九年级学生几何证明水平与数学学业成绩的关联性研究

发布时间：2018-01-27 05:48

本文关键词： 范希尔几何思维水平 SOLO分类理论几何证明九年级学生　出处：《广州大学》2016年硕士论文　论文类型：学位论文

【摘要】：在新课程改革的背景下,几何课程在编排与设置上发生了许多变化,但几何教学问题并没有因为几何课程的改革而减少,不少数学教师在教学中发现,有些学生对几何知识点的理解不存在认知障碍,但在解答证明题时却无法准确作答,这反映出学生的几何认知结构向思维结构的转化出现障碍,即学生的几何思维水平与其证明水平并不匹配。本研究采用了以定量为主的研究方法,以范希尔理论和SOLO分类理论为基础,首次提出几何证明水平层次可分为:水平1-直观证明,水平2-描述证明,水平3-关联证明,水平4-逻辑证明,水平5-优化证明,然后结合初中教材与《课程标准(2011版)》编制了几何证明水平测试卷,制定了相应的评价指标,并选取广州市某中学191名九年级学生作为研究样本,通过对相关测试的数据统计分析,不仅探讨了九年级学生在几何思维水平、几何证明水平的分布情形,而且也探究九年级学生的几何思维水平与证明水平的相关性、几何证明水平与学业成绩的关联性。主要结论有:1.12%的学生的几何思维处于水平三以下,80%以上的学生的几何思维达到了水平三甚至更高,整体的分布并不均匀,水平一至水平四分别为3.8%、8.2%、66.5%、14.3%,有7.1%的学生是违反范希尔理论的。另外,男女生在几何思维水平的发展上没有显著差异。2.16%的学生仍停留在低几何证明水平阶段,32%的学生处于中几何证明水平阶段,超过50%的学生达到高几何证明水平阶段,整体的分布不均匀,层次一至层次五分别为3.3%、12.64%、32.42%、42.86%、8.79%。另外,男女生在几何证明水平的发展上没有显著差异。3.在几何思维水平与几何证明水平的关联对比上,两者具有一定的相关性,不同的范希尔几何思维水平对应着若干个不同的几何证明水平,并可按一定的比例转换成相应的几何证明水平层次。4.几何思维水平与几何证明水平有强正相关性,两者之间的Spearman相关系数为0.822,几何证明水平与“一模成绩”、中考成绩有强正相关性,它们之间的Spearman两两相关系数分别为0.937、0.956。以此研究结论为基础,笔者通过对不同几何证明水平的学生进行认知分析,提出几何证明水平的层级结构与相应特点,并对不同几何证明水平的学生提出相应的教学建议如下:1.低几何证明水平学生应加强阅读与识图训练,教师在课堂上应有详细板书,让学生模仿学习;2.中几何证明水平学生可采用思维导图的方式,让学生写证明的思路分析,从而将知识加工成有联系的结构网;3.高几何证明水平学生要注意几何学习方法的归纳与总结,教师应进行针对性指导,并鼓励在解决原问题后提出新问题。本课题旨在为几何课程的改革、教材的编写和教师的教学提供有价值的参考依据,促使广大教师在教学实践中,能更加科学、有效地运用现代教育理念,组织并完善课堂教学。
[Abstract]:Under the background of the new curriculum reform, many changes have taken place in the arrangement and setting of the geometry curriculum, but the problems in geometry teaching have not been reduced because of the reform of the geometry curriculum. Many mathematics teachers have found out in the course of teaching. Some students do not have cognitive barriers to the understanding of geometric knowledge points, but they can not answer the proof questions accurately, which reflects the obstacles in the transformation of students' geometry cognitive structure to thinking structure. That is, the level of students' geometric thinking does not match their level of proof. This study adopts a quantitative approach, based on Van Hell's theory and SOLO's classification theory. For the first time, the level level of geometric proof can be divided into: level 1-visual proof, horizontal 2-description proof, horizontal 3-correlation proof, horizontal 4-logic proof, horizontal 5-optimization proof. Then combined with the junior high school textbooks and "Curriculum Standards 2011 Edition)" compiled a geometric proof level test paper, and formulated the corresponding evaluation indicators. With 191 ninth grade students in a middle school in Guangzhou as the research sample, the distribution of geometric thinking level and geometric proof level of ninth grade students is not only discussed by statistical analysis of relevant test data. It also explores the correlation between the level of geometric thinking and the level of proof and the correlation between the level of geometric proof and academic achievement. The main conclusion is that 1.12% of the students are below the level of three levels of geometric thinking. The geometric thinking of more than 80% students reached the level of three or more, the overall distribution is not even, the level of one to level four is 3.88.2or 66.5%. In addition, there is no significant difference between boys and girls in the development of geometric thinking level. 2.16% of the students are still at the stage of low geometric proof level. 32% of the students were in the level of middle geometric proof, and more than 50% of the students had reached the stage of high geometric proof, and the distribution of the whole was not even. 32.42 / 42.86 / 8.79. in addition, there is no significant difference in the development of the level of geometric proof between male and female students. (3) there is no significant difference between the level of geometric thinking and the level of geometric proof. There is a certain correlation between them. Different levels of van hill's geometric thinking correspond to several different levels of geometric proof. The geometric thinking level has strong positive correlation with geometric proof level, and the Spearman correlation coefficient between them is 0.822. There is a strong positive correlation between the level of geometric proof and the "score of one mode", and the correlation coefficient of Spearman between them is 0.937 / 0.956 respectively, which is based on the conclusion of the study. Through the cognitive analysis of students with different levels of geometric proof, the author puts forward the hierarchical structure and corresponding characteristics of the level of geometric proof. The teaching suggestions for students with different levels of geometric proof are as follows: 1.The students with low level of geometric proof should strengthen the training of reading and reading map, and teachers should have detailed blackboard writing in class to allow students to imitate learning; 2. The students can use the way of thinking map to write the thought analysis of proof, so that the knowledge can be processed into a network of related structures. 3. Students with high level of geometric proof should pay attention to the induction and summary of geometric learning methods, and teachers should give targeted guidance and encourage them to raise new problems after solving the original problems. The purpose of this project is to reform the geometry curriculum. The compilation of teaching materials and the teaching of teachers can provide valuable reference for teachers to be more scientific and effective in their teaching practice and to organize and perfect classroom teaching.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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