论理解视域下的有理数运算

On Operation of Rational Numbers from the Perspective of Understanding

阐释了数学理解的两种模型——表征转化模型和类型层次模型.指出有理数运算的理解包括对有理数运算意义的理解,对有理数运算算理、法则的理解.认为使用上述理解模型,能够界定学生对有理数运算的理解,厘定学生的理解水平;进而能够基于学生的理解水平,制定适切的课程目标,划分合理的内容层次,实施有理解地教与学.

There are two models about mathematics understanding. First, understanding is reflected in the ability to make connection and translation within and between various representations. Second, understanding includes intuitive understanding, procedural understanding, abstract understanding, and formal understanding. Understanding operation of rational numbers includes understanding meanings, theories, and rules. Using these understanding models, the students＇ understanding levels can be investigated. On the basis of students＇ understanding levels, appropriate curriculum objectives can be designed, content can be arranged, and teaching and learning with understanding can be implemented.