笔者曾在拙文《给数学的一片美丽天空——课堂教学的几点思考》中,分析了几次示范课实例的得失,提出了为大家所熟知又常常为大家所忽视的几个观点:真正的学生意识、问题意识、简单化意识。再读《透视美国教育——20位旅美留美博士的体验与思考》(王定华主编,北京大学出版社2008年6月出版),感慨良深。尤其《鸡兔同笼》的课堂节录,促使笔者对数学教学中的学生意识、问题意识、简单化意识再次思考。这是一堂令笔者汗颜的数学课。它充满情趣、机巧与睿智, In my essay “A Beautiful Sky for Maths - Reflections on Classroom Teaching”, I analyzed the gains and losses of several demonstration class examples, and put forward several views which are well known and often overlooked by everyone: true Student awareness, problem awareness, simplistic awareness. Read “Perspectives on American Education - Experience and Thinking of 20 US-China Doctors in the United States” (edited by Wang Dinghua, Peking University Press, June 2008). In particular, “chickens and rabbits in the same cage” excerpts in the classroom, prompting the author of mathematics teaching students awareness, problem awareness, simplistic thinking again. This is a math class that makes me ashamed. It is full of fun, ingenuity and wisdom,