Research On The Infiltration And Application Of Mathematical Equation Thought In Senior High School

Equation thinking is an important way of thinking in high school mathematics teaching,and it is widely used in the problems of functions,trigonometry,three-dimensional geometry,and series,which are worth studying.In this thesis,we firstly use literature research method to compile and analyze the research on equation thinking,and then sort out the knowledge points that reflect equation thinking in the textbook of high school mathematics,based on the textbook of Human Education A version,to understand how equation thinking is presented in the textbook.Secondly,through interviews with teachers and students and analysis of the test papers provided by the school,we understand the current situation of high school students’ use of equation thinking.The results show that students are aware of using equation thinking in solving problems,and they can solve problems by constructing equivalence and simplifying equivalence,but there are still some problems in the process of modeling and transformation,such as not being able to construct the correct mathematical model,not having a good knowledge of mathematics which leads to the wrong solution of the equation and solving the equation carelessly.In the classroom,we propose the following strategies and methods for the penetration and application of equation ideas in teaching.（1）Infiltration in new lessons:① to understand the new knowledge with the idea of equation;② to apply the new knowledge with the idea of equation.（2）Application in exercise lessons:① application strategies of modeling.Focus on the known conditions,implicit information mining,and transfer the corresponding mathematical knowledge to build equivalence;② application strategies of transformation.The solution of basic equations and the use of other mathematical ideas,such as the thought of elimination,the thought of combining numbers and shapes,the thought of functions,the thought of the whole and the thought of classification and discussion to simplify equations.（3）Consolidation in review lessons:The teacher summarizes equation ideas in a comprehensive manner and to consolidate the meaning,role and application techniques of equation thought to students.Through repeated penetration in new lectures,exercises lessons and review lessons,students can better grasp and apply the thought of equations.Finally,we designed a new lesson and implemented a problem lesson with the strategy.After the implementation,we interviewed the teachers and students and found that the problem lesson was very effective and it gave students a better understanding of the meaning,role and application skills of equations.