解题中元认知与数学概念多元表征相结合的调查研究

发布时间：2018-05-12 07:01

本文选题：元认知 + 数学概念　；参考：《四川师范大学》2015年硕士论文

【摘要】：为了提高数学成绩,教师会归纳考点的典型例题,布置大量相关习题让学生模仿练习。而在如何分析条件和调整解题策略上,却并未给出具有可操作性的建议。因此,对元认知与数学概念多元表征相结合的调查研究,具有重要的理论价值和实践意义。解题时,需要提取题目中的关键信息,并进行恰当表征,同时元认知也要对该过程进行监控和调节。数学概念具有多元表征这一特性,每个数学概念的表征形式会形成一个表征空间,如何从中选择最恰当的表征形式就变得非常重要。在对教师和学生访谈后,发现该内容常常被忽略。因此,笔者通过文献分析法、口语报告法、调查访谈法、定量与定性分析等研究方法对此进行调查研究,旨在了解元认知对解题行为进行调控的情况。在文献综述的基础上,将数学概念多元表征界定为数学概念或语义单位的数学表达式的多元性,与通常意义下的多通道、多形式的多元表征意义区分开。据此,笔者将本研究的内容确定为:通过口语报告分析元认知调控数学概念多元表征的情况,包括元认知行为、数学概念多元表征空间、以及元认知对数学表达式选取的调节。研究得出如下结论:(1)元认知行为参与了解题活动,但对解题行为的调节程度不够;(2)被试没有建立完善的数学多元表征空间;(3)元认知与数学概念多元表征结合程度差。基于上述研究结论,给出了有益于提高元认知调控数学概念多元表征的教学策略,对解题能力、数学学习能力的提高能起到一定的启示作用。
[Abstract]:To improve math performance, teachers summarize typical examples of test sites and assign a large number of related exercises for students to imitate. However, there are no operable suggestions on how to analyze the condition and adjust the strategy of solving the problem. Therefore, the research on the combination of metacognition and multi-representation of mathematical concepts has important theoretical value and practical significance. In solving problems, the key information is extracted and properly represented, and the process is monitored and regulated by metacognition. The mathematical concept has the characteristic of multivariate representation, and the representation form of each mathematical concept will form a representation space, how to choose the most appropriate form of representation becomes very important. After interviews with teachers and students, it is found that this content is often ignored. Therefore, the author investigates this problem by the methods of literature analysis, oral report, investigation and interview, quantitative and qualitative analysis, in order to understand the regulation of metacognition on problem-solving behavior. On the basis of literature review, the multivariate representation of mathematical concepts is defined as the plurality of mathematical expressions of mathematical concepts or semantic units, which is distinguished from the multi-channel and multi-form representations in the general sense. Based on this, the author determines the content of this study as follows: through oral report, the author analyzes the multiple representations of mathematical concepts, including metacognitive behavior, multi-representation space of mathematical concepts, and the adjustment of metacognition to the selection of mathematical expressions. It is concluded that: 1) metacognitive behavior is involved in problem-solving activities, but the degree of adjustment to problem-solving behavior is not enough (2) the participants have not established a perfect space for mathematical multivariate representation / space / 3) the degree of combination of metacognition and mathematical concept multiple representation is poor. Based on the above conclusions, a teaching strategy which is beneficial to the improvement of multi-representation of metacognitive mathematical concepts is put forward, which can give some enlightenment to the improvement of problem-solving ability and mathematics learning ability.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【参考文献】