[cross-posted from Dan Meyer’s blog]
Eight years ago, this XKCD comic crossed
my desk, then
into my classes, onto my
blog, and through my professional development workshops.
That single comic has put thousands of students in a position to encounter the
power and delight of the coordinate plane. But I’ve never been happier
with those experiences than I was when my team at
Desmos partnered with the team at
CPM to create a lesson we call Pomegraphit.
It’s yours to use.
Here is how Pomegraphit reflects some of
the core design principles
of the teaching team at Desmos.
Ask for informal analysis before formal analysis.
Flip open your textbook to the chapter that introduces the coordinate plane.
I’ll wager $5 that the first coordinate plane students see
includes a grid. Here’s the top Google result for “coordinate
plane explanation” for example.
A gridded plane is the formal sibling of the gridless plane.
The gridded plane allows for more power and precision, but a student’s
earliest experience plotting two dimensions simultaneously shouldn’t
involve precision or even numerical measurement. That can come later. Students
should first ask themselves what it means when a point moves up, down, left,
right, and, especially, diagonally.
So there isn’t a single numerical coordinate or gridline in Pomegraphit.
Delay feedback for reflection, especially during concept development
activities.
It seemed impossible for us to offer students any automatic feedback here.
After a student graphs her fruit, we have no way of telling her, “Your
understanding of the coordinate plane is incomplete.” This is because
there is no right way to place a fruit. Every answer could be
correct. Maybe this student really thinks grapes are gross and
difficult to eat. We can’t assume here.
So watch this! We first asked students to signal tastiness and
difficulty using checkboxes, a more familiar representation.
Now we know the quadrants where we should find each student’s
fruit. So when the student then graphs her fruit, on the next screen
we don’t say, “Your opinions are wrong.” We say,
“Your graph and your checkboxes disagree.”
Then it’s up to students to bring those two representations
into alignment, bringing their understanding of both representations up to the
same level.
Create objects that promote mathematical conversations between teachers and
students.
Until now, it’s been impossible for me to have one particular
conversation about the tasty-easy graph. It’s been impossible for me to
ask one particular question about everyone’s graphs, because the answer
has been scattered in pieces across everyone’s papers. But when all of
your students are using networked devices using some of the best math edtech
available, we can collect all of those answers and ask the question I’ve
wanted to ask for years:
“What’s the most controversial fruit in the room? How can we find out?”
Is it the lemon?
Or is it the strawberry?
What will it be in your classes?
Find out
and let us know.
