Analyzing Mathematical Tasks: A Catalyst for Change?

In this study we investigate a strategy for engaging high school mathematics teachers in an initial examination of their teaching in a way that is non-threatening and at the same time effectively supports the development of teachers’ pedagogical content knowledge [Shulman (1986). Educational Researcher, 15(2), 4–14]. Based on the work undertaken by the QUASAR project with middle school mathematics teachers, we engaged a group of seven high school mathematics teachers in learning about the Levels of Cognitive Demand, a set of criteria that can be used to examine mathematical tasks critically. Using qualitative methods of data collection and analysis, we sought to understand how focusing the teachers on critically examining mathematical tasks influenced their thinking about the nature of mathematical tasks as well as their choice of tasks to use in their classrooms. Our research indicates that the teachers showed growth in the ways that they consider tasks, and that some of the teachers changed their patterns of task choice. Further, this study provides a new research instrument for measuring teachers’ growth in pedagogical content knowledge. An earlier version of this paper was presented at the American Educational Research Association Annual Meeting, New Orleans, LA, April 2002.     

职前教师教育中数学教育类课程的构建

基础教育数学课程改革对数学教师的素质提出了新的要求,作为培养基础教育数学师资的母机高校数学教育,就应采取积极的策略,构建与时俱进的、具有前瞻性数学教育类课程体系,培养高素质的数学教师,以适应新课程改革的需要。     

小学数学专家教师与普通教师的专业知识水平与表现的比较研究

通过对174名小学数学专家教师和307名小学数学普通教师的教师专业知识进行测查,研究者发现,总的来说,我国的小学数学教师在数学史、数学思想等方面的知识较差;小学数学教师的PCK总体水平较低,具体地说,教师缺乏“有关学习者”的知识,大部分小学数学教师缺乏探究的意识和解决开放性问题的能力;专家教师和普通教师在教师专业知识的几个大维度上有显著的差异。基于这个研究结果,研究者提出在小学数学教师培训课程中应该补充数学文化思想史方面的内容,鼓励教师参与学生数学学习方面的研究,提升教师的探究意识和问题解决能力,并形成优势互补、分层设计的教师培训课程模式。     

从高等代数教学改革实践谈高师数学教学改革

目前,义务教育数学课程正在进行深刻地变革,作为为义务教育培养合格数学师资的高师数学教育也应顺应时代发展,开展教学改革的探索与实践。以高等代数课程教学改革的实践为例,以培养学习者的数学素质为目标,探索高师数学教学改革模式,以期提升人才培养规格。     

数学教师专业化与高师数学教育专业课改

数学教师专业化是世界数学教师教育的发展潮流,其内涵包括:数学教师数学专业化、数学教师教育专业化和数学教师专业情意.当前高师数学教育在课程设置上不适应数学教师专业化要求,改革重点是构建合理的课程体系.     

Teachers' Conceptions of Proof in the Context of Secondary School Mathematics

Current reform efforts in the United States arecalling for substantial changes in the natureand role of proof in secondary schoolmathematics – changes designed to provideall students with rich opportunities andexperiences with proof throughout theentire secondary school mathematicscurriculum. This study examined 17 experiencedsecondary school mathematics teachers'conceptions of proof from their perspectives asteachers of school mathematics. The resultssuggest that implementing ``proof for all' maybe difficult for teachers; teachers viewedproof as appropriate for the mathematicseducation of a minority of students. Theresults further suggest that teachers tended toview proof in a pedagogically limited way,namely, as a topic of study rather than as atool for communicating and studyingmathematics. Implications for mathematicsteacher education are discussed in light ofthese findings.     

A Study Of Mathematics Anxiety in Pre-Service Teachers

The study investigated the changes in levels of mathematics anxiety among pre-service teachers in six different sections of a mathematics method courses for early childhood/elementary education pre-service teachers. The changes were a function of using Bruner’s framework of developing conceptual knowledge before procedural knowledge and using manipulatives and other activities to make mathematics concepts more concrete and meaningful. Data were collected using quantitative and qualitative measures. Two hundred forty-six pre-service teachers completed a 98-item Likert-type survey. Informal discussions, informal interviews, and questionnaire-guided narrative interviews were conducted with pre-service teachers. Data revealed a statistically significant reduction in mathematics anxiety in pre-service teachers (p < .001) who completed a mathematics methods course that emphasized Bruner’s model of concept development. Results of the study have implications for teacher education programs concerning how future teachers are trained, the measurement of mathematics anxiety levels among pre-service teachers, and the determination of specific contexts in which mathematics anxiety can be interpreted and reduced.     

高中数学教师专业知识研究--基于吉林省数学教师的调查

教师专业发展必然需要教师专业知识的有力支撑。对高中数学教师专业知识进行的问卷调查和访谈发现：目前高中数学教师基本上较好地掌握了常用的教师专业知识,但也存在一些问题：对数学学科知识的关注范围过于狭窄;运用数学教学知识进行教学时偏向于被动;对数学课程标准的理解存在偏差。另外,研究还发现：数学教学知识的增长并非是持续的;不同层级的教师之间、不同类别学校中的教师之间,其差异主要体现在数学学科知识与数学教学知识。进而对数学教师教育提出相应建议：数学教师应适当拓展数学学科知识的关注范围;应依据调查数据加强数学教师教育培养计划的针对性;关于教师一般教育学知识的评价方式亟需改进等。     

目前高中数学教改现状及高师院校数学专业课程设置的对策研究

为了深入了解目前高中数学的教改现状,使得高等师范院校数学专业的课程设置与中学教改相适应,采用走访一线教师和问卷调查的方式收集有关资料,通过定量分析与定性分析相结合的方法,找出高师院校数学专业课程设置与中学教改数学教学内容间不相适应的方面,在此基础上提出了高师院校数学专业应该联系中学实际充实数学主干课,适应中学需要开好数学选修课,创造条件举办好数学专题讲座,采取多种形式开展好数学实践活动等教学改革的基本对策。     

Teachers and Computers for Secondary Mathematics

In the first stage of a three-year study in which the effects of using computers for the teaching and learning of mathematics are being explored, a questionnaire was developed and administered to teachers of students in grades 7–10 in a representative sample of co-educational post-primary schools in Victoria, Australia. Using open and closed response formats, the information sought included data on the teachers' professional backgrounds, computer ownership and use, and their beliefs and practices in using computers for the teaching of mathematics. In this article, findings related to ownership, professional development, perceptions of technological skills, beliefs about the efficacy of computer use in mathematics, and data on how teachers are using computers for teaching secondary mathematics are presented and discussed.     

Contribution of mathematics in-service training course to the professional development of elementary school teachers in Israel

The present study aimed to explore the contribution of a mathematics in-service training course to elementary school teachers (1st–6th grades) in Israel. The study was conducted among 449 educators. They were required to respond to background questions. Moreover, they were asked to indicate their expectations from the in-service training course and, at its end, point out to what extent they benefitted from that course. The research findings illustrate that educators who teach mathematics at elementary school and attended the course are generally women in their 40s, holding a BEd degree and a teaching certificate not in mathematics, with an average 13-year seniority. The participating teachers indicated their wish to enrich their didactic knowledge in order to acquire varied tools for teaching mathematics to the entire pupil population as well as to gifted pupils and pupils with learning difficulties. Nevertheless, their demand to expand their mathematics knowledge was very limited. Based on the fact that most teachers have no mathematics education, this is a surprising finding as, in order to be a good teacher, one must be versed not only in Pedagogical Content Knowledge but also in Subject Matter Knowledge.     

浅谈数学教师专业化

数学教师专业是数学专业和教育专业的有机统一;科学设置对数学教师的专门教育内容;建立科学的对数学教师的终身教育机制;数学教师专业化是一个动态的发展过程.     

高师专科数学专业教育科研能力培养策略

当前,我国的基础教育课程改革蓬勃开展。教育科研在很大程度上已成为中小学提高教育教学质量的重要推动力。高师专科是培养未来小学教师的摇篮,然而高师专科数学专业对学生教育科研能力方面的培养却很薄弱,而且没有严格的量化考核指标。现有的高师生教育科研能力的研究大多局限于本科生。文章通过理论研究、问卷访谈发现高师专科数学专业学生的教育科研能力具有自身特色。据此给出高师专科数学专业教育科研能力的定义,提出高师专科数学专业教育科研能力培养策略,及量化考核的指标、方式。     

Elementary school mathematics teachers’ perception of their professional needs

This study explored Israeli elementary school mathematics teachers’ perceptions of their professional needs, with the purpose of developing in-service training courses which cater to these needs. Eighty-four teachers responded to the questionnaire and were interviewed. The results indicate that the respondents’ main needs are associated with strengthening their didactical knowledge capability of dealing with emotional aspects that relate to pupils’ learning of mathematics. Although most of the respondents lack formal mathematics education, they attribute less importance to their need to enhance knowledge in the field. In light of Israeli pupils’ relatively low attainments in mathematics, the authors believe that the education system should require teachers to expand their mathematics knowledge and that only teachers with appropriate knowledge will be permitted to teach the discipline.     

Pre-service versus in-service mathematics teachers’ opinions of mathematics reform in post-primary schools in Ireland

A new approach to the teaching and learning of mathematics has been introduced on a phased basis in post-primary education in Ireland. As part of the OECD PISA 2012, a survey was undertaken of in-service mathematics teachers in Ireland, with the aim of gathering data on the opinions of teachers about this reform. Here, a modified version of the survey was distributed to pre-service teachers immediately before and after a four-month teaching placement to ascertain if there were differences in the views expressed by pre-service and in-service teachers in relation to the teaching and learning of mathematics, and also if there were differences expressed by the pre-service teachers before and after their placement in post-primary schools. Analysis of the results showed considerable levels of agreement between all groups, with some exceptions in relation to confidence in teaching the reformed curriculum, emphasis on various teaching and learning activities, and usage of ICT in the classroom.     

What Counts and How: Mathematics Teaching in Culturally, Linguistically, and Socioeconomically Diverse Urban Settings

This article presents findings from an ongoing study of urban teachers' efforts to embrace mathematics reform with student populations that are culturally, linguistically, and socioeconomically diverse (CLSD). We investigate the teacher's role in providing accessible and valuable mathematical learning opportunities to diverse students. Through narrative vignettes of practice and analyses of the personal and intellectual resources teachers draw on in CLSD contexts, we examine the challenges and possibilities two third-grade teachers face as they attempt such reform. One teacher's strengths were in making cultural connections with her students; the other's strengths were in pursuing complex and meaningful mathematics with her students. Building on our analysis, we offer a framework for examining the work of attending to mathematical and cultural issues simultaneously. Our findings suggest that such work is complex; however, teachers are seldom supported in their efforts to integrate these two perspectives. Our aim is to examine the dimensions of culturally relevant mathematics teaching and explore where the fields of mathematics and bilingual-bicultural education need to speak to one another.     

What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems

School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual activity. In this study, the authors explored the problem-posing behavior of elementary prospective teachers, which entailed analyzing the kinds of problems they posed as a result of two interventions. The interventions were designed to probe the effects of (a) exploration of a mathematical situation as a precursor to mathematical problem posing, and (b) development of aesthetic criteria to judge the mathematical quality of the problems posed. Results show that both interventions led to improved problem posing and mathematically richer understandings of what makes a problem ‘good.’     

数学文化教育中教师的缄默知识探讨

数学文化素养的提高,教师素质是关键.数学文化知识是一种缄默知识.探讨数学教师的缄默知识的内涵、特点、教育意义及基于缄默知识的数学文化教育能力具有非常重要的意义.     

数学课程改革中教师角色的分析

从数学教育史的角度看,我国古代教师是一种原始状态下的课程设计者、实践者、研究者;在近代特定历史背景下的教育改革中,数学教师是一个主动研究者;在现代职业化进程中,数学教师逐渐成为课程改革中被动的参与者。从课程理论的角度看,教师的参与应该贯穿于数学课程改革的每个阶段;数学教师的总角色是“行动研究者”,并向“反思型”转变。     

The status and context of change in mathematics education in Malawi

This article analyses the context and status of mathematics education reform in Malawi. It describes four interrelated developments in the reform of secondary education in general, and mathematics education in particular, in Malawi. These developments are concerned with attempts to increase access to secondary education for a majority of Malawians and to provide a mathematical education that is relevant to the needs of the current society. Although these are promising developments in line with the political context of Malawi, and although they aim at developing a more suitable curriculum for Malawi, I suggest that they are limited in two ways. First, participation in these reform processes has involved only a few individuals and neglected teachers and students from distance education centres who comprise the majority of participants in secondary education in Malawi. Secondly, the reform processes have proceeded with little empirical justification and qualitative understanding of the realities of schooling in general, and mathematics education in particular, in Malawi. The analysis in this article suggests that these limitations in the reform process are a function of an inadequate understanding of the social-contextual aspects of mathematics learning and what it means to provide an education that more broadly recognizes its democratic nature.This revised version was published online in September 2005 with corrections to the Cover Date.