摘要通过学生关于数和数的表示形式认知情况的案例，论述了教师研究学生、了解学生的方法及对教学改革的启示．Based on case study, this paper talked about students' understanding of number and number's showing form.
3Freudenthal H. Major Problems of Mathematics Education [J]. Educational Studies in Mathematics, 1981, 12(2): 133-150.
4Panagiotou. Using History to Teach Mathematics: The Case of Logarithms [J]. Sci & Educ, 2011, (20): 1-35.
5Spencer H. Education: Intellectual, Moral, & Physical [M]. New York: Hurst & Company, 1862.
6[ Kline M. The Nncients Versus the Modems: A New Battle of the Books [J]. Mathematics Teacher, 1958, 51 (6): 418--427.
7Clement J. Algebra Word Problem Solutions: Thought Processes Underlying a Common Misconception [J]. Journal for Research in Mathematics Education, 1982, (13): 16-30.
8Bardini C, Radford L, Sabena C. Struggling with Variables, Parameters, and Indeterminate Objects or How to Go Inzanein Mathemaics [A]. In: Chick H L, Vincent J L. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education [C]. 2005, (2): 129-136.
9Hart K M, Kuchermann D. Children's Understanding of Mathematics: 11-16 [M]. London: John Murray, 1981.
10Harper E. Ghosts of Diophantus [J]. Educational Studies in Mathematics, 1987, (18): 75-90.
