关于数学文化视域中数学教学的若干思考

On Mathematics Teaching in the View of Mathematical Culture

依据数学文化视域中数学教学的基本理念尤其是其“综合数学论”，以及合格数学教师教学的“给予”水平、“发现”水平和“超越”水平之划分，对现实中数学教学的分析发现，“给予”水平的教师是在教数学，“发现”水平和“超越”水平的教师都是在教学生学数学，但也有“有待的发现”和“无待的追求”之本质区别。数学文化视域中的数学教师应该追求“超越”水平的数学教学，而这种“超越”水平的数学教学则应充分体现“整体、联系与转换”、“留有余地”和“备而不‘课”’等特征。

Based on the basic concepts of mathematics teaching in the view of mathematical culture, especially the ＂comprehensive mathematical theory＂, and the division of qualified mathematics teacher as ＂giving＂, ＂finding＂ and ＂transcending＂ level, it has been found that, ＂giving＂ teachers teach students mathematics, both ＂finding＂ teachers and ＂transcending＂ teachers teach students to learn mathematics, but the former are ＂finding with expectations＂ and the later are ＂pursuing the essence＂, through the analysis of mathematics teaching practice. Mathematics teachers in the view of mathematical culture should pursue the ＂transcendence＂ level of mathematics teaching, which are supposed to fully embody the features of ＂entirety, relations and transformation＂, ＂leaving room for students＇ learning＂ and ＂preparing but without a fixed teaching plan＂.