新课标背景下中学生数学建模素养的测评研究

A Study on the Measurement of Secondary School Students'Mathematical Modelling Competency in the Context of the New Curriculum

数学建模能力是学生理解数学知识与现实世界、解决复杂问题的必备能力,也是我国普通高中与义务教育阶段新课程重点关注的数学核心素养。新课标在小学、初中、高中阶段分别提出“模型意识”“模型观念”“数学建模”三个关键词,为数学建模素养培育指明路径。在此背景下,加快推进基础教育阶段数学建模教学与评价成为了一项紧急且艰巨的任务。本研究基于新课标理念与要求,设计测评工具,对全国5个城市1428名中学生的数学建模素养展开调查。基于三重编码体系,研究分析了我国八年级学生数学建模素养的整体水平及特征,为未来各学段的数学建模教学与评价提供实证依据。研究发现:学生尚不能适应开放且真实的数学建模问题;学生缺乏对数学建模过程的完整认知;学生建模能力的性别差异受建模过程的推进影响;学生具备创造性解决数学建模问题的潜力。基于此,研究对未来的数学建模测评与教学进行反思,并提出建议。

Mathematical modelling ability is an essential competency for students to understand mathematical knowledge in relation to the real world and to solve complex problems.It is also a core mathematical competency focused on in the new curriculum for general senior high schools and compulsory education stages in China.The new curriculum standards at the primary,junior high,and senior high school levels respectively introduce three key terms:“model awareness”,“model concept”,“mathematical modelling”,which indicate the pathway for cultivating mathematical modelling competency.Against this background,it has become an urgent and challenging task to promote the teaching and assessment of mathematical modelling at the basic education level.The study,based on the concepts and requirements of the new curriculum standards,designed assessment tools and conducted a survey on the mathematical modelling competency of 1,428 middle school students across five cities in China.Using a triple coding system,the study analyzed the overall level and characteristics of mathematical modelling competency among eighth-grade students in China,providing empirical evidence for future mathematical modelling teaching and assessment at various educational stages.The study found that students are not yet able to adapt to open and real mathematical modelling problems;they lack a complete understanding of the mathematical modelling process;gender differences in students'modelling abilities are influenced by the progression of the modelling process;and students have the potential to creatively solve mathematical modelling problems.Based on these findings,the study reflects on future mathematical modelling assessment and teaching,and makes recommendations.