Developmental Research on New Teaching Materials on Discrete Mathematics in Upper Secondary School

高中离散数学新教材的开发研究

• 批准号: 16300258
• 负责人: NAGASAKI Eizo
• 金额: $ 7.68万
• 依托单位: National Institute for Educational Policy Research
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16300258/
• 关键词: Discrete mathematics; Graph Theory; Pigeon Hole Principle; Development of Teaching Materials; Upper Secondary School Mathematics

The objectives of this research is to develop new teaching materials on discrete mathematics in upper secondary school and to evaluate the materials.During three years, the following studies were carried out. First, content to be able to learn on discrete mathematics in upper secondary school were selected and analyzed. Second, the present states of the content in curriculum and textbooks in other countries were analyzed. Third, opinions of mathematicians and mathematics teachers in upper secondary schools were collected and analyzed. Forth, teaching materials on discrete mathematics were developed based on the results before mentioned. And fifth, trails on the teaching materials were conducted in mathematics classrooms and how much students understood and their interests or concerns increased were evaluated. In the process, experimental teaching were conducted in secondary schools using experimental teaching plans on discrete mathematics and the plans were examined based on the results. And how to evaluate the teaching was investigated through classroom teaching in secondary schools. Teaching materials were pigeon hole principle, discrete graph and others. Evaluation were conducted through observation during classroom teaching, analysis of students' worksheets on application items, analysis of students' problem posing, and analysis of students' questionnaires on awareness and attitudes.In conclusion, introduction of discrete mathematics into upper secondary school was placed in accordance with aims of mathematics education and possibility to teach discrete mathematics in compulsory and selective courses was showed in upper secondary school. Content on discrete mathematics that can be taught in upper secondary school are discrete graphs and pigeonhole principle in compulsory course, and discrete graphs, and their algorithms and their application, pigeon hole principle and binary logic in selective course.

本研究的目的是开发新的高中离散数学教材并对其进行评价。三年来，进行了以下研究。首先，对高中离散数学能够学习的内容进行了筛选和分析。其次，分析了其他国家课程和教科书内容的现状。第三，收集并分析了高中数学家和数学教师的意见。第四，根据上述成果开发了离散数学教材。第五，在数学课堂上对教材进行试用，评估学生的理解程度和兴趣或关注点的增加程度。在此过程中，利用离散数学实验教学方案在中学进行实验教学，并根据实验结果对方案进行了检验。并通过中学课堂教学来探讨如何评价教学。教材有鸽子洞原理、离散图等。通过课堂教学观察、学生应用题作业分析、学生提出问题分析、学生认知态度调查问卷分析等方式进行评价。根据数学教育的目标，在高中的必修课和选修课中展示了教授离散数学的可能性。高中离散数学可以讲授的内容有必修课的离散图和鸽巢原理，选修课的离散图及其算法和应用、鸽巢原理和二元逻辑。