Consortium for Mathematics and its Applications

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Modeling - Based Calculus with R / mosaic

Author: Daniel Kaplan, Cecylia Bocovich & Randall Pruim

Introduction: Software for Calculus

The choice of software for teaching calculus depends on several objectives and constraints, including:
• availability;
• instructor experience;
• graphics, symbolic, and numerical capabilities;
• and steepness of the learning curve.
When calculus is taught from a modeling perspective, other objectives ought to be considered:
• support for a broad range of modeling techniques, and
• the potential for use of the software in other, non-calculus, modeling courses.

R/mosaic for Calculus

We describe a powerful, expressive, and free computing environment that few calculus instructors have explored: R with the mosaic package [Pruim 2011]
Although R is most closely associated with statistics and data analysis, R is designed to be extensible, and it contains capabilities for symbolic manipulation, differentiation, and integration.
The mosaic package provides commands to make it easier to teach and to learn introductory calculus, statistics, and modeling. The principle behind mosaic is that a notation can support learning more effectively when it
• draws clear connections between related concepts,
• is concise and consistent, and
• avoids distracting boilerplate.

Goals of mosaic for Calculus

The mosaic calculus features were developed to support a calculus course
with these goals:
• introduce the operations and applications of differentiation and integration (which is what calculus is about);
• provide students with the skills needed to construct and interpret useful models that can apply inter alia to biology, chemistry, physics, and economics;
• familiarize students with the basics of functions of multiple variables;
• give students computational skills that apply outside of calculus; and
• prepare students for the statistical interpretation of data and models relating to data.

©2015 by COMAP, Inc.
The UMAP Journal 36.1
29 pages

Mathematics Topics:

  • Statistics, Calculus 3, Calculus 2, Calculus 1, Calculus

Application Areas:

  • Software for Calculus

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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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