Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Interpretations of National Curricula: the case of geometry in textbooks from England and Japan

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.     

Asymptotic behavior of the correlation coefficients of transverse momenta in the model with string fusion

In the framework of the model with fusion of quark–gluon strings on the transverse lattice, we find the asymptotic behavior of the correlation coefficients between observables in separated rapidity intervals with a high string density in a realistic case with an inhomogeneous distribution of strings in the impact parameter plane. We calculate the asymptotic forms for three types of correlations: between the average transverse momenta of particles with rapidity in these intervals, between the average transverse momentum of particles in one rapidity interval and the multiplicity of particles in another, and also between the multiplicities of charged particles in these intervals. We show that the previously found independence of the asymptotic form of the correlation coefficient between the average transverse momenta from the variance in the number of particles produced in string fragmentation holds only in the case of a uniform distribution of strings in the transverse plane. We also show that the found general expressions for the long-range correlation coefficients in the particular case with a uniform distribution of strings in the transverse plane become the formulas previously obtained by another method applicable only in this simple case.     

Education for Operational Research. A Practitioner's Viewpoint

University education for operational research in Britain is making great and welcome strides forward, but there has been little open discussion of its aims in relation to the advance of the profession. Progress in operational research, and in its application to the really worth-while problems of industry in particular, depends primarily on strengthening the industrial operational research group in its “front line” role. We need a research study of the teaching and practice of industrial operational research, in relation to effectiveness. We need “collaborative” programmes of operational research education in which the university and the industrial operational research group each contribute, in a man's training over a period of years, in the ways in which each is most competent. We need emphasis on “breadth” as well as “depth” in operational research education, and greater attention to the mutual contributions of operational research, teaching and practice, and the teaching and development of management. An impressionist sketch of a programme which might meet these needs is put forward for discussion of principles and feasibility.     

On Problems in the Calculus of Variations in Increasingly Elongated Domains

This paper deals with minimization problems in the calculus of variations set in a sequence of domains, the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain constant. The authors study the asymptotic behavior of minimizers in various situations and show that they converge in an appropriate sense toward minimizers of a related energy functional in the constant directions.     

The Development of Comprehension of Chance Language: Evaluation and Interpretation

Comprehension of chance language, such as is found in newspapers, is a fundamental aspect of statistical literacy. In this study, students' understandings of chance language were explored through responses to two items in surveys administered to 2,726 students from grades 5 to 11. One item involved evaluating the chance expressed in phrases from newspaper headlines using a number line, and responses were described in four levels of chance language evaluation. The other item involved interpreting, in context, an expression of percent chance, and responses were described in four levels of chance language interpretation. Students in higher grades were more likely to demonstrate higher levels of both evaluation and interpretation. The association between levels of evaluation and interpretation was further explored generally and in relation to one of the headlines involving percent. Implications for mathematics educators in relation to chance language in the curriculum across the years of schooling are discussed.     

Reasoning about variation in the intensity of change in covarying quantities involved in rate of change

This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual could simultaneously attend to variation in the intensity of change in a quantity indicating a relationship between covarying quantities. The results document how a secondary student, prior to formal instruction in calculus, reasoned numerically and nonnumerically about covarying quantities involved in rate of change in a way that was mathematically powerful and yet not ratio-based. I discuss how coordinating covariational and transformational reasoning supports attending to variation in the intensity of change in quantities involved in rate of change.     

On slice hyperholomorphic fractional Hardy spaces

In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball.     

基于平行DEA模型的我国小学教育资源配置效率分析

小学教育是教育阶段的基础,也是我国强制教育的一部分。但如何在各省份性别比例相差较大的情况下,更加有效的提高各省份小学教育资源配置效率是一个值得思考的问题。为了避免性别带来的影响,可以通过平行结构DEA模型根据学生性别分为两个平行子系统,来衡量我国2012~2018年各省份小学教育的资源配置情况。研究发现大部分省份小学教育资源配置的总系统效率未达到有效边界,仍有需要改进的地方。男学生在小学教育阶段的效率通常优于女学生在小学教育阶段的效率,但随着近些年我国教育体制的日益完善,女学生在小学教育阶段的效率呈上升趋势。此外,我国西部地区的小学教育资源配置效率在一些年份普遍优于东部和中部地区,而中部地区和东部地区小学教育总系统效率相对稳定,西部地区小学教育总系统效率波动较大。     

Exponential dispersion relation and its effects on unstable propagating pulses in unidirectionally coupled symmetric bistable elements

The propagation of pulses in unidirectionally coupled symmetric bistable elements is studied. The speeds of unstable traveling pulse waves in a ring of elements increase with pulse width in an exponential manner. This dispersion relation causes exponential increases in the duration of transient propagating pulses and the noise-sustained propagation of pulses, which are qualitatively the same as those in a reaction-diffusion-convection equation and a ring of sigmoidal neurons. However, the speeds of pulse fronts in propagating pulses depend on the backward pulse width. Properties of pulse transmission in an open chain of elements then differ from those in the above two systems qualitatively.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

Rolling in the Higgs model and elliptic functions

Asymptotic methods in nonlinear dynamics such as, for example, the Krylov-Bogoliubov averaging method and the KAM theory are commonly used to improve perturbation theory results in the regime of small oscillations. But for a series of problems in nonlinear dynamics, in particular, for the Higgs equation in field theory, not only the small-oscillation regime but also the rolling regime is of interest. Both slow- and fast-rolling regimes are important in the Friedmann cosmology. We present an asymptotic method for solving the Higgs equation in the rolling regime. We show that to improve the perturbation theory in the rolling regime, expanding a solution known in terms of elliptic functions not in trigonometric functions (as with the averaging method in the small-oscillation regime) but in hyperbolic functions turns out to be effective. We estimate the accuracy of the second approximation. We also investigate the Higgs equation with damping.     

Solution Blowup for Nonlinear Equations of the Khokhlov–Zabolotskaya Type

We consider several nonlinear evolution equations sharing a nonlinearity of the form ?²u²/?t². Such a nonlinearity is present in the Khokhlov–Zabolotskaya equation, in other equations in the theory of nonlinear waves in a fluid, and also in equations in the theory of electromagnetic waves and ion–sound waves in a plasma. We consider sufficient conditions for a blowup regime to arise and find initial functions for which a solution understood in the classical sense is totally absent, even locally in time, i.e., we study the problem of an instantaneous blowup of classical solutions.     

Multiple structural changes in the tail behavior: Evidence from stock index futures returns

The study provides an approach of nonlinear analysis for detecting multiple structural changes in the tails of financial returns distributions. The proposed approach can simultaneously determine the number of structural breaks in a series of tail-indexes and estimate the mean tail-index levels in distinct regimes. The method is applied to the tail behavior of DJIA futures returns. The sample period covered various recent financial crises, and ran from October 1999 to December 2003, enabling assessment of the relationships between changes in the tail shape of returns distribution and known extreme events in financial markets. The empirical results demonstrate the existence of at least one break point in the left and common tails of the DJIA futures returns distribution during the sample period, and the mean tail-index levels in different regimes classified by estimated break points display an increase in the left and common tails that coincides the phenomenon of gradually decreasing financial turbulence in DJIA futures contracts. The empirical evidence indicates that the structural changes in the tail behavior of the distribution of DJIA futures returns are associated more with negative shocks than positive ones, creating differences in risk management between long and short investors in futures markets.     

Complex Strategic Analysis: A Hypergame Study of the Fall of France

It is argued that a crucial element in decision-making in conflicts is the need for adequate conceptual complexity in problem formulation. This is illustrated by reference to a disastrous military failure—the fall of France in 1940. A formal model of the strategic situation is constructed using the Hypergame approach, in which the usual game-theoretic assumption that all "players" see the same "game" is discarded. Using this model, further features of the case are explored, and some general conclusions discussed. It is suggested that Hypergame analysis can be of assistance in achieving adequate levels of problem-perception in complex, conflict-prone environments, in particular by helping in the generation of multiple models.     

Representations of Nature of Science in Selected Histories of Science in the Integrated Science Textbooks in China

This study aimed to examine the representations of nature of science (NOS) in the eight histories of science selected from three series of integrated science textbooks used in junior high school in China. Ten aspects of NOS were adopted in the analytical framework. It was found that NOS had not been well treated in the selected histories of science in the three series of science textbooks. Specifically, it was found that the empirical and inferential aspects were treated better than other aspects, and discrepancies existed among the three series of science textbooks and among the eight histories of science in terms of dealing with the target NOS aspects. Implications for addressing NOS in historical materials in science textbooks were discussed in the final part of this paper.     

Trends in basic mathematical competencies of beginning undergraduates in Ireland, 2003–2013

Deficiencies in beginning undergraduate students’ basic mathematical skills has been an issue of concern in higher education, particularly in the past 15 years. This issue has been tracked and analysed in a number of universities in Ireland and internationally through student scores recorded in mathematics diagnostic tests. Students beginning their science-based and technology-based undergraduate courses in the University of Limerick have had their basic mathematics skills tested without any prior warning through a 40 question diagnostic test during their initial service mathematics lecture since 1998. Data gathered through this diagnostic test have been recorded in a database kept at the university and explored to track trends in mathematical competency of these beginning undergraduates. This paper details findings surrounding an analysis of the database between 2003 and 2013, outlining changes in mathematical competencies of these beginning undergraduates in an attempt to determine reasons for such changes. The analysis found that the proportion of students tested through this diagnostic test that are predicted to be at risk of failing their service mathematics end-of-semester examinations has increased significantly between 2003 and 2013. Furthermore, when students' performance in secondary level mathematics was controlled, it was determined that the performance of beginning undergraduates in 2013 was statistically significantly below that of the performance of the beginning undergraduates recorded 10 years previously.