Foundational Research on Problem Mathematization in Undergraduate Physics

本科教授普遍抱怨学生的数学技能很差。研究表明，困难并不在于学生缺乏数学知识。有证据表明，大多数学生都很难解析一个单词问题，并以一种可以用计算器或计算机解决的形式表示出来。在物理学和其他领域，“数学化”——学生如何将对问题的概念理解转化为数学——是学生不仅在物理学，而且在应用科学、研究科学、工程和许多其他STEM学科中掌握的一项非常重要的技能。迄今为止，关于学生如何学习表达数学概念问题的研究还很少。这个综合性的、基础性的研究项目将侧重于四种基本的数学能力：建立积分、建立微分方程、使用近似和选择合适的坐标系。这些是解决问题的基本技能，不仅在本科物理课程中，而且在许多其他STEM课程中也是如此。该项目将以三个研究问题为指导。哪些可塑因素影响学生的数学化（教学可以改变的因素）？哪些调节因素影响学生的数学化（教学无法改变的因素）？学生的问题“数学化”能力将如何在学生的本科生涯中发展？该计划将通过分析学生在不同班级的学习情况，以及对个人进行为期三年的纵向研究，对这些技能的发展进行详细分析。除了更典型的视频分析外，PI还将创新地使用智能笔来捕捉小组作业的写作和讨论，PI之前有相关的编码和分析结果转录的经验。经验丰富的外部评估人员将使用形成性和总结性策略，包括1)评估项目完成研究的可行性，2)评估研究的可靠性和可复制性，以及3)检查项目对物理问题数学化的贡献。定性和定量方法以及多种评估研究方法将用于三角测量数据，以从评估中获得更可靠的发现，然后将与项目团队共享并用于改进计划活动。通过将项目文件和研究活动与项目目标结合起来，验证研究数据和开发评估的结果，检查评估策略复制的潜力，评估项目对STEM教育理论和方法的贡献，将记录项目的成功。

A common lament among undergraduate professors is that students have poor math skills. Research has shown that the difficulty does not lie in students lack of knowledge of math. Evidence indicates that most students struggle with parsing a word problem and representing it in a form that is solvable using a calculator or computer. Within physics and other fields 'Mathematization'-how students translate the conceptual understanding of a problem into mathematics-is a very important skill for students to master not only in physics but in applied science, research science, engineering, and many other STEM disciplines. To date, little research has been done to gain an understanding of how students learn to express conceptual problems in mathematics. This comprehensive, foundational, research project will focus on four essential mathematical abilities: setting up integrals, setting up differential equations, using approximations and choosing appropriate coordinate systems. These are essential skills for problem-solving not only in the undergraduate physics curriculum, but also in many other STEM courses of study.The project will be guided by three research questions. What malleable factors influence student's mathematization (factors that teaching can alter)? What moderating factors influence student's mathematization (factors that teaching cannot alter)? How will the ability of students' problem 'mathematization' evolve over the students' undergraduate career? The proposed effort will provide a detailed analysis of the development of these skills through analyzing student work across classes and by following individuals over three years in a longitudinal study. Along with the more typical video analysis the PI, who has relevant previous experience coding and analyzing the resulting transcriptions, will adapt an innovative use of smart pens for capturing group homework writing and discussion. An experienced external evaluator will utilize both formative and summative strategies that include 1) assessing the viability of the research studies to be completed by the project, 2) assessing research reliability and replicability, and 3) examining the project's contribution to problem mathematization in physics. Qualitative and quantitative methodologies and multiple evaluation research methods will be utilized to triangulate data for more robust findings from the evaluation, which will then be shared with the project team and used to refine program activities. Project success will be documented through aligning project documentation and research activities with project goals, validating the research data and the outcomes of the developed assessments and examining potential for replication of the assessment strategies and assessing the contribution of the project to the theory and methodology of STEM education.