Construction Of Mathematical Teaching Model Based On Mathematical Culture

At present, the researches on mathematical culture and mathematical education mainly prove the significance and value of pervasion of mathematical culture in teaching, but seldom concretely integrate mathematical cultural theories and educational practices, especially rare for the systematic studies on teaching strategies and operation flows of models. Teaching model is a middle range theory between teaching theories and practices, as an intermediary between theories and practices. For the sake, "the construction of mathematical teaching model based on mathematical culture" not only has the value of theory, but also has the meaning of practice.For a lack of ready-made modes to be examples, after defining the connotations of mathematical culture and mathematical teaching model, the article cards and concludes mathematical theories and practices in order to lay a foundation for the model from values of mathematical cultural education, ways and vectors of permeating ideas and related teaching models, which Corresponding to three problems about mathematical cultural education on "why to teach", "how to teach" and "what to teach". Based on the understanding of the mathematical culture conception, the article further establishes the theoretic basis and teaching goal. Around them, after two years action research and by element analysis of mathematical cultural cases and two phases exploration on mathematical teaching model based on mathematical culture in middle schools, the research formed the preliminary operation flow of the model gradually: to touch experiences—the understanding of mathematization—multi-domain infiltrated—review and introspection. Among them, "to touch experiences" requires "around the topic to arouse interest", "the understanding of mathematization" requires "abstract gradually, study in proceeding", "multi-domain infiltrated" means " core commanding, expand and sublimate, "review and introspection" include reviewing, concluding, integration, creative and so on. Besides these, the article makes consideration and exploration on the scope of application, precautions and implement conditions, for example, teaching style, teaching principles, teaching method, principles of material selection and so on by classroom observation method and interview method.In order to make students feel the charm of mathematics as a culture and teachers vividly understand mathematical cultural education and ways of permeating mathematical cultural ideas, the article puts forward that the mathematical teaching model based on mathematical culture has the features of openness, process, culture and integration, by lesson study in middle schools. In the research of "mathematical induction"lesson, such features embody clearly and the model not only motivates students' participating enthusiasm and contribute degree, but also let teachers' understanding of mathematical cultural education from "blankness" turn to "searching and sublating". Finally, it is worthy to point out that the teaching model based on mathematical culture is still at primary stage, so there still exist several conclusions must to be validated.