作　　者： ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;

机构地区： 澳门大学

出　　处： 《数学教育学报》 2008年第6期21-28,共8页

摘　　要： 变式在数学教育研究中具有突出地位，变式通过“变中发现不变”来学习抽象化和“以不变应万变”来学习公理化．中国课程常常采用一题多解，而美国课程出现“一题多解”机会较少．“一题多解”作为问题解法变式，是长期存活于中国本土文化土壤的中国数学教学的小策略，但任何数学内容都可以借助问题变式，使得方法理解得以深化和广化，推广到全部数学方法体系建构．“一题多解”的理论和实践价值主要有：效果真实而有效；能够更广义地构建数学方法体系；有实践之根，因而能有效地应用于实践；有本土之脉，因而有长期存活于本土文化的可能． This study was to explore the possible opportunities for effectiveness of a theoretical model （known as Spiral Variation curriculum based on practical activity of ＂one problem with multiple solutions （OPMS））. There was a great contrast of effectiveness to the traditional teaching, providing only one or two methods of proofs, more than ten new methods in proving ＂Mid-point theorem＂ were carried out by students in University of Macao by stressing OPMS practice, one of rationales of spiral variation curriculum design theory. This again ensured that OPMS can promote teaching practice to go further. The study further discussed about the potential of OPMS to be developed into a theory for guiding teaching practice. In fact, spiral variation curriculum is not a new model but a curriculum framework stressing variations （Bianshi）, which are identified as an important element of learning/teaching mathematics in China by some researchers, educators, and teachers in recent years. The curriculum framework specially filtered and rationalized problem variations with multiple conceptions connection （known as ＂one problem with multiple solutions in China ）or multiple solutions connection （known as ＂one problem multiple changes （OPMC） from Chinese own teaching experience from its own mathematics curriculum practice. In fact the notion of one problem multiple solutions is widespread, and well known, but still far from uplift into a curriculum design framework guiding our teaching practice in the world. Just to declare that practice with one problem multiple solutions will not help much, if we cannot specify a curriculum design frame and suggest well-founded scaffolding tool. Although spiral variation curriculum is a simple framework, it is important and helpful for curriculum practice, Without a framework we have to rely only on intuition, experience and common sense. This case show it could take us far, and indeed it did.

关 键 词： 一题多解 中国数学教学传统 三角形中位线定理 问题解决

领　　域： [文化科学] [文化科学] [文化科学]