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

本研究旨在开发高中离散数学新教材，并对教材进行评价。首先，对高中离散数学学习的内容进行了选择和分析。其次，分析了国外课程和教材内容的现状。第三，收集和分析了高中数学家和数学教师的意见。第四，在前述研究成果的基础上，编制了离散数学教材。第五，在数学课堂上对教材进行实验，评估学生的理解程度和兴趣或关注的增加程度。在此过程中，使用离散数学实验教学计划在中学进行了实验教学，并根据结果对计划进行了审查。并以中学课堂教学为例，对如何评价教学进行了探讨。教材有鸽子洞原理、离散图等。通过课堂教学观察、学生应用项目作业单分析、学生问题提出分析、学生意识与态度问卷分析等方式进行评价，得出结论：将离散数学引入高中是符合数学教育目标的，在高中开设离散数学必修课和选修课是可行的。高中离散数学的内容包括必修课上的离散图和鸽子洞原理，选修课上的离散图及其算法及其应用，鸽子洞原理和二进制逻辑。

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.