This article discusses four mathematically rich settings with origins in the elementary, middle, and secondary school curricula. Depending on the questions asked and the connections made within each setting, the problem spaces allow the instructor to import tools leading to sophisticated extensions appropriate for college-level study. These topics include the Heaviside function, randomness, symmetry, modular arithmetic, the generalized Pythagorean Theorem, and the theory of groups. Given the potentially extensive ground covered by these settings, they serve to reward those students who are inherently curious while highlighting the coherence in the curriculum as one progresses through the grades. The mathematical experiences invite disciplinary and interdisciplinary connections and encourage discourse and productive struggle.
Nabb, Keith A. and Murawska, Jaclyn M.
"Coherence and enrichment across the middle and secondary levels: Four mathematically authentic learning experiences,"
The Mathematics Enthusiast: Vol. 14
, Article 15.
Available at: http://scholarworks.umt.edu/tme/vol14/iss1/15