Research On Comparison Of Mathematics Problem-Solving Schema Induction

This research referred two experiments.Experiment 1 was performed by a 2(numbers of source problems)×2(whether participants compare source problems with others or not),completely randomized multiple factorial design. First,participants were divided into 4 groups and asked to solve 2 or 4 different source problems,then 2 of them were asked to compare these source problems with each other,while the other 2 groups did not.At last,all 4 groups were asked to solve one target problem.The analysis of variance showed that both two factors mentioned above had significant effects on target problem performance, and with the increasing number of source problems,the performance of target problem of automatic groups will be as good as participants of controlled induction groups.This result justified the "multiple-trace memory model" theory:schema induction can be both automatic and controlled.The main purpose of experiment 2 was to compare superior students who had done well in mathematics with inferior students.In order to determine whether the way of schema induction is different between them,experiment 2 was performed by a 2(student's types)×2(ways of assuming target problem) completely randomized multiple factorial design.The analysis of variance showed a significant difference between them:superior students were decline to be eliminative induction,while inferior students mostly performed conservative induction.As a result,after schema induction,for one thing,what is in superior students' minds are structural information,and for another,superficial information are at last kept in inferior students' minds.This leads different performance of target problem solving between the 2 types of students.This result supports neither of the 2 schema induction theories.At least,whether schema induction is conservative or eliminative depends on the types of student (superior or inferior).