初中数学教材代数内容的国际比较研究

International Comparative Study on Algebra of Secondary Textbook

对中国、美国、澳大利亚、英国、法国与新加坡6个国家现行的初中数学教材代数内容中的代数式、方程与不等式、函数3大块,从知识广度、知识呈现方式、例题与习题4个方面进行了比较研究.研究发现：广度上美国最广,中国次之,国家之间差异比较大;六国教材知识呈现以直观描述为主,类比归纳为辅;例题相对简单是共性,但呈现方式差异大;习题数量教材之间差距大,类型以封闭性为主,国家之间难度差距明显.通过比较,获得了一些启示：体现知识的数学化过程;注重数学的应用;概念呈现注重引导性材料的设计;继续保持习题难度水平;进一步优化例题设计.

To compare the algebra among different textbooks in an international perspective, textbooks were selected from China, United States, Australia, Britain, France and Singapore in this study. Algebra expressions, equation and inequality, and function as the main algebra content were considered. The range of knowledge, the presentation of knowledge, and the difficulty of worked examples and exercises were compared. The results included： the textbooks of United States had the largest range in knowledge and there was big differentia among countries; the mainly presentation of knowledge was visual description rather than in a generalizing way; the difficulty of worked examples was not high in all cou0ntries but had different presentation; and there was big gap between countries in the amount and difficulty of exercises which were mainly closed questions. These results indicated that mathematical process and application should be focused more; contextual materials should be implemented in learning concepts; keep the same difficulty level of exercise; and design more reasonable worked examples for the future textbooks designing.