Shelley Carranza is a math coach in Northern California and uses our free
Activity Builder as
much as anybody we know. Previously, she has posted
a long list of activities
mapped to the free EngageNY curriculum. In a recent post, she has offered
her top four tips
for making great use of those activities in the classroom, starting with:
Open up the teacher dashboard on an iPad or tablet so that you can monitor
student work as you circulate the class. During my last lesson I also kept a
post-it note with me so I could take down names of student work to share
with the class during debrief time. Doing this also helped me decide when we
should debrief and keep track of time.
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.
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.
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.
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.
