilibrium of the damaged plate structure under the combined state of loading are obtained using the variational principle and solved numerically to compute the deflection values. Further, the convergence test has been performed by refining the numbers of elements and validated through comparing the present results with available published values. The usefulness of the proposed formulation has been discussed by solving the different kind of numerical examples including the size, location and position of delamination.

Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation

NASA Astrophysics Data System (ADS)

Masuda, Hiroshi; Kanda, Yutaro; Okamoto, Yoshifumi; Hirono, Kazuki; Hoshino, Reona; Wakao, Shinji; Tsuburaya, Tomonori

2017-12-01

It is very important to design electrical machineries with high efficiency from the point of view of saving energy. Therefore, topology optimization (TO) is occasionally used as a design method for improving the performance of electrical machinery under the reasonable constraints. Because TO can achieve a design with much higher degree of freedom in terms of structure, there is a possibility for deriving the novel structure which would be quite different from the conventional structure. In this paper, topology optimization using sequential linear programming using move limit based on adaptive relaxation is applied to two models. The magnetic shielding, in which there are many local minima, is firstly employed as firstly benchmarking for the performance evaluation among several mathematical programming methods. Secondly, induction heating model is defined in 2-D axisymmetric field. In this model, the magnetic energy stored in the magnetic body is maximized under the constraint on the volume of magnetic body. Furthermore, the influence of the location of the design domain on the solutions is investigated.

Tablets and Applications to Tell Mathematics' History in High School

ERIC Educational Resources Information Center

Dias, Eduardo Jesus; Araujo, Carlos Fernando, Jr.; Ota, Marcos Andrei

2017-01-01

In this article, we suggest that the history in Mathematics Education combined with mobile technology, can provide analysis of concepts, theories and significant logical structures in the process of teaching and learning of Mathematics, as the main objective of this study is to analyze the students' motivation and learning using tablets in the…

The Mental Representation of Integers: An Abstract-to-Concrete Shift in the Understanding of Mathematical Concepts

ERIC Educational Resources Information Center

Varma, Sashank; Schwartz, Daniel L.

2011-01-01

Mathematics has a level of structure that transcends untutored intuition. What is the cognitive representation of abstract mathematical concepts that makes them meaningful? We consider this question in the context of the integers, which extend the natural numbers with zero and negative numbers. Participants made greater and lesser judgments of…

Exploring a Structure for Mathematics Lessons That Foster Problem Solving and Reasoning

ERIC Educational Resources Information Center

Sullivan, Peter; Walker, Nadia; Borcek, Chris; Rennie, Mick

2015-01-01

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks…

High School Learners' Mental Construction during Solving Optimisation Problems in Calculus: A South African Case Study

ERIC Educational Resources Information Center

Brijlall, Deonarain; Ndlovu, Zanele

2013-01-01

This qualitative case study in a rural school in Umgungundlovu District in KwaZulu-Natal, South Africa, explored Grade 12 learners' mental constructions of mathematical knowledge during engagement with optimisation problems. Ten Grade 12 learners who do pure Mathemat-ics participated, and data were collected through structured activity sheets and…

Matriculation Mathematics, Pure Mathematics - Test Papers. Circular of Information to Secondary Schools.

ERIC Educational Resources Information Center

Victoria Education Dept. (Australia).

This document consists of test questions used in three state high schools teaching the new Matriculation pure mathematics course (approximately grade 12). This material was circulated to all schools teaching this course as a teacher resource. The questions are arranged in 14 papers of varying structure and length. Most questions are of the essay…

Teachers' Concerns and Efficacy Beliefs about Implementing a Mathematics Curriculum Reform: Integrating Two Lines of Inquiry

ERIC Educational Resources Information Center

Charalambous, Charalambos Y.; Philippou, George N.

2010-01-01

This study brings together two lines of research on teachers' affective responses toward mathematics curriculum reforms: their concerns and their efficacy beliefs. Using structural equation modeling to analyze data on 151 elementary mathematics teachers' concerns and efficacy beliefs 5 years into a mandated curriculum reform on problem solving,…

The Culture of Exclusion in Mathematics Education and Its Persistence in Equity-Oriented Teaching

ERIC Educational Resources Information Center

Louie, Nicole L.

2017-01-01

In this article, I investigate the influence of the dominant culture characterizing mathematics education--which I term the "culture of exclusion"--on efforts to teach for equity. Analyzing a year of observations in an urban high school mathematics department, I found that this culture structured everyday instruction even for teachers…

Attracting Primary School Children to Mathematics: The Case of a City Mathematical Marathon

ERIC Educational Resources Information Center

Applebaum, Mark; Freiman, Viktor

2013-01-01

In this paper we report on the first year of an online competition in which 480 students took part. After a brief presentation of the organizational structure of the marathon and general data about students' participation, we discuss findings from questionnaires about participants' attitudes towards mathematics, technology, and their perception of…

Improving Mathematics: An Examination of the Effects of Specific Cognitive Abilities on College-Age Students' Mathematics Achievement

ERIC Educational Resources Information Center

Taub, Gordon E.; Benson, Nicholas; Szente, Judit

2014-01-01

This study investigated the effects of general intelligence and seven specific cognitive abilities on college-age students' mathematics achievement. The present investigation went beyond previous research by employing structural equation modeling. It also represents the first study to examine the direct and indirect effects of general and specific…

A bio-physical basis of mathematics in synaptic function of the nervous system: a theory.

PubMed

Dempsher, J

1980-01-01

The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction results in a change in form of both energy and matter. There are at least six mathematical operations in a simple synaptic region. It is believed the form of both energy and matter are specific, and their interaction is specific, that is, function in most of the 'mind' and placed where it belongs - in nature and the synaptic regions of the nervous system; it results in both places from a precise interaction between energy (in a precise form) and matter ( in a precise structure).

An information driven strategy to support multidisciplinary design

NASA Technical Reports Server (NTRS)

Rangan, Ravi M.; Fulton, Robert E.

1990-01-01

The design of complex engineering systems such as aircraft, automobiles, and computers is primarily a cooperative multidisciplinary design process involving interactions between several design agents. The common thread underlying this multidisciplinary design activity is the information exchange between the various groups and disciplines. The integrating component in such environments is the common data and the dependencies that exist between such data. This may be contrasted to classical multidisciplinary analyses problems where there is coupling between distinct design parameters. For example, they may be expressed as mathematically coupled relationships between aerodynamic and structural interactions in aircraft structures, between thermal and structural interactions in nuclear plants, and between control considerations and structural interactions in flexible robots. These relationships provide analytical based frameworks leading to optimization problem formulations. However, in multidisciplinary design problems, information based interactions become more critical. Many times, the relationships between different design parameters are not amenable to analytical characterization. Under such circumstances, information based interactions will provide the best integration paradigm, i.e., there is a need to model the data entities and their dependencies between design parameters originating from different design agents. The modeling of such data interactions and dependencies forms the basis for integrating the various design agents.

Optimization of numerical weather/wave prediction models based on information geometry and computational techniques

NASA Astrophysics Data System (ADS)

Galanis, George; Famelis, Ioannis; Kalogeri, Christina

2014-10-01

The last years a new highly demanding framework has been set for environmental sciences and applied mathematics as a result of the needs posed by issues that are of interest not only of the scientific community but of today's society in general: global warming, renewable resources of energy, natural hazards can be listed among them. Two are the main directions that the research community follows today in order to address the above problems: The utilization of environmental observations obtained from in situ or remote sensing sources and the meteorological-oceanographic simulations based on physical-mathematical models. In particular, trying to reach credible local forecasts the two previous data sources are combined by algorithms that are essentially based on optimization processes. The conventional approaches in this framework usually neglect the topological-geometrical properties of the space of the data under study by adopting least square methods based on classical Euclidean geometry tools. In the present work new optimization techniques are discussed making use of methodologies from a rapidly advancing branch of applied Mathematics, the Information Geometry. The latter prove that the distributions of data sets are elements of non-Euclidean structures in which the underlying geometry may differ significantly from the classical one. Geometrical entities like Riemannian metrics, distances, curvature and affine connections are utilized in order to define the optimum distributions fitting to the environmental data at specific areas and to form differential systems that describes the optimization procedures. The methodology proposed is clarified by an application for wind speed forecasts in the Kefaloniaisland, Greece.

DAISY: a new software tool to test global identifiability of biological and physiological systems

PubMed Central

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D’Angiò, Leontina

2009-01-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/. PMID:17707944

Finite element techniques in computational time series analysis of turbulent flows

NASA Astrophysics Data System (ADS)

Horenko, I.

2009-04-01

In recent years there has been considerable increase of interest in the mathematical modeling and analysis of complex systems that undergo transitions between several phases or regimes. Such systems can be found, e.g., in weather forecast (transitions between weather conditions), climate research (ice and warm ages), computational drug design (conformational transitions) and in econometrics (e.g., transitions between different phases of the market). In all cases, the accumulation of sufficiently detailed time series has led to the formation of huge databases, containing enormous but still undiscovered treasures of information. However, the extraction of essential dynamics and identification of the phases is usually hindered by the multidimensional nature of the signal, i.e., the information is "hidden" in the time series. The standard filtering approaches (like f.~e. wavelets-based spectral methods) have in general unfeasible numerical complexity in high-dimensions, other standard methods (like f.~e. Kalman-filter, MVAR, ARCH/GARCH etc.) impose some strong assumptions about the type of the underlying dynamics. Approach based on optimization of the specially constructed regularized functional (describing the quality of data description in terms of the certain amount of specified models) will be introduced. Based on this approach, several new adaptive mathematical methods for simultaneous EOF/SSA-like data-based dimension reduction and identification of hidden phases in high-dimensional time series will be presented. The methods exploit the topological structure of the analysed data an do not impose severe assumptions on the underlying dynamics. Special emphasis will be done on the mathematical assumptions and numerical cost of the constructed methods. The application of the presented methods will be first demonstrated on a toy example and the results will be compared with the ones obtained by standard approaches. The importance of accounting for the mathematical assumptions used in the analysis will be pointed up in this example. Finally, applications to analysis of meteorological and climate data will be presented.

Can Mathematics be Justified by Natural Logic?

NASA Astrophysics Data System (ADS)

Schreiber, Lothar; Sommer, Hanns

2010-11-01

Charles Darwin claimed that the forms and the behaviour of living beings can be explained from their will to survive. But what are the consequences of this idea for humans knowledge, their theories of nature and their mathematics?. We discuss the view that even Plato's objective world of mathematical objects does not exist absolutely, without the intentions of mathematicians. Using Husserl's Phenomenological Method, cognition can be understood as a process by which meaning is deduced from empirical data relative to intentions. Thereby the essential structure of any cognition process can be detected and this structure is mirrored in logic. A natural logic becomes the direct result of cognition. Only in a second step, mathematics is obtained by abstraction from natural logic. In this way mathematics gains a well-defined foundation and is no longer part of a dubious 'a-priori knowledge' (Kant). This access to mathematics offers a new look on many old problems, e.g. the Petersburg problem and the problem 'P = NP?'. We demonstrate that this new justification of mathematics has also important applications in Artificial Intelligence. Our method provides a procedure to construct an adequate logic to solve most efficiently the problems of a given problem class. Thus, heuristics can be tailor-made for the necessities of applications.

A study of rural preschool practitioners' views on young children's mathematical thinking

NASA Astrophysics Data System (ADS)

Hunting, Robert P.; Mousley, Judith A.; Perry, Bob

2012-03-01

The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

NASA Technical Reports Server (NTRS)

Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

1973-01-01

A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

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.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

PubMed

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

PubMed Central

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

Mathematics and engineering in real life through mathematical competitions

NASA Astrophysics Data System (ADS)

More, M.

2018-02-01

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

Student perception of the impact of mathematics support in higher education

NASA Astrophysics Data System (ADS)

Fhloinn, E. Ní; Fitzmaurice, O.; Bhaird, C. Mac an; O'Sullivan, C.

2014-10-01

Mathematics support in higher education has become increasingly widespread over the past two decades, particularly in the UK, Ireland and Australia. Despite this, reliable evaluation of mathematics support continues to present challenges for those working in this area. One reason is because ideally, properly structured support should function as an integral part of the overall educational experience of the student, in tandem with lectures and tutorials. When this occurs, it makes it difficult to isolate the impact of mathematics support from these other entities. In this paper, the results of a large-scale nationwide survey conducted with first-year service mathematics students in nine higher education institutes in Ireland are considered, exploring students' perceptions of the impact of mathematics support upon their retention, mathematical confidence, examination performance and overall ability to cope with the mathematical demands they face. Students were extremely positive about the effectiveness of mathematics support in all of these areas, providing valuable insights into the value of learning support in mathematics.

Advances in engineering science, volume 2

NASA Technical Reports Server (NTRS)

1976-01-01

Papers are presented dealing with structural dynamics; structural synthesis; and the nonlinear analysis of structures, structural members, and composite structures and materials. Applications of mathematics and computer science are included.

Multiple methods integration for structural mechanics analysis and design

NASA Technical Reports Server (NTRS)

Housner, J. M.; Aminpour, M. A.

1991-01-01

A new research area of multiple methods integration is proposed for joining diverse methods of structural mechanics analysis which interact with one another. Three categories of multiple methods are defined: those in which a physical interface are well defined; those in which a physical interface is not well-defined, but selected; and those in which the interface is a mathematical transformation. Two fundamental integration procedures are presented that can be extended to integrate various methods (e.g., finite elements, Rayleigh Ritz, Galerkin, and integral methods) with one another. Since the finite element method will likely be the major method to be integrated, its enhanced robustness under element distortion is also examined and a new robust shell element is demonstrated.

Early Career Teachers' Ability to Focus on Typical Students Errors in Relation to the Complexity of a Mathematical Topic

ERIC Educational Resources Information Center

Pankow, Lena; Kaiser, Gabriele; Busse, Andreas; König, Johannes; Blömeke, Sigrid; Hoth, Jessica; Döhrmann, Martina

2016-01-01

The paper presents results from a computer-based assessment in which 171 early career mathematics teachers from Germany were asked to anticipate typical student errors on a given mathematical topic and identify them under time constraints. Fast and accurate perception and knowledge-based judgments are widely accepted characteristics of teacher…

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

ERIC Educational Resources Information Center

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

Analysing the Correlation between Secondary Mathematics Curriculum Change and Trends in Beginning Undergraduates' Performance of Basic Mathematical Skills in Ireland

ERIC Educational Resources Information Center

Treacy, Páraic; Faulkner, Fiona; Prendergast, Mark

2016-01-01

The phenomenon in which students enter university under-prepared for the mathematical demands of their undergraduate courses, regularly referred to as the 'Maths Problem', has been widely reported in Ireland, UK, Australia, and the US. This issue has been of particular concern in Ireland recently, with beginning undergraduates' performance of…

A Comparison of Teacher and Lecturer Perspectives on the Transition from Secondary to Tertiary Mathematics Education

ERIC Educational Resources Information Center

Hong, Ye Yoon; Kerr, Suzanne; Klymchuk, Sergiy; McHardy, Johanna; Murphy, Priscilla; Spencer, Sue; Thomas, Michael O. J.; Watson, Peter

2009-01-01

The transition from school to tertiary study of mathematics comes under increasing scrutiny in research. This article reports on some findings from a project analysing the transition from secondary to tertiary education in mathematics. One key variable in this transition is the teacher or lecturer. This article deals with a small part of the data…

Pokémon Battles as a Context for Mathematical Modeling

ERIC Educational Resources Information Center

McGuffey, William

2017-01-01

In this article I explore some of the underlying mathematics of Poke´mon battles and describe ways that teachers at the secondary level could explore concepts of mathematical game theory in this context. I discuss various ways of representing and analyzing a Poke´mon battle using game theory and conclude with an example of applying concepts of…

Proceedings of the International Conference of the International Group for the Psychology of Mathematics Education (8th, Sydney, Australia, August 16-19, 1984).

ERIC Educational Resources Information Center

Southwell, Beth, Ed.; And Others

This document contains 53 plenary and contributed papers presented at the eighth Psychology of Mathematics Education (PME) meeting. Two plenary addresses focused on mathematics research in Australia and Japan, and problem solving and symbolism. Contributed papers were classified under 13 headings including: teaching and learning theory; cognition;…

Building innovative and creative character through mathematics

NASA Astrophysics Data System (ADS)

Suyitno, Hardi; Suyitno, Amin

2018-03-01

21st century is predicted as the century with rapid development in all aspects of life. People require creative and innovative character to exist. Specifically, mathematics has been given to students from the kindergarten until the middle school. Thus, building character through mathematics should begin since the early age. The problem is how to build creative and innovative character through mathematics education? The goal expected from this question is to build innovative and creative characters to face the challenges of the 21st century. This article discusses the values of mathematics, the values in mathematics education, innovative and creative character, and the integration of these values in teaching mathematics that support the innovative and creative character building, and applying the values in structurely programmed, measurable, and applicable learning activities.

Laser-induced plasma spectroscopy (LIPS): use of a geological tool in assessing bone mineral content.

PubMed

Andrássy, László; Gomez, Izabella; Horváth, Ágnes; Gulyás, Katalin; Pethö, Zsófia; Juhász, Balázs; Bhattoa, Harjit Pal; Szekanecz, Zoltan

2018-02-17

Bone may be similar to geological formulations in many ways. Therefore, it may be logical to apply laser-based geological techniques in bone research. The mineral and element oxide composition of bioapatite can be estimated by mathematical models. Laser-induced plasma spectrometry (LIPS) has long been used in geology. This method may provide a possibility to determine the composition and concentration of element oxides forming the inorganic part of bones. In this study, we wished to standardize the LIPS technique and use mathematical calculations and models in order to determine CaO distribution and bone homogeneity using bovine shin bone samples. We used polished slices of five bovine shin bones. A portable LIPS instrument using high-power Nd++YAG laser pulses has been developed (OpLab, Budapest). Analysis of CaO distribution was carried out in a 10 × 10 sampling matrix applying 300-μm sampling intervals. We assessed both cortical and trabecular bone areas. Regions of interest (ROI) were determined under microscope. CaO peaks were identified in the 200-500 nm wavelength range. A mathematical formula was used to calculate the element oxide composition (wt%) of inorganic bone. We also applied two accepted mathematical approaches, the Bartlett's test and frequency distribution curve-based analysis, to determine the homogeneity of CaO distribution in bones. We were able to standardize the LIPS technique for bone research. CaO concentrations in the cortical and trabecular regions of B1-5 bones were 33.11 ± 3.99% (range 24.02-40.43%) and 27.60 ± 7.44% (range 3.58-39.51%), respectively. CaO concentrations highly corresponded to those routinely determined by ICP-OES. We were able to graphically demonstrate CaO distribution in both 2D and 3D. We also determined possible interrelations between laser-induced craters and bone structure units, which may reflect the bone structure and may influence the heterogeneity of CaO distributions. By using two different statistical methods, we could confirm if bone samples were homogeneous or not with respect to CaO concentration distribution. LIPS, a technique previously used in geology, may be included in bone research. Assessment of element oxide concentrations in the inorganic part of bone, as well as mathematical calculations may be useful to determine the content of CaO and other element oxides in bone, further analyze bone structure and homogeneity and possibly apply this research to normal, as well as diseased bones.

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Mathematical Description of Dendrimer Structure

NASA Technical Reports Server (NTRS)

Majoros, Istvan J.; Mehta, Chandan B.; Baker, James R., Jr.

2004-01-01

Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.

Discrete structures in continuum descriptions of defective crystals.

PubMed

Parry, G P

2016-04-28

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular, I provide a quite general list of 'plastic strain variables', which quantifies inelastic behaviour, and exhibit rigorous connections between discrete and continuous mathematical structures associated with crystalline materials that have a correspondingly general constitutive specification. © 2016 The Author(s).

Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?

PubMed

Muñoz-Tamayo, R; Puillet, L; Daniel, J B; Sauvant, D; Martin, O; Taghipoor, M; Blavy, P

2018-04-01

What is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODEs) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and, moreover, highly informative experiments via optimal experiment design. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design.

Examining the Interactions between Mathematical Content and Pedagogical Form: Notes on the Structure of the Lesson

ERIC Educational Resources Information Center

Karp, Alexander

2004-01-01

Research conducted during the Trends in International Mathematics and Science Study (TIMSS) and later (Stigler et al. 1999; Stigler and Hiebert 1999) undertook a thorough analysis of lessons in the United States, Japan, and Germany. This article focuses on certain aspects of mathematics lessons in Russia. Specifically, the attempt is made to…

The Acquisition of Problem-Solving Skills in Mathematics: How Animations Can Aid Understanding of Structural Problem Features and Solution Procedures

ERIC Educational Resources Information Center

Scheiter, Katharina; Gerjets, Peter; Schuh, Julia

2010-01-01

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

Developing Mathematical Knowledge and Skills through the Awareness Approach of Teaching and Learning

ERIC Educational Resources Information Center

Cherif, Abour H.; Gialamas, Stefanos; Stamati, Angeliki

2017-01-01

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

Separate but Correlated: The Latent Structure of Space and Mathematics across Development

ERIC Educational Resources Information Center

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

2016-01-01

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…

Structural Model of the Effects of Cognitive and Affective Factors on the Achievement of Arabic-Speaking Pre-Service Teachers in Introductory Statistics

ERIC Educational Resources Information Center

Nasser, Fadia M.

2004-01-01

This study examined the extent to which statistics and mathematics anxiety, attitudes toward mathematics and statistics, motivation and mathematical aptitude can explain the achievement of Arabic speaking pre-service teachers in introductory statistics. Complete data were collected from 162 pre-service teachers enrolled in an academic…