Des-blog

[cross-posted to dy/dan]

Sometimes I see a worksheet online and I say to myself, “That should stay a worksheet. Paper is the right home for that math. Any possible benefit from moving that math to a computer is more than outweighed by the hassle of dragging out the laptop cart.”

Other times I see a worksheet and it seems clear to me that a different medium would add – you name it – breadth, depth, interest, collaboration, etc.

That’s the case with Joshua Bowman’s implicit differentiation worksheet, which he shared on Twitter. It’s great in worksheet form. But the Desmos Activity Builder can add a lot here while subtracting very little. Activity Builder is the right home for this math.



Here is the activity I built in Activity Builder:



And here are some differences, from small to large:

Simplify Assignment Collection

Bowman is asking his students to do their work in Desmos anyway and then copy and paste their calculator link into a Google Doc for feedback.



Activity Builder simplifies that collection process. Students do their work in the Desmos activity. Desmos sends you all of their graphs, quickly clickable.



Ask More Questions

When students see worksheets with seventeen questions running (a) through (q), they lose their mind. Let’s lighten their cognitive load and keep question (q) out of their visual space while they’re considering question (a).

This isn’t necessarily an improvement, especially if my new questions just ask students to repeat the same dreary work several hundred times. So:

Ask More Interesting Questions

I added six more questions to Bowman’s worksheet, and they share particular features.

First, they ask students to work at several different levels, from informal to formal. For example, I wanted to ask questions about:

• a blank graph – "What do you think the shape of the graph will be?“
• the graph – "Add up all the intercepts. What is that sum?”
• the graph and some tangent lines – “Multiply their slopes. What is the product?”

These questions move productively from informal understandings to formal understandings, but they don’t live well together on the same piece of paper. You can’t ask students, “What do you think the shape of the graph will be?” when the graph is farther down the page.

Another example:

Bowman’s worksheet asks students to find the equation of the tangent lines to the intercepts of the graph. Some students may use sliders, other students may differentiate implicitly.



I can quickly figure out which group is which by asking them to multiply their slopes together and enter the product in a new question. Which students differentiated and which students experimented?



Long before I ask students to calculate that product, I ask them to simply estimate its sign. Envision the tangent lines in your head. Without knowing their exact slopes, what will their product be? That’s an informal understanding that assists later, formal understandings.

So again:

• Simplify assignment collection.
• Ask more questions.
• Ask more interesting questions.

Best of all, this Desmosification took minutes. Start somewhere. The tools are all free forever. Thanks, Joshua, for sharing your worksheet and letting us take a crack at it.

by Christopher

If you teach algebra, you probably teach transformations of functions. If you teach transformations of functions and use Desmos, you have probably gotten the idea that this topic and this tool—like chocolate and peanut butter—would go pretty well together.

At present, we have twelve activities in our Activity Builder search pool having to do with transformations of functions.

Each of these is worth looking at—either because you can use it as-is in your classroom, or because you can learn something that applies to building your own activity. Today, I want to look at What’s My Transformation? by Sheri Walker and Meg Craig.

The activity consists of a series of transformation challenges using function notation. The challenges increase in difficulty as the activity proceeds, and there are several reflection questions sprinkled amongst them.

What’s My Transformation? helps to highlight some important things about classrooms and Desmos activities:

1. Teachers need to know whether their students are ready for the activity.

The first two screens discuss function notation and its relationship to transformations, but they don’t serve as anything like a complete introduction. Students will need to have some experience with the meaning of function notation (e.g. f(x) and f(x-2)) before they do this activity.

The overview on the first two screens can signal the necessary prerequisite knowledge to a teacher browsing these lessons. As a classroom teacher I would ask myself, Will my students be able to make sense of this information with what they know right now? and How can I ensure they’ll know it when we do this activity?

2. Thinking about thinking is important.

All of the activities we build (and nearly all that we curate for search) ask students to think about their thinking. We didn’t build a tool for multiple-choice quizzes. We built a tool for activity, and activity requires reflection. This activity asks three such questions:

a. Does this work? This introduces a two-step strategy that may help some students break their work down into smaller pieces.

b. Help Dan out! This asks students to focus on and explain an important difference—a difference they may struggled with themselves.

c. How did you decide? This is a different form of question b. While this is a multiple-choice question, its purpose isn’t to get the right answer, it is to compare the answers and consider why the right one is right. The wrong answers are not distractors, they are ideas that students in any class are likely to try. The wrong answers have similarities, and their differences require attention.

3. Bonus challenges are fun!

The activity ends with two “Bonus challenges”. These turn out to have simple-looking solutions that actually require careful, clever analysis to resolve.

In another post later this week, I’ll share some summaries of the kind of student work we’ve seen in this activity in order to dig deeper into classroom practice and better understand effective use of Activity Builder.

Over the last year, we’ve developed some powerful new tools for classrooms. With all those advances, we’ve needed to revisit our company goals, our terms of service, and our privacy policy.

First, the goal: Desmos wants to help every student learn math and love learning math. That goal isn’t new for us.

We understand our limits, though. We’re a small handful of designers, engineers, and teachers. For us to come anywhere close to that goal, we need to enlist the teachers of all those students, or rather invite those teachers to enlist us. We need to connect those teachers and all their efforts through curriculum, code, and community.

Here are some updates on our efforts:

Activity Builder & Search

We have designed a small handful of activities ourselves – lessons like Function Carnival and Polygraph. Those efforts will continue. We have been dazzled, though, by the outpouring of creativity and pedagogical innovation in our Activity Builder, even in that tool’s infancy.

We want to help every teacher find the best activities built by every other teacher, both so teachers can learn from each other and also so teachers don’t unnecessarily duplicate their efforts. Teachers can currently share their activities with anybody, anywhere, through emails, tweets, and blog posts. But now teachers can also search through the community’s activities. Our three faculty members – Christopher Danielson, Michael Fenton, and Dan Meyer – are combing through every activity created, curating them, and polishing them in collaboration with their authors. They’re available for search and use now.

Legal & Financial

Until today, we haven’t articulated terms around use of the Activity Builder. We built and released the tool without clearly stating what it will cost to use that tool or what will happen to everything you create with that tool. That lack of clarity may have inhibited the growth and vibrancy of our community and we’re changing that today.

Of course you should read our updated terms of use, but here are some important points which we hope will allow this community to continue to flourish:

• We won’t ever sell your activities without your permission. If your activities are public, anyone can use them without cost. We are creating a community, not a marketplace.
• While we’re still uncertain where the Activity Builder fits into our plan for long-term sustainability, we can promise this: we won’t ever charge you to edit or use your existing activities. If you’ve built it for free, you will always be able to edit it and run it for free.
• If you make your activity public, you are saying, “Yes, I want to participate in this community.” Community participation requires that you allow anyone to copy your activity and make edits to that copy. People will eventually be able to add screens, change screens, correct misspellings, and localize it, either for their native language or particular class of students. Desmos teaching faculty can also copy it and make polishes to bring it in line with our house style for inclusion in our search results. You will always receive credit on the copied activity’s landing page. Additionally, anyone who copies your activity must allow other people to copy that activity – share and share alike.
  

We have subjected all of these community expectations – both what we promise to our community members and what membership in that community requires – to debate inside and outside Desmos. We have been grateful, throughout that process, for our critical friends who have pushed us to develop and articulate these ideals. Now we ask for your support and encouragement to live up to them.