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Teaching Calculus Minus Computation, Plus Understanding

Nikolay Brodskiy
Organization: The University of Tennessee

Wolfram Technology Conference 2011
Conference location

Champaign, Illinois, USA

Wolfram|Alpha and Mathematica take care of all computational problems in a multivariable calculus class. That frees significant time to be spent on a conceptual understanding of calculus. Such a fundamental change in the course raises a whole spectrum of questions: from content-specific questions like "What is the fundamental theorem of multivariable calculus?" to technical questions of managing homework assignments completed by students in the Mathematica notebook format.

In this talk, I will briefly mention a theorem I proved that can be considered as the fundamental theorem of multivariable calculus. That would illustrate the complexity of mathematical questions that need to be resolved before we teach calculus at a higher conceptual level. I would like to share my experience of using Wolfram|Alpha together with Google Docs for homework assignments and tests. I have incorporated a significant conceptual component into tests, making the tests more coherent with my concepts-oriented teaching. Students read my lecture notes as notebook files and complete an online homework assignment before I talk about the corresponding material in class. This fall semester I will take it even further: all my lectures will be recorded and made available on YouTube. I will spend class time mostly on doing projects with students when they have to apply calculus to their favorite topic.

My website contains most of the materials I use for teaching calculus, including video lectures recorded during the 2011 summer semester.

*Mathematica Technology
Downloads Download Wolfram CDF Player

TeachingCalculusMinusComputationPlusUnderstanding.cdf (91.3 KB) - CDF Document
TeachingCalculusMinusComputationPlusUnderstanding.nb (90.6 KB) - Mathematica Notebook