上海与台湾初中数学“三角形”内容习题认知难度比较——以沪教版和康轩版为例

Comparative Study on the Cognitive Difficulty of Triangle Context Exercises in Junior School between Shanghai and Taiwan——Taking Hujiao Version in Shanghai and Kangxuan Version in Taiwan as Example

在前人认知理论研究的基础上,结合数学学习特点,初步构建条件个数、条件辨识度、知识点个数、知识点辨识度和认知负荷五维指标的数学习题认知难度的分析框架.以"三角形"为例,分析了上海和台湾地区的数学习题,得到如下结论:(1)两地区的学生在数学习题的练习上占用的时间比欧美发达国家多,尤其是上海;(2)通过深入分析,两地区的数学习题认知难度的平均水平在各个指标上基本一致,但在习题认知难度分层中,两地区在习题不同认知难度层次的分配上表现出较大的差异,如上海较台湾有更多低水平的数学习题.

Based on the study of J. Sweller and others researches, and combined the chanters of mathematic learning, a five-dimensional frame of cognitive difficulty （CD） according to mathematics items, composed of number of conditions （NC）, conditions recognition （CR）, number of knowledge point （NP）, knowledge point recognition （PR） and cognitive load （CL） was set up. Then we labeled the item-difficulty-values the exercises related to triangle context in the Shanghai and Taiwan. We got the conclusions as follows： （I） The students from Shanghai and Taiwan sped much more time than the students from developed countries. （II） Then the analysis on the average value of CD indexes, they showed big difference on the analysis on the level of CD in the two regions, such as the CD level of exercises in Shanghai was much more than Taiwan.