关系与数量:分数概念理解的不同视角

Relationship and quantity:different perspectives on fraction understanding

分数是小学数学的重点也是难点.国内外教学与基础认知领域都对分数的教与学进行了较为丰富和详细的研究.对比这些研究成果发现,分数概念宏观上可以分为关系概念和数量概念.分数理解的困难主要源于每种关系概念自身的抽象性、关系间转换的复杂性;数量概念的相对性、稠密性、无限性;关系概念和数量概念交织的教学同构性.因此,教学中需适度区分分数各种关系概念的结构,找到关系概念之间以及关系概念与数量概念的联系,丰富学生的分数认知,构建完备的数概念系统.

ion and the transformation between relationships has complexity.Secondly,the concept of quantity has relativity,denseness and infinity.Thirdly,there should be the teaching isomorphism based on Concepts of relationship.and quantity.Therefore,in the process of teaching,we need to improve the structure of the relationship of fraction and find the connection between the concept of relationship and the concept of quantity,which can effectively break the barriers of fraction learning and construct the structure of fraction teaching as a whole.