Foundational Research on Problem Mathematization in Undergraduate Physics

Kansas State University, Manhattan KS

Investigators

Abstract

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.