The Investigation On Pupils' Problem-solving Representation Characteristic

Representation has become an important problem solving ability, understanding, converting, constructing problems have played a huge role, many psychologists and educators began to concern of problem representation. This study wants to do research on pupils'problem presentation characteristic, conclude the characteristics of characterizing for front-line math teachers. Specifically, the aim of the research is concluded as follows:(1) Primary application of the general characteristics of problem representation issue:grade characteristics of problem representation capacity, gender difference in problem representation, the features of problem representation mode.(2) Comparing the difference of problem representation between excellent students and poor students:Characterization of mathematical characteristics of excellent students, poor students learn mathematical characterization of features. (3) According to pupils'the characteristics of problem presentation, proposing teaching strategies to guide teaching practice on application questions. This study uses interview, oral report, questionnaire method to investigate pupils in Grade Four,Five and Six in the three primary schools in Hangzhou, conclusions are as follows:(1)Pupils'ability of solving problems has gradually improved with the higher grades. (2)The ability of application problem representation was no significant difference between boys and girls.(3) Primary school students use more semantic structure analysis method for the characterization of schematic representations, repeating and mapping representation, especially the value of representation, literal representation, characterized by applying a similar approach, the formula representation, characterized by the use of other specific topics based on the type selection.(4) Excellent representation of groups tend to use semantic structure representation, schematic representations, repeat representation, image representation, problem-solving using a higher proportion of diverse representation; poor tend to use the literal representation representation, special values of representation, apply a similar method in characterizing, the formula representation, they tend to use a single characterization of problem solving or trying too Representation.(5) Excellent, and poor groups in the semantic structure characterization, schematic representations, special values of representation, repeat representation, literal representation, to apply a similar method in characterizing the use of significant differences in the formula representation, image representation, and other characterization methods used There is no significant difference.(6) excellent students tend to use semantic structure characterization, schematic representations, repeat representation, image representation, problem-solving using a higher proportion of diverse representation; school tend to use the literal representation of poor students, special values of representation, apply a similar approach characterized by the formula representation, they tend to use a single characterization of problem solving or trying too Representation.(7) Excellent and poor at language righteousness structure analysis token, chart type token, especially be worth token, complex to say token and transliterate existence of the token, set use used similar method token show Zhao discrepancy, didn't show discrepancy on the use of formula token, picture token, other token methods.This conclusions can provide reference frame for research of cognition psychology, guide front-line teachers to deeply understand to the students' thinking characteristics,at the same time improve teaching strategies.