Number And Shape Of The Psychological Mechanism

As an important ideas and methods of mathematic problem solving , numeric-graphic combination not only is a guide ideas and concrete method to every teachers and students ,but also is a focus of study to every investigator .Nowadays ,the study is focusing on how to applying numeric-graphic combination to solving problem and the applying principle and the wrong way of using .All these study have made some harvest .But there still are song problems in the study , reflecting in the most paper's structure is singleness as "view+example"; the content and view of this study are repeated ;the study method is just analyzing typical example. There are only small part of study work studying the mentality process of numeric-graphic combination.Studying numeric-graphic combination from the view of psychology point is benefit to make clear of the mentality process ,which offer effective considering way and method guide to using it. Based on these thinking ,my study will study the mentality process of numeric-graphic combination by using the harvest of psychology study.Mathematic problem has two representation forms ,one is algebraic representation the other is graphic representation, numeric-graphic combination reflects the communication and conversion of these two forms .We divide numeric-graphic combination into two kinds according to the conversation way of representation. One kind is have obvious corresponding relation between the two representations ,the other is not have obvious corresponding relation between the two representations, which need construct other representation according to the structure of problem . This is a more difficult kind of numeric-graphic combination. We call this as constructing representation numeric-graphic combination. In my study work I will emphasis study the mental process of this kind of numeric-graphic combinationAnalogy is the main thinking pattern of constructing representation numeric-graphic combination. There are two analogy forms , one is experience analogy ,the other is creative analogy. Experience analogy regard the solved problem which have the same structure with the solving problem (target problem )as the base problem and use it solving way to solve the target problem. Experience analogy is the portrait analogy in the same knowledge system. The key tache of this kind analogy is retrieval the base problem according to deep-seated similarity of relation and sameness of quality . creative analogy is using the essential similarity of two system's relation and quality to make the direct analogy ,which is the transverse analogy between different knowledge systems. Such as make analogy between algebra and geometry structure systems. The similarity of two system's relation and quality is the substance of this kind analogy. Structure mapping is the primary shape of the analogy. The analogy's mental process of constructing representation numeric-graphic combination are seven taches ,which are apperceive—representation ( homomorphism inner representation )—retreval—combination- representation ( different exterior representation )—self-examination—problem solving. From representation (homomorphism inner representation) to representation ( different exterior representation ) is the key tache of achieving the numeric-graphic combination and simply principle.There are two different level perception analogy when student use numeric-graphic combination to solve problem. One is low-level-perception analogy which use the similarity of appearance structure to make analogy and which make partial structure mapping. The other is high-level-perception analogy which use the similarity of essence structure to make analogy and which make integer structure mapping.In my paper also validate the conclusion, according geometry representation to think algebra representation is easier than according algebra representation to create geometry representation. The main reason is according geometry representation to think algebra representation which make a logical consequence that is according the ubiety and quantity relation in the graphics. The main think mode in according algebra representation to create geometry representation is analogy ,which is a creative think mode.