高中生数学程序性知识认知理解过程的研究

发布时间：2018-05-26 14:16

本文选题：数学程序性知识 + 数学理解　；参考：《山东师范大学》2016年硕士论文

【摘要】：数学程序性知识是高中生数学学习的重要组成部分,它不仅能够影响到学生的学习成绩,而且对学生学习信念和学习积极性等各方面都有一定影响。现实的情况是部分高中生不能够理解数学程序性知识,因此,研究高中生数学程序性知识认知理解过程是非常重要的。当前关于数学理解的研究多集中在数学理解的内涵、层次、特点、功能、以及调查研究等方面,而对于数学认知理解的研究比较少,特别是对理解程序性知识的心理过程的研究几乎没有。本人在前人研究的基础上,结合当前高中生数学程序性知识的学习情况,深入研究了高中生数学程序性知识认知理解心理过程,并且在研究基础上提出了相应的教学要求和教学建议。本文主要采用了文献分析法、访谈法和口语报告法等研究方法。本文的研究顺序是:第一,阅读大量与数学理解有关的文献,对国内外数学理解的已有研究进行综述;第二,阅读大量与程序性知识和数学认知理解有关的文献,并且做相关的理论分析;第三,制定教师访谈提纲,并通过访谈初步确定影响高中生数学程序性知识认知理解的因素;第四,制定学生访谈提纲,并通过对学生的初步访谈最终确定影响高中生数学程序性知识认知理解的因素;第五,对学生进行访谈,确定影响高中生数学程序性知识认知理解的关键因素是什么;第六,对学生进行访谈,在影响高中生数学程序性知识认知理解的关键因素的基础上,总结出高中生数学程序性知识认知理解的过程、特点和模型;第七,根据以上的研究结果和结论,提出相应的教学要求和教学建议。本文研究得出的主要结论有:一、影响高中生数学程序性知识认知理解的因素主要有六个,分别是新旧知识之间的联系、数学程序性知识相关历史、数学程序性知识相关证明、数学程序性知识相关应用、数学程序性知识相关原则和数学程序性知识相关适用范围;二、影响高中生数学程序性知识认知理解最关键的因素是新旧知识之间联系;三、高中生数学程序性知识认知理解过程具有积极主动性、连续性、顺序性、迟缓性、惰性和迅捷性的特点;四、高中生数学程序性知识认知理解的过程主要是学生认知结构当中产生式系统的不断完善。具体如下:学生遇到新的数学程序性知识后积极主动的搜索认知结构当中与之相关的命题网络,并经过一定的操作之后形成产生式,通过筛选组合产生式形成简单的产生式系统,如果学生满足于简单的产生式系统,那么他将处于假理解状态,如果不满足于当前状态就会继续积极主动搜索认知结构当中的命题网络,并最终筛选组合成完整的产生式系统,达到实理解状态。最后,根据以上的研究结果和结论,提出的教学要求为:一、教师要加强自身知识储备量;二、根据具体数学程序性知识制定具体的教学过程;三、了解高中生的数学程序性知识认知理解水平,关注学生的心理机制;四、认识到教师的主导地位且把这种地位发挥的正确有效;五、注重学生的主体地位;六、注重对学生学习动机和学习积极性的激发。提出的教学建议为:一、不要给予解题模板,引导学生真正理解数学程序性知识;二、引导学生反思,促进程序性知识的理解与获得;三、积极与学生进行交流,对学生学习情况进行及时评价;四、制定恰当的教学情境和教学内容;五、引导学生加强新旧知识联系,促进学生知识系统化;六、发现学生对数学程序性知识理解力的不同,做到因材施教和个性化教学;七、更多的教授数学程序性知识的相关原则、相关应用和相关历史等各方面相关知识;八、利用合适材料促进学生从假理解到实理解状态的转换。
[Abstract]:The mathematical programming knowledge is an important part of the high school students' mathematics learning. It not only affects the students' academic achievements, but also has some influence on the students' learning beliefs and learning enthusiasm. The actual situation is that some high school students can not understand the mathematical programming knowledge. Therefore, the study of high school students' mathematical programming knowledge is studied. The process of understanding cognitive understanding is very important. The current research on mathematical understanding is mainly focused on the connotation, levels, characteristics, functions, and investigation and research of mathematical understanding, and there are few studies on cognitive understanding of mathematics, especially the research on the process of understanding procedural knowledge. On the basis of this, combined with the current high school students' learning of mathematical programming knowledge, this paper deeply studies the cognitive process of cognitive understanding and understanding of high school students' mathematical programming knowledge, and puts forward the corresponding teaching requirements and teaching suggestions on the basis of the study. This paper mainly adopts the methods of literature analysis, interview and oral report method. The following order is: first, reading a large number of literature related to mathematical understanding, summarizing the existing research on mathematical understanding at home and abroad; second, reading a large number of documents related to procedural knowledge and cognitive understanding of mathematics, and making relevant theoretical analysis; third, formulating an outline of teacher interview, and preliminarily determining the number of high school students through interviews. Learn the factors of cognitive understanding of procedural knowledge; fourth, make an outline of student interview, and finally determine the factors that affect the cognitive understanding of the mathematical procedural knowledge of high school students through the preliminary interview to the students; fifth, interview the students to determine the key factors that affect the cognitive understanding of the mathematical procedural knowledge of the high school students; sixth, to the students. In the interview, on the basis of the key factors affecting the cognitive understanding of high school students' mathematical programming knowledge, the process, characteristics and models of the cognitive understanding of high school students' mathematical programming knowledge are summed up. Seventh, according to the results and conclusions above, the corresponding teaching requirements and teaching suggestions are put forward. There are six main factors affecting the cognitive understanding of the high school students' mathematical programming knowledge, which are the links between the old and the new knowledge, the related history of the mathematical programming knowledge, the related proof of the mathematical programming knowledge, the application of the mathematical programming knowledge, the related application of the mathematical procedural knowledge and the mathematical procedural knowledge, and the influence of the two. The most important factor in cognitive understanding of high school students' mathematical programming knowledge is the connection between old and new knowledge. Three, the process of cognitive understanding of mathematical procedural knowledge of high school students has the characteristics of active initiative, continuity, sequence, sluggishness, inertia and rapidity; and four, the process of cognitive understanding of the mathematical procedural knowledge of high school students is mainly the cognition of students. As the students meet new mathematical programming knowledge, the students are actively searching for the related propositional networks in the cognitive structure after encountering new mathematical programming knowledge, and form a production form after a certain operation, and form a simple production system by screening the combination generation, if the students are satisfied with the simple production. In a system of birth, he will be in a state of false understanding. If he is not satisfied with the current state, he will continue to actively search the propositional network in the cognitive structure, and finally filter it into a complete production system to achieve the actual understanding. Finally, according to the results and conclusions of the above research, the teaching requirements are as follows: first, teachers should add Strong self knowledge reserves; two, according to specific mathematical programming knowledge to formulate specific teaching process; three, to understand the level of cognitive understanding of mathematical procedural knowledge of high school students, pay attention to the psychological mechanism of students; four, understand the teacher's dominant position and make the position of this position correct and effective; five, pay attention to the main position of the students; six, pay attention to the right The students' motivation of learning and the motivation of learning enthusiasm are: first, do not give the template to solve the problem, guide students to truly understand the mathematical programming knowledge; two, guide students to reflect, promote the understanding and acquisition of procedural knowledge; three, actively and students to make a timely evaluation of students' learning situation; four, make the appropriate work. The teaching situation and content of teaching; five, guide the students to strengthen the old and new knowledge connection, promote the systematization of students' knowledge; six, find the students' different understanding of the mathematical programming knowledge, to teach students in accordance with their aptitude and individualized teaching; seven, more relevant principles of teaching mathematical programming knowledge, related applications and related history, and so on. Knowledge; eight, use appropriate materials to promote students' conversion from false understanding to real understanding.
【学位授予单位】：山东师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

【参考文献】