#### Presentation Title

Student Understanding of Ordinary Differential Equations in Physics

#### Faculty Mentor

Michael Loverude

#### Start Date

23-11-2019 9:45 AM

#### End Date

23-11-2019 10:00 AM

#### Location

Markstein 208

#### Session

oral 1

#### Type of Presentation

Oral Talk

#### Subject Area

physical_mathematical_sciences

#### Abstract

Ordinary differential equations (ODEs) are an important tool for physicists who want to model dynamic systems, i.e., systems that undergo change. Undergraduate physics majors are usually introduced to ODEs early in the elementary calculus sequence (2^{nd} semester single-variable calculus). Despite this introduction, we feel that physics majors’ understanding of ODEs need to be improved.

The recognition for this need for improvement stemmed primarily from the analysis of several semesters’ worth of student written responses in a mathematical methods course for junior-level physicists. A consistent point of struggle throughout was that the solving of ODEs presented little problem when familiar symbols from previous courses were used, but that students struggled when asked to solve a similar ODE but with the familiar symbols removed. This suggested that student understanding is substantially weaker when it came to applying ODEs to a novel physical context than when rote-solving decontextualized ODEs.

Future work will first be focused on enlarging our data set through the gathering of student responses. A larger data set will allow for more insight into how students think of ODEs as well as possibly allow for the development of more rigorous survey methods. This work is supported by the NSF through grant PHYS-1405616 and by the Dan Black Family Foundation.

Student Understanding of Ordinary Differential Equations in Physics

Markstein 208

Ordinary differential equations (ODEs) are an important tool for physicists who want to model dynamic systems, i.e., systems that undergo change. Undergraduate physics majors are usually introduced to ODEs early in the elementary calculus sequence (2^{nd} semester single-variable calculus). Despite this introduction, we feel that physics majors’ understanding of ODEs need to be improved.

The recognition for this need for improvement stemmed primarily from the analysis of several semesters’ worth of student written responses in a mathematical methods course for junior-level physicists. A consistent point of struggle throughout was that the solving of ODEs presented little problem when familiar symbols from previous courses were used, but that students struggled when asked to solve a similar ODE but with the familiar symbols removed. This suggested that student understanding is substantially weaker when it came to applying ODEs to a novel physical context than when rote-solving decontextualized ODEs.

Future work will first be focused on enlarging our data set through the gathering of student responses. A larger data set will allow for more insight into how students think of ODEs as well as possibly allow for the development of more rigorous survey methods. This work is supported by the NSF through grant PHYS-1405616 and by the Dan Black Family Foundation.