Learning mathematics and learning to teach: Learning cycles in mathematics teacher education

The reconceptualization of mathematics teacher education based on current mathematics education reform efforts necessitates the elaboration of theoretical frameworks to guide both the practice of and research on teacher education. The author presents a framework which has been useful in shaping two major mathematics teacher education research and development projects. This framework for mathematics teacher learning builds recursively on a framework for mathematics learning which derives from a social constructivist view of learning and incorporates aspects of French didactical theory using the organizing structure of the Karplus Learning Cycle. The framework can be used to think about the content and organization of a particular lesson or of an entire course or program for teachers. Further, it describes the interconnection between different domains of teacher knowledge.     

信息与计算科学专业开设《数学建模实验》课程教学研究和实践

研究了理科数学建模实验教学模式,给出了建模实验教学大纲,介绍了实验教学方法,考核方式及实践后的认识与体会,说明数学建模实验课程与数学建模课程一样,将日益受到考核的重视.     

Developing mathematics teacher knowledge: the paradidactic infrastructure of “open lesson” in Japan

In this paper, we first present a theoretical approach to study mathematics teacher knowledge and the conditions for developing it, which is firmly rooted in a systemic approach to didactic phenomena at large, namely the anthropological theory of the didactic. Then, a case of open lesson is presented and analysed, using this theoretical approach, to show how the format of open lesson contributes to the construction and diffusion of didactic knowledge in the community of mathematics teachers in Japan. The basic idea of this format is that teachers from other schools are invited to observe a class taught by a teacher then participate in a discussion session with him on the details of the lesson. For the case study, we analyse the lesson plan prepared for an open lesson, the observed lesson and the teachers’ discussion. As a result, an open lesson session has been described as a specific form of post-didactic practice related directly to an actual observed lesson, and aiming specifically at elaborating the theoretical aspects of teacher’s didactic practice in the lesson and beyond it.     

Introducing a symbolic interactionist approach on teaching mathematics: the case of revoicing as an interactional strategy in the teaching of probability

This study examines an interactional view on teaching mathematics, whereby meaning is co-produced with the students through a process of negotiation. Further, teaching is viewed from a symbolic interactionism perspective, allowing the analysis to focus on the teacher’s role in the negotiation of meaning. Using methods inspired by grounded theory, patterns of teachers’ interaction are categorized. The results show how teachers’ actions, interpretations and intentions form interactional strategies that guide the negotiation of meaning in the classroom. The theoretical case of revoicing as a teacher action, together with interpretations of mathematical objects from probability theory, is used to exemplify conclusions from the proposed perspective. Data are generated from a lesson sequence with two teachers working with known and unknown constant sample spaces with their classes. In the lessons presented in this article, the focus is on negotiations of the meaning of chance. The analysis revealed how the teachers indicate their interpretations of mathematical objects and intentions to the students to different degrees and, by doing so, create opportunities for the students to ascribe meaning to these objects. The discussion contrasts the findings with possible interpretations from other perspectives on teaching.     

THE INTERACTIONAL ACCOMPLISHMENT OF NOT KNOWING IN ELEMENTARY SCHOOL SCIENCE AND MATHEMATICS: IMPLICATIONS FOR CLASSROOM PERFORMANCE ASSESSMENT PRACTICES

The day-to-day business of being a science or mathematics teacher involves the continuous assessment of students. This, in turn, is an inherently discursive process. The aim of the present study is to examine some of the specific discursive practices through which science and mathematics knowing is jointly produced through classroom interaction. In particular, we examine the coproduced nature of two students’ not knowing—one in an outdoor elementary school science lesson and the other in an elementary school mathematics lesson. Our analysis is based on ideas in discursive psychology and challenges conventional interpretations of students’ academic performance in school science and mathematics.     

小学数学课堂教学评价的质性研究

Through the qualitative interviews of five implementers of primary school mathematics curriculum, this study addresses the ways in which mathematics lessons are evaluated. Results show that each evaluator recognizes different aspects of a “good lesson,” however, among all criteria, the design of the lesson plan, realization of the lesson goals, active student participation, and mathematical thinking are seen as key indicators in lesson evaluation. The study also shows that student performance is a major point of concern in lesson evaluation, and some extreme teaching practice has drawn attention and being reflected by some implementers of the New Mathematics Curriculum.     

中学数学教学的说课活动

针对目前中学数学教研中“说课”环节薄弱,不少人错误地将“说课”与“复述教案”、“简介教学过程”混为一谈的现状,阐明了说课的科学涵义与类型,结合实例讨论了数学说课的内容及实践意义,指出了培养数学说课能力所应遵循的原则。     

成人"经济数学基础"课教学探索

"经济数学基础"是成人高校经济学科各专业一门必修的重要基础理论课,教学中要面对学员的学习现状,改变以往的教学观念,注重提高学员的数学素养,使学员掌握一定的数学技巧和技能,以不断满足社会需求,并使学员今后在不同的领域中,具备应用数学解决实际问题的能力.     

Reports on Books

OfSTED's criteria for inspection are published and available to all. However, it is quite possible that there will be a mismatch between schools' interpretations of what OfSTED means by good practice in primary mathematics and those of the inspectors who come to inspect them. The research reported here focuses on the responses of a small set of primary schools to the inspection of their mathematics: their anticipation of issues, their expectations of what would be found and their views of how the inspection would contribute to the development of good practice. Inspectors' reports seemed frequently to match the expectations of the schools. Interpretations appeared to coincide, but in some cases there appeared to be mismatch and disagreement which raised questions about expertise or interpretations of both inspector and mathematics co-ordinator and might, in turn, affect the development of mathematics following inspection.     

《电气控制及PLC》教学改革的探索与体会

可编程控制器是工业自动化领域中不可缺少的一种逻辑控制器,已经成为高等学校自动化、机械电子工程等专业的必修课。由于该课程具有较强的实践性,本文旨在现有的教学研究基础上,探索一种新的教学方法,使学生理论联系实际,着力提高学生的实践能力。     

电子书包与初中数学教学深度融合的模式与策略研究

本文结合电子书包的课堂教学应用实践,提炼电子书包与初中数学教学深度融合的课堂教学模式,明确了新授课及练习课、复习课的基本教学流程;提出电子书包与初中数学教学深度融合的"电子书包多组件参与探究"等教学策略,以及电子书包与初中数学教学深度融合的"班级空间与微信平台融合"等家校互联学习策略,以期为电子书包环境下创新教师的教学...     

中学数学教学方法创新思维辩证论

中学数学的教学,是关系到学生数学思维形成的重要阶段。在这个特殊时期,引领学生掌握数学学习的基本方法,探讨对于数学问题的不同的解释,都是极其重要的。涉及到数学教学的创新,需要教育工作者不断总结,在实践中避轻就重,在总结的基础上创新。     

浅谈高等数学的教学原则

高等数学是大学理工科及经济学专业的一门基础课，为教好和学好它，对教学原肘进行探讨很有必要。教学原则可分理论课与习题课并重的原则；单项训练与综合训练相互结合的原则；经典的、基本的内容与现代数学的方法尽量结合的原则；直觉想象和审慎推敲相互结合和转化的原则。     

Middle school teachers’ differing perceptions and use of curriculum materials and the common core

Eight middle school mathematics teachers’ perceptions and uses of curriculum materials and the Common Core State Standards for Mathematics (CCSSM) were investigated. Adapting a noticing framework and models of dialogic instruction and direct instruction, teachers’ noticing practices with curriculum materials and the CCSSM when planning, enacting, and reflecting on lessons were examined. Teachers who were committed to implementing the CCSSM and who were using one of two substantively different curriculum programs were purposefully selected. Data sources included multiple forms of interviews and classroom observations. The teaching evidenced three distinct noticing patterns. These patterns indicated that teachers’ curriculum materials were associated with how teachers perceived and enacted the CCSSM. Teaching with a curriculum program that was designed as a thinking device prioritized the Standards for Mathematical Practice of CCSSM evidenced noticing that was consistent with dialogic instruction. Teaching with a curriculum program that was designed as a delivery mechanism prioritized the Content Standards of CCSSM and evidenced noticing consistent with direct instruction. Findings indicated that the designated curriculum and contributed to differing interpretations of CCSSM and served as a lens for noticing. However, a dialogic curriculum program was not sufficient to support dialogic approaches in practice. One pattern showed teachers planning dialogic lessons, but the lesson enactments were not consistent with teachers’ plans, with evidence that the teachers were not aware that their practices differed from dialogic approaches. Implications for research and practice are discussed.     

The role of attention in expert classroom practice

In this paper we outline a new theoretical model of expert practice that identifies the importance of attentional skills. We report on a small-scale pilot study of the classroom practice of experienced teachers of mathematics based on this model, through which a method of articulating aspects of classroom practice has been developed. This study took place in England, where current policy in teacher education places considerable emphasis on lesson planning. Our study raises issues about the relationships between the different kinds of knowledge that we see as constituting expert practice.     

《数学教学论》教学中实施模拟课堂教学实践的探讨

模拟课堂教学实践就是学生在教师的指导下,以数学教学理论为指导,充分发挥教师的创造性,自行设计教学方案,并模拟中学数学课堂对其中的一个教学设计方案进行教学实践。模拟课堂教学实践分为前期准备、课堂教学设计、模拟课堂实施和总结评价四个阶段。它充分调动学生自主学习的积极性,有效地促进学生之间的相互学习;创造理论与实践相结合的机会,深化学生对数学教学理论的理解;提供训练教学技能的平台,促进学生数学教学能力的初步形成。