Writing-to-Learn Activities to Provoke Deeper Learning in Calculus

Abstract

For students with little experience in mathematical thinking and conceptualization, writing-to-learn activities (WTL) can be particularly effective in promoting discovery and understanding. For community college students embarking on a first calculus course in particular, writing activities can help facilitate the transition from an “apply the formula” approach to problem-solving, to a “conceptual understanding of the formula” to initiate mathematical knowledge-building. Community college students face several common challenges in a beginning calculus course, including difficulties using mathematical notation, applying theorems, and understanding the language of proof. Several WTL assignments are discussed, ranging from low-stakes assignments to more formal assignments with a chance for revision, which effectively addressed these difficulties. Samples of students’ work are presented to highlight the learning objectives different writing tasks help attain, student’s understanding of concepts, and the benefits of frequent, low-stakes writing assignments. An analysis of individual students’ work shows that WTL activities not only help students cement mathematical knowledge, deepen understanding, and develop appreciation for the rigor and concision of mathematical language, but also enable them to develop learning habits essential to their success in any field.

Keywords:

• Calculus
• writing-to-learn mathematics
• community college

ACKNOWLEDGEMENTS

The author would like to thank her colleagues Yelena Baishanski for agreeing to run the study in her Calculus I section, Nichole Shippen and Nancy Berke for carefully reading the final version of the manuscript, and Jenny Zhu from the office of Institutional Research & Assessment for promptly providing the requested data. She is also grateful to the Core Competencies seminar leaders organized by LaGuardia’s Center of Teaching and Learning for providing feedback and suggestions on some assignments.

Additional information

Notes on contributors

Reem Jaafar

Dr. Reem Jaafar holds a Ph.D. in Theoretical Physics from the CUNY Graduate School and is currently an Associate Professor in the Mathematics, Engineering and Computer Science Department at LaGuardia Community College. During her tenure at LaGuardia, she was the recipient of four grants, co-founded the Math Society, trained LaGuardia students to compete in regional and national mathematics competitions, organized interdisciplinary STEM talks, and supervised undergraduate student researchers. She conducts in-depth pedagogical research about effective classroom practices in mathematics education across all college-level courses. She has co-authored 15 papers in peer-reviewed journals and has presented her work in theoretical physics and mathematics pedagogy at over 13 conferences. Dr. Jaafar’s current areas of research are nanomagnetism and mathematics pedagogy.