高中生数形结合数学思维能力提升途径探索

发布时间：2018-10-18 12:36

【摘要】：提高数学思维能力是数学教育的重要目标,而是否掌握数学思想方法是数学思维能力高低的一个表现.数学是研究空间形式和数量关系的科学,数形结合思想是基本的数学思想方法,是提升学生思维能力的重要途径之一.然而在实践教学中发现,不会思考、不愿意思考是目前数学教学中的重要的问题,学生的思维水平没有完全随着知识的增长而得到有效的提升.另外一方面,学生对数学思想方法的掌握情况也不太乐观.本研究对两者的联系进行了探索,试图从数形结合的教学入手,以期提升数学思维能力.本研究主要采用文献分析法、访谈法、案例分析法三种研究方法,对当前高中生的数形结合思想掌握情况和思维状况进行了调查,并提供了相应的教学设计.研究分为三部分:第一部分通过文献分析,对国内外的数形结合思想的研究进行了整理和分析;并从心理学对思维的研究来分析数形结合与数学思维的关联性,找到影响数学思维提升的因素以及数形结合对数学思维的作用.第二部分采用问卷法和访谈法对高中生的数形结合思想的掌握情况进行调查和分析,得出主要结论如下:(1)数形结合整体掌握情况并不理想;(2)习惯于代数解法,较少用图;(3)能够认识到图形在解题中的重要性,但不擅长作图;(4)学生思维有一定的懒惰性,不愿动脑去想一题多解;(5)缺乏解题方法的比较和优化.第三部分在访谈和测试结果的基础上,分别以平面向量和数列进行了案例设计,以此说明如何在数形结合思想的教学中培养思维能力.最后,对数形结合的教学提出一些建议.
[Abstract]:It is an important goal of mathematics education to improve the thinking ability of mathematics, and whether or not to master the method of thinking in mathematics is an expression of the ability of thinking in mathematics. Mathematics is a science that studies the relationship between space form and quantity. The idea of combining number and form is the basic method of mathematical thought and one of the important ways to improve students' thinking ability. However, in practical teaching, it is found that not thinking and unwilling to think is an important problem in mathematics teaching at present, and the students' thinking level has not been improved effectively with the increase of knowledge. On the other hand, students are not very optimistic about how to master mathematical thinking methods. This study explores the relationship between the two and tries to improve the mathematical thinking ability by teaching the combination of numbers and shapes. This research mainly adopts three research methods: literature analysis method, interview method and case analysis method, to investigate the mastering situation and thinking state of the current high school students' numeral-form combination thought, and to provide the corresponding teaching design. The research is divided into three parts: in the first part, through the literature analysis, the research on the combination of numbers and shapes at home and abroad is arranged and analyzed, and the relationship between the combination of number and form and the thinking of mathematics is analyzed from the psychological study of thinking. Find out the factors that affect the promotion of mathematical thinking and the effect of the combination of numbers and shapes on mathematical thinking. In the second part, questionnaire and interview are used to investigate and analyze the mastering of the idea of numeral-form combination in senior high school students, and the main conclusions are as follows: (1) the overall grasp of numeral-form combination is not ideal; (2) it is accustomed to algebraic solution. (3) being able to realize the importance of graphics in solving problems, but not good at drawing; (4) students have a certain laziness in thinking, they do not want to think about more than one problem; (5) lack of comparison and optimization of problem-solving methods. In the third part, based on the results of interviews and tests, the author designs cases with plane vectors and series of numbers to show how to train the thinking ability in the teaching of the combination of numbers and shapes. Finally, some suggestions on the teaching of the combination of numbers and shapes are put forward.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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