Consortium for Mathematics and its Applications

Product ID: Teaching Modeling
Supplementary Print

Guiding Students to Discover Counting Formulas - With a Modeling Twist

Author: Kristen Barnard, Kayla Blyman & Carl W. Lee


In undergraduate mathematics classes, counting is often taught by presenting
formulas for students to memorize so they can solve a standard set
of problems.

We provide an alternative to this approach in the form of an activity that
is appropriate to use in any course that covers counting. It is designed to
allow students to discover counting formulas by engaging in data-gathering
simulations, with each simulation representing one of 12 mathematicallydistinct
counting problems. Ultimately, students may discover the entirety
of Gian-Carlo Rota and Joel Spencer’s “Twelvefold Way,” which we
present in the Appendix.

© 2022, COMAP, Inc.
UMAP Journal 43.2
22 Pages

Mathematics Topics:

  • Finite Mathematics

Application Areas:

  • Education

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COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.

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