基于因子分析的学生数学建模能力结构研究  

A Structural Research on Mathematical Modeling Ability of Students Based on Factor Analysis

作　　者：林子植 胡典顺[1] LIN Zi-zhi;HU Dian-shun(School of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China;College of Mathematics and Computer Science,Jiangxi Science and Technology Normal University,Nanchang 330013,China)

机构地区：[1]华中师范大学数学与统计学学院,湖北武汉430079 [2]江西科技师范大学数学与计算机科学学院,江西南昌330013

出　　处：《数学的实践与认识》2020年第4期50-58,共9页Mathematics in Practice and Theory

基　　金：教育部人文社会科学研究规划基金项目——中小学核心素养测评的模型建构与实证研究(19YJA880012);2017年度江西省教育厅科学技术一般研究项目——B样条曲线曲面的数据压缩技术研究(课题编号GJJ170679).

摘　　要：通过编制测试卷对深圳市龙岗区17327名初中生进行数学建模能力测试.根据测试数据,利用探索性因素分析,探索初中生数学建模能力的整体结构和组成因素,对于探索出的数学建模能力结构模型分别利用一阶和二阶验证性因素分析验证其合理存在性.研究表明,我国初中生数学建模能力包含模型建立能力,模型阐释能力,模型计算能力和模型评估能力四个组成因素,每个组成要素包含若干数学基本技能,该能力模型可以与现有数学建模能力理论形成三角互证.最后,根据初中生的数学建模能力结构模型,提出三个相应的教学策略,以期帮助学生提高数学建模能力.About 17327 junior middle school students in Longgang District of Shenzhen have taken part in the test for assessing the mathematical modelling ability.According to examination data,the structure of junior middle school students’ mathematical modelling ability is explored by using exploratory factor analysis,and we also use confirmatory factor analysis to confirm the validity and reliability of the modelling ability structure.Study has shown that the mathematical modeling ability of junior high school students in China includes four components:model building ability,model interpreting ability,model calculation ability and model evaluation ability,each component contains several mathematical basic skills.Finally,three teaching strategies are proposed to improve their mathematical modeling ability according to the structure and composition elements.

关 键 词：数学建模能力 探索性因素分析 验证性因素分析 数学建模过程 教学策略 

分 类 号：G633.6[文化科学—教育学]