Research On Mathematics Problem-Solving Analogical Transfer And Teaching

Research on transfer mainly focused on the problems of transfer of learning early, and in problem-solving study field, which was one of advanced studying types, the phenomena of transfer were not paid enough attention. Recently, with the development of research on problem-solving in the cognitive psychology, people have paid more and more attention on the problem-solving analogical transfer in the transfer field since 1980s. Combined with the characteristics of mathematics, the analogical transfer law in the problem-solving field was studied in this paper.Mathematics problem-solving analogical transfer was defined by the conception of analogical transfer in this paper, and was compartmentalized five kinds: mathematics knowledge analogical transfer, mathematics means analogical transfer, structures analogical transfer, numbers and graphs analogical transfer, relationships analogical transfer, every kind of mathematics problem-solving analogical transfer was explained by examples of mathematics in this paper.From the cognitive psychology angle, Combined with the division of sub-processes of analogical transfer, this paper brought forward that the usual cognitive process of mathematics problem-solving analogical transfer include three sections:"create the representation of the mathematics problem","retrieval base mathematics problem , concretely match","schema induction, optimize the old cognitive structure", and explain the process by mathematics example. About the mechanism of mathematics problem-solving analogical transfer, the theories of problem-solving analogical was used to explain the mechanism of mathematics problem-solving analogical transfer in this paper. This section includes two parts: on the one hand, conclusions and disputes existed about the mechanism of problem-solving analogical transfer were analyzed. On the other hand, Combined with the examples of mathematics, the mechanism of mathematics problem-solving analogical transfer was explained by three theories-"structure-mapping theory","pragmatic schema theory","exemplar theory", at the same time the characteristics of mathematics was taken into account.The influential factors of mathematics problem-solving analogical transfer are one of the important contents of mathematics problem-solving analogical transfer study. In the paper, the author considered the objective influential factors include three parts: the similarities between the mathematics problems; exoteric hint, guidance; the examples'design, presentation modes of examples, and the subjective influential factors include four parts: mathematics learning motive; mathematical self-monitoring ability; mathematics knowledge; level of consciousness of the related isomorphic mathematics problems.The author took an investigation on the existence condition of students'mathematics problem-solving analogical transfer, and the four subjective influential factors: mathematics inner learning motive; mathematics exterior learning motive mathematics self-efficacy; mathematics self-monitoring ability. Questionnaire method and examination method were mainly used in the study. The effectual sample is 412. The results of the analysis show that questionnaire and examination paper in the study have a good reliability and validity. From statistical analysis of the data, the following conclusions were drawn: there are no significant differences between the male and the female participants on mathematics problem-solving analogical transfer ability; there are no significant differences between city and country on the male's mathematics problem-solving analogical transfer ability, but there are on the female's; there are significant differences between science and arts on mathematics problem-solving analogical transfer ability; there are no significant differences between city and country on the science's mathematics problem-solving analogical transfer ability, but there are on the arts'; there are significant differences between city and country, and between different achievement groups; the level of mathematics self-monitoring and mathematics self-efficacy has effect on mathematics problem-solving analogical transfer ability; mathematics inner learning motive and mathematics exterior learning motive are all influential factors of mathematics problem-solving analogical transfer; there exists a positive linear connection between mathematics problem-solving analogical transfer achievements and mathematics achievements.Based on theory study and survey analysis, the author brought forward some advices to the mathematics problem-solving analogical transfer teaching: design teaching from the angle mathematics problem-solving analogical transfer; attach importance to the students'grasp of the mathematics knowledge; teach the mathematics idea means to students gradually. Some advices were also given to improve mathematics problem-solving analogical transfer ability in this paper: improve the level of students'mathematics self-monitoring and mathematics learning motive; foster students'mathematics self-efficacy.