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.
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.
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.
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.
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 to use it whether it is worth the investment. As I mentioned the goal of the syntax is to be easy, but there is still a learning curve here. Personally, I typically teach only the basics with my students for them to create plots themselves, and then if I want to cover something more complicated, I share a template for them to play with.
Of the two, DESMOS I find slightly easier to learn and with a cleaner interface for plotting 2D plots. However, Geogebra has a lot more functionality built in, such as the ability to do 3D plots, statistics, etc. Ultimately, I ended up using primarily DESMOS for Calculus I/II and Geogebra for Multivariable and Vector Calculus because of the need for lots of 3D plots.
Both can shared either with a url or embedded as an html iframe. For instance, I include embedded versions in my LMS so that they are visually prominent and paired beside the rest of the content in a module in my LMS. Similarly, they could be embedded inside a PreText or other OER website. One note is some institutions can have issues with embedding due to firewall issues and would need to whitelist the two domains (an email to computer help desk fixed this at my institution), but there is always the backup of just sharing a url.
Both Geogebra and DESMOS can be used without creating an account. However, any usage that involves asking students to create accounts (for instance to save to the cloud) would not be FIPPA compliant (for instance they do no use exclusively Canadian servers). I highly recommend speaking with your institution’s privacy office for best practices in terms of protecting your students’ data.
I recommend these resources to be used in courses in the first-year engineering common curriculum as a supplemental resource. As interactive tools they can help student actively engage in visualizing the concepts of Calculus courses and many others.
