数学师范生高中概率概念的认知水平研究

发布时间：2018-09-15 19:43

【摘要】：概率是数学课程中的一个重要的模块,它广泛运用于航天、医学、农业等多个领域,对社会的发展有着不可忽视的作用。学生对概率的学习很大程度上取决于教师概率知识系统的完善程度。本文旨在探讨数学师范生对高中概率概念的认知水平,通过调查找出师范生认知现状及存在的主要问题,并提出具有针对性的建议。在大量文献分析的基础上确定本文测试的内容为高中概率的三种定义,即:统计定义、古典概型、几何概型,并对相关概念进行了明确的界定。研究的主体部分为以下四步:第一步编制预测卷,测试试卷的可行性;第二步制成正式测试卷,并对204名大三的数学师范生进行测试;第三步用SOLO分析法对试卷的回答进行水平划分,并统计结果;第四步进行个案研究。测试对象是西华师范大学和乐山师范学院的部分大三学生。测试结果分别在第四章、第五章、第六章进行分析和总结,在第七章对几份具有代表性的测试卷作个案研究,并在第八章展示研究结论。研究表明:针对于样本,师范生对古典概型的总体认知水平较高,其次是几何概型,而对于统计定义的认知水平则相对偏低。存在的主要问题:对概率和频率的理解模糊不清;混淆古典概型与几何概型;重运算,轻理解;对随机事件、基本事件等基本概念的理解还停留在中学阶段;数形结合思维能力不足,数学知识板块之间的联系不够紧密。最后,基于研究结论提出若干建议,并得出了师范生概率概念认知框架。
[Abstract]:Probability is an important module in mathematics curriculum. It is widely used in many fields, such as aerospace, medicine, agriculture and so on. It plays an important role in the development of society. Students' learning of probability depends to a great extent on the perfection of teacher's probabilistic knowledge system. The purpose of this paper is to probe into the cognition level of mathematics normal students to the concept of high school probability, to find out the cognitive status quo and the main problems of the normal school students through the investigation, and to put forward some pertinent suggestions. On the basis of a lot of literature analysis, it is determined that the contents of this paper are three definitions of high school probability, that is, statistical definition, classical probability type, geometric probability type, and the related concepts are clearly defined. The main part of the study consists of the following four steps: the first step is to compile the forecast paper to test the feasibility of the test paper, the second step is to make the formal test paper, and to test 204 math normal students in junior high school. The third step uses the SOLO analysis method to divide the answer level of the test paper and the statistical result; the fourth step carries on the case study. The subjects are some junior students of Xihua normal University and Leshan normal College. The test results are analyzed and summarized in chapter 4, chapter 5 and chapter 6 respectively. In chapter 7, some representative test papers are studied, and the conclusions are shown in chapter 8. The results show that normal students have a higher overall cognitive level of classical probability type, followed by geometric probability type, and relatively low level of cognition about statistical definition. The main problems are: vague understanding of probability and frequency; confusion between classical probability and geometric probability; heavy operation, light understanding; understanding of basic concepts such as random events and basic events are still in the middle school stage; The combination of number and form thinking ability is not enough, mathematical knowledge between the plate is not close enough. Finally, some suggestions are put forward based on the conclusions of the study, and the conceptual cognitive framework of normal school students' probability is obtained.
【学位授予单位】：西华师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6;G652.4

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