中美数学教材设计的一项比较研究——以“勾股定理及其逆定理”为例

A Comparative Study for Design of Mathematics Texts for Students of China and the United States——Taking Pythagorean Theorem and Its Inverse Theorem as an Example

中小学数学教材中对知识的设计和处理方式在数学教学中起着重要作用.通过比较美国教材《发现几何》与国内人教版《初中数学》在"勾股定理及其逆定理"设计上的差异,发现2本教材在设计上各有优势,前者设计注重学生的动手操作,侧重学习者的个性学习,力求在做中学,关注学习者对几何的兴趣;后者设计注重知识的完整体系,对演绎推理的要求比重明显大于对合情推理的要求,关注学习者和教师严谨、准确的数学体验.

Important effect has been made in mathematics teaching that design of mathematics textbook in middle and primary schools in China and the United States. In this paper, by contracting the difference of design between the American textbook of Discovering Geometry and the Chinese textbook of Junior Mathematics （Edition of People＇s Education Press）. Both books have their advantage. In the design of Discovering Geometry, emphasis has been laid on student＇s hands-on operation, with extra emphasis on personality study of learner, aiming at learning by doing and at learner＇s interesting about geometry. And in the design of Junior Mathematics （Edition of People＇s Education Press）, much more claims have been raised on proportion of deductive inference than that on intuitive inference obviously, with emphasis on knowledge＇s global system.