The Influence Factors Of Pattern Recognition Research In Mathematical Problem Solving

Cognitive process of solving mathematical problem can be divided into four stages: problem presentation, pattern recognition, transfer, and self-control. Here, the "pattern" refers to mathematical patterns, such as kinds of concepts, systems, theory, rules, and methods. In mathematical problem solving, a kind of problems which have the same structure or solving method can be called a pattern. Pattern recognition refers that when confronting a mathematical problem, indivduals can sort the problem so that it matches a kind of mathematical pattern in his/her cognitive struction. In this systerm, pattern recognition, as the second stage of mathematical problem solving process, is based on problem presentation, and is the precondition of transfer, through which we can see the important role of pattern recognition in mathematical problem solving. In mathematical problem solving, how individuals recognize the patterns learned, and what factors influnence the pattern recognition, and then instruction strategy of pattern recognition is explored. In these sense, the study on pattern recognition in mathematical problem solving has realistic need.This study employs documentary analysis, quantitative analysis, qualitative analysis, and structural equation model to study the factors influencing pattern recognition.First, on the basis of summarizing researches on pattern recognition in the field of sensory perception and mathematical problem solving at home and abroad, the concept of "pattern recognition in mathematical problem solving" is proposed, that is, the thinking and cognitive process of matching the problem and a kind of mathematical pattern in his/her cognitive struction when individuals confronting a mathematical problem.Second, chaper3,4,6respectively explored the factors influencing pattern recognition in mathematical problem solving by qualitative analysis, structural equation model and quantitative analysis, which achieve the stable methodological triangulation. Study1in chaper3, analysizes problem solvers’strategy of pattern recognition by questionnaire survey, and study2,3,4interview problem solvers’cognitive process of pattern recognition. Study5in chaper4explored the relationship between individuals’ pattern recognition, self-control, thinking quality and mathematical problem solving achivevment using structural equation model. Study6,7,8in chaper6explored the factors influencing pattern recognition by experimentation.Thirdly, chaper7examines an outstanding classroom and propose that reflective practice is the practice pathway of pattern recognition in mathematical problem solving.Results:(1) pattern quality is the basis and predetermination element of pattern recognition, and self-control and thinking quality is the conditional factor.(2) the cognitive process of pattern recognition of different kinds of problems can be explained with different models; pattern recognition in mathematical problem solving has the characteristic of bottom-top and top-bottom.(3) self-control and thinking quality have direct influence on pattern recognition. Their influence on mathematical problem solving achievement is partly direct and partly indirect through pattern recognition.(4) acquisition way and problem kind significantly influence pattern quality, and their interaction influence pattern quality significantly.(5) self-explanation level significantly influence pattern quality in mathematical problem solving, and interaction of self-explanation level and problem kind influence pattern quality significantly.(6)for cross-over problems, there is no significant difference in pattern recognition between high-sense group and mid-sense group, while significant difference exist between high-sense group and low-sense group, and between mid-sense group and low-sense group.