Teaching Modeling-Based Calculus

Presented by

Daniel Kaplan & Daniel Flath (Macalester College), Randall Pruim (Calvin College), Eric Marland (Appalachian State University)

Tuesday, January 3rd, 2012


The MAA/CRAFTY reports recommended a strong emphasis on modeling in early university-level math courses, as well as much greater attention to statistics and computing. This workshop will show some techniques for teaching an introductory calculus course that is genuinely based on the process of modeling. By this, we mean using the concepts of calculus to help develop and interpret models of diverse phenomena in biology, economics, physics, etc. There will be a strong link made between calculus and statistical models. And, rather than using technology to carry out traditional symbolic calculus operations, we'll show how technology can be used to aid the modeling process. The workshop will include a general introduction to teaching modeling, several examples of classroom activities and homework projects that help develop modeling concepts and skills, and a broad introduction to the use of computing to support modeling. Participants should bring their laptops with the software they would like to use in their teaching. Recognizing that the choice of software is often determined by external factors including the preferences of colleagues and budgets, we will be ecumenical about software. In addition to providing a basic introduction to two free mathematical software systems --- R and Sage --- we'll try to support participants who would rather work with Mathematica, Maple, and Matlab. The workshop is an outreach activity of Project MOSAIC (NSF DUE-0920350) as well as CAUSE --- the Consortium for the Advancement of Undergraduate Statistics.

Participants should bring a laptop computer to the workshop, if possible. Lunch will be provided.

There is no workshop registration fee and advance registration is required. You will receive notification of acceptance. There will be no on-site registration; walk-ins on the day of the workshop will not be accommodated.

About the presenters

Daniel KaplanDaniel Kaplan is DeWitt Wallace Professor at Macalester College where he teaches applied statistics, mathematics, and computer science. He is the author of several textbooks, including Introduction to Statistical Modeling. (See www.mosaic-web.org/StatisticalModeling.) He won Macalester's annual Excellence in Teaching award in 2006.

Daniel FlathDaniel Flath, Professor of Mathematics at Macalester College, teaches the gamut of the undergraduate math curriculum. For twenty years his focus has been on new ways to teach calculus, coauthoring a calculus textbook and constantly trying new things in his classes. An undergraduate degree in electrical engineering is perhaps behind Flath's commitment to the centrality of mathematical modeling in basic mathematics courses.

Randall PruimRandall Pruim is Professor of Mathematics and Statistics and Director of the Integrated Science Research Institute at Calvin College. He is author of several books, including Gems of Theoretical Computer Science (with Uwe Schöning) and Foundations and Applications of Statistics: an Introduction using R (published by the AMS in 2011). He also maintains several R packages on CRAN, including the mosaic package which provides numerous utilities to simplify teaching statistics and calculus using R.