The Effects Of Pupils' Mathematical Word-problem Representation Type On Problem-solving

Based on previous studies, we classified the types of problem representation, chose four kinds of word-problems, and defined fitting representation, preference representation and preference representation. Four experiments were carried out for exploring pupils'types of problem representation and its influence on their word-problem solving.Experiment 1 aimed to investigate how many types pupils have in solving four kinds of word-problems, the relations between Word-problem Type and Problem Representation Type, and how the different problem representation influence pupils'word-problem solving. 60 Grade-4 pupils as objects, and four different word-problems as material, individual tests were performed. Experiment 2 aimed to investigate the different influence between fitting representation and ill-fitted representation on four kinds of word-problems. 120 Grade-4 pupils were distributed into four Problem Representation Group, that's Word Representation Group, Relation Representation Group, Picture Representation Group and Schema Representation Group. They were asked to use the only one type of problem representation to solve all four kinds of word-problems.Experiment 3 aimed to investigate how difficulty of the word-problems influences Grade-4 pupils'choice of problem representation, and the word-problem solving. Two different difficulty levels were designed, one was low difficulty level, and the other was high difficulty level, in order to explore how 60 Grade-4 pupils'problem representation changed under different difficulty condition.Experiment 4 aimed to investigate the developmental characteristics of Grade 4 to Grade 6 pupils'problem representations in four kinds of word-problem solving, especially the change of pupils'application frequency about preponderant representation.The main conclusions were drawn follow:(1) Grade-4 pupils have four different types of problem representation in solving word-problems, that is Word Representation, Relation Representation, Picture Representation and Schema Representation.(2) Every kind of word-problem have corresponding problem representation type: Compare Problem and Ratio Problem have Diction Representation as fitting representations, Tree Planting Problem and Distance Problem have Figure Problem as fitting representations. Fitting representation is useful in solving corresponding wore-problems.(3)Math-difficulty students lean to use Word Representation and Picture Representation, math-better students lean to use Relation Representation and Schema Representation.(4)Fitting Representation Group have high score in wore-problem solving than Ill-fitted Representation Group and pupils in Choice condition.(5)Under high difficulty condition, Grade-4 pupils'numbers of problem representation types deduce; Grade-4 pupils lean to use Word Representation and Picture Representation, less use Relation Representation and Schema Representation.(6) Under high difficulty condition, Grade-4 pupils lean to use Word Representation in solving Compare Problem and Ratio Problem; use Picture Representation in solving Tree Planting Problem and Distance Problem.(7) Under high difficulty condition, Word Representation and Picture Representation have lower scores in solving word-problems, but Relation Representation and Schema Representation have similar scores in solving word-problems.(8) Grade-4 to Grade-6 pupils more and more use Relation Representation and Schema Representation, less and less use Word Representation and Picture Representation in solving all four kinds of word-problems.(9) Grade-4 pupils have Word Representation and Picture Representation as preponderance representation, Grade-5 pupils have Relation Representation and Picture Representation as preponderance representation, Grade-6 pupils have Relation Representation and Schema Representation as preponderance representation.(10) Grade-4 to Grade-6 pupils'correction ratio has gradual increase. That is, Relation Representation has more and more scores in solving Compare Problem and Ratio Problem, and Schema Representation does so in solving Tree Planting Problem and Distance Problem.