[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.
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.
- 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.