RESEARCH IN MATHEMATICS EDUCATION: SOME ISSUES AND SOME EMERGING INFLUENCES

In this article, I introduce a typology of forms of algebraic thinking. In the first part, I argue that the form and generality of algebraic thinking are characterised by the mathematical problem at hand and the embodied and other semiotic resources that are mobilised to tackle the problem in analytic ways. My claim is based not only on semiotic considerations but also on new theories of cognition that stress the fundamental role of the context, the body and the senses in the way in which we come to know. In the second part, I present some concrete examples from a longitudinal classroom research study through which the typology of forms of algebraic thinking is illustrated.     

A TRANSNATIONAL COMPARISON OF PRIMARY MATHEMATICS TEXTBOOKS: THE CASE OF MULTIPLICATION

This paper centres around a transnational comparison of primary mathematics textbooks. The focus is on the similarities and differences between the ways in which images related to multiplication are represented in textbooks. The results of the study show that the English and USA texts analysed place less emphasis on mathematical structure and the linking of mathematical representations than the texts from France, Hungary and Singapore.     

VISUALISATION AND THE INFLUENCE OF TECHNOLOGY IN ‘A’ LEVEL MATHEMATICS: A CLASSROOM INVESTIGATION

The study reported here is part of a wider study, which aims to investigate the potential of the graphical calculator for mediating the development of students’ abilities to visualise the graphs of functions at GCE Advanced level. This paper focuses on how the graphical calculator influenced six particular students’ work with functions. Initial results have illuminated ways in which the technology can have a positive impact on students’ visualisation capabilities. It is proposed that visual thinking forms a significant part of many students’ mathematical reasoning, enabling students to derive richer meaning from given problems. It is suggested further that use of the technology mediates the development of students’ visual capacities, by helping to highlight the links between complementary modes of representation.     

论事理数理学的发展

我们谈论事理数理学的发展 ,是对数学和运筹学发展简况的回顾后作出的 ,是以人们多年来逐步发现若干事理与数理有重要联系的经验为基础来谈论的。从这种观点来看 ,事理数理学的发展 ,尚处于初始阶段。从事理与数理的联系来研究问题 ,特别是研究经济发展中的理论问题 ,是大有可为的。这种研究 ,既要以经济中有关的经验、理论、统计资料为基础 ,又要有相应的计算手段 ,还要研究出一些新的数学理论和方法 ,特别是能用来处理有相互影响的数量关系的方法 ,以及用来研究包含有矛盾的事理的数学方法。本文在谈论事理数理学的一些初步研究经验之后 ,以山东大学运筹组的两项研究工作为例 ,谈谈一些实际的应用研究的经验。其中一项是在一定的简化了的情况下 ,从理论上论述如何能解决国家计划与市场经济结合的问题     

THE NATURE OF PARTICIPATION AFFORDED BY TASKS,QUESTIONS AND PROMPTS IN MATHEMATICS CLASSROOMS

This paper reports on the development of an analytical instrument which identifies mathematical affordances in the public tasks, questions and prompts of mathematics classrooms. The aim is to become more articulate about mathematical activity. I have explored the use of several frameworks which identify learning outcomes, structures of knowledge, mental actions, teaching actions and intentions and found that none of them give me access to the detail of what makes one mathematics lesson different from another for learners. From the experience of using these I devised a new analytical tool which unfolds patterns of participation afforded in mathematics lessons. This tool has been tested on several videos of lessons, and has been used by pre-service teaching students to analyse their own lessons.     

SCHOOL OR COLLEGE MATHEMATICS AND WORKPLACE PRACTICE: AN ACTIVITY THEORY PERSPECTIVE

This paper reports on a case study in which we detail how a college mathematics and chemistry student struggles to make sense of the graphical output of an experiment in an industrial chemistry laboratory. The student's attempts to interpret unfamiliar graphical conventions are described and contrasted with those of college mathematics. Our analysis of this draws on activity theory to assist in understanding the position of the student in both the college and the workplace. This highlights the limitations of the experience of the student at college and we question how the mathematics curriculum might be adapted to assist students in making sense of workplace graphical output.     

COMPARISON, SYMMETRY AND MONOTONICITY RESULTS FOR SOME DEGENERATE ELLIPTIC OPERATORS IN CARNOT－CARATHEODORY SPACES

This paper studies the properties of solutions of quasilinear equations involving the p-laplacian type operator in general Carnot-Caratheodory spaces.The authors show some com-parison results for solutions of the relevant differential inequalities and use them to get somesymmetry and monotonicity properties of solutions,in bounded or unbounded domains.     

AN IRREGULAR OBLIQUE DERIVATIVE PROBLEM FOR SOME NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

1FormulationofirregularObliqueDerivativeProblemLetDbean(N 1)-connecteddomainwithboundaryr=UU=,r,6Cj(0相似文献   

SOME CONDITIONS FOR THE EQUIVALENCE OF WEAK AND STRONG F-REGULARITY

ABSTRACT

We show that all forms of F-regularity are equivalent for rings in which a sufficiently large symbolic power of an anti-canonical ideal has small enough analytic spread. We also show that if R is weakly F-regular and has a two-generated anti-canonical ideal then R is strongly F-regular. Both of these results then have implications for the existence of test elements.     

多元位置和散布的 PP 型估计的几个性质

Donoho (1982)应用投影寻踪(Projection Pursuit)思想对多元位置和散布提出了一类仿射同变估计并讨论了其样本崩溃点.本文给出了相应于这类估计的度量多元位置和散布的泛函,讨论了其合理性和同变性,证明了该类泛函在一定条件下的弱连续性,从而得到这类估计的定性稳健性和相合性.     

多叶解析函数族子类的一些结果(英文)

本文研究了在单位开圆盘U={z:|z|1}内多叶解析的函数族G_(p,c)~*(a,b,σ)的性质.利用函数论的方法,获得了G_(p,c)~*(a,b,σ)族相关的准哈达玛乘积的一般化结果及G_(p,c)~*(a,b,σ)的极值点与支撑点.推广了先前相应的一些研究工作。