通过数学任务提高美国职前教师的数学成熟性

Advancing U.S. Pre-service Teachers’ Mathematical Sophistication Via Mathematical Tasks

在美国,大多数学校讲授的数学是学校"数学",它与数学家所从事的数学有着本质的不同.为此要区分以下4种差异:(1)约定俗成的数学与学校数学之间的差异;(2)理解方式与思维方式之间的差异;(3)成熟的学习者与被动的学习者之间的差异;(4)知识传授与知识参与这两种教学模式之间的差异.根据Harel的对偶原则来设计一个数学任务时,应该考虑学生已有的思维方式和理解方式,如激发学生学习某一特定概念的需要,促进理想的思维方式,阻止不合适的思维方式以及评估学生的概念性理解.

This article is based on the seminar that the author presented for the Hong Kong Association for Mathematics Education at the Hong Kong Baptist University on May 22,2008. In this article,the author differentiates(a) between institutionalized mathematics and school mathematics,(b) between ways of understanding and ways of thinking as two complementary subsets of mathematics that students should develop,(c) between sophisticated learners and passive learners,and(d) between knowledge dissemination and knowledg...