Free Resources: Desmos Calculator and Geogebra
Free Resources Reviewed: DESMOS and Geogebra
Reviewer: Trefor Bazett, Assistant Teaching Professor, Department of Mathematics and Statistics, University of Victoria
This review focuses on two open access computational tools that could augment in-class or online learning: DESMOS (https://www.desmos.com/) and Geogebra (https://www.geogebra.org). I’m going to focus on their use in Calculus courses in this review, but they could be used far beyond just that.
What are DESMOS and Geogebra?
From the perspective of a Calculus student, both are online graphing calculators. Type y=x^2 into either and out comes the plot. However, they are also both much more powerful than that, able to create entire interactive graphics students can play around with to help them viualize. For example, one could make slider which demonstrated how secant lines approached a tangent line as the points got close together.
Each project in DESMOS and Geogebra is saved in the cloud and can be shared with students to modify, or even included in more of an interactive workbook style that walks through a full lesson that combines text with these interactive graphics.
How can I use DESMOS and Geogebra?
There are a lot of options. I have used them in a few ways. Firstly, I’ve used them in class during a demonstration when I want students to have dynamic visualizations (as opposed to drawing a static picture on a chalkboard). For instance, it is nice to visualize how a curve can be rotated around an axis to form a surface. Secondly, also in class, students working in small groups are given the link to an activity and asked to manipulate it. Thirdly, online I’ve used them to help develop a concept as part of a pre-class module in a flipped classroom where they establish the foundational ideas before class. Finally, now that I’m teaching in a fully online context, they are playing a larger role as one type of activity students are asked to play around with between asynchronous videos.
How hard is it to learn for instructors?
There is a syntax – in effect its own programming language – needed to create a DESMOS or Geogeba activity. I personally find it pretty quick and straightforward to figure out the basics of creating a slider or adjusting colours, etc. For most standard Calculus topics you can simply type, say, ‘secant line DESMOS’ into Google and find many existing examples of someone who has already made a very nice activity you can use or modify yourself. Both systems have clearly taken care to minimize the dependency on learning lots of syntax and make this as easy is possible. So I think it isn’t completely trivial, but also shouldn’t be a large barrier.
How hard is it to learn for students?
The larger question is whether to also teach students how to do this. Most pickup the basics like plotting y-x^2 more or less immediately, but it would take time to demonstrate more of the functionality. This probably depends on how deeply you want