基于APOS理论的高一数学习题教学的调查与实验研究

发布时间：2018-04-30 16:24

本文选题：APOS理论 + 解题　；参考：《闽南师范大学》2015年硕士论文

【摘要】：学习数学离不开解题,学好数学就意味着善于解题,而教学内容以解题为主的习题课在数学课程中就显得尤为重要。但是,由于受到应试教育及“熟能生巧”传统思想的影响,习题课教学现状不容乐观,主要表现之一就是缺少解题理论的科学指导。杜宾斯基提出的APOS理论可以为数学习题课教学提供理论基础,为数学习题课教学寻求新途径,并对一线教师的习题课教学有所帮助。而且,APOS理论是为数不多的依据数学学科特点而建立的教学理论,对此理论进行深入的研究也是十分有意义的。本文先采用问卷调查的研究方法从两方面了解学生在数学习题课中的学习现状。一方面以问卷的形式了解学生学习水平的现状,分析存在的主要问题;另一方面以测试题的形式,依据APOS理论调查学生的认知水平的现状,发现以下问题:(1)80%的学生已达到活动阶段和过程阶段;(2)45%-60%的学生达到对象阶段;(3)仅有20%-40%的学生达到图式阶段。针对上述对习题课学习的调查现状,基于APOS理论对数学习题课教学进行优化实践,开展微型教学实验,并通过数学成绩和出声思维测试两方面来检验实验效果。研究结果表明:(1)基于APOS理论的数学习题课教学效果明显优于传统教学效果;(2)个别学生由于认知水平偏低、数学基础差等原因还不能掌握解题思路探索方法,实验效果不明显。在调查研究和实验研究的基础上,针对数学习题课教学,依据APOS理论分析学生在解题时的内部思维过程,体会对数学习题课教学活动的启示,并探讨基于APOS理论的数学习题课教学策略:(1)呈现解题思路探索过程;(2)引导学生学会建构完整的知识图式;(3)培养学生解题后积极反思的习惯。
[Abstract]:Learning mathematics is inseparable from solving problems, learning mathematics well means being good at solving problems, and the lesson of problem solving is especially important in mathematics course. However, due to the influence of examination-oriented education and the traditional thought of "practice makes perfect", the present situation of exercise teaching is not optimistic. One of the main manifestations is the lack of scientific guidance of problem solving theory. The APOS theory put forward by Dobinsky can provide a theoretical basis for the teaching of mathematics exercises, seek a new way for the teaching of mathematics exercises, and be helpful to the teaching of exercises for first-line teachers. Moreover, APOS theory is one of the few teaching theories established according to the characteristics of mathematics, so it is very meaningful to study this theory deeply. In this paper, the present situation of students' study in mathematics exercises is studied from two aspects by means of questionnaire survey. On the one hand, the present situation of students' learning level is understood by questionnaire, and the main problems are analyzed. On the other hand, the present situation of students' cognitive level is investigated according to the APOS theory by the form of test questions. It is found that 80% of the students have reached the activity stage and the process stage, and 60% of the students have reached the target stage. Only 20% -40% of the students have reached the schema stage. In view of the above investigation on the study of exercise course, this paper optimizes the teaching practice of mathematics exercise course based on APOS theory, carries out micro-teaching experiment, and tests the effect of the experiment through two aspects: mathematics achievement and sound thinking test. The result shows that the teaching effect of the mathematics exercises course based on the APOS theory is obviously better than that of the traditional teaching method. Because of the low cognitive level and poor mathematical foundation, some students can not grasp the method of exploring the thinking of solving problems, and the experimental results are not obvious. On the basis of investigation and experimental research, according to the APOS theory, this paper analyzes the inner thinking process of students in solving problems, and experiences the enlightenment to the teaching activities of mathematics exercises. This paper also discusses the teaching strategy of mathematics exercises class based on APOS theory: 1) presents the thinking of solving problems 2) guides students to learn to construct complete knowledge schemas and 3) cultivates students' habit of active reflection after solving problems.
【学位授予单位】：闽南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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