Echoes of the Instructor’s Reasoning: Exemplars of Modeling for Homework

Abstract

In this paper, we tell a story of iterative design and continual improvement of an asynchronous technological resource, pencasts, to support development of students’ modeling skills while studying at home. Our students were typically engineering majors, enrolled in differential equations as a prerequisite for their subsequent engineering courses. The course used a modeling-first approach to teaching the differential equations content. In this paper, we share four aspects of the students’ reactions to the pencasts: the students’ self-assessments of the helpfulness of the pencasts, how they used pencasts, why the students chose (not) to use them, and the relationship between pencast usage and achievement.

Keywords:

• Mathematical modeling
• differential equations
• engineering students
• instructional technology

Notes

1 We used the brand Livescribe Echo, but many brands are available.

Additional information

Notes on contributors

Jennifer A. Czocher

Jennifer Czocher is an assistant professor in the Department of Mathematics at Texas State University. Her research interests include students' mathematical thinking and cognition, research in undergraduate mathematics education (RUME), the influence of mathematical modeling tasks on students’ mathematical thinking, and how mathematical reasoning supports STEM education.

Jenna Tague

Jenna Tague is an assistant professor in the Department of Mathematics at California State University, Fresno. Her research focuses on retention of underrepresented students in mathematics. She also studies students’ understandings of rate of change and how their understandings impact their learning of later coursework.

Greg Baker

Greg Baker is a recently retired professor emeritus in the Mathematics Department with a courtesy appointment in the College of Engineering at The Ohio State University. His educational goals were to create more effective and relevant mathematics instruction for engineering students by finding ways to integrate mathematical modeling into his differential equations classes.