数学文化的教育学解读--基于“理解取向”文化观的分析

Pedagogical Interpretation of"Mathematical Culture":An Understanding-oriented Cultural View

在深入推进基础教育课程改革的背景下,如何真正将“数学文化”融入课程教学,是数学教育工作者必须关注的一个重要论题。已有“数学文化”的涵义可概括为基于学科主义立场的“事实覆盖”型数学文化观,不适应“素养培育为本”的数学学科教育实践要求,因此需要重新解读“数学文化”的涵义。杜威提出的文化定义代表了一种基于教育学立场的“理解取向”文化观。这种文化观具有三方面的特点:(1)文化是“三元合一”的;(2)文化是理解取向的;(3)文化是动态发展的。以“理解取向”文化观为指导,可以把“数学文化”解读为:学生在学习数学知识的数学活动中,理解数学的思想(方法)、观点、精神等数学观念意义,并内化为数学素养,这种数学理解的过程和结果统称为数学文化。基于数学学科的特点,“数学文化”具有三种层次结构:第一层次,是从经验感受到数学认识模式的“数学明理化理解”;第二层次,是从数学认识到数学理性模式的“数学理性化理解”;第三层次,是从数学理性到数学悟性模式的“数学道理化理解”。教师应树立数学课堂才是“数学文化”主阵地的意识,积极探索“数学文化”融入课堂教学的有效路径,发挥数学育人的重要作用。

In the context of deepening the curriculum reform of basic education,the question of how to integrate"mathematics culture"into the curriculum content is an important topic for mathematics educators.The existing definition of"mathematical culture"can be summarized as the"fact covering"mathematical culture view based on the position of subjectivism.However,it does not meet the needs of"literacy cultivation oriented"mathematical discipline education practice,so it is necessary to re-interpret the meaning of"mathematical culture".The definition of culture proposed by Dewey represents a kind of"understanding-oriented"cultural view based on pedagogy.This cultural view has three characteristics.First,culture is"three-in-one".Second,culture is understanding-oriented.Third,culture is developing dynamically.Within the framework of understanding-oriented cultural view,"mathematical culture"could be interpreted as a situation in which students in their learning of mathematics understand the ideational meaning of mathematics,including the mathematic thoughts(methods),views,and concepts of,and internalize this understanding as the mathematical literacy.The process and result of mathematical understanding iswhat we call mathematical culture.According to the characteristics of mathematics,there are three levels of"mathematical culture".The first level is"reasoning understanding",involving mathematical experience to mathematical knowledge.The second level is"rationalization understanding",involving mathematical knowledge to mathematical rationality.The third level is"creation understanding",involving mathematical rationality to creative mathematical thinking.Teachers should form the idea that mathematics class is the major locus of"mathematics culture",explore ways of integrating"mathematics culture"into classroom teaching,and play an important role in educating people through mathematics.