Research On The Penetration And Application Of Geometric Transformation Ideas In Junior High School Geometry Teaching

Geometry transformation as an important modern geometry thought,its essence is the thought of motion transformation and invariant.According to the Mathematics Curriculum Standards for Compulsory Education(2011 Edition),geometric proof has changed from emphasizing the Euclidean geometric axiom system to the nature and transformation based on graphs.How to permeate and apply the idea of geometric transformation in middle school geometry teaching effectively? This paper focuses on the study of the penetration and application of the idea of geometric transformation in the geometry teaching process of the ninth grade.This paper studies the following four questions:1、What is the current situation of the penetration and application of geometric transformation in junior high school geometry teaching?2 、 What are the effective methods to permeate the idea of geometric transformation in the geometry teaching of Grade 9?3、What are the promoting effects of the teaching of the idea of geometric transformation on the geometry learning of Grade 9 students?4、For students of different levels,are these promoting effects different to some extent?In this paper,the literature research method is adopted to analyze the research status of geometric transformation and determine the research ideas of this paper.First of all,through the questionnaire survey,we understand the current situation of geometry transformation thought penetration in junior high school geometry teaching.By means of the geometry test,we can understand the students’ practical situation of solving geometry problems by using geometric transformation,and therefore we establish the realistic foundation of the research.Secondly,in this paper,we excavate the knowledge and exercise carriers that can permeate the geometric transformation in the teaching materials,determine the teaching target levels and methods,design teaching cases,and conduct the quasi-experimental research on the geometry teaching that permeates and applies the geometric transformation thought.Two parallel classes were selected to conduct an experiment between single factor subjects.Through the experiment,it was tested whether the penetration and application of geometric transformation thought could improve students’ attention to and application of geometric transformation,whether it could cultivate students’ ability to look at problems from the perspective of motion transformation,and whether it could improve students’ ability of geometric exploration and divergent thinking.Finally,through the questionnaire survey of the students before and after the experiment,the quantitative analysis of the five mathematical test results,after the experiment on the experimental class students "thinking aloud" geometry test,and after the experiment test results of the qualitative analysis of case comparison,we obtain the experimental conclusion.The study reached the following conclusions:1.In junior middle school geometry teaching,teachers hold a positive attitude towards the infiltration and application of geometric transformation thought.However,due to various reasons,the current situation of the infiltration and application of geometric transformation thought by teachers in actual teaching needs to be improved.Corresponding students do not pay enough attention to geometric transformation,and the application of transformation in actual problem solving is also inadequate.2.In the teaching process,teachers should pay more attention to the idea of geometric transformation and consciously infiltrate it step by step.Specifically,the idea of geometric transformation can be understood by combing the permeating carrier in teaching,cutting and piecing graphics,and exploring the transformation relationship.Through the exploration of a problem,the idea of geometric transformation is mastered.Through the exploration of problem solving,the geometric transformation thought is flexibly applied.3.By permeating the geometry teaching with the thought of geometric transformation,students’ attention to the thought of geometric transformation can be improved,students’ geometry concept of movement can be cultivated,students’ understanding of the nature of mathematical knowledge can be deepened,and students’ ability of exploration and geometry thinking can be improved.Short-term experiment has no significant effect on the improvement of performance,while long-term experiment has significant effect on the improvement of performance.4.The case comparison of the test results shows that there are certain differences in the acceptance of the idea of geometric transformation among students with different academic performance.It is difficult for the underachieving students to accept the idea of geometric transformation and they cannot solve geometric problems by geometric transformation.Middle-level students and top students are easier to accept the idea of geometric transformation.Middle-level students can see problems from multiple angles and can add auxiliary lines with geometric transformation.Top students have improved their ability of geometric exploration.When solving complex geometric problems,they can grasp the core of the problems,flexibly use geometric transformation to expand the study of geometric problems,and make decisions on the test questions from the perspective of test makers.