Mathematical Problem-solving Transfer And Its Teaching Study

Based on the studies of transfer and problem-solving transfer, the article initially studies the process and mechanism of the mathematical problem-solving transfer, and studies the influential factors of the mathematical problem-solving transfer, in which the Mathematics Idea Means' affections are studied especially. In the end, helpful suggestions of the mathematical teaching are offered to improve the students' abilities of mathematical problem-solving transfer. So, it's a significant subject.Mathematical problem-solving transfer is a kind of problem-solving transfer which is in the domain of mathematics, and the studies of mathematical problem-solving transfer is the sub-study of the studies of problem-solving transfer. So. the characteristic of this article are, on the one hand, based on the foregone theories of problem-solving transfer, on the other hand, emphasize the mathematical character of mathematical problem-solving transfer, which is shown from the object of mathematical problem-solving transfer - the mathematical problem, and the media of mathematical problem-solving transfer - the cognitive structure of mathematical problem solving.From the cognitive psychology angle, this article bring forward that the usual cognitive process of mathematical problem-solving transfer include four sections: l.creat the mental representation of the mathematical problem", 2. "analogize and associate, create the mathematical problem space", 3. "concretely match, change the mathematical problem space", 4. "generalize the experience of mathematical problem solving, recreate the old cognitive structure". In the process of mathematical problem-solving transfer, the front three sections run again and again, until the mathematical problem-solving transfer success, then the forth section runs.About the mechanism of mathematical problem-solving transfer, this article mainly transfers the theories of problem-solving transfer to explain the mechanism of mathematical problem-solving transfer. This section include two parts, on the one hand, explain the mechanism of mathematical problem-solving transfer by themechanism of analogical transfer, which mainly uses three theories to explain the mechanism of mathematical problem-solving transfer - "structure-mapping theory", "pragmatic schema theory", "exemplar theory", at the same time the character of mathematics is taken into account. On the other hand, explain the mechanism of mathematical problem-solving transfer by the mechanism of cognitive skill transfer. mathematical problem-solving transfer is intellectual skill transfer, the theory of common elements is the main theory of explaining the mechanism of skill transfer. But "four factors theory of transfer", which based on the theory of common elements, explains the mechanism of skill transfer more synthetically. So in this article, "the four factors theory of transfer" is chosen to explain the mechanism of mathematical problem-solving transfer.The influential factor of mathematical problem-solving transfer is one of the important contents of mathematical problem-solving transfer study. In this article, the author considers the subjective influential factors include three parts: 1. the mathematical problem solver's intelligence, age and attitude; 2. the elements of "the cognitive structure of mathematical problem solving", such as the knowledge and experience system of the mathematical problem solving, the cognitive operating system of the mathematical problem solving and the metacognition system of the mathematical problem solving; 3. the good organization and generalization of the mathematical cognitive structure. The objective influential factors include two parts: 1. exoteric hint, guidance and the example's design; 2. the similarities between the mathematical problems' exterior character and the deeply structure.It's acknowledged that the Mathematics Idea Means is helpful for mathematical study transfer, the author considers that the effects of the Mathematics Idea Means in the mathematical study is mainly embodied...