思维可视化在圆锥曲线复习教学中的实验研究

发布时间：2018-11-16 17:45

【摘要】：圆锥曲线是高中数学解析几何的核心内容,学习圆锥曲线可以发展学生的数学思维,培养学生逻辑推理能力、思维创新能力以及运算求解能力等。《普通高中数学课程标准(实验)》中提出了高中数学课程应该注重提高学生的数学思维能力的教学目标。而思维可视化技术与教学的整合可以促进学生思维的发展以及知识的建构。因此,思维可视化教学顺应了数学教学发展的趋势。这项研究以M中学高三文科学生为研究对象,从以下两方面探索高中圆锥曲线复习策略对学生学习的影响:首先,调查高三学生圆锥曲线的学习现状,并对圆锥曲线的统一性进行研究,结合调查结论提出圆锥曲线的复习策略;其次,开展高三圆锥曲线复习中思维可视化复习策略的实验研究,结合教学实践对复习策略的可行性及有效性进行检验,从而改进复习策略。这项研究的主要结论有:首先,通过问卷调查得到学生对圆锥曲线知识的理解水平不高,知识点易混淆,综合能力弱,思维不灵活,缺乏主动性和总结反思意识等;其次,通过实验研究得到学生接受圆锥曲线复习策略,并积极参与学习,同时思维可视化复习策略有利于学生对圆锥曲线内容的深刻理解和内化,有利于提高学生的学习兴趣、探究意识及解题能力,有利于促进学生思维的发展和提高,但短时间内数学成绩无明显差异。通过这项研究获得了一些有意义的结果,希望在数学教学中,教师更加注重学生思维的培养,使学生能够可视化和结构化的思考,以提高学习效率。同时,希望能为教师研究和学习思维可视化与数学学科的整合提供一定帮助,为高中数学教师的教学提供参考。
[Abstract]:Conic curve is the core content of analytic geometry in senior high school mathematics. Learning conic curve can develop students' mathematical thinking and develop students' logical reasoning ability. In the ordinary Senior High School Mathematics Curriculum Standard (experiment), it is pointed out that the high school mathematics curriculum should pay attention to the teaching goal of improving the students' mathematical thinking ability. The integration of visual thinking technology and teaching can promote the development of students' thinking and the construction of knowledge. Therefore, visual thinking teaching conforms to the development trend of mathematics teaching. This study takes the students of the third liberal arts in M Middle School as the research object, and explores the influence of the strategy of reviewing the conic curve on the students' learning from the following two aspects: first, investigate the current situation of the learning of the conic curve of the senior high school students. The unity of conic curve is studied, and the review strategy of conic curve is put forward in combination with the investigation conclusion. Secondly, an experimental study of the visual review strategy of thinking in the review of the third conic curve is carried out, and the feasibility and effectiveness of the review strategy are tested in combination with the teaching practice, so as to improve the review strategy. The main conclusions of this study are as follows: firstly, the students' understanding of conic knowledge is not high, the knowledge points are easy to be confused, the comprehensive ability is weak, the thinking is not flexible, the students are lack of initiative and the consciousness of summing up reflection, etc. Secondly, through the experimental study, we can get the strategy of accepting the conic curve and actively participating in the study. Meanwhile, the visual review strategy of thinking is beneficial to the students' deep understanding and internalization of the conic curve content, and it is helpful to improve the students' interest in learning. Inquiry consciousness and problem-solving ability can promote the development and improvement of students' thinking, but there is no obvious difference in mathematics achievement in a short period of time. It is hoped that in mathematics teaching, teachers will pay more attention to the cultivation of students' thinking so that students can visualize and think structurally so as to improve their learning efficiency. At the same time, the author hopes to provide some help for teachers' research and integration of thinking visualization and mathematics subject, and provide reference for the teaching of senior high school mathematics teachers.
【学位授予单位】：云南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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