I went to the California Math Council – South conference last weekend, and saw Eli Luberoff speak on intellectual need and the Desmos Activity Builder. Eli referred to Guershon Harel’s work on intellectual need and his paper here. Harel posits that for students to learn, they must have an intellectual need for what we are teaching — they must experience a problematic situation, and the drive to resolve this situation motivates learning.
Eli argued that Desmos activities provide an effective example of creating an intellectual need for math. I think that many activities do this well — the activities provide a gateway to perplexing situations with a low barrier to access. I can’t find the example Eli used during the conference, but it’s very similar to this activity by Desmos teaching faculty:
I love this activity. It goes further to motivate systems of equations, but it starts by provoking very simple questions for students — “I wonder what shape all of the points will form?” This is pure, mathematical intellectual need at its best.
All that said, provoking intellectual need isn’t what I primarily use Desmos Activity Builder for. First, a quick detour:
I read this post by Jonathan Claydon at the end of the summer on how the Activity Builder is best used. It was pretty influential for me, and this quote sticks out:
My big reservation: permanence. This is part of the reason I’ve never gotten into whiteboarding, the associated work never gets saved. Students could dutifully complete my match the graph activity but wouldn’t take anything home with them at the end of the day.
Jonathan offers one solution — the follow up worksheet, where students take something with them that codifies the learning from Activity Builder. I think it’s a great addition to Activity Builder, and provides a really great opportunity to connect representations and formalize strategies.
So two approaches to Desmos Activity Builder here. First, that it effectively puts students in a situation of intellectual need. Second, a reservation about permanence and the follow-up worksheet to codify the learning.
I have a different takeaway, however. Having spent a ton of time tinkering with both the graphing calculator and Activity Builder trying to build some lessons for my students, I realized that I struggle to build activities that successfully introduce a new concept to students. Desmos is great at illustrating stuff — but there’s a pretty significant transaction cost (at least in my classroom) to get every student onto a computer and onto the correct page. By that point, some kids or groups are well ahead of others. And the reality is, they’re going to have questions, and many students will have the same questions. The more their paths through the activity diverge, the harder it is to orchestrate meaningful discourse or jump in to provide a missing piece of knowledge and I inevitably end up leaving students behind.
Instead, I see the greatest value of Activity Builder in formative assessment. Desmos provides a hugely powerful tool to explore new ideas. A bit of instruction, the old-fashioned way, to introduce the big ideas of a new concept goes a long way. Desmos provides the power to explore these ideas more deeply, apply them in a new way, connect them to new representations, and the whole time give me a great bird’s-eye view of what students do and don’t understand to drive instruction moving forward. Students aren’t necessarily keeping a token from the lesson, although I do accompany many activities with a follow-up worksheet. The primary purpose is to deepen their understanding of an idea that’s been introduced, and help me decide where to go next.
This can perpetuate intellectual need, but that’s not the primary purpose. I think I can do that better with my usual pencil, paper and projector schtick. And it avoids the challenge of giving students a place to make their learning permanent — a well placed formative activity comes after they’ve been introduced to key ideas, but with time to reteach and remediate as the data from the activity suggests. Oh, and Desmos is just plain fun for students to play with.
Some examples that I’ve used an have gotten excited about:
Students need to know how to construct a rational function with specific x-intercepts, asymptotes, and end behavior to attempt this activity, but that basic knowledge and a willingness to experiment are plenty to further their understanding.
This activity won’t teach students the Mean Value Theorem, but it will see if they can apply it visually in a few different ways, and underscore important principles of derivatives at the same time.
Students won’t learn vertex form from Match My Parabola, but it’s effective practice with writing quadratic functions, and does an excellent job pushing students’ knowledge around the leading coefficient of a quadratic.
I don’t meant to bash Activity Builder here. It’s an incredible tool, and it’s made a nontrivial difference in my classroom this year. But handing over the key moments in learning new content to a self-guided activity is too much for me right now, and when it goes bad, it can be hard to put the brakes on. This structure is perfect for pushing student understanding and giving me a view of what they know as I figure out what to do next.