koholman
Jan 9, 2023
"Once I was asked, 'why are you so bad at shapes?'
I replied, 'I'll triangle back to that later'" (Cue Learn Pvt. Ltd.).
Geometry is my jam! I wrote my master's thesis on geometry (specifically, the isoperimetric property of the circle, combined with some really cool stuff involving triangles). I fell in love with geometry in the 9th grade and have been captivated since.
One of the groups I participate in is a community of Math Mamas. My peers are mostly mathematics professionals in academia, and while we talk about parenting struggles, women's issues, glass ceilings, and a host of other topics, we also share resources for teaching.
I first heard of Geogebra there. I'd been meaning to check it out but hadn't gotten around to it; then, we used it for one of the projects in mathematical modeling earlier this summer. I wasn't completely sold on it, even though Coach Hall kept hyping it up, and I made a mental note (which was quickly forgotten) to play with it some more.
Learning the power and extent of Geogebra's capabilities in this course was amazing! Yes, there's value in knowing how to calculate the area of a shape or find the distance between points, but sometimes that's not the goal of the lesson. Because Geogebra is dynamic, when objects (e.g., points, lines, shapes) are connected/associated, you can move one and see how the change affects the others.
Geogebra has some fantastic capabilities with only a few simple clicks (table is non-exhaustive):
The dynamic manipulations employed by Geogebra lend themself to relational understanding (Skemp, 1978) and is a creative, innovative way to move through the van Hiele Levels (Shaughnessey & Burger, 1985).
One of the reasons I like Geogebra is that it brings geometry to life. Geometry is an inherently visual discipline, and by adding a dynamic geometry system to the curriculum we are able to dig deeper into the relationships that ...
Gif by Giphy
Additionally, when we use a tool like Geogebra, we can assess students' learning by asking them at least three kinds of questions as they move through an exercise: problem thinking, making the mathematics visible, and encouraging reflection and justification (Principles to Actions [PTA], 2014). For "problem thinking" questions, we might ask students how an object was constructed (PTA, 2014, p. 36). Possible questions about "making the mathematics visible" could be about the visual similarities and differences of objects or to describe an object's transformation (PTA, 2014, p. 37). When we want to "[encourage] refection and justification" we may ask a student to demonstrate a construction while they provide reasoning for each step (PTA, 2014, p. 37). Questions like these require more than a few seconds to answer and are conducive to a focused questioning pattern allowing us to get them thinking on a deeper level about the task (PTA, 2014).
Geogebra has other features that might better handled by another MAT overall, but if the context is geometry, staying within one program is better for students: no screen swapping, less troubleshooting data migration, fewer programs to focus on leaving more time to do the work. These include built-in spreadsheets and computer algebra system. If we want to analyze and compare geometric objects, these are handy! If we are working with random data and statistical analyses, however, there are other MATs which are better suited.
I like Geogebra. It's a great tool and I'm grateful to have spent time exploring it in-depth!
References
Cue Learn Pvt. Ltd. (n.d.). Geometry puns: Geometry jokes: Circle puns and more! Geometry puns. Retrieved July 28, 2022, from https://www.cuemath.com/learn/geometry-puns/
Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9-15.
Shaughnessy, J. M., & Burger, W. F. (1985). Spadework Prior to Deduction in Geometry. The Mathematics Teacher, 78(6), 419–428.
Principles to Actions. (2014). National Council of Teachers of Mathematics.
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