Research On Problem-Solving Teaching Under The Guidance Of Thought Of Transformation

Thought of transformation is very important.It is not only an important way of thinking in solving mathematical problems,but also a very common mathematical thinking method.Teachers of senior secondary mathematics can realize the importance of thought of transformation in problem-solving,but in practice,they still only focus on the results of the solution and lack the analysis and guidance of the solution ideas.Aiming at this situation,this paper discusses the problem-solving teaching design of thought of transformation using the conic sections comprehensive question as to the carrier and provides a reference for the problem-solving teaching guidance of thought of transformation.This research organizes and summarizes the research results of mathematical thinking method,thought of transformation,and conic sections problem-solving teaching sorts out the connotation and principle of thought of transformation and combines typical examples to carry out conic sections solution under the guidance of thought of transformation.The current situation of conic sections problem-solving teaching in senior high school and the application of thought of transformation in conic sections problem-solving teaching are investigated through test paper analysis method,interview recording method,and case study method.Three designs for solving problems by using thought of transformation have been designed for the three stages of training thought of transformation in the exercise lessons,and the effectiveness and operability of the designs have been tested through teaching practice.The survey shows that although students attach importance to the content of conic sections,there are still many problems with their learning attitudes and habits,and the current situation of understanding and applying thought of transformation is not optimistic.Teachers are conscious of the need to teach thought of transformation but lack systematic teaching design.They teach by explaining how the conditions are transformed,but they do not specify the object,the pathway and the goal of the transformation,leading students to memorize the solution process in steps.Research has shown that conic sections’ comprehensive question can be divided into three basic types of problems:equations and trajectories of curves,definition and basic properties of conic sections,and straight-line and conic sections problems.The study shows that after three stages of training: multiple gestation,initial formation,and comfortable application,students can consciously apply the idea of a reduction in solving problems with conic sections.In addition,this series of training can also effectively improve students’ problem-solving skills,develop their thinking skills,make them think independently to form solutions,reflect on the process of solving problems,and build and improve their problem-solving schemas.