When we’re modeling in our own lives, we have to make decisions about what information is necessary and how we’ll get it. We start with no data at all, just a purpose that’ll eventually require data. (That’s only for modeling, though.)

I liked this a lot and went googling around to see what other folks had to say. Found an old Jo Boaler paper with this gem: “School mathematics remains school mathematics for students when they are not encouraged to analyze mathematical situations and understand which aspects are central.”

Dan:

Two: how can we best enact mathematical modeling in the classroom with teachers of varying quality?

Script one of your 3-Act pieces out word for word: every question you’d ask, every misconception you’d anticipate, etc.. That’d be top-tier PD for lots of us.

One improvement to a lot of textbook modeling problems is to remove as much data as possible. But how much data removal is too much data removal?

When we’re modeling in our own lives, we have to make decisions about what information is necessary and how we’ll get it. We start with no data at all, just a purpose that’ll eventually require data.

So on its own, if the question is “How much data removal is too much data removal in a modeling task?” my answer is “You can’t remove enough data.” (That’s only for modeling, though.)

Kate introduces another variable – teacher quality. Optimizing for both of those variables will lead us to different conclusions w/r/t scaffolding. I think we should consider the two questions separately, though.

One: what does mathematical modeling look like?

Two: how can we best enact mathematical modeling in the classroom with teachers of varying quality?

One improvement to a lot of textbook modeling problems is to remove as much data as possible. But how much data removal is too much data removal? You’ve done such useful, provocative work exploring this, and I really liked Kate Nowak’s recent description of the Mathalicious process:

“…scaffold too little, and the lesson becomes too hard for too many teachers. Scaffold too much, and the lesson does too much of the cognitive work for the student, robbing them of the chance at the learning that comes from insight.”

Another improvement might be to invite criticism of the assumptions the authors make (e.g. “What are the risks of holding the rate constant? Why might they have chosen to neglect air resistance? What other variables might we add or discard?”)