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Developing Learning Activities That All Students Enable to Construct Mathematical Thinking Flows Like "Story-Constructing"

开展让所有学生都能构建数学思维流程（如“故事构建”）的学习活动

基本信息

批准号：
11680183
负责人：
YANAGIMOTO Shigekazu
金额：
$ 1.86万
依托单位：
Fukui University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2002
项目状态：
已结题

项目摘要

One of the most important goals of instruction in classroom mathematics is to insure that each student experiences the deductive development of new facts. In many traditional mathematics classes, if some students are already familiar with a proposition and its proof, and their teacher wants to teach the students how to use deduction to develop the proposition, those students who are already familiar with the proposition and its proof, are unlikely to learn anything new during the teaching-learning process.Students such as the ones described above, may not need to take the class, and they might be called over-prepared for the class. On the other hand, again in traditional geometry classes, teachers routinely assume that all students already know certain facts that are necessary for understanding the teacher's explanations in a lesson. If there are some students that don't know these facts, these students cannot understand the teacher's explanation, and they consequently cannot benefit f … More rom their teacher's instruction. These students might be called under-prepared, and if the teacher tries to meet the needs of under-prepared students, then there is often minimal progress in meeting the goals of the lesson in the classroom.So, the teacher faces a dilemma in trying to meet the needs of both under- and over-prepared students. If the teacher tries to meet the needs of over-prepared students, then the under-prepared students cannot understand the teacher's explanation.The under- and over-prepared students essentially inhibit each other from making progress in the math class.This is one of the most serious problems in traditional geometry classes, and it is not a problem with an easy solution. We have developed a principle of mathematics lesson which satisfies the following conditions :(1) Both under- and over-prepared students can deduce new facts on the basis of (old) facts they know in their own way ; and(2) Each student can construct a new line of reasoning (or flow of reasoning) by combining the results of his/her reasoning with those of other students. Less

课堂数学教学最重要的目标之一就是确保每个学生都能体验到新事实的演绎发展。在许多传统的数学课堂上，如果一些学生已经熟悉了一个命题及其证明，而他们的老师想要教会学生如何利用演绎来发展这个命题，那么那些已经熟悉了这个命题及其证明的学生，不太可能在教与学的过程中学到任何新的东西。如上所述的学生可能不需要上这门课，他们可能被称为为这门课做了过度准备。另一方面，同样是在传统的几何课堂上，老师通常认为所有的学生都已经知道了理解老师在一节课上的解释所必需的某些事实。如果有一些学生不知道这些事实，这些学生就不能理解老师的解释，因此他们不能受益于…更多的是听从老师的教导。这些学生可能被称为准备不足，如果老师试图满足准备不足的学生的需求，那么在实现课堂上的课程目标方面往往进展甚微。因此，教师在努力满足准备不足和准备过度的学生的需求方面面临两难境地。如果老师试图满足准备过度的学生的需要，那么准备不足的学生就听不懂老师的解释。准备不足和准备过度的学生本质上是相互抑制的，在数学课堂上取得进步。这是传统几何课堂上最严重的问题之一，也不是一个容易解决的问题。我们开发了一种满足以下条件的数学课原则：(1)准备不足和准备过度的学生都可以用自己的方式根据他们所知道的(旧的)事实来推断新的事实；(2)每个学生都可以通过将他/她的推理结果与其他学生的推理结果相结合来构建一条新的推理(或推理流程)。较少