或许是受笔试的影响,一个不争的事实是,数学思考一直被老师们所青睐,而数学交流则遭到有意或无意的忽视。其实,数学思考和数学交流是相辅相成的。一方面,数学思考为数学交流提供有力的支撑,另一方面,数学交流可以使数学思考更加条理化、结构化、深刻化。尤其是,当课堂内各种相异性构想能够相互碰撞、彼此激荡时,数学交流 Perhaps influenced by the written test, an indisputable fact is that mathematical thinking has always been favored by teachers, while mathematics exchanges have been intentionally or unintentionally ignored. In fact, mathematical thinking and mathematical exchange are complementary. On the one hand, mathematical thinking can provide strong support for the exchange of mathematics. On the other hand, mathematical exchange can make mathematics thinking more organized, structured and profound. In particular, when the various forms of dissent in the classroom collide with each other and stimulate one another, mathematical exchange