数学习题课的导学功能初探——以“平行四边形复习课”为例

在数学的教学过程中,习题课教学是必不可少的.那么,数学习题课教学,应该如何进行,又应该让学生通过习题课学到什么呢？笔者认为,数学习题课的功能不仅是对数学概念、命题的复习巩固,也应该是对数学解题方法的总结提炼,甚至应该起到对学生后续学习的引导作用.     

浅谈数学习题课的教学

浅谈数学习题课的教学刘汉顶（安徽枞阳中学２４６７００）习题课是数学教学中经常运用的一种教学形式．通过习题课的教学，帮助学生巩固、深化有关概念，消除某些困惑，纠正存在的问题，梳理知识结构，完善知识系统，从而使学生掌握有关知识和某些解题方法，达到培养学生...     

习题课教学要充分体现“四性”

习题课教学要充分体现“四性”杨瑛芳（甘肃民乐一中７３４５００）培养学生的思维能力是数学教学的目的之一．在数学教学中思维能力的培养有赖于对数学问题的解决，而中学阶段的数学问题主要表现形式为习题，所以解题教学是帮助学生思维能力提高的重要途径．为了使习题能...     

促进数学习题课教学有效性的实践与思考

本文针对习题课教学谈谈提高课堂有效性的实践与思考.通过习题课的教学,落实素质教育,已成为数学教学的重要任务.通过多年研究后发现,在一些传统单一的基础数学习题课等教学训练模式体系中,加入一些开放性、探究性问题,可以比较有效地培养学生的思维创新开拓意识、创新思维训练和计算机应用综合能力,切实做到使学生关注于自身的各项实际能力得到发展,从而提高数学习题课的教学有效性.     

关于数学习题课的思考

本文对数学习题课教学进行了深入的探讨 ,对如何提高习题课的教学质量作了一些研究     

关于数学习题课的思考

本对数学习题课教学进行了深入的探讨,对如何提高习题课的教学质量作了一些研究。     

利用课本习题上好习题课例谈

利用课本习题上好习题课例谈２２６６００江苏海安中学张亚东，李红习题课教学是学生获得数学知识，掌握解题技巧，理解所涉及的数学思想方法的主要渠道．课本每章节都精心安排有一定数量的习题和复习题，如何充分利用这些习题，深入挖掘它们的潜在教学功能来发展学生思维...     

在典型例题的习题课教学中培养学生的创新能力

教学实践表明,数学习题课是培养学生数学修养,提高创新能力的一种十分有效的教学形式.本文结合一道典型数学例题,尝试数学习题课在培养大学生的质疑态度,否定意识,一题多解,类比分析,逻辑推理,以及追根寻源的探索精神等方面的重要作用.这些方面都是通常所说创新能力的重要组成部分.     

初中数学习题课变式教学初探

习题课是初中数学教学的一种重要形式,学生通过习题课对已学知识进行再认识,并进一步从数学思想方法的高度认识知识的本质和内在的联系,从而使所学的知识融会贯通,运用自如.     

注重思维过程是提高数学教学效率的关键

本文针对数学教学中常存在的两种倾向，提出了两方面的建议．数学理论知识的教学要注重思维过程，强调思维过程是数学教学的本质；习题课的教学要注重选题的典型性，使之既成为理论教学的巩固和延伸，也成为思维训练的继续和发展．并以等比数列的教学为例，对两方面的建议分别进行了说明．     

Teaching routines and student-centered mathematics instruction: The essential role of conferring to understand student thinking and reasoning

We compare two lessons with respect to how a teacher centers student mathematical thinking to move instruction forward through enactment of five mathematically productive teaching routines: Conferring To Understand Student Thinking and Reasoning, Structuring Mathematical Student Talk, Working With Selected and Sequenced Student Math Ideas, Working with Public Records of Students’ Mathematical Thinking, and Orchestrating Mathematical Discussion. Findings show that the lessons differ in the enactment of teaching routines, especially Conferring to Understand Student Thinking and Reasoning which resulted in a difference in student-centeredness of the instruction. This difference highlights whose mathematics was being centralized in the classroom and whether the focus was on correct answers and procedures or on students’ mathematical thinking and justifying.     

Assessing and understanding U.S. and Chinese students' mathematical thinking

If the main goal of educational research and refinement of instructional program is to improve students' learning, it is necessary to assess students' emerging understandings and to see how they arise. The purpose of this paper is to address issues related to assessments of students' mathematical thinking in cross-national studies and then to discuss the lessons we may learn from these studies to assess and improve students' learning. In particular, the issues related to assessing U.S. and Chinese students' mathematical thinking were discussed. Then, this paper discussed the findings from two studies examining the impact of early algebra learning and teachers' beliefs on U.S. and Chinese students' mathematical thinking. Lastly, the issues related to interpreting and understanding the differences between U.S. and Chinese students' thinking were discussed.     

Studying sample lessons rather than one excellent lesson: A Japanese perspective on the TIMSS videotape classroom study

The findings of the TIMSS Videotape Classroom Study include aspects of mathematics lessons showing a strong resemblance between Germany and the US in difference to Japan. This paper discusses some of the features that appear to make Japanese lessons different from the other two countries. In particular, the paper examines the goals of lessons described by Japanese teachers, how lessons are structured and implemented, and the emphasis on alternative solutions to a problem in the teaching and learning processes. The characteristics of Japanese lessons identified by the TIMSS Videotape Classroom Study can naturally be interpreted as indications of teachers' efforts to foster students' mathematical thinking in the classroom.     

Carpenter,tractors and microbes for the development of logical–mathematical thinking – the way 10th graders and pre-service teachers solve thinking challenges

The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical–mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th graders was higher than that of the pre-service teachers. Unlike the 10th graders, some of whom used various strategies for representing the problem, most of the pre-service teachers’ answers were based on a technical algorithm, without using control processes. The obvious conclusion drawn from the findings supports and recommends expanding and enhancing the development of logical–mathematical thinking, both in specific lessons and as an integral part of other lessons in pre-service frameworks.     

Using Sociocultural Theory to Teach Mathematics: A Vygotskian Perspective

This study describes an elementary teacher's implementation of sociocultural theory in practice. Communication is central to teaching with a sociocultural approach and to the understanding of students; teachers who use this theory involve students in explaining and justifying their thinking. In this study ethnographic research methods were used to collect data for 4 1/2 months in order to understand the mathematical culture of this fourth‐grade class and to portray how the teacher used a sociocultural approach to teach mathematics. To portray this teaching approach, teaching episodes from the teacher's mathematics lessons are described, and these episodes are analyzed to demonstrate how students created taken‐as‐shared meanings of mathematics. Excerpts from interviews with the teacher are also used to describe this teacher's thinking about her teaching.     

Teachers' Considerations of Students' Thinking During Mathematics Lesson Design

Teachers' abilities to design mathematics lessons are related to their capability to mobilize resources to meeting intended learning goals based on their noticing. In this process, knowing how teachers consider Students' thinking is important for understanding how they are making decisions to promote student learning. While teaching, what teachers notice influences their decision‐making process. This article explores the mathematics lesson planning practices of four 4th‐grade teachers at the same school to understand how their consideration of Students' learning influences planning decisions. Case study methodology was used to gain an in‐depth perspective of the mathematics planning practices of the teachers. Results indicate the teachers took varying approaches in how they considered students. One teacher adapted instruction based on Students' conceptual understanding, two teachers aimed at producing skill‐efficient students, and the final teacher regulated learning with a strict adherence to daily lessons in curriculum materials, with little emphasis on student understanding. These findings highlight the importance of providing professional development support to teachers focused on their noticing and considerations of Students' mathematical understandings as related to learning outcomes. These findings are distinguished from other studies because of the focus on how teachers consider Students' thinking during lesson planning. This article features a Research to Practice Companion Article . Please click on the supporting information link below to access.     

Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective

This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.     

Educating rational decision-makers about uncertainty using US social security investment economics

We make a case for improving the education of future rational decision-makers who will incorporate probabilistic thinking and not simply deterministic thinking in their processes of making decisions. The power of a system, systems thinking, and the power of thinking spatially, symbolically, and distributionally will be more naturally internalized by students who routinely use the tools of rational decision-making in both their coursework and their professional careers. Using the recent Social Security debate in the United States as a case example, we demonstrate how to enlarge the frame of the discussion, and hence change the course of the debate, to include uncertainty, market volatility, and the security of investments, not just their average rate of return. An important issue is identified and addressed by the use of a simple mathematical model based on difference equations and generating functions, which was implemented in Microsoft Excel along with the @RISK Monte Carlo Simulation program. The lessons learned can be used in many decision-making frameworks.