八年级学生数学概念表征及其对学业成绩的影响机制——基于Z省的大规模测试

Eighth Graders’ Mathematical Conceptual Representation and Its Impact Mechanism on Academic Performance: Large-Scale Test in Z Province

依托大规模纸笔测试,以Z省34 412名八年级学生为被试考察数学概念表征及其对学业成绩的影响机制.结果表明,概念表征得分排序从高到低依次是符号表征、语言表征、图象表征及结构表征;男生结构表征显著优于女生,女生在其它表征方面均显著优于男生;结构表征通过其它表征对数学学业成绩及各内容领域成绩的间接影响均达显著,且贡献大于直接影响;在间接影响路径中,通过符号表征的影响最大,通过语言表征的影响次之;概念表征对三大内容领域的影响机制存在差异.对课程与教学的建议有：关注学生数学体系的整体建构;培养学生多元表征及其相互转化的能力;重视数学符号意识及数学交流能力的培养;关注概念表征对不同内容领域学业成绩影响的差异;关注概念表征的性别差异.

The present large-scale test chose 34 412 eighth graders from Z province as the subjects to investigate mathematical conceptual representation and its impact mechanism on academic performance. The results shown that eighth graders＇ propensity of conceptual representation from high to low was symbolic representation, pictorial representation, linguistic representation and structural representation; Males shown preference to structural representation while females tend to others; The indirect impact mediated by other representations from structural representation to mathematics score and three content scores were both significant, and the effect size was bigger than direct impact; Among the indirect impact paths, the effect size was highest when mediated by symbolic representation, and linguistic representation followed; The impact mechanism was different among different content areas. Suggestions to curriculum and instruction were that, to cultivate students＇ ability of multiple representation and the transformation among them; To help students constructing their own mathematics system; To attach attention to the symbols consciousness and mathematical communication ability; To pay attention to the influential path among different content areas; To pay attention to gender difference in conceptual representation.