Bonita High School’s Teacher of the Year for 2015, Kari Redman, asked me into her class during prep period.
So, once I texted Kaplinksy to say, “Your training went so well, you’re now a verb,” I scooted over to room 202 and she handed me this:
“A bunch of my students don’t get it. Every year. I wanna make it more… graspable,” Kari said with a grin.
We chatted for a bit about how similar it is to the Performance Task on the CAASPP test, and how one of the goals is student perseverance through the steps. Kari wants her students to have big Performance Task muscles.
I am a flawed individual. It’s a challenge for me to keep from curling up my nose at these types of problems. A rag-tag band of math teachers are creating great math tasks that are accessible online for free, yet this pseudocontext is prominent throughout math education.
That mean voice in my head now scoffs when I see these problems, since I so enjoy prepping, teaching, and debriefing deep, rich tasks.
There’s a condescending math-task hipster in my head, and it’s a bummer.
Kari is an awesome teacher with a safe class culture for experimentation and learning, so of course I wanted our first task together to go well so she’ll let me mooch her class sometime next year.
We discussed the difference between an open-ended task and one with a clear expected flow. I debated in my head turning this into a tailless problem, but instead, we went to YouTube and found this.
Now we’re talking. While Kari thought about how that video changes the flow of the task, I built this and walked her through it.
“Let’s start with giving the students very little; let’s show the video and ask, ‘What questions do you have?’ or ‘What do you notice? What do you wonder?’ They will get a lot of the framework down for us. Instead of us directing them, they’ll lead and we can steer.”
“Yeah…” Kari says, staring into space, her wheels turning. “My students who don’t catch on to the problem quickly will be on board if we start with something like that.”
“Exactly,” I agreed. “It’s often the students who don’t know how to start that get stuck, and something like that will offer a low door for entry. Here’s a possible flow for the lesson.”
1. Show them the video and this graph.
Ask them, “What do we know so far?”
They’ll likely mention the soccer ball and the hoop. They might mention that the hoop is lower.
2.) Ask them to draw what we have so far.
They’ll likely draw a parabola-shaped path of the ball, draw the ball, draw the hoop, draw the grass. If this is in pencil, they can make revisions later. Or, even better, give a fresh graph at the end and let them make a “pretty version” once they know everything.
3.) Ask them, “What do we still need?” and let them ask you for information.
They’ll probably ask for how steep the hill is; what a great time to remind them of slope.
They may ask how tall the arc of the ball is; we don’t know, but what a great time to remind them of vertex form of a quadratic.
They might ask how tall the hoop is; what a great time to say, “I don’t know. Google it.”
4.) Once they have the stuff they need, assist them in plugging it in.
All of those steps are helpful in understanding and defining the problem, and this part of the process is often ignored or under-represented in math class.
Here’s where the math hipster has to bite his tongue; the equation still appears out of thin air.
Maybe next year, this is where a teacher could detour into Will It Go In The Hoop? or something similar. In this case, that’s not the point of Kari’s lesson, so the math task hipster can keep quiet.
The equation and Desmos offer a visual to understand the problem, but the Performance Task is still focused on the algebraic solution to the system of equations.
I’m stoked for the moment when they realize that the equation for the grass line doesn’t include the basketball hoop, and they have to add something on the end of the linear function.
What do you think? What’s missing?
UPDATE 19 April 2016: She’s also the one who has her Algebra II Students build these after testing:
— Matt Vaudrey (@MrVaudrey) April 20, 2016
UPDATE 29 April 2016: Kari taught sixth period, which went much better than my lesson, first period. We realized (during a debrief third period) that I was attempting to warp math around a context that didn’t demand it, something my inner math hipster accuses textbooks of doing. Instead, a more guided lesson went pretty well when Kari slid into what was a more comfortable class flow.