MathTech: GeoGebra & UDL, for special education


by Kate Fanelli

Kate Fanelli

Kate Fanelli

In my November 2014 Special Ed Tech column, I wrote about calculators and how they can be used as universal supports for learning. Today I suggest using one particular calculator, GeoGebra, as part of Universal Design for Learning (UDL).

UDL is a way of teaching that comes to education from architecture. When architects build accessibility features into their designs from the beginning, they not only proactively address needs of people with disabilities (for example, curb cutouts, elevators, or ramps), but they do so seamlessly with the design of the rest of the structure, and inadvertently support the needs of people without disabilities, such as people making deliveries using carts or caretakers pushing strollers.

With UDL, teachers proactively build accessibility features into their lessons that align with strengths and difficulties of students with disabilities, but at the same time address learner variability within their entire classroom by making those accessibility features available to everyone. UDL involves offering students multiple means of representation (teachers present information in a variety of ways), multiple means of expression (students may demonstrate understanding in a variety of ways), and multiple means of engagement (teachers offer a variety of motivations for learning).

geogrebra logoRecently I have been playing around with GeoGebra, a free graphing calculator app with computer algebra system (CAS) capabilities. GeoGebra is available on-line and as an app and can do just about everything I used Texas Instruments (TI) Nspire calculators for with my high school students with severe emotional impairments, including side by side dynamic, connected representations of algebraic functions; collecting like terms; substitution of values in an expression; and geometric constructions. Like TI, GeoGebra also allows educators to build and program lessons that can be shared among users.

Image from Plotting Points - GeoGebra - Snoopy

Image from Plotting Points – GeoGebra – Snoopy

With the shift to online standardized assessments, I would be hesitant to create dependency on handheld calculators that are not allowed on such tests. However, GeoGebra would not only give my students experience with using onscreen calculators, but would also allow for flexible methods of representation and expression, and could be motivating to those students who enjoy working with technology. While TI products are still state of the art, cutting edge technology with many features that enhance, support, and assess instruction, for those on a budget, GeoGebra shows promise as a viable alternative.



GeoGebra training happens all over the world on an ongoing basis, but a quick visit to their website shows that a 2-day workshop will be offered in Ohio this summer. For those in the Midwestern United States, this would be a great opportunity to learn more about how to use this free resource. I am told by those who have gone to two day GeoGebra conferences before that it is just as helpful to novices as experienced users.

For more information on Universal Design for Learning, visit or download the free online book containing over 10 years of research and application of UDL at

Kate Fanelli is the math accessibility specialist for Michigan’s Integrated Mathematics Initiative (Mi)2, a state of Michigan initiative that promotes and supports high quality mathematics education for ALL students. Follow (Mi)2 on Facebook ( or on Twitter (@MI2_Math). Contact Kate at


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