The Research of the Effective Use of CAI for Algebraic Education in University Mathematics

[1]大学生代数教育的新视点代数理论对情报学概念学习和/或理论建构具有重要的借鉴意义。计算机能力在大学生代数教育中的作用主要体现在以下两个方面。(1)总结试错经验，从具体实际出发，形成概括性、系统性的理论。(2)从已建立的理论中提取问题解决策略作为启发式策略。[2]计算机支持的课程CSC(CSC)的实施由首席调查员F.Terada提出，并在一所高中进行了实验实施。尤其是对于计算机教育这样一个高技术、高复杂性的教育，系统的评价更是不可或缺。通过SS(语义结构)分析对上述CSC的实验实施进行了评估。[4]问题解决过程和多元学习环境的分析我们总是根据学生的实际行为来设计问题解决过程的结构。学生利用数学知识和策略知识。数学知识是一组数学真理，即定义、公式、定理等。在此基础上，我们在计算机模拟上实现了数学知识和策略知识，并构建了支持学生问题解决过程的多元学习环境框架。该系统提供了检查学生答案，指出他们的误解，并指导他们解决问题的设施。

[1] The new viewpoint for algebraic education for university students The theory of algebra is important as a good example for the concept learning and/or for the theory structuring in informatics. We have concluded Computer capabilities play the following two roles in the algebraic education for the university students. (1) To give the experience of trial and error to make the generalized and systematic theory from specific facts. (2) To give the problem solving strategies which are extracted from the established theory as the heuristics.[2] The implementation of CSC( Curriculum Supported by Computer ) The CSC, which has been proposed by the head investigator F.Terada, was experimentally implemented in an upper secondary school.[3] The application of the evaluation theory to mathematical education Needless to say, the teaching techniques should always be evaluated to improve. Particularly the systematic evaluation is indispensable for the highly technological and complicated one as the computer based education. The experimental implementation of CSC which was described above was evaluated by SS( Semantic Structure ) analysis.[4] The analysis of problem solving process and the multiple learning environment We always the structure of the problem solving process based on the actual students' behavior. Students utilize two kinds of knowledge, MK( Mathematical knowledge ) and SK( Strategic Knowledge The MK is a set of mathematical truths, i.e. defines, formulas, theorems, and so on.Based on our analysis, we implemented the MK and the SK on a computer simulation and built the framework for the multiple learning environment to support students' problem solving process. This system provides the facility to check students' answers, to point out their misunderstanding, and to guide their problem solving.