数学思想方法在高中数学教与学中的运用研究

【作者】 张雪；

【导师】 徐罗山； 邓友祥；

【作者基本信息】 扬州大学 ， 学科教学（数学）（专业学位）， 2018， 硕士

【摘要】 在高中数学教材中,许多内容不单单是知识点的介绍,更多的是知识与数学思想方法的有机融合。高中数学教育受到越来越多关注和重视的同时,数学思想方法也跟着受到重视。但是对于教师来说想要达到良好的课堂教学效果却不是那么容易,对学生来说,数学学习过程中灵活运用数学思想方法也不易。所以,这就需要教师在教给学生数学知识的同时,也要引导学生更好地接受数学思想,运用数学思想方法到数学学习中。本论文首先采用文献分析法对相关概念进行了界定,对高中数学教材进行研读,梳理得到了高中阶段所涉及到的数学思想和方法,其中常见的数学思想有函数与方程思想、转化与化归思想、分类讨论思想和数形结合思想等,常见的数学方法有数学归纳法、待定系数法、类比法、辅助元法等。其次,对高中生数学思想方法的认知水平和接受程度进行了测试,得知高中生学习数学思想方法的现状;并对高中数学教师进行了访谈,了解到高中数学教师数学思想方法教学现状。根据试题测试数据和目前数学思想方法教与学的现状,对教师提出了引导学生运用数学思想和方法的几点策略及注意事项。具体策略有:更新观念,重视数学思想方法教学;挖掘教材中数学思想方法,做到“有的放矢”;教学各环节积极渗透数学思想和方法等。具体注意事项有:教师更新观念同时,培养学生重视数学思想方法;加强解题研究,不能“生搬硬套”等。最后,分别对高中数学概念教学和解题教学进行了教学案例分析,说明了本论文提出的策略及注意事项的具体运用。本文共分为五章。第一章为绪论,主要讲述了研究背景、研究内容和意义、对数学思想与数学方法概念进行了界定。第二章介绍了高中阶段常见的数学思想与数学方法。第三章是数学思想和方法在高中阶段教与学的现状调查分析,对学生进行了试题测试,对教师进行了访谈。第四章是引导学生运用数学思想方法的策略及注意事项。第五章是教学案例分析。更多还原

【Abstract】 In high school mathematics textbooks,many contents are not only introductions of knowledge,but also are interactions of knowledge and mathematical ideas and methods.More attentions in high school mathematics education are paid,and mathematics ideas and methods are also emphasized.However,it is not easy for teachers to achieve good classroom teaching effects;it is not easy for students to use mathematical ideas and methods in mathematics learning.Therefore,it is needed for teachers not only to teach students maths knowledge but also to well guide students to accept math ideas and using maths methods into their maths study.Firstly,we defined the related concepts by the literature analysis method.We picked up main mathematics ideas and mathematical methods involved in senior high school by studying mathematics textbooks.Familiar mathematics ideas include function and equation idea,transforming and reduction,discussing in cases,combining of algebra and geometry,etc.Familiar mathematical methods include the mathematical induction,pending coefficient method,analogy method and auxiliary elements method,etc.Secondly,the cognitive level and acceptance degree of mathematics ideas and methods of senior high school students were tested.The present student’s learning situations of mathematics ideas and methods in senior high school was obtained.Mathematics teachers in senior high school were interviewed to get the teaching situations of mathematics ideas and methods of senior high school.The present situation of mathematics idea method teaching.According to the testing data and the present situations,the thesis put forward strategies and matters needing attention to guide students to use mathematical ideas and methods.Concrete strategies:renewing ideas and attaching importance to teaching of mathematical ideas and methods,digging the mathematical idea methods in textbooks to get targeted,actively implanting mathematical ideas and methods in every link of teaching.Concrete matters needing attentions include:on renewing ideas,on training students to pay more attention to mathematical ideas and methods,strengthening study of solving problems without "copying mechanically".Finally,cases of mathematics concept teaching and problem-solving teaching in senior high school were analysed to explain applications of strategies and matters needing attention above.This thesis has five chapters.Chapter I includs backgrounds,contents and significance of the thesis,as well as definitions of mathematical ideas and methods.Chapter II introduces familiar mathematical ideas and methods in senior high school.Chapter III presents investigations and analysis of present situation of teaching and learning in senior high school.Students are tested and teachers are interviewed.Chapter IV poses strategies and matters needing attention to guide students to use mathematical ideas and methods.Chapter V is teaching cases analysis.更多还原