The Effect And Mechanism Of Representation On Mathematical Problem Solving In Primary Students

It is very important to develop primary students' ability to solve mathematical word problems in learning.Recruiting 194 primary school students from grade two to five,this research divided four types of mathematical word problems: difficult visual problems,difficult non-visual problems,easy visual problems and easy non-visual problems.By using mathematical word problem test and individual interview,this study aimed to investigate the effect and mechanism of representation on mathematical problem solving among pupils.Experiment 1 adopted mixed experimental design,measuring the mathematical word problem scores and representation scores of students in grade 2,grade 3,grade4 and grade 5.The results showed that: with the increase of grade levels,the frequency of students' pictorial representation decreased,while the frequency of students' schematic representation increased and there was no grade difference in mixed representation.Based on the mathematical word problem test in experiment 1,experiment 2 further analyzed the amount of effective information which related to word problem solving contained in schematic,pictorial and mixed representation used by students.Corsi Block Tapping task was added to measure spatial working memory ability.The results showed that: Spatial working memory played an important role in mathematical word problem through two paths.One was directpath and the other was indirect path,with schematic presentation and effective information as mediators.Combining above these two experiments,this study found that the students' scores of word problems,visual-spatial representation,schematic presentation and effective information in grade two to three were significantly improved,which indicated that this stage was a critical period for students to learn mathematical word problem in primary school.In addition,the difficulty of word problem and the degree of visualization had a significant interaction on visual-spatial representation,schematic representation,pictorial representation and effective information.This implied that students used more schematic representation when dealing with visual word problems,more pictorial representation when dealing with non-visual word problems and easy word problems were more susceptible to visualization than difficult word problems.In conclusion,this study completed previous studies and provided theoretical support for mathematical word problem teaching in primary school.