Foundational Research on Problem Mathematization in Undergraduate Physics

本科生教授中普遍存在的一个抱怨是，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，大多数学生都难以解析一道应用题，并将其用计算器或计算机解决。 在物理学和其他领域的“数学化”-学生如何将问题的概念理解转化为数学-是一个非常重要的技能，学生不仅要掌握物理学，而且要掌握应用科学，研究科学，工程和许多其他STEM学科。迄今为止，很少有研究已经做了了解学生如何学习表达数学概念问题。 这个综合性的基础研究项目将侧重于四个基本的数学能力：建立积分，建立微分方程，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，而且在许多其他STEM课程的研究。该项目将由三个研究问题指导。什么样的可塑性因素影响着学生的认知化？ 哪些调节因素影响学生的自我认同（教学不能改变的因素）？ 大学生的问题“抽象化”能力在大学生涯中会如何演变？ 拟议的努力将提供这些技能的发展，通过分析跨类学生的工作，并通过以下个人超过三年的纵向研究的详细分析。 沿着更典型的视频分析，PI将采用智能笔的创新使用来捕获小组作业写作和讨论，PI具有相关的编码和分析结果transmitting的先前经验。一位经验丰富的外部评估员将利用形成性和总结性策略，包括1）评估项目完成的研究的可行性，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，以便从评价中获得更有力的结果，然后将这些结果与项目小组分享，并用于完善方案活动。 项目的成功将通过调整项目文件和研究活动与项目目标，验证研究数据和开发的评估结果，并检查评估战略的复制潜力和评估项目对STEM教育理论和方法的贡献来记录。

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.