A Descriptive Study on Progressof 8th Graders' Proof-Conception in School Mathematics of Japan

最后，本研究以日本国中八年级学童为研究对象，以数学真的相关概念为基础，透过证明教学，描述其证明概念的发展历程。本研究的目标包括：目标1：明确开发基于相对真概念的数学证明教学材料的理论背景;目标2：开发基于相对真概念的数学证明教学材料;目标3：开发基于相对真概念的数学证明教学材料;目标4：开发基于相对真概念的数学证明教学材料。通过自然观察法收集八年级学生在数学真理相关概念证明教学中的部分小组数据。目标4通过社会学和心理学的方法对数据进行分析，描述八年级学生证明概念的发展过程。关于目标1，我讨论了以下几点：讨论1-a：数学中相对真概念的背景和意义;讨论1-B：日本学校数学课程的动向;讨论1-c：初中教科书中证明的介绍 关于我们 日本国中数学教科书的证明教学中命题真值的概念。对于讨论1-c，我得到了以下结论。在日本初中数学教材中，一个证明定义中的论证规则与一组证明的论证之间并不一致，或者说不能判断是否一致。作为不一致的原因，一个标准的正确性（correspondenceto facts学生可以获得）被应用于一个命题之前的几何领域在8年级，和其他标准（连贯性来什么假设）被故意应用于同一命题在该领域。此外，这两个标准的应用是由于不仅采用证明或解释作为证明的功能，而且还采用了八年级几何领域之前所学的命题的局部系统化。关于真理的意义，可以提出两个概念：命题在学生能够认识的范围内的适用性，以及他们的真理对已证明命题的依赖性。关于真理的标准，可以提出以下概念：对一个命题应用哪一个标准是预先确定的，与学生能够认识到的事实相对应，或者在预先确定的用法区分下从假设中推导出来。少

The study finally aims to describe the progress of 8th graders' proof-conception by proof instructions based on relative concept of truth in mathematics in Japan. The aim involves the following goals.Goal 1 : Clarifying the theoretical background to developmaterials for proof instruction based on relative concept of truth in mathematics.Goal 2 : Developing materials for proof instruction based on relative concept of truth in mathematics.Goal 3 : Collecting data of some small groups of 8th grader throughout proof instruction based on relative concept of truth in mathematics by natural observation.Goal 4 : Describing the progress of 8th graders' proof-conception by analyzing the data by sociological / psychological method.Regarding Goal 1, I discussed the following points.Discussion 1-a : Background & significance of relative concept of truth in mathematics.Discussion 1-b : Movement of curriculum in school mathematics of Japan.Discussion 1-c : Introduction of proof in textbooks of junior … More high school mathematics in Japan.Discussion 1-d : Conceptions of truth of a proposition in proof instruction following tectbooks of junior high school mathematics in Japan.As to Discussion 1-c, I got the following conclusion. In textbooks of junior high school mathematics in Japan, there is no consistency between regulations of argument in a definition of proof and a set of arguments of proof, or we cannot judge whether there is a consistency or not. As a reason of no consistency, One criterion of correctness (correspondenceto facts students can acquire) is applied for a proposition before the field of geometry in 8th grade, and the other criterion (coherence to comewhat assumptions) is applied intentionally for the same proposition in the field. Furthermore, the application of two criterions is causedby adapting not only justification or explanation as functions of proof, but also local systemization of the propositions learned before the field of geometry in 8th grade.As to Discussion 1-d, I got the following conclusion. Regarding the meaning of truth, two conceptions is possible to brought up : the applicability of propositions in the range students can recognize, and the dependence of their truth on the proved propositions. Regarding the criterion of truth, the following conception is possible to be brought up : it is pre-established which criterion should be applied to a proposition, the correspondence to the facts students can recognize or the deduction from assumptions under the pre-established distinction of usage. Less