Development of teaching materials for facilitating students' action proof in mathematical inquiry

证明和证明是数学活动的核心，因此应该是所有年级学生数学经验的中心。然而，数学教育研究表明，许多学生在学习证明和证明方面存在困难。为了改善这种学习状况，本研究提出了“行动证明”的概念，旨在探索如何鼓励学生在数学探究中运用行动证明。特别是，本研究通过查阅现有研究，分析材料，并对五年级和九年级学生进行和分析教学实验，得出了一些旨在促进学生活动的教材开发的指导方针。

Proof and proving are at the core of mathematical activities, and therefore should be the center of students' mathematical experiences at all grades. However, mathematics education researches have revealed that many students feel difficulties in learning proof and proving. In order to improve this learning situation, this study focuses on a notion of" action proof", and aims to explore how we can encourage students to utilize action proof in mathematical inquiry. In particular, this study derives some guidelines for developing teaching materials which intend to facilitate students' activities, by examining the existing researches, analyzing materials, and conducting and analyzing teaching-experiments with fifth and ninth graders.