Monday, February 18, 2019

Using Desmos in a Classroom Environment



I've recently been exploring online software for use in a classroom. While I was familiar with using GeoGebra for a variety of geometry and graphical representations, I was amazed with the other applications of Desmos as a powerful resource for teachers and students to explore. Apparently, Desmos has built a wide variety of classroom explorations. These are actually fairly high quality explorations, and I am actually going to continue exploring Desmos in a few explorations in the near future, so keep your eyes open for those.

In 2016 NCTM published an article about increasing class participation through online resources. While it was written by authors of Desmos curriculum, I feel like it gives great information and suggestions for math teachers. It's a little outdated, one of the activities that they describe has lost native Desmos software support, but the principles are pretty useful to think about. The article can be found here (or here if you have a BYU Learning Suite account).


Summary


This article, it seems, was written primarily to discuss the benefits of using online technologies in a math classroom. That being the case, one major benefits of using online softwares (particularly Desmos) in a classroom is that students can receive iterative feedback- feedback that comes extremely fast and not too leading. Online tools are also useful in that students can share with each other in additional ways, making student collaboration and peer to peer learning much more likely. Beyond just student feedback, teachers also have more information, often being able to observe the entire process of learning instead of just viewing the final result. The article then explores two Desmos activities and how they achieve these aims of online software tools.

As I discussed this with a few of my fellow students, we were amazed with the tools that are available for the teacher as students accomplish these tasks. This eventually progressed past a discussion of the article, and I will actually discuss these benefits in an upcoming blog post. However, we also discussed how online tasks should not and cannot replace classroom discussion led by a teacher. While student's interaction and peer teaching is extremely useful, we must also be able to "steer" the class in the correct direction, keeping students from "guessing and checking" when they do not understand the material. This is actually possible in any Desmos activity: the teacher has the control to "pause" all their student's screens, inserting teaching and discussion where otherwise students might get caught in a learning trap.

Critique

While this was an interesting article, I feel that it was much too focused on the benefits and value of Desmos. No other software was mentioned in the article, while I know that there are a variety of other softwares and online mathematical tools for the classroom. The article itself also didn't mention the need for heavy teacher involvement in a classroom full of devices, it almost seemed to me that the article was implying that the class would teach itself with Desmos. This makes sense as it was written by some authors of Desmos, but it was lacking in power by not addressing all parts of this important issue.

I do wonder about the discussion that we had and if we are all a bit naive. While our discussion focused on the ideal classroom environment, I do wonder how long it will take us to actually come anywhere near that in our teaching. Teachers who have been teaching for years may be able to know where each of their 200 students are in their understanding and address needs well, but I worry about being able to do that in my classroom. However, I do feel like online activities will give us additional information on student understanding and the excitement that our discussion had for the tools of Desmos is deserving. Being able to pause an activity is an extremely powerful tool, and recognizing that was a great benefit from our discussion.

Connections

I think that technology can be extremely useful in the mathematics classroom. For example, when I was in high school, I programmed my graphing calculator to solve a quadratic equation using the quadratic formula. I knew how to plug numbers into an equation, I'd done that hundreds of times and probably will a few thousand times more. However, for ease, I used my calculator and would get onto more "interesting" mathematics instead of wasting my time with something that I already understood.

The other day, I was observing in a classroom and watched as a teacher had students graph (on their graphing calculators) an exponential function versus its' derivative. Students then used that to estimate what the formula for the derivative of an exponential function from that graphical representation. This could have been very useful for these students, but I feel like it wasn't presented in an exploratory manner, making it a "plug and chug" method for many students. I think if it had been presented in a way such as through Desmos or other exploratory software students could have discovered and understood the concepts a lot better than they did.

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