Intellectual Need, Formative Assessment, and Desmos Activity Builder

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:

Screenshot 2015-11-11 at 11.28.55 AM
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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.

Screenshot 2015-11-11 at 3.03.04 PM

Write a function that has the x-intercepts and asymptotes shown.

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.

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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.

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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.

5 thoughts on “Intellectual Need, Formative Assessment, and Desmos Activity Builder

  1. Dan Meyer

    Thanks for your thoughts here, Dylan. My team found it very provocative. No one on our team disputed your main points. Certainly not me.

    A teaching pattern I’m warming to w/r/t Activity Builder is this: ask the students to do something informal and concrete, pause the lesson and help contextualize what they did in formal, abstract mathematical structures.

    The simple “find two numbers that sum to 12” activity is a helpful illustration. The class is adding points and more points. Pause the class. Have a conversation about what all the points will look like. Entertain arguments and counterarguments. Verify.

    I’m not optimistic that any curriculum – digital or print – will ever fully encapsulate that conversation and those arguments. My best hope (today) is that Desmos will do such a great job with the first step in that pattern that the second step becomes much, much easier for the teacher.

    1. dkane47 Post author

      I think that’s a great use for the Activity Builder. My biggest challenge on that front is that internet is inconsistent in rural Colorado, and I get much more consistent mileage out of activities that are a bit more self-directed by students, and don’t require me to pull the class back early on. That’s unique to my situation, though. The other part here is that those activities are hard to come by. Doesn’t make them any less worthwhile, but I have plenty more ideas for lessons that come a little later in the learning cycle. That’s part of why I’m so excited about search — finding some more of those activities and figuring out what that process looks like. None of this invalidates the importance of intellectual need or the opportunity to create great activities in that area, just that it’s hard to do right.

      I think what Desmos adds to any of these lessons is a low barrier for entry and an opportunity to experiment and get some authentic feedback. That’s what I care most about, and what I’ll be looking to continue experimenting with.

  2. Bob Lochel

    I appreciate the thoughtfulnheness of this post Dylan. I have struggled with finding the place where Activity Builder lies in my teaching. What I’ve determined is that I don’t want Activity Builder to be a hammer and nails – do this, do that, and now here are a bunch of traditional problems which do the same thing. I’d say my uses of Builder fall into 2 subgroups:
    1. An opportunity to explore, then crowdsource later. The overlay feature, for my money, is the best part of AB. I feel having the opportunity to have many students contribute to a prompt, then discuss our contributions, leads to deeper understanding if I facilitate that discussion effectively.
    2. Planting seeds for discussion. Questions like “what happens if you drag this…?”, “how are these the same / different?” or “what do you think if…” allow discussions of content to begin with context, rather than cold.
    I agree that the follow-up here is crucial. I’d like to see Desmos build pauses into an activity, or perhaps opportunity to re-visit, revise. It’s easy for AB’s to feel like one-offs. I’m appreciating the discussions of best-practice our community is having here.

    1. dkane47 Post author

      Thanks, Bob. I really like these ideas for promoting discussion, and I need to keep working on these structures in my class. I especially like the focus on what Activity Builder can do, but other modes of instruction can’t. The point isn’t just to import what we do with pencil and paper into Activity Builder because it’s fun to use, but to make use of that platform for things it does particularly well — like the overlay, and low-barrier exploration before introducing context.

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