In recent time, the foundmental education are reforming thoroughly in our country. An importantaim of this reform is to change the traditional studying approach of simple imitation and to build a new active studying method to foster students with creating spirits. In this thesis, we establish a mathematical teaching mode with mutual exploration and pose five teaching strategies: construct problems with correspondant circumstances, form conjections by exploring and discussion, demonstrating and resoning, evaluate by self and learn with depth creating with cyclic raising. We also give teaching cases as applications of the above teaching strategies.Our teaching experiments show that the teaching mode of mutual exploration is efficient to encourage student's study interests and build confidences. It is also efficient to forter students subjective senses in teaching and studying.
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