从数学活动论看数学教育思想的转变

从数学活动论的角度去阐述21世纪在素质教育意义下的数学教育思想或模式的转变。     

From natural numbers to numbers and curves in nature - II

In this second part of the article we discuss how simple growth models based on Fibbonachi numbers, golden section, logarithmic spirals, etc. can explain frequently occuring numbers and curves in living objects. Such mathematical modelling techniques are becoming quite popular in the study of pattern formation in nature.     

在初中数学中蕴藏着的数形结合思想

揭示在初中数学的有理数、应用题、不等式、函数及其图像、统计初步、平面几何内容中所蕴藏着的数形结合思想 ,以及应用数形结合思想解决相关内容中考试题的思路。     

师范院校数学教学更应注重合情推理

就当前一些师范院校数学教育存在的问题及师范院校的特殊性质在教材的编写和课堂教学中实施合情推理教学法提出一些具体的建议,以期达到对学生起潜移默化的作用,使之在真正意义上提高师范院校的数学教育质量.     

从“失败国家”到“脆弱国家”:概念发展与政策演变

过去二十年,国家功能的失效和衰退问题被视为安全和发展援助领域的重大挑战.20世纪60年代的民主化、现代化危机和80年代末大量的内战冲突使“失败国家”进入政策视野.“脆弱国家”概念则由发展援助机构提出和推广使用.20世纪90年代末对发展—安全联结的热烈讨论,使“脆弱国家”框架开始纳入安全维度.作为国家机制衰败的极端表现,“失败国家”也出现被并入内涵更大、更易被接受的“脆弱国家”概念的趋向,特别是在发展、人道主义援助与建设和平领域.不论“失败国家”还是“脆弱国家”,都加大了西方干预的可能性,存在很多问题和改进的空间,尤其要打破两个概念背后所蕴含的西方中心主义迷恋,真正地关注“当地”.     

从大数据到计算教育学：概念、动因和出路

在大数据时代,计算社会科学是社会科学发展的必然走向,教育学作为社会科学的重要分支,同样面临着向计算教育学转型的形势。计算社会科学的兴起催生出一系列亟待明确的核心概念,极大地超越了传统社会科学研究范式。从新计算社会学出现的过程、从大数据时代的背景和特征、从传统研究范式的局限,足以见出计算教育学出现的必然性。在这一过程中需着重处理好四个关键问题:积极适应计算教育学的思维方式;技术繁荣与理论繁荣齐头并进;增强数据挖掘能力以争取话语权;变被动为主动回应时代和政策要求。     

Factors shaping community attitudes to school mathematics: Implications for future curriculum change

The goals of mathematics education are pressured by political, social, and economic forces that are often expressed through the medium of public opinion. Public opinion is formed largely by the preceptions of what is rather than the reality itself which may be known by only a few. The recommendations of committees of enquiry are activated in the world of average people and typical teachers — not the rarefied world of specialised professional knowledge in which the recommendations are typically incubated.This paper reports on community perceptions of school mathematics with respect to the four areas of content, individual values, attitudinal aspects, and folklore. Factor analysis identified five predictor variables (derived from the respondents' own backgrounds), and five criterion variables (describing their views and values as to what school mathematics should be). Analysis of variance was used to explore the contribution of the predictor variables and selected demographic variables to the criterion factor scores. The results are discussed in relation to their implications for the effective implementation of recommendations for change in mathematics education.     

From failure to success: Changing the experience of adult learners of mathematics

For the last few years, the author has been part of a team developing a mathematics course for students most of whom are women, many of whom are black and all of whom are attempting to gain entry to a teacher-training course by successfully completing a one year re-entry course. It is a requirement that teacher-training students should have attained a suitable standard in mathematics. Further Education colleges where re-entry courses are sited have a sad history of student failure in mathematics. The theoretical environment in which the development of this course took place is described in order to place the course in context. In particular, attention is drawn to the re-definition of mathematics which encourages student enquiry and experimentation in order to establish a basis for understanding the subject, and to the teaching/learning model which creates an environment of respect and confidence. The roles of students and staff in a learning environment of this kind are discussed. Particular attention is paid to the attitudes and feelings of the students and the effects on their expectations.     

基本概念隐喻与诗歌隐喻——从认知语言学视角对诗歌隐喻的解读

认知语言学提出概念隐喻理论,认为基本概念隐喻是人类组织概念系统的基础。通过分析基本隐喻与诗歌隐喻的关系,可知后者是以前者为基础展开的,其展开途径表现为拓展对应关系、增加细节描述、整合多个隐喻和质疑常规隐喻四种。     

Reflective, systemic and analytic thinking in real numbers

The aim of this paper is to propose a theoretical model to analyze prospective teachers?? reasoning and knowledge of real numbers, and to provide an empirical verification of it. The model is based on Sierpinska??s theory of theoretical thinking. Data were collected from 59 prospective teachers through a written test and interviews. The data indicated that mathematical tasks on real numbers, based on Sierpinska??s theory, could be categorized according to whether they require reflective, systemic or analytic thinking. Analysis of the data identified three different groups of prospective teachers reflecting different types of theoretical thinking about real numbers. The interviews confirmed the empirical data from the written test, and provided a better insight into the thinking and characteristic features of the prospective teachers in each group. The analysis also indicated that the participants were more successful in tasks requiring systemic and analytic thinking, and only when this was achieved were they able to solve problems which required reflective thinking. Implications for teaching related to the findings of the study are discussed.     

Applying mathematics with real world connections: metacognitive characteristics of secondary students

This paper reports an intensive study of problem-solving activity of female students at the senior secondary level. The study focussed both on the mathematical processing and the underlying cognitive and metacognitive activities that led to that processing. Response maps were used to analyse and categorize the written responses from individual students while videotaped problem solving sessions and structured and free response interviews probed the students' metacognitive knowledge, strategies, decision making, beliefs and affects. Metacognitive activities were involved in all phases of the solution process with key points in students' solutions identifiable in terms of the cognitive-metacognitive framework of Garofalo and Lester (1985). On average more time was spent on orientation and execution activities with little time being spent on organisation and verification activities, however, the successful groups spent less time on orientation than the other groups. All successful groups displayed a high number of key points where metacognitive decisions could influence cognitive action. Success was accompanied by a tendency to engage in a high number of organisational activities, regulation of execution activities and evaluation activities particularly evaluation of execution but fewer opportunities where metacognitive decisions could influence cognitive actions during orientation.     

From ideal to real: Understanding the development of new educational settings

Summary and Conclusion In this paper we presented a framework for viewing the development of new educational settings. We also postulated the necessity of two conditions for the creation of a coherent self-renewing educational program: the development of a community, especially in a linguistic sense, and on-going practical dialog that defines and redefines the setting over time in light of collective action and experience. In doing so, we took the position that educational program and program development mean something more than what is implied in most theories of organizational and program development. We argued that a collection of educational activities constitutes a program only when the activities are grounded in a commonly perceived core of beliefs and values about what is and what ought to be.Clearly, we have only begun to sketch out the nature and operation of the processes by which a new educational setting evolves and develops into an organization. We need to know why development and growth through the application of the dialectic are typically not present in new programs. Our future research efforts are oriented in this direction and we hope that by setting forth our tentative ideas at this point we may encourage others to react to them and perhaps to pursue a similar line of inquiry.OISE     

Conceptual change strategies and cooperative group work in chemistry

This study conducted at a suburban community college tested a method of conceptual change in which treatment students worked in small cooperative groups on tasks aimed at eliciting their misconceptions so that they could then be discussed in contrast to the scientific conceptions that had been taught in direct instruction. Categorizations of student understanding of the target concepts of the laws of conservation of matter and energy and aspects of the particulate nature of gases, liquids, and solids were ascertained by pre- and posttesting. Audiotapes of student verbal interaction in the small groups provided quantitative and qualitative data concerning student engagement in behaviors suggestive of the conditions posited to be part of the conceptual change process (Posner, Strike, Hewson & Gertzog, 1982). Chi-square analysis of posttests indicated that students in treatment groups had significantly lower (p < 0.05) proportion of misconceptions than control students on four of the five target concepts. Students who exhibited no change in concept state had a higher frequency of verbal behaviors suggestive of “impeding” conceptual change when compared to students who did change. Three factors emerged from qualitative analysis of group interaction that appeared to influence learning: (a) many students had flawed understanding of concepts that supported the target concepts; (b) student views towards learning science affected their engagement in assigned tasks, (c) “good” and “poor” group leaders had a strong influence on group success.