新课程理念下的初中数学思想方法教学的思考

初中数学思想方法教学活动在遵循目标性、层次性、计划性、系统性、参与性原则下,应结合数学课程标准,努力提高数学教师自身的数学思想方法素养;结合数学知识,将数学思想方法有机地渗透到教学计划和教案内容之中;结合数学问题,在问题解决的探究过程中激活数学思想方法;结合“过程教学”模式,把发现和创造的思维与方法教给学生。     

The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice

Case studies were conducted to investigate the conceptions of mathematics and mathematics teaching held by three junior high school teachers. Examination of the relationship between conceptions and practice showed that the teachers' beliefs, views, and preferences about mathematics and its teaching played a significant, albeit subtle, role in shaping their instructional behavior. Differences among the teachers in their conceptions and practices are explained followed by a discussion of properties of their conceptual systems.This paper is based on the author's doctoral dissertation which was directed by Professor Thomas J. Cooney of the University of Georgia and was partly supported by a grant from San Diego State University. I wish to express my appreciation to the teachers who participated in the study and their administrators.     

In the workplace mathematics does not announce itself: towards overcoming the hiatus between mathematics education and work

After improving enrolment rates significantly, many developing countries such as Peru are facing the challenge to increase learning levels among students. Over the past few years, many researchers have turned to teacher-related variables as a way to better understand classroom processes that may help increase learning levels among students. In this study, we analyze one of these, that falls under what Shulman (Educational Researcher, 15 (2), 4–14, 1986) called pedagogical content knowledge (PCK). Specifically, in this study, we analyze one of the areas of PCK which is knowledge of content and students. This was measured through a test where teachers were asked to explain students’ mistakes and predict responses in similar mathematics exercises. We explore if PCK is associated with the socioeconomic status of children and if it has an effect on children’s achievement. Additionally, we analyze which teacher characteristics are associated with higher scores in PCK. The analysis uses the Young Lives longitudinal survey for Peru. We found that students’ socioeconomic status at age 1 and maternal education were positively associated with their teachers’ PCK by the time students were enrolled in fourth grade, thus depicting a very unequal education system. Furthermore, teachers’ PCK was positively associated with student achievement, but only when a threshold for the PCK test was established. For our sample, male teachers, who were younger, and Spanish speakers had higher PCK scores.     

Undergraduates’ conceptions of mathematics teaching and learning: an empirical study

Educational Studies in Mathematics - Previous research in mathematics education has explored teachers’ conceptions of mathematics and its teaching and learning, and how their instructional...     

Motivating adults to learn mathematics in the workplace: a trade union approach

ABSTRACT

The aim of this qualitative study is to explore adults’ motivation to learn mathematics in the workplace and the role that the trade union education approach promoted in the United Kingdom plays in that motivation. The findings draw on data from 20 semi-structured in-depth interviews with adults learning mathematics, organised through their trade union representatives. Trade unions promote education which uses teaching and learning approaches based on collectivist and activist principles, which is different from mainstream education, so the research explores what might be learnt from this approach. The findings show that the trade union-led approach enables even long-held negative feelings towards mathematics to become positive. The research finds a strong link between supportive social networks, including Union Learning Representative, as well as positive social and emotional encounters in the classroom that develop adult learners’ confidence, increasing their motivation to both learn and use mathematics in their everyday lives. This change in feelings and motivation is termed an Affective Mathematical Journey. These findings, while taking place in a non-traditional context, nevertheless are relevant to practitioners working with adults in both traditional (school and college) and non-traditional (workplace and community) settings. There are also indications of the positive influence this learning has on the relationship between individual members and their trade union organisations.     

Prospective teachers' initial conceptions about pupils' understanding of science and mathematics

Earlier reports have shown that prospective teachers' conceptions about teaching science to a high degree are resistant and do not change substantially during the teacher‐training programme. In our investigation we elucidate the prospective teachers' initial conceptions about pupils' understanding of science and mathematics. We applied ‘The Lesson Preparation Method' and used a phenomenographic approach in order to reveal the range of conceptions that the prospective teachers hold. A third of the prospective teachers did not consider pupils' conceptions when planning lessons. The rest of the 32 participants expressed awareness; some of the prospective teachers even referred to subject‐specific teaching experience. Also regarding the prospective teachers' conceptions about pupils' knowledge and beliefs, as well as about pupils' difficulties, there was a significant diversity. By raising these issues about pedagogical content knowledge the prospective teachers' conceptions can be extended and developed during the education.     

The influences of conceptions of mathematics and self‐directed learning skills on university students' achievement in mathematics

This study tested the mediating role of self‐directed learning skills (SDL) between students’ conceptions of mathematics and their achievement in mathematics using a structural equation model. Data were collected using the “Conceptions of Mathematics Questionnaire” and the “Self‐Rating Scale of Self‐Directed Learning”, together with students’ achievement in mathematics. A sample of 440 first year university students at King Saud University participated in the study. The findings confirm the moderating role of students’ self‐directed learning skills between their conceptions of mathematics and their achievement in mathematics. Students who have a highly fragmented conception of mathematics tended to have low SDL skills, and in turn low mathematics achievement (partial mediation), whereas students who have a highly cohesive conception of mathematics tended to have high self‐directed learning skills, and in turn high mathematics achievement (full mediation). Mathematics educators should be aware that students’ conceptions of mathematics may be influential, but not sufficient to predict achievement in mathematics. Equipping students with appropriate conceptions of mathematics and self‐directed learning skills is key to enhancing their performance in mathematics.     

The emerging of teachers' conceptions of new subjects inserted in mathematics programs: the case of informatics

The changes in mathematical curricula induced by the introduction of informatics in school represent the general framework of this research. In particular we focus on the teacher's role by analysing the different choices taken by mathematics teachers when faced with a curriculum reform induced by the introduction of informatics in secondary school courses (age 14–16). Our hypothesis is that these choices are the consequence of conceptions teachers have about informatics and its teaching in relation to the teaching of mathematics. Thus, through a case study research method, we focus on mathematics teachers' conceptions of informatics and its teaching. An attempt is made at outlining a typology of these conceptions, based on the different orientations identified.     

A comparison of Hungarian and English teachers' conceptions of mathematics and its teaching

This paper reports on a statistical study of English and Hungarian teachers' conceptions of mathematics and its teaching. A questionnaire was developed and distributed to teachers of mathematics in 200 English and40 Hungarian schools teaching children in the 11–14 age range. Factor analyses identified four conceptions of mathematics and five of mathematics teaching. These were compared with those yielded by an earlier study involving the same English teachers and found to be consistent indicating the existence of similar conceptions in different educational systems. Differences and similarities in the strengths with which those conceptions are held were suggestive of both global and national conceptual traditions. The significant similarity to emerge concerned teachers from both countries sharing, with similar strengths, a general conception of mathematics teaching incorporating the teaching of mathematical skills, a variety of classroom approaches including investigations and problem-solving, and a recognition that mathematics provides an essential lifetool. Multi-dimensional scaling indicated that English teachers have their perspectives informed by two underlying, and possibly conflicting, traditions– pedagogic relevance and mathematical utility. The Hungarians appeared concerned only with notions of pedagogic relevance – those practices perceived to facilitate effective learning of a subject which is untainted by utilitarian perspectives. This revised version was published online in July 2006 with corrections to the Cover Date.     

小学数学学习习惯培养的实践探索

习惯是个人在成长过程中逐渐养成且不易改变的一种行为或者倾向,小学阶段是人们学习和成长的重要时期,养成良好的学习习惯,不仅能帮助人们树立正确的思想道德观念,更对人们以后的成长具有重要的意义。本文主要阐述了目前我国小学生数学学习习惯的现状,从四个方面探讨了如何培养小学生养成良好的数学学习的习惯。     

Exploring the NATURE OF MATHEMATICAL activity: USING theory, research and `working hypotheses' to broaden conceptions of mathematics knowing

What proficiencies are brought tobear when students work on mathematicsproblems? And to what extent may these becaptured by knowledge categories? These arequestions that I consider in this article,as I explore notions of competency, that gobeyond knowledge to include themathematical `dispositions' that studentsbring to problems and the `practices' withwhich they engage. This exploration willdraw from two frameworks that have recentlybeen introduced in the US. In addition, Iconsider the ways in which researchknowledge is conceived and developed,reflecting upon the important role oftheory and the potential of `workinghypotheses' for connecting with practice innew ways.     

Tablet-based AR technology: Impacts on students’ conceptions and approaches to learning mathematics according to their self-efficacy

Most studies of Augmented Reality (AR) in education have considered students’ learning outcomes and motivation. Previous studies have revealed that AR has the potential to help students learn abstract conceptions in mathematics. In this paper, a series of statistics and probability lessons using AR installed on tablets was designed and developed to examine the effect of the AR technology by comparing the conceptions and learning approaches of junior high school students with different levels of self-efficacy. A total of 101 students were divided into two groups based on their mathematics learning self-efficacy. The analysis of the results shows that AR applications in mathematics courses can help students with higher self-efficacy to pay closer attention to higher level conceptions. It can also help higher self-efficacy students to apply more advanced strategies when learning mathematics.     

"问题解决"教学在数学教学中的实践

“问题解决”教学是实施素质教育,进行数学教育改革的一种有效教学模式。在数学课堂教学中如果能根据教学目标,设计并提出系列具有趣味和魅力的问题和任务,向学生提出智力挑战,引起学生的思考,将激发学生参与整个教学过程,最终达到学生主动发现、积极探索,深层次理解并掌握和应用隐含于问题背后的知识,提高解决问题的能力。     

独立学院高等数学分层教学的实践与思考

高等数学是高等院校一门必修课,其具有高度的抽象性和严密的逻辑性。随着高等教育的普及,要兼顾不同层次学生的数学学习,高等数学教学改革势在必行。分层教学是高等数学教学改革的一项重要内容。本文结合独立学院的实际,从必要性、实施以及效果三个方面对分层教学作了简要论述。     

数学"自主探究"教学的实践与体会

以笔者几年来的亲身实践,来谈谈数学课堂教学中"自主探究"教学的实践与体会,并对如何有效开展"自主探究"教学活动提出个人的若干观点.     

提高小学数学教学有效性的几点做法

提高小学数学教学的有效性可从以下几方面着手：一、备课要精心,尽心;二、有效的组织教学过程;三、开展有效的讨论;四、为学生提供形式多样的课堂练习;五、教学反思及时有效。     

Making sense of and with mathematics: the interface between academic mathematics and mathematics in practice

This article summarises what we can learn from research into workplace practice and vocational preparation to inform the design of mathematics education curricula for learners in general education undertaking compulsory schooling. Key findings about workplace practices are identified and explicated through the report of a case study from research in which researchers, students, teachers and workers explored workplace and mathematical practices together. Further to this, issues of learning and personal development are considered and explored from a point of view that sees learning as practice (doing) and identity development (becoming). This leads to a proposal for principles that provide a strategic vision for curriculum design. A potential approach to tactical design that facilitates curriculum structuring is illustrated in the particular instance of understanding developing measures as a modelling activity. Overall, the exercise, whilst providing some insight into possible ways forward in curriculum development, also suggests areas that require further research and development.     

Individuals,Communities of Practice and the Policy Context: School teachers' learning in their workplace

Current theorising about learning at work comes from a predominantly participatory perspective, emphasising the social and communal dimensions of learning. This paper seeks to develop such a perspective further, devoting particular attention to the interrelationships between individual worker dispositions to learning, community of practice and wider organisational and policy contexts. This is done through the case study examination of the learning of one secondary school teacher, and of the art department of which she was part.