初中生几何证明中目标选择性联结能力的调查研究

发布时间：2018-05-09 15:08

本文选题：初中生 + 几何证明　；参考：《山东师范大学》2017年硕士论文

【摘要】：美国数学教师协会在《数学课程标准(2000年)》中首次提出了数学联结能力,其“中介”的特质可以很好地将学生头脑中储备的相关信息调配运用起来。而目标选择性联结能力是基于数学联结的多向性和复杂性提出的,重在以问题目标为导向进行选择性联结。本文通过对数学联结能力以及目标选择性联结相关文献的分析,在联结主义、认知主义以及相关数学教育心理学的基础上,结合几何证明的特点,提出初中生几何证明中目标选择性联结能力的概念,即初中生能以问题目标为导向,联结到数学学习中的相关的概念、命题、方法等,并积极主动地作出正确、合理的筛选和加工,能监控自己的选择性联结对证明过程产生的影响,并能对自己选择性联结行为进行调节的一种个性心理特征。它是一种以解决几何证明问题为特定任务的数学解题能力,既包括对几何模块学习中的知识进行选择联结、重组加工等认知成分,也包括对自己的目标选择性联结的过程进行计划、监控、调节等元认知成分。本文通过对初中生几何证明中目标选择性联结能力进行调查,了解初中生几何证明中目标选择性联结能力水平,以及目标选择性联结对初中生几何证明的影响,并据此提出培养初中生几何证明中目标选择性联结能力的对策。本文的研究顺序主要有以下几点:第一,确定研究方向。首先对目标选择性联结等相关文献进行分析,得出相关研究成果,并确定研究的内容。第二,建构相关理论。根据相关心理学和数学教育心理学的理论建构了几何证明中目标选择性联结能力的理论基础,并对其内涵以及能力成分进行界定。第三,设计调查并实施。本次调查以调查问卷和几何证明测试题相结合的形式进行调查。第四,得出调查结论。根据调查统计结果,得出初中生在几何证明中目标选择性联结能力的现状和水平,以及对解决几何证明问题的影响,并做出反思,提出培养几何证明中目标选择性联结能力的必要性。第五,提出培养策略。本文研究的结论主要有以下几点:第一,初中生在几何证明中目标选择性联结意识表现中等,两级差异大。第二,在目标选择性联结能力中,在联结和目标转化中性别差异显著,主要表现在女生比男生更尽可能地解读题目已知信息和思考相关证明思路。另外,女生比男生更有目标导向意识。第三,在解决几何证明题的具体解题过程中,初中生目标导向能力不足。主要体现在不能很好的以待证明的结论为导向,将待求证的结论转化成结论等价链,缩小问题空间。同时,初中生在几何证明中目标转化的小步性和反思性方面表现欠佳,未能结合已知信息将结论等价链进行小步论证,同时推理过程不严谨,不能对证明过程合理验证。另外,不能及时对目标转化的方向进行修正。第四,初中生几何证明中目标选择性联结能力对初中生在几何证明测试题中的成绩有显著影响,尤其是对于难度越大的几何证明题,初中生的目标选择性联结能力越高,其在几何证明测试题中的表现越好。最后,为加强初中生几何证明中目标选择性联结能力,从几何证明中目标选择性联结能力的构成成分角度提出相关培养对策。在知识联结方面,构建知识网络,夯实基础知识;积累基本解题经验,促进知识迁移。在目标转化方面,培养目标导向意识,促进逆推分析能力;构建等价或半等价命题体系,促进目标转化。在解题监控方面,增强反思意识,养成“推理有据”的习惯;加强解题监控训练,提高解题监控水平。
[Abstract]:The American Association for mathematics teachers first put forward the ability to connect mathematics in the mathematics curriculum standard (2000). Its "intermediary" characteristics can well apply the related information stored in the students' minds. The ability of the target selection is based on the multi nature and complexity of the mathematical connection, and the emphasis is on the goal of the problem. Based on the analysis of mathematical connectionism and the related literature of target selection, this paper, based on connectionism, cognition and related mathematical education psychology, combines the characteristics of geometric proof, and puts forward the concept of selective binding ability of junior middle school students' geometric proof, that is, junior high school students can The problem goal is oriented, connects to the relevant concepts, propositions, methods, etc. in mathematics learning, and actively and actively make the correct and reasonable selection and processing, can monitor the influence of their selective connection to the process of proof, and can adjust the behavior of their selective connection. It is a kind of solution. The problem of geometric proof is a mathematical problem solving ability for a specific task, which includes the selection of knowledge in the learning of the geometric modules, the cognitive components of the reorganization process, and the process of planning, monitoring and adjusting the metacognitive components of the process of the selection of their own targets. In order to understand the level of target selection in junior middle school students' geometric proof and the effect of target selection on the geometric proof of junior high school students, the paper puts forward the countermeasures to cultivate the ability of target selection in junior middle school students' geometric proof. First, the relevant literature of the target selection is analyzed, the relevant research results are obtained, and the content of the research is determined. Second, the relevant theory is constructed. Based on the theory of related psychology and mathematics educational psychology, the theoretical basis of the objective selective connection in the geometric proof is constructed, and its connotation and ability components are bound. Third, design investigation and implementation. This survey is conducted in the form of a combination of questionnaires and geometric proof tests. Fourth, draw the conclusion of the investigation. According to the results of the survey, the status and level of the junior middle school students' ability to join the geometric proof in the geometric proof are obtained, and the influence on the problem of solving the geometric proof is made and made. Fifth, put forward the training strategy. The main conclusions of this study are as follows: first, the junior middle school students are medium in the geometric proof, and the two level difference is large. Second, in the ability of the target selection, the combination and the goal transformation are in the target selection. The difference of neutral difference is significant, which mainly shows that girls are more likely to interpret the known information of the topic and think about the related ideas. In addition, the female students have more goal oriented consciousness than the boys. Third, in the process of solving the problem of geometric proof, the junior middle school students' goal orientation is insufficient. The main manifestation is that it is not good to be proved. At the same time, the junior middle school students are not good at the small step and reflective aspects of the target transformation in the geometric proof, and fail to demonstrate the equivalent chain of the conclusion in combination with the known information. At the same time, the process is not rigorous, and the process of proof can not be properly verified. In addition, the direction of the target transformation can not be corrected in time. Fourth, the goal selective connection ability of junior high school students has a significant influence on the achievement of junior high school students in the geometric proof test questions, especially for the more difficult geometric proof questions, the higher the ability of the junior middle school students to join in the selection of the target, the higher the ability of the junior middle school students' goal selection. The better the performance is. Finally, in order to strengthen the goal selective connection ability of the junior high school students' geometric proof, the relevant training countermeasures are put forward from the angle of the composition of the target selection ability of the geometric proof. In the knowledge connection, the knowledge network is constructed, the basic knowledge is rammed, the basic knowledge solving experience is accumulated and the knowledge transfer is promoted. Face, train target oriented consciousness, promote the ability to push back analysis, build an equivalent or semi equivalent proposition system, promote target transformation, strengthen the consciousness of reflection, develop the habit of "reasoning with evidence", strengthen the training of problem solving monitoring and improve the level of problem solving and monitoring.

【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

【参考文献】