Using Geogebra in Calculus

Last week Thursday I gave a colloquium talk at a local college on some of my favorite results in the area of mathematics known as “the geometry of polynomials.”  During the talk, I used a couple of demonstrations built in Geogebra.  When I did so, I asked my audience of approximately 50 students (almost all math majors) and 10 faculty:  “who here is a Geogebra user?”  Not one student hand went up, and just one faculty hand did.

It therefore occurs to me that it’s still worth advertising this fantastic free software.  So here goes.  While comparable in capabilities to Geometer’s Sketchpad, it can be downloaded freely for local use, or even just run through a browser.  See http://www.geogebra.org/cms/ for details.  There is also an incredible community of active users, with a giant repository organized on GeogebraTube at http://www.geogebratube.org/.  You can even follow Geogebra on Twitter: @Geogebra.

In an earlier post, I wrote about how I’ve used Marc Renault’s outstanding collection of Geogebra applets for calculus in my textbook.  But in my own calculus classroom, I also have my students work with Geogebra directly themselves.  I especially like having students learn to use the slider bars and spreadsheet mode.  The former enables them to easily build their own applets, and the latter gives an easy-to-use way to investigate numerical patterns.  It’s also incredibly simple to work with functions in Geogebra:  if you want to define a rule by g(x), you type “g(x) = …”  If you then want to work with the derivative, all you do is refer to g'(x).  I’m delighted that it looks like my own department is moving in the direction of using Geogebra as the primary software for calculus 1 and 2 instead of the proprietary and [insert your own criticism here] Maple.

I’ve posted a couple of sample files that show how I use Geogebra with my calc I students:  an introduction to GGB that involves ideas with limits and continuity, and a more advanced use of GGB to instantiate Newton’s Method.  Students find the program intuitive and easy to use, and its graphics are fantastic and easy to export.  For the introductory lab, you can find the file in Word or .pdf, as well as the supporting .ggb file; for the Newton’s Method lab, the file students receive is posted in Word or .pdf.

If you’d like to use any of these files, please feel free to use and modify as you see fit.  I’d appreciate you acknowledging my role in their development in some way.  But they, like Geogebra, are completely free, even if I did a double-take when I saw what certain K12 teachers are doing with their lesson plans.

Finally, a disclaimer:  I am a relatively novice Geogebra user.  You’d do well to check out my colleague John Golden’s work, which is often featured on his excellent blog.

Again, if you’ve not used Geogebra, please try it.  It’s free, and it’s awesome.

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