“问题化”:数学“史学形态”转化为“教育形态”的实践路径

Problematization: the Practical Approach of “Historical Morphology” of Mathematics Transforms into “Teaching Morphology”

充分发挥数学史教育功能的基本理路是将数学的＂史学形态＂转化为＂教育形态＂.将数学史料＂问题化＂则是把数学＂史学形态＂转化为＂教育形态＂的有效路径.数学史料＂问题化＂是指通过深入挖掘蕴涵于数学史料背后的数学知识与育人要素,并将其转化为有利于促进学生数学学习的一系列问题.＂问题化＂是数学＂史学形态＂向＂教育形态＂转化的方法论创新,是数学文化价值向育人价值转化的内在价值突破,并能促进数学课堂教学内在规律的良性实现.史料选择、问题设置、教学设计则是数学史料＂问题化＂的实践策略.

A basic route to fully perform mathematics history＇s functions of education was to transform the ＂historical morphology＂ of mathematics into ＂teaching morphology＂. Problematization was a practical approach to make the transformation effectively. The meaning of problematization was to excavate the mathematics knowledge and educational factors concealed into the mathematics history, and turn them into a series of problems which may promote students＇ mathematics learning. Problematization offered methodology innovation for the transformation of ＂historical morphology＂ into ＂teaching morphology＂, and made inherent value breakthrough from cultural value to educational value, and promote the mathematics teaching follows the innate laws of classroom teaching. Based on the lesson of Perfect Number, the study provides practical strategy on the selection of mathematical history, the setting of mathematical problems and the design of mathematics teaching.