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

本研究的目的是开发新的高中离散数学教材，并对教材进行评价。在三年的时间里，进行了以下研究。首先，对高中离散数学可以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的内容现状。第三，收集和分析了高中数学家和数学教师的意见。第四，在此基础上开发离散数学教材。第五，在数学课堂上对教材进行了测试，并评估了学生理解的程度以及他们的兴趣或关注的增加程度。在此过程中，利用离散数学实验教案在中学进行了实验教学，并根据实验结果对实验教案进行了检验。并通过中学课堂教学对教学评价进行了探讨。教材有鸽洞原理、离散图等。通过课堂教学观察、学生应用项目作业分析、学生问题提出分析、学生意识态度问卷分析等方式进行评价。综上所述，离散数学在高中的引入符合数学教育的目标，并且在高中的必修课和选修课中教授离散数学的可能性。高中离散数学的教学内容有必修课中的离散图和鸽子洞原理，选修课中的离散图及其算法和应用、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.