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Rasmussen, Chris; Dunmyre, Justin; Fortune, Nicholas; Keene, Karen – PRIMUS, 2019

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

Descriptors: Mathematical Models, Teaching Methods, Mathematics Instruction, Inquiry

Zazkis, Dov; Rasmussen, Chris; Shen, Samuel P. – PRIMUS, 2014

The Riemann sum definition of integration is ubiquitous in college calculus courses. This, however, is not the only possible way to define an integral. Here, we present an alternative mean-based definition of integration. We conjecture that this definition is more accessible to students. In support of this proposition we first present a…

Descriptors: College Mathematics, Mathematics Instruction, Calculus, Mathematical Concepts