“乘除比翼”:倍认识的新视角

Multiplication and Division:a New Angle of Teaching Time

倍,是儿童思维由加法结构上升到乘法结构的台阶,是儿童数学认知结构中的一个生长结点,它起着承上启下的、构筑儿童数学知识大厦的基础作用。"倍"概念的建立和理解,需要学生克服加法结构的影响,即需调整已有认知结构,是对原认知的顺应。再者,教材的改编引起学生的已有认知发生了巨大的改变,教师应借助乘除比翼的合力来重新定位和整合倍的认识的教学:通过乘除抽取学生原有的思维;借助"找"、"圈"、"数"以达到学生对倍概念的掌握与内化。

Time in primary school math means a step from an additive structure to multiplicative one, which is a base for children to build math knowledge in their cognitive structure. To have the concept of time and understand it needs children＇s adjustment to new cognitive structure, and teachers could make use ofknowledge of multiplication and division to guide children, that is, abstracting children＇s original thinking and borrowing methods of finding, circling and counting helps children understand and makes the concept internalized.