Wolfram|Alpha: Recalculating Teaching and Learning

Maria H. Andersen

Muskegon Community College

Abstract

For at least a decade, we have had the ability to let CAS software perform computational mathematics, yet computational skills are still a large portion of the mathematics curriculum.  Enter Wolfram|Alpha. Unlike traditional CAS systems, Wolfram|Alpha has trialability: Anyone with Internet access can try it and there is no cost. It has high observability: Share anything you find with your peers using a hyperlink.  It has low complexity: You can use natural language input and, in general, the less you ask for in the search, the more information Wolfram|Alpha tends to give you. Diffusion of innovation theories predict that these features of Wolfram|Alpha make it likely that there will be wide-spread adoption by students. What does this mean for math instructors?
	This could be the time for us to reach out and embrace a tool that might allow us to jettison some of the computational knowledge from the curriculum, and give math instructors greater flexibility in supplemental topics in the classroom.  Wolfram|Alpha could help our students to make connections between a variety of mathematical concepts.  The curated data sets can be easily incorporated into classroom examples to bring in real-world data.  On the other hand, instructors have valid concerns about appropriate use of Wolfram|Alpha. Higher-level mathematics is laid on a foundation of symbology, logic, and algebraic manipulation.  How much of this "foundation" is necessary to retain quantitative savvy at the higher levels?  Answering this question will require us to recalculate how we teach and learn mathematics.