Research On The Application Of Mathematical Thinking Methods In High School Mathematics Teaching And Learning

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.