指向几何直观,完善教学设计--建立“异分母分数”加法法则的视点

Focusing on geometric intuition,perfecting the teaching design:a view point of establishing the addition rule of"different denominator fractions"

数学知识主要指的是数理逻辑知识,具有抽象性的特点.发生逻辑知识认识的来源在于“反省抽象”,它是指对于发生知识认识的主体操作信息活动中的“活动”的抽象.处于具体运演阶段的小学生,必须要操作具体的事物才能发生“活动”.因此,在教学设计及其课堂实施中,对于稍微抽象的数学知识,必须要将其转化为学习主体所具有的对象性信息后再进行操作,几何直观就是这种对象性信息.据此,几何直观被列入义务教育数学课程目标的确是实至名归.文章以建立“异分母分数”加法法则的教学为例说明之.

Mathematics knowledge mainly refers to the knowledge of mathematical logic,characteristic of abstraction.The source of the cognition of logical knowledge originates from"reflection abstraction",which refers to the abstraction of"activity"in the operation of information activities by the subject of knowledge cognition.Elementary school students in the stage of concrete performances must manipulate concrete things in order to have"activity".Therefore,in instructional design and its classroom implementation,when teaching a slightly abstract mathematical knowledge,it must be transformed into the object information that is already possessed by the learning subject before it is operated and geometric intuition is the very kind of this object information.According to this,it is right to the point that geometric intuition is included in the goal of compulsory education mathematics curriculum.The article takes the teaching of establishing the addition rule of"different denominator fractions"as an illustrating example.