| Problem characterization is a key part of problem solving.It is of great significance to study problem characterization in the subject teaching to improve students' ability to solve problems.This paper adopts literature research and investigation to study the influence of external representations of mathematics problems on the problem solving to junior students in the dimension of representation and knowledge.The research contents include:related theories and experimental research of representation;The analysis of the influence of the representation mode on the problem solving of junior students;the analysis of the impact of knowledge areas and representation methods on student problem solving.Based on this,this paper proposes effective and reasonable teaching suggestions for students1 troubles in problem solving.The experiment resulted in the following conclusions:1.The external representation of the problem has a significant difference in the student's problem solving.In the topic of situation representation,the prefermance of student is the best,followed by the topic of graphic representation.In the topic of situation representation and graphic representation,students'perfermance is more concentrated.In the topic of namely text representation,the students' problem solving results are more decentralized and significantly lower than the solution of the situational representation.2.In different areas of knowledge,the external representation has a significant difference in students' problem solving.(1)In the fields of number and algebra knowledge,students have higher scores in situation representation than the topics of graphical representation and namely representation.(2)In the field of graphics and geometry knowledge,the external representation has no significant difference with the student's problem solving.(3)In the field of probabilistic and statistical knowledge,students have higher scores in solving graphical representations and situational representations than namely representations.3.Different external representations have an impact on the internal representation.In the topic of contextual representation,the internal representation of students in the process of solving problems tends to be algebraic representation;in the topic of graphical representation,the internal representation of students is biased towards geometric representation;For the topic of representation,students use algebraic representations and geometric representations.4.The knowledge area has a significant influence on the internal representation of students.(1)In the field of number and algebra knowledge,students are good at using algebra representation to solve problems in the topic of contextual representation;and there are many students with geometric representation and algebraic representation for the problem of graphical representation;in the topic of graphic representation,students are good at using geometric representation to solve problems.(2)In the field of geometric and graphic knowledge,students solve problems by geometric representations.Only a few students use algebraic representation to solve problems in namely presentation.(3)In the field of probability and statistical knowledge,students basically use algebraic representation to solve problems.Only a few students use geometric representations to solve problems in text representation.Finally,aiming at the trouble that arise in problem solving,we put forward reasonable and effective teaching suggestions.Teachers should consciously expand the topics of different external representations during the teaching process,attach importance to the cultivation of students,ability to express mathematical problems,and focus on cultivating students' problem-solving abilities. |
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