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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

Apkarian, Naneh; Bowers, Janet; O'Sullivan, Michael E.; Rasmussen, Chris – PRIMUS, 2018

This article presents a case study that details the successes and lessons learned by faculty and administrators at San Diego State University (SDSU) who are in the process of implementing a substantial improvement to the Precalculus to Calculus 2 sequence. Improvement efforts have been informed by national studies of successful programs and center…

Descriptors: Case Studies, Mathematics Instruction, Calculus, College Faculty

Zandieh, Michelle; Wawro, Megan; Rasmussen, Chris – PRIMUS, 2017

In this paper we address practical questions such as: How do symbols appear and evolve in an inquiry-oriented classroom? How can an instructor connect students with traditional notation and vocabulary without undermining their sense of ownership of the material? We tender an example from linear algebra that highlights the roles of the instructor…

Descriptors: Algebra, Mathematics, Mathematics Instruction, Mathematics Education

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

Wawro, Megan; Rasmussen, Chris; Zandieh, Michelle; Sweeney, George Franklin; Larson, Christine – PRIMUS, 2012

In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and…

Descriptors: Algebra, Definitions, College Mathematics, Mathematics Instruction

Rasmussen, Chris; Keynes, Michael – PRIMUS, 2003

The purpose of this paper is to describe an instructional sequence where students invent a method for locating lines of eigenvectors and corresponding solutions to systems of two first order linear ordinary differential equations with constant coefficients. The significance of this paper is two-fold. First, it represents an innovative alternative…

Descriptors: Prediction, Concept Formation, Equations (Mathematics), Generalization