# Kansas State University

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## Department of Physics

Physics Department
116 Cardwell Hall
1228 N. Martin Luther King Jr. Drive
Manhattan, KS 66506-2601

785-532-6786
785-532-6806 Fax
office@phys.ksu.edu

### Mathematization

#### What is "mathematizing"?

Mathematizing is a part of problem solving where students convert a physics problem into a form on which they can "do math". Learning how to mathematize is an important part of learning physics. It's vital in homework during university studies, and it's also necessary for reaching conclusions in all types of work undertaken by scientists and engineers.

In this project, we investigate how students' mathematizing changes as they move from first-year students to seniors.

#### Goals

Only a few limited studies have been undertaken to attempt to understand how students mathematize and the difficulties that they encounter while doing it. Thus, the results of this research will provide new insights into the problem solving process that must be developed by scientists and engineers.

This research will result in new models of student development of important STEM problem solving capabilities. The novel focus will provide a unique way to investigate the problem solving process. Our data and results will help physics education researchers and practitioners generalize and create models of the process and thus create new teaching strategies. These new strategies will enable students to learn important components of the problem solving process better. Thus, a broader impact of this work will be improved STEM education which will serve the students beyond their undergraduate years. The research methods which are developed during the project will be applicable to similar studies in other STEM disciplines.

#### Design

Our research questions are large:

• What malleable and moderating factors influence students' mathematization?
• How does students' problem mathematization evolve over the students' undergraduate career?

Our prior research shows that students struggle with parsing a word problem and representing it in a form that is solvable using algebra, calculus, or calculational devices: they lack adequate mathematizing skills. Building on these studies, we zoom in from our previous research on problem solving to problem mathematization. We identify the following mathematizing strands that are important across multiple sub-disciplines in physics and that require further research:

• setting up integrals,
• setting up differential equations,
• using approximations, and
• choosing appropriate coordinate systems.

This study looks at mathematizing across the full range of the undergraduate physics curriculum from the introductory calculus-based course to senior-level efforts. We use both cross-sectional studies (all the students in Mechanics, for example), and longitudinal ones.

To delve into these questions, we engage in three kinds of data collection:

• natural, in situ observations of classroom activities;
• contrived research settings like think aloud interviews and focus group interviews;
• written artifacts of students' work, like exams and homework.

We triangulate among these three kinds of data to build a strong picture of how students' mathematizing changes as they move up the four-year physics curriculum.

This project is funded by the NSF IUSE program.