高一学优生与普通生数学问题表征的差异研究
发布时间：2018-11-02 19:45
【摘要】：问题表征是解题的中心环节,随着认知心理学的发展,问题表征受到众多研究者的关注。在数学问题解决中,由于表征层次过低或不够全面等原因,学生不能将问题合理准确地转化为平时学过的熟悉的公式、概念等解答的图式,影响问题的解决。在学科领域中开展问题表征的研究有利于学生问题解决能力的提高,因此,研究的焦点逐渐集中于学科问题上。在文献分析的基础上,本文对问题表征进行了概述,指出了开展问题表征研究的意义;阐述了问题表征在一般学科和学科问题领域的研究情况,对研究课题的确定指明了方向。本文在借鉴一般数学问题解决的步骤以及其它学科问题表征层次划分的基础上,提出了数学问题解决表征层次的划分。本研究采用文献研究法、口语报告法对课题进行了探讨。首先,分析学优生与普通生对问题中隐含信息的表征情况。其次,比较学业成绩不同的两类学生对同一道数学题所经历的问题表征层次上的差异(动态差异和静态差异)与各个层次之间的相关性,同时也对不同被试外部表征形式的运用与转化上进行了比较分析。最后,针对学生问题解决中出现的实际困难,提出合理有效的教学建议。通过研究得出结论:(1)高一学优生对隐含信息的表征更加全面,并且能够将隐含信息进行成功转译,而大部分普通生不能将隐含信息做到有效表征。(2)高一学生会经历相同的表征层次(文字表征、情境表征、数学表征、数量表征),在表征层次上存在动态差异与静态差异,经检验情境表征与数学表征无显著性差异(P0.05),不同层次的被试在情境表征阶段差异显著(P0.05),文字表征与数量表征,经检验与情境表征和数学表征差异显著(P0.05),所以整个解题过程,情境表征与数学表征占据了数学问题解决的主要过程,静态差异主要是被试在知识结构、表征转化、问题空间建构上的差异。(3)学优生习惯于多种外部表征形式的运用与转化,而大部分普通生往往习惯于用题目中给出的表征形式去表征问题,外部表征形式单一。教学建议:实现认知结构的整体优化;促进学生形成问题图式;引导学生去挖掘隐含条件;完善学生的CPFS结构系统;提高学生表征转换的能力。
[Abstract]:Problem representation is the central link of problem solving. With the development of cognitive psychology, problem representation has been concerned by many researchers. In mathematical problem solving, students can not reasonably and accurately transform the problem into familiar formula, concept and other solution schema, which influence the solution of the problem because the representation level is too low or not comprehensive enough and so on. The research on problem representation in the subject field is beneficial to the improvement of students' problem solving ability, so the focus of the research is gradually focused on the subject problem. On the basis of literature analysis, this paper summarizes the problem representation, points out the significance of the research on problem representation, expounds the research situation of problem representation in the general discipline and subject problem field, and points out the direction of the research subject. On the basis of drawing lessons from the steps of general mathematical problem solving and the division of representation levels of other disciplines, this paper puts forward the division of representation levels of mathematical problem solving. This research uses the literature research method, the spoken language report method to carry on the discussion to the topic. Firstly, it analyzes the representation of implicit information in the problem between gifted students and ordinary students. Secondly, the correlation between the difference in representation level (dynamic difference and static difference) between the two types of students with different academic achievement to the same mathematical problem was compared. At the same time, the use and transformation of the external representation of different subjects were compared and analyzed. Finally, some reasonable and effective teaching suggestions are put forward in view of the practical difficulties in solving students' problems. The conclusions are as follows: (1) the eugenics of a senior high school have a more comprehensive representation of the implied information and can successfully translate the implied information. However, most ordinary students can not effectively represent implicit information. (2) Senior one students will experience the same level of representation (literal representation, situational representation, mathematical representation, quantitative representation). There were dynamic and static differences in the level of representation, there was no significant difference between the test situation representation and mathematical representation (P0.05), different levels of participants in the stage of situation representation significant difference (P0.05), text representation and quantitative representation. There were significant differences between test and situational representation and mathematical representation (P0.05), so the whole problem solving process, situational representation and mathematical representation occupied the main process of mathematical problem-solving, the static difference was mainly in the knowledge structure, representation transformation. Differences in problem space construction. (3) gifted students are used to the use and transformation of many forms of external representation, while most ordinary students tend to use the form of representation given in the topic to represent the problem, and the external representation form is single. Teaching suggestions: to achieve the overall optimization of cognitive structure; to promote the formation of problem schemata; to guide students to explore hidden conditions; to improve students' CPFS structure system; to improve students' ability of representation and transformation.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
本文编号：2306773
[Abstract]:Problem representation is the central link of problem solving. With the development of cognitive psychology, problem representation has been concerned by many researchers. In mathematical problem solving, students can not reasonably and accurately transform the problem into familiar formula, concept and other solution schema, which influence the solution of the problem because the representation level is too low or not comprehensive enough and so on. The research on problem representation in the subject field is beneficial to the improvement of students' problem solving ability, so the focus of the research is gradually focused on the subject problem. On the basis of literature analysis, this paper summarizes the problem representation, points out the significance of the research on problem representation, expounds the research situation of problem representation in the general discipline and subject problem field, and points out the direction of the research subject. On the basis of drawing lessons from the steps of general mathematical problem solving and the division of representation levels of other disciplines, this paper puts forward the division of representation levels of mathematical problem solving. This research uses the literature research method, the spoken language report method to carry on the discussion to the topic. Firstly, it analyzes the representation of implicit information in the problem between gifted students and ordinary students. Secondly, the correlation between the difference in representation level (dynamic difference and static difference) between the two types of students with different academic achievement to the same mathematical problem was compared. At the same time, the use and transformation of the external representation of different subjects were compared and analyzed. Finally, some reasonable and effective teaching suggestions are put forward in view of the practical difficulties in solving students' problems. The conclusions are as follows: (1) the eugenics of a senior high school have a more comprehensive representation of the implied information and can successfully translate the implied information. However, most ordinary students can not effectively represent implicit information. (2) Senior one students will experience the same level of representation (literal representation, situational representation, mathematical representation, quantitative representation). There were dynamic and static differences in the level of representation, there was no significant difference between the test situation representation and mathematical representation (P0.05), different levels of participants in the stage of situation representation significant difference (P0.05), text representation and quantitative representation. There were significant differences between test and situational representation and mathematical representation (P0.05), so the whole problem solving process, situational representation and mathematical representation occupied the main process of mathematical problem-solving, the static difference was mainly in the knowledge structure, representation transformation. Differences in problem space construction. (3) gifted students are used to the use and transformation of many forms of external representation, while most ordinary students tend to use the form of representation given in the topic to represent the problem, and the external representation form is single. Teaching suggestions: to achieve the overall optimization of cognitive structure; to promote the formation of problem schemata; to guide students to explore hidden conditions; to improve students' CPFS structure system; to improve students' ability of representation and transformation.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
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