Foundational Research on Problem Mathematization in Undergraduate Physics

本科生教授普遍抱怨的是，学生的数学能力很差。研究表明，困难并不在于学生缺乏数学知识。有证据表明，大多数学生很难分析一道应用题，并用计算器或计算机可以解决的形式来表示它。在物理和其他领域，学生如何将对问题的概念理解转化为数学是一项非常重要的技能，不仅是在物理领域，而且在应用科学、研究科学、工程和许多其他STEM学科中都是如此。到目前为止，对学生如何学习表达数学概念性问题的研究还很少。这个综合性的基础研究项目将集中于四个基本的数学能力：建立积分，建立微分方程式，使用近似和选择适当的坐标系。这些都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。影响学生数学化的可塑性因素(教学可以改变的因素)？什么是影响学生数学化的调节因素(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演变？这项拟议的工作将通过分析学生在课堂上的作业，并通过三年多的纵向研究跟踪个人，提供对这些技能发展的详细分析。除了更典型的视频分析，PI之前有相关的编码和分析结果的经验，他将适应智能笔的创新使用，以捕捉小组作业写作和讨论。一位经验丰富的外部评估者将利用形成性和终结性策略，包括1)评估项目将完成的研究研究的可行性，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。将利用定性和定量方法以及多种评价研究方法对数据进行三角测量，以获得更可靠的评价结果，然后将这些数据与项目小组分享，并用于改进方案活动。将通过使项目文件和研究活动与项目目标保持一致、验证研究数据和制定的评估结果、审查复制评估战略的可能性以及评估项目对STEM教育理论和方法的贡献来记录项目的成功。

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.