基于知识空间理论的线性代数的关键学习路径

On the Key Learning Path of Linear Algebra Based on Knowledge Space Theory

合理利用线性代数中知识点之间的组织和依赖关系,可以提高学生学习效率及教师的教学质量,然而目前针对线性代数构建知识空间的研究甚少。针对本科生在线性代数学习中的问题,为教育评价提供了一种有效的科学方法,即将知识点与集合论中的元素建立对应关系,基于知识点间的组织和依赖,寻求知识点集合的最小支撑网,利用知识空间理论给出一种线性代数中快速自优化测试过程,使学生能够准确高效地对自己的知识结构、认知缺陷等更细节性内容有一个清晰明确的认识。最终测试结果可以为教师的因材施教提供理论指导,以达到全面了解学生学习状态的目的,同时学生还可以基于已有的测试结果实时掌握个人学习状况,并以此设计符合自己实际情况的学习方案。

Reasonable use of the organization and dependence between knowledge points in Linear Algebra can improve students’learning efficiency and teachers’teaching quality.However,there is little research on the construction of knowledge space in Linear Algebra.In this paper,we provide an adequate scientific method for education evaluation,the knowledge points,which establishes the corresponding relationship between the elements in the set theory.And we seek knowledge points set,the minimum supporting network based on knowledge points.Meanwhile,we give the Linear Algebra optimization test process using the idea of knowledge space,so as to let students have a clearer understanding of what they have learned,such as their knowledge structure and cognitive deficits.The final test results can provide theoretical guidance for teachers to teach students according to their aptitude to achieve a comprehensive understanding of their learning status.At the same time,students can also master their learning status in real time based on the current test results and design their learning plan according to their actual situation.