Comparing the use of the empty number line in England and the Netherlands

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed that the English use of the ENL differs from that of the Dutch. In this study curriculum guidance materials are examined to investigate these differences. Two examples of teaching sequences are provided to illustrate them further. It is proposed that the different uses stem from different pedagogical principles. The implications of the English use are discussed in relation to the presentation of mental calculation strategies in an algorithmic way.     

Achievement of English as New Language Learners in Monitor Status: A Cross Sector Comparison from Denver

This study uses administrative data to measure the effect of attending a charter school in Denver, Colorado on the achievement of reclassified English as New Language (ENL) students during their monitor period in the mainstream classroom environment. We utilize school choice data from Denver’s Common Enrollment System (CES) to control for each school a family selected entering grade six, a typical time for a structural move, in order to better control of unobserved variable bias. Results indicate charter attendance increases achievement in mathematics and English on state testing. Charter school success in the CES environment provides insights for districts serving large numbers of ENL students.     

多媒体技术与数学"情境-问题"教学

如何将现代教育技术与"情境-问题"教学结合起来是摆在我们面前的重要课题,为此可以从以下几方面进行尝试:创设合作实验情境、动态变化情境、空间想象情境、游戏扮演情境,以促使学生通过主动的心理建构活动,获得真实反映客观规律的认知结构,形成有效解决问题的认知能力.     

基于建构主义的数学概念转变学习

概念转变学习是学生原有概念的改变、发展和重建,是学生的前概念向科学概念的转变.日常概念、概念意象、迁移等因素是数学概念转变学习中产生错误概念的主要原因.根据概念转变的途径、机制和条件理论,概念转变学习的教学策略:(1)了解学生已有知识经验,促进日常概念向科学的数学概念转变;(2)引发认知冲突,辨清新旧界限以实现数学概念转变学习;(3)重视概念生成的凝聚,构建概念网络.     

中重度智障学生大小比较测试与数概念测试相关性研究

中重度智障学生数学知识的理解和运用能力水平低,学生之间存在的差异大,在教和学的过程都存在极大困难。解决这些问题需要对智障学生进行科学的评价,从而找到教学的起点和缩小差距的办法。本研究把数概念的评估作为解决问题的切入点,采用相关性研究来证明10以内大小比较测试方法与数概念测试存在相关性,这种方法能为智障学生的入学筛查和实际教学计划的制定服务。     

函数概念的演变及其对高中函数教学的启示

函数是数学中最基本的概念,也是高中数学的核心内容,函数的思想方法贯穿高中数学课程的始终。根据历史发生原理,数学教育取向的数学史研究的主要目的之一就是获取相关知识点(概念、公式、定理)的教学启示。基于函数概念演变阶段与发展动力的分析,高中函数教学给我们的启示是:从丰富的现实背景及具体的函数入手抽象概括函数的本质;注重从不同角度认识函数概念;注重对运动、变化的体现与分析;从数学史料中精选函数教学材料。     

DETERMINANTS OF GIRLS' CHOICE OF MATHEMATICS

Questionnaires concerning the self‐concept and evaluations of maths and French, as well as an intelligence test, were administered to secondary school students more than six months before they had to decide whether or not to take maths courses during the following school year. At the same time their school grades for maths and French were recorded. Students’ decisions were related to self‐concept, evaluations of maths and French, and aptitude measures, by means of discriminant analyses. Results indicated that sex, in combination with students’ (positive) evaluations of mathematics, their achievements in mathematics and their intellectual abilities, as well as a focus on French and self‐concept of French abilities, could adequately predict their choice of mathematics courses. No interaction effects were found between sex and the other predictor variables. These results suggest that stimulating more girls to choose mathematics during their secondary school years should focus upon achievement, self‐concept and evaluations of mathematics in comparison with other options.     

Research-based interventions in the area of proof: the past,the present,and the future

The concept of proof has attracted considerable research attention over the pastdecades in part due to its indisputable importance to the discipline of mathematics and tostudents’ learning of mathematics. Yet, the teaching and learning of proof is an instructionallyarduous territory, with proof being recognized as a hard-to-teach and hard-to-learn concept atall levels of education. Prior research has examined, documented, and cast light on theprocesses underpinning different problems of classroom practice in the area of proof, buthas paid less emphasis on acting upon such problems to generate possible solutions throughresearch-based interventions in mathematics classrooms. In this Editorial, we first situate thecontributions in this Special Issue in a brief chronological account of scholarly work on research-based interventions in the area of proof, and we conclude with a proposal for somehigh-leverage directions for future research.     

试论形而上学与数学的关系——以笛卡尔为例

形而上学与数学有怎样的联系?这是西方哲学研究中的一个重要的问题.从西方哲学家泰勒斯、毕达哥拉斯、柏拉图、亚里士多德的哲学中可见出数学对其形而上学的影响.笛卡尔采用数学的方法,建立了他的知识论形而上学.数学与笛卡尔的知识论形而上学相互影响、互为根据.     

基于生活化理念创新初中数学教学

新课程在改革过程中,提出了生活化教学的理念,也就是将教学活动与现实生活构建起来,依托于生活素材或工具,实现教学活动的生活化构建.针对初中数学课程而言,实现生活化教学,能够带来多方面的积极作用,这一点需要数学教师清楚认识.本文便对此展开分析,探讨了生活化理念内涵及其对初中数学教学的作用,然后分析初中数学教学基于生活化理念实现创新应该关注的要点,最后提出初中数学教学生活化构建的具体措施,以供参考.     

STEAM教育理念下高职学生合作性学习行为探析

STEAM教育理念正处于蓬勃发展阶段,体现了集科学、技术、工程、艺术、数学多学科融合的综合教育特点。对STEAM教育中高职学生合作性行为的分析,显示该行为对促进新型教学模式建构、推动个性化教学、促进心理健康发展等方面具有重要作用。可运用建立积极的相互依赖、促进面对面互动、强调个体责任与团体责任、练习优化协作技能、建立合作求助基地、倡导基于问题的学习等多种方式促进合作性学习行为建构,从而促进STEAM教育理念与高职学生合作性行为深度融合。     

基于核心素养的小学数学教材资源整合探讨

新课改要求教师摒弃以教材为本的旧观念,树立以学生发展为本的新观念。整合教材资源,培养学生的数学核心素养,成了教师首先要解决的问题。本文从数学教材与信息技术整合、数学教材与游戏整合、从生活中挖掘数学教材资源三个方面,探讨基于核心素养的小学数学教材资源整合问题。     

Globalized curriculum or global approach to curriculum reform in mathematics education

The mathematics education community has shown considerable awareness of the international status of their discipline. While internationalization of the discipline is not a new phenomenon, globalization is a relatively recent term in educational discourse. This paper presents a theoretical model towards the study of globalization and internationalization in mathematics education based on previous publication by the authors. Secondly, it identifies some key issues that have been discussed in the literature and that may require further discussion and research in the field. In particular it discusses the issue of similarity of mathematics education curricula around the world. The concept of a global curriculum is rejected in favor for more internationalized approach to curriculum reform based on collaboration between mathematics educators.     

Towards a unified theory for HIV/AIDS counselling

The paper explores the introduction of an unified theory for HIV/AIDS counselling. To date the provision of HIV/AIDS counselling has been largely based upon the behavioural theory of counselling. This theory has been adopted by WHO/GPA and its main aims have been the prevention of HIV infection and the psychosocial support for those already infected. It is argued that future counselling interventions should be redirected from a disease-centred approach to a person centred approach. This redirection can be facilitated by the adoption of the self concept as the central measure for evaluating change. It is argued that various ideas should be selected from the behavioural, psychoanalytical and humanistic theories of counselling. These ideas should be amalgamated into a unified theory which provides the theoretical foundation upon which a comprehensive counselling intervention can be based.     

高职院校应用数学教学改革初探

在高职院校学生数学基础参次不齐、兴趣缺乏的现状下,教学改革势在必行。本文现从教学理念、教学方法以及学生学习等几个方面对高职应用数学教学改革进行了探索和思考。     

The necessity of each phase of the learning cycle in teaching high school physics

The learning cycle is a method of teaching—it is also a curriculum organization principle and is derived directly from the mental functioning model invented by Piaget. Although Jean Piaget contributed to the formation of the learning cycle (Piaget, 1973), its present structure has to be attributed to Dr. Robert Karplus and the persons who developed the materials of the Science Curriculum Improvement Study (SCIS). It was through the SCIS activities that many of us learned how to develop curricula and teach with the learning cycle. The learning cycle is built upon the premise that three distinct phases are necessary in developing understanding of a concept, that those phases have a definite sequence, and each phase has a definite structure or form. The research done in testing the form variable has already been reported in this journal (Renner, Abraham, & Birnie, 1985). This report explores whether or not each learning-cycle phase is necessary in learning a concept.     

Making the transition to formal proof

This study examined the cognitive difficulties that university students experience in learning to do formal mathematical proofs. Two preliminary studies and the main study were conducted in undergraduate mathematics courses at the University of Georgia in 1989. The students in these courses were majoring in mathematics or mathematics education. The data were collected primarily through daily nonparticipant observation of class, tutorial sessions with the students, and interviews with the professor and the students. An inductive analysis of the data revealed three major sources of the students' difficulties: (a) concept understanding, (b) mathematical language and notation, and (c) getting started on a proof. Also, the students' perceptions of mathematics and proof influenced their proof writing. Their difficulties with concept understanding are discussed in terms of a concept-understanding scheme involving concept definitions, concept images, and concept usage. The other major sources of difficulty are discussed in relation to this scheme.This article is based on the author's doctoral dissertation completed in 1990 at the University of Georgia under the direction of Jeremy Kilpatrick.     

以生活情境为导向的小学数学教学微视频探析

最近几年,在小学数学课堂教学中逐步渗入互联网微视频,要实现其有效的意义与价值,离不开以生活情境为导向的明灯来指引小学数学教学走向更有效的方法和路径。本文主要从以下几方面着手,探析以生活情境为导向的小学数学教学微视频的核心概念、存在意义及使用措施。     

数学与思维机械化之路

在人类的脑力劳动中，数学具有特殊的和典型的地位。数学是其他科学的基础。数学化，正成为现代科学技术发展日益明显的趋势。因此，数学机械化对于整个脑力劳动的机械化来说也具有特殊的甚至是关键的意义。通过数学思维的机械化来实现更广泛意义上的脑力劳动机械化，这是人类长期梦寐以求的目标。文章探讨并力图简明地概括数学思维机械化的历史源流。     

我国大学生心理素质研究20年的回顾与反思

20世纪80年代心理素质及其教育受到我国心理学界关注,大学生心理素质及其教育问题已经成为教育学和心理学的研究热点之一。我国一批学者在大学生心理素质的概念、结构、发展状况、教育训练等方面进行了有益探索,积累了丰富的研究成果。然而,大学生心理素质研究还存在一些问题,主要表现为理论研究缺乏整合、实证研究薄弱、研究方法单一、测量工具不够完善、教育研究有效性不高。对这些问题的反思,有助于我们明确该领域未来研究的发展方向。