Understanding Mathematical Induction by Writing Analogies

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Published: Aug 6, 2019
DOI: https://doi.org/10.31719/pjaw.v3i2.38

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Andrew A. Cooper
Department of Mathematics, North Carolina State University

Abstract

Mathematical induction has some notoriety as a difficult mathematical proof technique, especially for beginning students. In this note, I describe a writing assignment in which students are asked to develop, describe in detail, critique, defend, and finally extend their own analogies for mathematical induction. By putting the work of explanation into the students' hands, this assignment requires them to engage in detail with the necessary parts of an inductive proof. Students select their subject for the analogy, allowing them to connect abstract mathematics to their lived experiences. The process of peer review helps students recognize and remedy several of the most common errors in writing an inductive proof. All of this takes place in the context of a creative assignment, outside the work of writing formal inductive proofs.

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How to Cite
Cooper, A. A. (2019). Understanding Mathematical Induction by Writing Analogies. Prompt: A Journal of Academic Writing Assignments, 3(2). https://doi.org/10.31719/pjaw.v3i2.38
Issue
Vol. 3 No. 2 (2019)
Section
Articles

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References

Bahls, P. (2012). Student writing in the quantitative disciplines: A guide for college faculty. San Francisco: Jossey-Bass.

Bodnar, I. (2006). Aristotle’s natural philosophy. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy.

Cooper, A. A. (2018). Incorporating critical and creative thinking in a transitions course.

Holden, J. (2015). Why induction is like ice cream: Writing about analogies in discrete mathematics courses.

Katz, V. J. (2009). A history of mathematics. Pearson.

Paul, R., & Elder, L. (2012). The nature and functions of critical and creative thinking. Tomales, CA: Foundation for Critical Thinking Press.

Peano, G. (1960). Formulario mathematico. Rome: Edizioni Cremonese.

Plotker, K. (2009). Mathematics in India. Princeton: Princeton University Press.

Stokes, P. (2005). Creativity from constraints: The psychology of breakthrough. New York: Springer.