| There exist a lot of similarities and differences between Taiwan and the Mainland,owing to the same cultural heritage for thousands of years and different development way in the past decades. Each forms unique characteristics of education. Basal education also show very prominent performance in the area of basic education. This paper makes a comparative study of junior middle school mathematical exercises between Shanghai and Taiwan, to explore the superiority and weakness of basic mathematical education of each other. It will be significant for the two areas and even the nation to elevate educational level.This study based on the Cognitive Task Analysis(CAT) model, which was adopted and adjusted properly. A five-dimensional frame of cognitive difficulty(CD),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. We labeled the item-difficulty-values for examples and exercises related to triangle. Thus, we analyzed and compared CD and relevant indexes of textbooks,workbooks, and tutoring materials in the Shanghai and Taiwan.The author selected the chapter of triangle as study object in two areas. First of all,contents and standards related to the chapter was analyzed and compared. It is found that there is great similarity in course content arrangement and curriculum standards between Shanghai and Taiwan. However, these two regions differ greatly in teaching goal. Then, we labeled and analyzed examples and exercises’ cognitive difficulty of textbooks, exercise-book and extra-exercises in the two region. From the discussion on the results of prior evaluation of cognitive difficulty, the conclusion is as follows:ⅰ) There is same quantity of textbooks, but slight difference in the concrete quantity of examples and exercises. However, Shanghai possesses much more exercises of exercise-book and extra-exercises than Taiwan;ⅱ) Average of CD and relevant index of textbook exercises has hardly any differences in these two region. However, the CD mean of exercise-book exercises’ and extra-exercises’ in Taiwan is bigger than Shanghai.ⅲ) In term of exercises’ CD pattern, both of these two regions present the similar pattern bobbing up and down near to mean. Exercises’ CD shows distinct spiral trends in Shanghai, but the opposite situation appears in Taiwan, even becoming easier and easierⅳ) Concerning CD in layers, textbook’s exercises don’t show difference. But exercise-book show great difference in CD in layers, Taiwan speeds more time to basic exercise. The exercise-book’s basic and the top questions setting was less in Shanghai than Taiwan. Shanghai’s extra-exercise possesses much more exercises than Taiwan’s. Taiwan’s percentage of high degree of CD is more than the Shanghai.From above we may come to conclusions, the students’ schoolwork was excessively heavy, corresponding to national current situation. The author analyzes deeply exercises’ CD. The results show that Shanghai’s students do too many exercises mainly about basic knowledge and concept. This just agrees with double-base teaching in mainland.In a word, the arrangement of mathematical exercises result in a series of questions well worth of considering and investigating. Mathematical content is arranged casually in Taiwan. For example, more difficult content is set at the beginning of the chapter, which makes student lose learning enthusiasm. The Shanghai’s spiral trend deserves Taiwan to learn and imitate. However excessive schoolwork make students get school-weary psychology easily. To achieve good score in this way is not worth. It is worth us to rethink and try our best to change the status.This is exactly what is called “you cannot know the shape of a mountain when you stand on it”. And for exactly that reason, we can demonstrate clearly superiority and weakness of mathematics education between Shanghai and Taiwan by means of comparative study. And then, this can provide reference and idea for curriculum reform. |
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