Research On Junior High School Mathematics Problem Solving Teaching Based On The Perspective Of Representation

Representation is a basic concept of cognitive psychology,which has an important influence on clarifying students' psychological cognition and optimizing teaching activities.The representation of question is one of the key factors to solve the question,and it is the externalized carrier of knowledge transfer between teachers and students.Studying question-solving teaching from the angle of representation can help teachers to make good use of classroom time,improve teaching efficiency,perfect teaching methods,promote students' change of mathematical representation,and cultivate their question-solving ability and creative spirit.This paper is based on the actual investigation of a school in Benxi City,Liaoning Province,and from the angle of representation,taking mathematical question-solving as the carrier,this paper aims to study the current situation of the use of representation in question solving by junior middle school students and the teaching situation of teachers in problem-solving teaching,then the author puts forward some suggestions on question-solving teaching from the angle of representation.This paper mainly discusses three aspects: first,the present situation of junior high school mathematics question-solving teaching from the angle of representation;second,the suggestion of junior high school mathematics question-solving teaching under the representation angle of view;third,how to carry on mathematics question-solving teaching design.In view of the above three problems,firstly,through the research of literature,this paper clarify the background of junior middle school mathematics question-solving teaching and the present research situation at home and abroad,and then uses classroom observation,test investigation and interview research methods to understand the current situation of junior high school mathematics question-solving teaching representation,and finds that there are the following problems:for students,understanding tends to be intuitive,lack of representation internal translation;ignoring the transformation between representations,there are obstacles in question-solving;the knowledge structure is not perfect,and the ability of representation transformation is low;teachers also have some difficulties in implementing the teaching process of multi-representation question-solving,which mainly lies in the low classroom efficiency of using representations to solve problems,it is difficult to combine with modern information technology,and students' limited cognitive ability to accept multiple representations is not strong.In view of the problems existing in question-solving teaching,according to the cognitive load theory,dual coding theory,multiple intelligences theory,cognitive theory of mathematical multi representation learning and Polya's theory of question solving,etc.,this paper puts forward some suggestions on the question-solving teaching in junior high school from the angle of representation: to perfect the cognitive structure and arouse the knowledge and experience;to identify the types of problems by combining the knowledge and experience;to reduce the obstacles in question-solving and to pay attention to multi-representation;combining cognitive characteristics,teaching students according to their aptitude,refining classroom content,appropriate cognitive load.Finally,based on the above suggestions,the author designs the typical mathematics knowledge in junior middle school,and present a new style of junior high school mathematics teaching based on the perspective of representation.