Using Cumulative Homework in Calculus Classes

Abstract

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the testing effect and spacing effect in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional opportunities to recall old material. Effects were analyzed by comparing the final exam scores of randomized groups of students, which showed small positive gains for students who had the experimental homework design. Additionally, students were split into the categories of low-scorers and high-scorers based on their first test score, prior to the intervention. Low-scoring students saw more benefits than the high-scoring students.

Keywords:

• Cumulative
• testing effect
• spacing
• exams
• homework
• mathematics teaching

Acknowledgements

The authors wish to thank the other members of the faculty learning community on applying memory science to the classroom and on the scholarship of teaching and learning: Nora Belzowski, Kieth Carlson, Melissa Desjarlais, Randa Duvick, Laurie Eberhardt, Tiffany Kolba, and Karl Schmitt.

Additional information

Notes on contributors

Jonathan Beagley

Jonathan Beagley received his B.S. from Illinois Institute of Technology in Chicago, IL and M.S. and Ph.D. at George Mason University in Fairfax, VA. His dissertation work was over discrete and convex geometry, but has broad interests in combinatorics and the scholarship of teaching and learning. He enjoys spending time with his wife Callie and son Gabriel, two cats, and dog.

Mindy Capaldi

Mindy Capaldi attended Georgetown College in Georgetown, KY before moving on to graduate school at North Carolina State University in Raleigh, NC. Although she studied algebraic topology for her dissertation, Mindy’s interests now include mathematics education and the scholarship of teaching and learning. She likes to think about how to be a better teacher and bounce those ideas off of her husband, Professor Alex Capaldi. When not contemplating work, Mindy is usually playing with son Henry, reading, or cuddling with her cats.