Research On Mathematics Problem Solving Teaching In Senior High School From The Perspective Of Representation

Problem-solving teaching is the core content of mathematics education,which has strong practical significance and is one of the hot issues in mathematics education research.Representation is an important part of cognitive psychology,which has a strong influence on revealing students' psychological cognition and optimizing teaching activities.Mathematical representation is the representation in the field of mathematics.In recent years,the study of mathematical representation has become an increasingly important content.It is of great value to combine it with problem-solving teaching in order to better serve mathematical problem-solving.Studying the problem-solving teaching of high school mathematics from the perspective of representation plays an important role in organic combination of classroom teaching,reasonable presentation of learning materials,and close to students' cognitive characteristics and level.Reasonable mathematical representation can improve the quality of problem-solving teaching,but there are still many problems in the educational research of problem-solving teaching from the perspective of representation.There are still many shortcomings in how to guide problem-solving teaching from the perspective of representation.This paper intends to study this topic in order to provide reference for problem-solving teaching.Mathematical representation refers to the expression of various information records used in the process of information inflow or outflow in mathematics,including graphical representation,symbolic representation,linguistic representation,operational representation and situational representation.The characteristics of five kinds of representation used by teachers and students in problem-solving teaching are the important content of this paper.Through natural observation and interviews,the following problems are found in the teaching of high school mathematics problem-solving from the perspective of mathematical representation: students' single representation;lack of attention to multiple representation;confusion of multiple representation;low ability of representation transformation.From the perspective of teachers' representation,problem-solving teaching shows: inefficient classroom;inflexible use of modern information technology;lack of in-depth study of test questions.In view of the problems existing in problem-solving teaching,according to the cognitive load theory and Polya's problem-solving theory,the teaching of high school mathematics problem-solving from the perspective of representation should follow the following principles: design principles at the macro level,taking into account the cognitive load of students,so as to achieve the best cognitive load in the overall classroom effect;selecting the important representation forms that fit the overall content of the curriculum;We should adhere to the principle of representation with prominent main line.On the medium level,the design principles of specific classroom content presentation should embody the pluralistic representation principle of content presentation,and in the process should be based on the representation principle of penetrating the transformation ability of representation.At the micro level,the design principles and problem solving process conform to the representation principles of understanding intuition;the representation principles of thinking conversion;the representation principles of solving rigor;and the representation principles of reviewing modelling.