The Influence Of Schematic Representation Strategy On Elementary Students' Mathematical Problem-Solving Ability

Mathematical problem-solving ability as a main objective of contemporary education, it is not only reflected in the mathematical problem-solving scores also reflected in the mathematical problem-solving transfer. Strategy plays an important role in mathematical problem-solving, and it has a direct impact on his ability to solve mathematical problems. When elementary students face mathematical problems, especially more complex word problems, they fist represent the problem. Schematic representation strategy is elementary students often used representation strategy, which has an important role in mathematical problem-solving. Schematic representation strategy related to metacognition and its application only reached metacognitive level can be transferred. So metacognition has close relations with schematic representation strategy and elementary students'mathematical problem-solving ability.Participants in our studies were the former 269 and the latter 218 grade 5 students. We used both natural empirical and questionnaires research to test the influence of schematic representation strategy on elementary students'mathematical problem-solving ability, and the role of metacognition in schematic representation strategy influenced elementary students'mathematical problem-solving ability. The main findings are as follows:1 After strategy learning, for elementary students'schematic representation strategy level and mathematical problem-solving scores were significantly enhanced.2 There was main effect on schematic representation strategy influenced elementary students'mathematical problem-solving scores. Students with high strategy level had higher scores in mathematical problem-solving test than students with average and low strategy level, and students with average strategy level had higher scores than students with low strategy level. 3 Excluding the effect of pre-test mathematical problem-solving scores, there was interaction between strategy level and feedback in post-test mathematical problem-solving scores. Sample effect showed that students with feedback had higher scores than students without feedback in low strategy level.4 There was significant difference among the transfer of three different conditions. Students had higher transfer scores in surface-feature-same-and-essential- feature-same and surface-feature-different-but-essential-feature-same than in surface-feature- same -but- essential- feature- different.5 There was main effect on schematic representation strategy influenced elementary students'mathematical problem-solving transfer. In surface-feature-same -and-essential-feature-same and surface-feature-different -but-essential-feature-same, students with high and average strategy level had higher scores in mathematical problem-solving transfer test than students with low strategy level. In surface-feature-different-but-essential-feature-same and total transfer questionnaires, students with high strategy level had higher scores in mathematical problem-solving transfer test than students with average and low strategy level, and students with average strategy level had higher scores than students with low strategy level.6 Schematic representation strategy on elementary students'mathematical problem-solving ability was mediated by metacognition.The present study provided a new perspective to the study of mathematical problem-solving and some new theoretical basis and guiding ideas to the development of elementary students'mathematical problem-solving ability.