Experimental Research On Analytic Geometry Teaching In Senior High School Based On Analogical Transfer Theory

The essence of analytic geometry is to use "number" to solve the problem of "shape",that is,to analyze geometric problems by means of coordinates.With a wide range of contents,analytic geometry,infiltrated with other knowledge and consisting of abundant mathematical thoughts,plays a significant role in the College Entrance Examination.Students,who are not eqipped with a strong ability to observe “shape”,an excellent ability of mathematical modeling as well as a powerful calculation ability,will encounter great difficulty in learning this module.Complicated as it is,close connections and features of similarities exist among different sections.Teachers can make use of this feature to guide students to solve new problems by searching the existing knowledge base and learning ability.If there is scientific theoretical guidance on this basis,it will make the teaching method more scientific,more systematic,and make teaching more effective.Analogical migration refers to the fact that when people encounter a new problem(target problem),they will recall similar problems solved in the past(source problem)and use the solution and steps of source problem to solve the target problem.Therefore,the author will take the analytic geometry teaching as the carrier to carry on the experimental research to the high school mathematics teaching under the analogy transfer theory.Based on the theme of "application and effect of analogical transfer theory in analytic geometry teaching",the following work was carried out :(1)a preliminary investigation was conducted on the application status of analogical transfer theory by teachers and students,and experimental classes and control classes were selected according to the monthly examination and final score.(2)Conduct pre-experiment questionnaire survey and pre-experiment test for the experimental class and the control class.(3)According to the literature research and the preliminary investigation results,a 4-month experimental study of analytic geometry teaching based on the theory of analogical transfer was carried out.(4)Sort out and analyze the experimental results and draw a conclusion.Through the investigation of the current situation of analytic geometry learning of the students in grade two of senior high school(mainly pre-test results and supplemented by questionnaires),it is found that the students' analytical geometry results are not ideal;Lack of confidence in learning analytic geometry.Through teachers' questionnaire survey and the author's own teaching practice,we know that teachers have the consciousness of analogy transfer in teaching,but their understanding of it is one-sided,let alone systematically applying the theory of analogy transfer in teaching.Through 4-month analytical geometry teaching based on analogical transfer theory in the experimental class,the specific methods are as follows: Teachers put forward new problems,guides the student to find similar content,guides the student to review the concept of knowledge,guide the student to review the exploration methods,students explore new problem,students refine concepts,teachers were revised,teachers and students together to complete the application summary knowledge concept,to explore the method of the lesson homework assignments(basic knowledge to change type training to comprehensive training).The results showed that :(1)there was no significant difference between the experimental class and the control class in pre-test scores and pre-test questionnaire results.(2)There are significant differences between the post-test scores of the experimental class and the control class,the post-test questionnaire results and the pre-test scores of the experimental class,while there are no significant differences between the pre-test scores of the control class.(3)Students in the experimental class have higher attention,interest,confidence and satisfaction in learning analytical geometry than those in the control class.