Research Into Students' Mathematic Activity Experience

Students' mathematic activity experience is an important part in their personal experience, is one of the important. bases in learning mathematics and improving mathematics quality. The process of its production and formation is actually a process for students to experience mathematic activity. However, our traditional mathematic class based on Basic Knowledge and Skills show more respect to the result, and the process of leaning mathematics has been neglected, this leads to the result that students' experiences from mathematics activity play marginal position in mathematics class, are coincident incidents. Under the contexts of new mathematics reform, Mathematics Curriculum Standards of national compulsory education put forward to requirements to mathematic activity experience based on curricular target. Changes of Curriculum target, especially, some mathematicians, such as, Shing Ningzhong, Zhang Dianzhou's concerns about mathematic activity experience, draw mathematics educators' consideration and exploration to mathematic activity experience. From literature review, studies are mainly personal views on connotation of mathematics activity experience, quite few of studies relating to mathematic activity experience have been done in its and theory and practice. Therefore, a complete and systematic study on mathematic activity experience from its connotation, forms and teaching strategy should be carried out, it not only helps to enrich the fundamental theory, but also promotes to provide suggestions for deepening the reforms of Basic Mathematics Education.By the analysis of documents, attending lectures, records of class teaching, interview, analysis of cases and theory, the research focuses on the connotation and forms, the process, arrangements, influencing factors and teaching strategies of mathematic activity experience. The following conclusions can be drawn:(1) Further understanding of connotation: Broad Mathematic activity experience means students obtain feeling, understanding, comprehending and experiences about the aim of teaching activity, mathematics contents, mathematics activity behaviors and transformation of forms and mathematics activity surroundings from the process of mathematics activity, and the combined experiences of mathematic knowledge, skills, wisdom, affection and ideas. Mathematics activity experience can be broadly classified into process and result mathematic activity, can also be simply divided into idea, cognitive, affective and action skills. It can be said that narrow mathematic activity means idea and affective experience.(2) Specific contents: By analyzing the students' memory, mathematic writing, and the use of metaphor, mathematics activity experience includes:①memory of the process of mathematic activity experience;②the actual mathematics knowledge, skills, methods and strategies from activity;③the comprehension from activity;④affective experience, by observing class and interview, main contents of mathematic activity experience from one mathematics class can be induced:①Students' specific mathematic activity,②Experience from the process, it is the experience of mathematic activity process, perception and gradually forming point of view and opinion, and some judgments of value on mathematic activity process,③acquired actual knowledge and proceeding knowledge from mathematic activity experience;④Methods and skills of how to conduct a reasonable mathematic observation, finding and guess, how to verify, how to induce, communicate and discuss.(3) Process construction: Students' knowledge, affection, meaning and practice from mathematic activity experience is a process of supplementing and supporting each other; It is also a process of socialization situation perception; It is a cycling process "from activity to experience" and " from experience to new activity again"; It is a process of experience reformation. So, the process that students obtain mathematic activity experience should be through the following steps: preliminary experience stage; renewed experience stage; recognition experience stage; conception experience stage; participation of diversified teaching activities, conception experienced schema stage by gradual internalization. Accordingly, according to its degree of abstractness from the lowest to highest degree, students' mathematic activity experience can be through the following stages: preliminary stage, renewed stage, recognition stage and conception stage.(4) The influencing factors of obtaining mathematic activity experience are mainly from students themselves, teachers and mathematic activity experience itself. From students' perspective, factors can be cognitive style, students' past experiences, memory, attention, cognitive strategy and self-adjustment factors, intention, motivation, affective, belief, efficacy, self-awareness and ways of involving in mathematic activity; From teachers' perspective, factors include teaching belief, teaching behavior and teaching style, reply and response to students' performance, management between teachers' supervision and students' independent study, providing teaching scene and teaching tasks, fairness between forms and opportunity of activity; From the perspective of teaching activity, factors contain arrangements of teaching activity scene, teaching tasks and classroom cultural atmosphere, etc..(5) The following basic teaching strategies should be carried out to cultivate teaching of mathematic activity experience:①stimulating strategies of mathematic activity experience;②generating strategies of mathematic activity experience;③systematical implementation strategies of mathematic activity experience ;④transformation strategies of mathematic activity experience;⑤extending strategies of mathematic activity experience;⑥optimizing strategies of mathematic activity experience.Many researches have been done on activities and experiences, but just few on mathematic activity, especially on the study of influencing factors and teaching strategies that students obtain mathematic activity experience, therefore data and resources are quite rare, and make the research more difficult. The paper conduct a preliminary arrangement of the connotation of meaning of mathematic activity experience, and attempts to construct the framework for analyzing contents of mathematic activity experience; By memory, metaphor and comparison, the paper studies specific contents of mathematic activity experience(These are quite rare in the study of the field). The paper makes a preliminary exploration of construction process and influencing factors, and presents teaching strategies for cultivating mathematic activity experience.