中国、新加坡与英国初中几何教材认知复杂程度的比较研究

发布时间：2018-01-13 21:00

本文关键词：中国、新加坡与英国初中几何教材认知复杂程度的比较研究　出处：《西南大学》2017年硕士论文　论文类型：学位论文

【摘要】：本研究以中国、新加坡与英国三国初中几何教材中三角形、四边形与圆部分的数学问题为研究对象,围绕以下两个问题进行比较研究:(1)中国、新加坡与英国三国初中几何教材认知复杂广度的比较研究;(2)中国、新加坡与英国三国初中几何教材认知复杂深度的比较研究。通过比较中、新、英三国初中数学教材中的三角形、四边形与圆相关例、习题的认知复杂程度,发现三套教材具有一定相似之处:(1)就广度而言,三国教材几何部分均较重视利用计算法则或程序解决问题,另外其认知广度种类均不够丰富。(2)就深度而言,三国教材几何部分认知水平要求较高的做数学型任务均相对较少,且其图形复杂程度总体上均不高。除相似之处外,三国教材的认知复杂程度具有一定的差异性,主要体现在:(1)就广度而言,中国教材对知识的实际背景应用和数学推理的重视超过其他两国,且给学生提供了更加丰富的机会参与不同广度种类的问题;新加坡教材较其他两国更加侧重于利用计算法则或程序解决问题;英国教材对于表述型知识问题的设置重视程度强于其他两国。(2)就深度而言,认知要求水平方面,中国教材具有最高层次的认知要求水平,其次为新加坡教材,英国教材最低;图形复杂程度方面,总体上中国教材几何问题所需点线变化量最高,其次为新加坡教材,英国教材所需点线变化量最低;问题解决复杂程度方面,中国教材程度最高,其次为新加坡教材,英国教材程度最低。根据结论,最后向教材编写者与教师提出一定的建议:加强表述型知识的设置以加深学生对于几何性质本质的理解;适当增加做数学型任务(C4)的设置满足高层次水平要求;加强带有图示几何问题的图形复杂程度;教师应当提供补充性材料满足学生的不同认知水平层次需求;教师应当合理分配课时以满足数学问题不同的认知复杂程度。
[Abstract]:This study focuses on the mathematical problems of triangular, quadrilateral and circular parts in junior high school geometry textbooks of China, Singapore and Britain, and makes a comparative study on the following two questions: 1) China. A Comparative study on the Cognitive complexity of Geometry textbooks in Singapore and Britain; 2) A comparative study on the complex cognitive depth of geometry textbooks in junior high schools in China, Singapore and Britain. The cognitive complexity of the exercises, found that the three sets of textbooks have certain similarities) in terms of breadth, the geometric part of the three textbooks pay more attention to the use of calculation rules or procedures to solve problems. In addition, the types of cognitive breadth are not rich. (2) in terms of depth, the geometry part of the three textbooks requires a higher cognitive level of mathematics tasks are relatively less. In addition to the similarities, the cognitive complexity of the textbooks has some differences, mainly reflected in the breadth of the scope. Chinese textbooks pay more attention to the practical application of knowledge and mathematical reasoning than the other two countries, and provide students with more opportunities to participate in different kinds of problems. Singapore teaching materials are more focused on the use of algorithms or procedures to solve problems than the other two countries; British textbooks pay more attention to the issue of expressive knowledge than the other two countries) in terms of depth, the level of cognitive requirements, Chinese textbooks have the highest level of cognitive requirements. The next is Singapore textbook, the British textbook is the lowest; On the whole, the geometric problem of Chinese textbooks requires the highest change of point line, followed by Singapore textbook, and the British textbook requires the lowest change of point line. In terms of the complexity of problem-solving, the Chinese textbook is the highest, the Singapore textbook is the second, and the British textbook is the lowest. According to the conclusion. Finally, some suggestions are put forward to the textbook writers and teachers: strengthening the setting of expressive knowledge in order to deepen the students' understanding of the nature of geometry; Appropriate increase in the number of mathematical tasks (C4) set up to meet the high level requirements; Enhance the complexity of graphics with graphical geometry problems; Teachers should provide supplementary materials to meet the needs of students at different levels of cognition; Teachers should allocate class hours reasonably to meet the different cognitive complexity of mathematical problems.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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