数学理解水平的划分

The Division of the Level of Mathematical Understanding

基于经典的数学理解内涵的阐释以及已有各家理解水平的划分,将学生数学理解划分为工具性理解、关系性理解、创造性理解、文化性理解4个水平,并以均值不等式为典型案例,详细解读学生各数学理解水平的内涵和表现形态.工具性理解水平的价值不能忽视.学生个体数学理解水平是发展变化的,学生间的数学理解水平是有差异的.在力所能及的范围内,鼓励学生追根问底式地深层次学习,达到“关系理解”的水平;鼓励学生对知识进行自我建构,达到“创造性”理解水平;鼓励学生在历史文化、审美情趣、人文关怀中进行熏陶,达到“文化性理解”的水平.

Based on the interpretation of the connotation of classical mathematical understanding and the division of existing understanding levels,students’mathematical understanding is divided into four levels:instrumental understanding,relational understanding,creative understanding and cultural understanding.Taking the mean value inequality as a typical case,this paper interprets the connotation and manifestation of students’various levels of mathematical understanding in detail.The value of the level of instrumental understanding cannot be ignored.The level of students'individual mathematical understanding is developing and changing,and the level of students’mutual mathematical understanding is different.Within the scope of the ability,students are encourage to pursue in-depth learning,to achieve the level of“relational understanding”.Students are encouraged to self-construct knowledge and to achieve the“creative understanding”level;they are encouraged to be nurtured in history and culture,aesthetic taste and humanistic care,so as to reach the level of“cultural understanding”.