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## Mathematics
Kinds of Mathematics
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## Selected Abstracts## MATHEMATICS OF KIN- AND GROUP-SELECTION: FORMALLY EQUIVALENT? EVOLUTION, Issue 2 2010Arne TraulsenEvolutionary game theory is a general mathematical framework that describes the evolution of social traits. This framework forms the basis of many multilevel selection models and is also frequently used to model evolutionary dynamics on networks. Kin selection, which was initially restricted to describe social interactions between relatives, has also led to a broader mathematical approach, inclusive fitness, that can not only describe social evolution among relatives, but also in group structured populations or on social networks. It turns out that the underlying mathematics of game theory is fundamentally different from the approach of inclusive fitness. Thus, both approaches,evolutionary game theory and inclusive fitness,can be helpful to understand the evolution of social traits in group structured or spatially extended populations. [source] ## ON NATURALIZING THE EPISTEMOLOGY OF MATHEMATICS PACIFIC PHILOSOPHICAL QUARTERLY, Issue 1 2009JEFFREY W. ROLANDIn this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered. [source] ## A digital simulation of the vibration of a two-mass two-spring system COMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 3 2010Wei-Pin LeeAbstract In this study, we developed a computer program to simulate the vibration of a two-mass two-spring system by using Visual BASIC. Users can enter data for the two-mass two-spring system. The software will derive the eigenvalue problem from the input data. Then the software solves the eigenvalue problem and illustrates the results numerically and graphically on the screen. In addition, the program uses animation to demonstrate the motions of the two masses. The displacements, velocities, and accelerations of the two bodies can be shown if the corresponding checkboxes are selected. This program can be used in teaching courses, such as Linear Algebra, Advanced Engineering Mathematics, Vibrations, and Dynamics. Use of the software may help students to understand the applications of eigenvalue problems and related topics such as modes of vibration, natural frequencies, and systems of differential equations. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 563,573, 2010; View this article online at wileyonlinelibrary.com; DOI 10.1002/cae.20241 [source] ## Framing French Success in Elementary Mathematics: Policy, Curriculum, and Pedagogy CURRICULUM INQUIRY, Issue 3 2004FRANCES C. FOWLERABSTRACT For many decades Americans have been concerned about the effective teaching of mathematics, and educational and political leaders have often advocated reforms such as a return to the basics and strict accountability systems as the way to improve mathematical achievement. International studies, however, suggest that such reforms may not be the best path to successful mathematics education. Through this qualitative case study, the authors explore in depth the French approach to teaching elementary mathematics, using interviews, classroom observations, and documents as their data sets. They apply three theoretical frameworks to their data and find that the French use large-group instruction and a visible pedagogy, focusing on the discussion of mathematical concepts rather than on the completion of practice exercises. The national curriculum is relatively nonprescriptive, and teachers are somewhat empowered through site-based management. The authors conclude that the keys to French success with mathematics education are ongoing formative assessment, mathematically competent teachers, policies and practices that help disadvantaged children, and the use of constructivist methods. They urge comparative education researchers to look beyond international test scores to deeper issues of policy and practice. [source] ## A Perspective on Achieving Equality in Mathematics for Fourth Grade Girls: A Special Case CURRICULUM INQUIRY, Issue 2 2001Christine G. RenneHow can and do teachers create equal access within everyday classroom lessons and establish opportunities for girls to participate fully? What contexts contribute to equity? In contrast to classrooms where boys receive more attention, encouragement, and content-area instruction, Ms. Jeffreys conducts whole class lessons in her fourth grade classroom where girls participate equally and successfully with boys during mathematics. To ascertain what contributes to the equal participation, I use interactional analysis to closely examine two mathematics lessons. Part of Ms. Jeffreys' success lies in altering normative classroom discourse and in the assertive context created and sustained by the math, science, and technology magnet school setting. However, another layer of complexity is introduced: to teach her students at their instructional level, Ms. Jeffreys groups her students by their ability to pass timed multiplication tests. By instituting a form of tracking, Ms. Jeffreys also legitimates girls as knowledgeable, both socially and academically, by their membership in the top math group. While policy guidelines exhort teachers to provide equal access to curriculum, actually accomplishing a first step of access to participation in the routine day-to-day classroom talk remains extremely difficult. [source] ## Mathematics for Humans: Kant's Philosophy of Arithmetic Revisited EUROPEAN JOURNAL OF PHILOSOPHY, Issue 3 2002Robert HannaFirst page of article [source] ## p-FEM2000,International Conference on p and hp Finite Element Methods: Mathematics and Engineering Practice INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2002Guest Editor, Zohar Yosibash Conference ChairmanNo abstract is available for this article. [source] ## On pressure separation algorithms (PSepA) for improving the accuracy of incompressible flow simulations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009S. TurekAbstract We investigate a special technique called ,pressure separation algorithm' (PSepA) (see Applied Mathematics and Computation 2005; 165:275,290 for an introduction) that is able to significantly improve the accuracy of incompressible flow simulations for problems with large pressure gradients. In our numerical studies with the computational fluid dynamics package FEATFLOW (www.featflow.de), we mainly focus on low-order Stokes elements with nonconforming finite element approximations for the velocity and piecewise constant pressure functions. However, preliminary numerical tests show that this advantageous behavior can also be obtained for higher-order discretizations, for instance, with Q2/P1 finite elements. We analyze the application of this simple, but very efficient, algorithm to several stationary and nonstationary benchmark configurations in 2D and 3D (driven cavity and flow around obstacles), and we also demonstrate its effect to spurious velocities in multiphase flow simulations (,static bubble' configuration) if combined with edge-oriented, resp., interior penalty finite element method stabilization techniques. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Positive-definite q -families of continuous subcell Darcy-flux CVD(MPFA) finite-volume schemes and the mixed finite element method INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Michael G. EdwardsAbstract A new family of locally conservative cell-centred flux-continuous schemes is presented for solving the porous media general-tensor pressure equation. A general geometry-permeability tensor approximation is introduced that is piecewise constant over the subcells of the control volumes and ensures that the local discrete general tensor is elliptic. A family of control-volume distributed subcell flux-continuous schemes are defined in terms of the quadrature parametrization q (Multigrid Methods. Birkhauser: Basel, 1993; Proceedings of the 4th European Conference on the Mathematics of Oil Recovery, Norway, June 1994; Comput. Geosci. 1998; 2:259,290), where the local position of flux continuity defines the quadrature point and each particular scheme. The subcell tensor approximation ensures that a symmetric positive-definite (SPD) discretization matrix is obtained for the base member (q=1) of the formulation. The physical-space schemes are shown to be non-symmetric for general quadrilateral cells. Conditions for discrete ellipticity of the non-symmetric schemes are derived with respect to the local symmetric part of the tensor. The relationship with the mixed finite element method is given for both the physical-space and subcell-space q -families of schemes. M -matrix monotonicity conditions for these schemes are summarized. A numerical convergence study of the schemes shows that while the physical-space schemes are the most accurate, the subcell tensor approximation reduces solution errors when compared with earlier cell-wise constant tensor schemes and that subcell tensor approximation using the control-volume face geometry yields the best SPD scheme results. A particular quadrature point is found to improve numerical convergence of the subcell schemes for the cases tested. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Creative Mathematics by H. S. Wall INTERNATIONAL STATISTICAL REVIEW, Issue 3 2009Jorma Kaarlo MerikoskiNo abstract is available for this article. [source] ## Mathematics and Common Sense: A Case of Creative Tension by Philip J. Davis INTERNATIONAL STATISTICAL REVIEW, Issue 2 2007Jorma Kaarlo MerikoskiNo abstract is available for this article. [source] ## Mathematics for Biological Scientists JOURNAL OF ANATOMY, Issue 4 2010Michael DoubeNo abstract is available for this article. [source] ## Trends of the bonding effect on the performance of DFT methods in electric properties calculations: A pattern recognition and metric space approach on some XY2 (X = O, S and Y = H, O, F, S, Cl) molecules JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 2 2010Christos ChristodouleasAbstract A test set of 10 molecules (open and ring forms of ozone and sulfur dioxide as well as water and hydrogen sulfide and their respective fluoro- and chloro-substituted analogs) of specific atmospheric interest has been formed as to assess the performance of various density functional theory methods in (hyper)polarizability calculations against well-established ab initio methods. The choice of these molecules was further based on (i) the profound change in the physics between isomeric systems, e.g., open (C2v) and ring (D3h) forms of ozone, (ii) the relation between isomeric forms, e.g., open and ring form of sulfur dioxide (both of C2v symmetry), and (iii) the effect of the substitution, e.g., in fluoro- and chloro-substituted water analogs. The analysis is aided by arguments chosen from the information theory, graph theory, and pattern recognition fields of Mathematics: In brief, a multidimensional space is formed by the methods which are playing the role of vectors with the independent components of the electric properties to act as the coordinates of these vectors, hence the relation between different vectors (e.g., methods) can be quantified by a proximity measure. Results are in agreement with previous studies revealing the acceptable and consistent behavior of the mPW1PW91, B3P86, and PBE0 methods. It is worth noting the remarkable good performance of the double hybrid functionals (namely: B2PLYP and mPW2PLYP) which are for the first time used in calculations of electric response properties. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010 [source] ## The Utility of Third International Mathematics and Science Study Scales in Predicting Students' State Examination Performance JOURNAL OF EDUCATIONAL MEASUREMENT, Issue 4 2004Nick SofroniouTo examine the predictive utility of three scales provided in the released database of the Third International Mathematics and Science Study (TIMSS) (international plausible values, standardized percent correct score, and national Rasch score), information was obtained on the performance in state examinations in mathematics and science in 1996 (2,969 Grade 8 students) and in 1997 (2,898 Grade 7 students) of students in the Republic of Ireland who had participated in TIMSS in 1995. Performance on TIMSS was related to later performance in the state examinations using normal and nonparametric maximum likelihood (NPML) random effects models. In every case, standardized percent correct scores were found to be the best predictors of later performance, followed by national Rasch scores, and lastly, by international plausible values. The estimates for normal mixing distributions are close to those estimated by the NPML approach, lending support to the validity of estimates. [source] ## Constructing a Universal Scale of High School Course Difficulty JOURNAL OF EDUCATIONAL MEASUREMENT, Issue 2 2003Dina BassiriThis study examined the usefulness of applying the Rasch rating scale model (Andrich, 1978) to high school grade data. ACT Assessment test scores (English, Mathematics, Reading, and Science Reasoning) were used as "common items" to adjust for different grading standards in individual high school courses both within and across schools. This scaling approach yielded an ACT Assessment-adjusted high school grade point average (AA-HSGPA) on a common scale across high schools and cohorts within a large public university. AA-HSGPA was a better predictor of first-year college grade point average (CGPA) than the regular high school grade point average. The best model for predicting CGPA included both the ACT composite score and AA-HSGPA. [source] ## An Empirical Investigation Demonstrating the Multidimensional DIF Paradigm: A Cognitive Explanation for DIF JOURNAL OF EDUCATIONAL MEASUREMENT, Issue 2 2001Cindy M. WalkerDifferential Item Functioning (DIF) is traditionally used to identify different item performance patterns between intact groups, most commonly involving race or sex comparisons. This study advocates expanding the utility of DIF as a step in construct validation. Rather than grouping examinees based on cultural differences, the reference and focal groups are chosen from two extremes along a distinct cognitive dimension that is hypothesized to supplement the dominant latent trait being measured. Specifically, this study investigates DIF between proficient and non-proficient fourth- and seventh-grade writers on open-ended mathematics test items that require students to communicate about mathematics. It is suggested that the occurrence of DIF in this situation actually enhances, rather than detracts from, the construct validity of the test because, according to the National Council of Teachers of Mathematics (NCTM), mathematical communication is an important component of mathematical ability, the dominant construct being assessed. However, the presence of DIF influences the validity of inferences that can be made from test scores and suggests that two scores should be reported, one for general mathematical ability and one for mathematical communication. The fact that currently only one test score is reported, a simple composite of scores on multiple-choice and open-ended items, may lead to incorrect decisions being made about examinees. [source] ## Identifying Sources of Differential Item and Bundle Functioning on Translated Achievement Tests: A Confirmatory Analysis JOURNAL OF EDUCATIONAL MEASUREMENT, Issue 2 2001Mark J. GierlIncreasingly, tests are being translated and adapted into different languages. Differential item functioning (DIF) analyses are often used to identify non-equivalent items across language groups. However, few studies have focused on understanding why some translated items produce DIF. The purpose of the current study is to identify sources of differential item and bundle functioning on translated achievement tests using substantive and statistical analyses. A substantive analysis of existing DIF items was conducted by an 11-member committee of testing specialists. In their review, four sources of translation DIF were identified. Two certified translators used these four sources to categorize a new set of DIF items from Grade 6 and 9 Mathematics and Social Studies Achievement Tests. Each item was associated with a specific source of translation DIF and each item was anticipated to favor a specific group of examinees. Then, a statistical analysis was conducted on the items in each category using SIBTEST. The translators sorted the mathematics DIF items into three sources, and they correctly predicted the group that would be favored for seven of the eight items or bundles of items across two grade levels. The translators sorted the social studies DIF items into four sources, and they correctly predicted the group that would be favored for eight of the 13 items or bundles of items across two grade levels. The majority of items in mathematics and social studies were associated with differences in the words, expressions, or sentence structure of items that are not inherent to the language and/or culture. By combining substantive and statistical DIF analyses, researchers can study the sources of DIF and create a body of confirmed DIF hypotheses that may be used to develop guidelines and test construction principles for reducing DIF on translated tests. [source] ## Between ends and fibers JOURNAL OF GRAPH THEORY, Issue 2 2007C. Paul BonningtonAbstract Let , be an infinite, locally finite, connected graph with distance function ,. Given a ray P in , and a constant C , 1, a vertex-sequence is said to be regulated by C if, for all n,,, never precedes xn on P, each vertex of P appears at most C times in the sequence, and . R. Halin (Math. Ann., 157, 1964, 125,137) defined two rays to be end-equivalent if they are joined by infinitely many pairwise-disjoint paths; the resulting equivalence classes are called ends. More recently H. A. Jung (Graph Structure Theory, Contemporary Mathematics, 147, 1993, 477,484) defined rays P and Q to be b-equivalent if there exist sequences and VQ regulated by some constant C , 1 such that for all n,,; he named the resulting equivalence classes b-fibers. Let denote the set of nondecreasing functions from into the set of positive real numbers. The relation (called f-equivalence) generalizes Jung's condition to . As f runs through , uncountably many equivalence relations are produced on the set of rays that are no finer than b -equivalence while, under specified conditions, are no coarser than end-equivalence. Indeed, for every , there exists an "end-defining function" that is unbounded and sublinear and such that implies that P and Q are end-equivalent. Say if there exists a sublinear function such that . The equivalence classes with respect to are called bundles. We pursue the notion of "initially metric" rays in relation to bundles, and show that in any bundle either all or none of its rays are initially metric. Furthermore, initially metric rays in the same bundle are end-equivalent. In the case that , contains translatable rays we give some sufficient conditions for every f -equivalence class to contain uncountably many g -equivalence classes (where ). We conclude with a variety of applications to infinite planar graphs. Among these, it is shown that two rays whose union is the boundary of an infinite face of an almost-transitive planar map are never bundle- equivalent. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 125,153, 2007 [source] ## Mathematics in chemical engineering: A 50 year introspection AICHE JOURNAL, Issue 1 2004Doraiswami RamkrishnaAbstract A review is made of the role of mathematics in the field of chemical engineering in the latter half of the twentieth century. The beginning of this era was marked by the concerted effort of a few to raise the mathematical consciousness of the profession to think fundamentally about processes. We have accomplished this review by providing a rough structure of the areas of mathematics, deliberating on how each area has matured through growing applications, to conclude that mathematics is the main medium to meditate not only about processes, but even about materials and products. As we are clearly entering another era where the domain of chemical engineering is expanding into new areas with a focus on discovery oriented high throughput technology, modeling and rapid computation must provide the guidelines for rational interpretation of multitudes of observations. © 2004 American Institute of Chemical Engineers AIChE J, 50: 7,23, 2004 [source] ## PISA 2006: An assessment of scientific literacy JOURNAL OF RESEARCH IN SCIENCE TEACHING, Issue 8 2009Rodger BybeeAbstract This article introduces the essential features of the science component of 2006 Program for International Student Assessment (PISA). Administered every 3 years, PISA alternates emphasis on Reading, Mathematics, and Science Literacy. In 2006, PISA emphasized science. This article discusses PISA's definition of scientific literacy, the three competencies that constitute scientific literacy, the contexts used for assessment units and items, the role of scientific knowledge, and the importance placed on attitude toward science. PISA 2006 included a student test, a student questionnaire, and a questionnaire for school administrators. The student test employed a balanced incomplete block design involving thirteen 30-minute clusters of items, including nine science clusters. The 13 clusters were arranged into thirteen 2-hour booklets and each sampled student was assigned one booklet at random. Mean literacy scores are presented for all participating countries, and the percentages of OECD students at the six levels of proficiency are given for the combined scale and for the competency scales. © 2009 Wiley Periodicals, Inc. J Res Sci Teach 46: 865,883, 2009 [source] ## Using data mining to predict K,12 students' performance on large-scale assessment items related to energy JOURNAL OF RESEARCH IN SCIENCE TEACHING, Issue 5 2008Xiufeng LiuThis article reports a study on using data mining to predict K,12 students' competence levels on test items related to energy. Data sources are the 1995 Third International Mathematics and Science Study (TIMSS), 1999 TIMSS-Repeat, 2003 Trend in International Mathematics and Science Study (TIMSS), and the National Assessment of Educational Progress (NAEP). Student population performances, that is, percentages correct, are the object of prediction. Two data mining algorithms, C4.5 and M5, are used to construct a decision tree and a linear function to predict students' performance levels. A combination of factors related to content, context, and cognitive demand of items and to students' grade levels are found to predict student population performances on test items. Cognitive demands have the most significant contribution to the prediction. The decision tree and linear function agree with each other on predictions. We end the article by discussing implications of findings for future science content standard development and energy concept teaching. © 2007 Wiley Periodicals, Inc. J Res Sci Teach 45: 554,573, 2008 [source] ## Undergraduates' attitudes and beliefs about subject matter and pedagogy measured periodically in a reform-based mathematics and science teacher preparation program JOURNAL OF RESEARCH IN SCIENCE TEACHING, Issue 8 2002J. Randy McGinnisThis study describes the design and use of a valid and reliable instrument to measure teacher candidates' attitudes and beliefs about mathematics and science and the teaching of those subjects. The instrument, Attitudes and Beliefs about the Nature of and the Teaching of Mathematics and Science, was developed for the Maryland Collaborative for Teacher Preparation (MCTP), a statewide, standards-based project in the National Science Foundation's Collaborative in Excellence in Teaching Preparation (CETP) Program. We report on two applications of the instrument: (a) a contrast between MCTP teacher candidates' and non-MCTP teacher candidates' attitudes and beliefs about mathematics and science as they initially encountered reform-based instruction in their undergraduate courses, and (b) a landscaping of how the MCTP teacher candidates' attitudes toward and beliefs about mathematics and science evolved over a 2.5-year period. In support of current reform in science and mathematics teacher education, we determined that over an extended period the MCTP teacher candidates' attitudes and beliefs moved substantively and significantly in the direction intended. However, we also found that the non-MCTP teacher candidates in the same reform-based courses did not mirror this improvement in their attitudes and beliefs about mathematics and science or the teaching of those subjects. © 2002 Wiley Periodicals, Inc. J Res Sci Teach 39: 713,737, 2002 [source] ## Scopus's source normalized impact per paper (SNIP) versus a journal impact factor based on fractional counting of citations JOURNAL OF THE AMERICAN SOCIETY FOR INFORMATION SCIENCE AND TECHNOLOGY, Issue 11 2010Loet LeydesdorffImpact factors (and similar measures such as the Scimago Journal Rankings) suffer from two problems: (a) citation behavior varies among fields of science and, therefore, leads to systematic differences, and (b) there are no statistics to inform us whether differences are significant. The recently introduced "source normalized impact per paper" indicator of Scopus tries to remedy the first of these two problems, but a number of normalization decisions are involved, which makes it impossible to test for significance. Using fractional counting of citations,based on the assumption that impact is proportionate to the number of references in the citing documents,citations can be contextualized at the paper level and aggregated impacts of sets can be tested for their significance. It can be shown that the weighted impact of Annals of Mathematics (0.247) is not so much lower than that of Molecular Cell (0.386) despite a five-f old difference between their impact factors (2.793 and 13.156, respectively). [source] ## Extending Responsiveness to Intervention to Mathematics at First and Third Grades LEARNING DISABILITIES RESEARCH & PRACTICE, Issue 1 2007Lynn S. FuchsResponsiveness to intervention (RTI) is an innovative approach to the identification of learning disabilities (LD). The central assumption is that RTI can differentiate between two explanations for low achievement: poor instruction versus disability. If the child responds poorly to validated instruction, then the assessment eliminates instructional quality as a viable explanation for poor academic growth and instead provides evidence of a disability. For children who do respond nicely, RTI serves a critical prevention function. Most of RTI research has been focused on early reading. In this article, we describe two ongoing programs of research on RTI in the area of mathematics: one on a comprehensive mathematics curriculum at first grade and the other focused on word problems at third grade. For each research program, we describe the sample, explain how students are identified as at risk for mathematics disability, provide an overview of the interventions to which responsiveness is gauged, and describe some results to date. [source] ## Middle School Mathematics Teachers' Beliefs About Inclusion of Students with Learning Disabilities LEARNING DISABILITIES RESEARCH & PRACTICE, Issue 2 2006Janet R. DeSimoneThe purpose of this descriptive study was to investigate middle school general education mathematics teachers' beliefs and self-perceived knowledge regarding teaching students with learning disabilities (LD) in inclusive classrooms. Teacher beliefs regarding administrative support and higher education teacher preparation were also examined. The Survey on Teaching Mathematics to Students With Learning Disabilities in Middle School was completed by 228 sixth-, seventh-, and eighth-grade general education mathematics inclusion teachers from 19 states. In addition, telephone interviews were conducted with a subset of 26 survey respondents. Frequency analyses were performed on the survey data, with ,2 tests comparing teachers on demographic variables. Follow-up interview responses were summarized to elaborate on the major research questions. The findings revealed three central issues: (1) teachers had a limited understanding of the mathematics learning needs of students with LD, (2) teacher collaboration was judged to be the most beneficial and available resource by general educators teaching students with LD in inclusive mathematics classrooms, and (3) teachers did not feel that teacher education programs at the preservice level and professional development at the inservice level were adequate in preparing them for teaching students with LD in inclusive mathematics classrooms. Implications and recommendations for teacher preparation and program implementation are provided. [source] ## Promoting Strategic Learning by Eighth-Grade Students Struggling in Mathematics: A Report of Three Case Studies LEARNING DISABILITIES RESEARCH & PRACTICE, Issue 3 2005Deborah L. ButlerParticipants were three eighth-grade students enrolled in a learning assistance classroom who were of at least average intelligence but who were performing significantly below grade level in mathematics. These case studies document the processes by which these students were supported to self-regulate their learning in mathematics more effectively. We begin by outlining important instructional foci in mathematics education for intermediate or secondary students with learning disabilities, along with what research indicates are effective instructional processes. In that context, we introduce the theoretical principles underlying the instructional model used here,Strategic Content Learning (SCL). Based on analyses of case study data, we describe how SCL instruction was structured to promote strategic learning. Throughout the discussion, intervention processes are described in sufficient detail to be of use to practitioners. [source] ## Literacy in the secondary curriculum LITERACY, Issue 1 2001David WrayThe much-signalled extension of the National Literacy Strategy from primary to secondary schools is now in full swing and many secondary teachers are actively looking for practical guidance on ways forward with this national priority. One way of providing such guidance is to outline a common language with which secondary teachers of all subjects can discuss the role of literacy within their subjects. This article puts forward one possible way of developing this common language, by building on the work of Freebody and Luke (1990) in Australia who suggest a literacy resource model. This model is applied to the teaching of literacy within the three core subjects of English, Mathematics and Science. [source] ## Global existence of weak-type solutions for models of monotone type in the theory of inelastic deformations MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2002Krzysztof CheThis article introduces the notion of weak-type solutions for systems of equations from the theory of inelastic deformations, assuming that the considered model is of monotone type (for the definition see [Lecture Notes in Mathematics, 1998, vol. 1682]). For the boundary data associated with the initial-boundary value problem and satisfying the safe-load condition the existence of global in time weak-type solutions is proved assuming that the monotone model is rate-independent or of gradient type. Moreover, for models possessing an additional regularity property (see Section 5) the existence of global solutions in the sense of measures, defined by Temam in Archives for Rational Mechanics and Analysis, 95: 137, is obtained, too. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Beyond Conceptual Change: Using Representations to Integrate Domain-Specific Structural Models in Learning Mathematics MIND, BRAIN, AND EDUCATION, Issue 2 2007Florence Mihaela SingerABSTRACT, Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for promoting representational change across cognitive development. I provide an example of an integrated structural model that highlights the underlying cognitive structures that connect numbers, mathematical operations, and functions. The model emphasizes dynamic multiple representations that students can internalize within the number line and which lead to developing a dynamic mental structure. In teaching practice, the model focuses on a counting task format, which integrates a variety of activities, specifically addressing motor, visual, and verbal skills, as well as various types of learning transfer. [source] ## Mathematics in Economics: An Austrian Methodological Critique PHILOSOPHICAL INVESTIGATIONS, Issue 1 2010Robert WutscherEven the briefest and most superficial perusal of leading mainstream economics journals will attest to the degree that mathematical formalism has captured the economics profession. Whereas up to the early 20th century virtually all of the output of the dismal scientists was in the literary format, by the early 21st century this is not at all any longer the case. Mathematical formalism is supposed to serve economics, and yet now true economic insight has been crowded out by the math. If mainstream neoclassical economics is to come back to its proper path, a far less central role for mathematical economics, statistics and econometrics will have to be fashioned. [source] |