Dan Meyer’s work on mathematical modeling has been instrumental in shaping my own understanding. I’m super thankful for Dan’s commitment to SMP #4 over the years.
So when he recently posted that he was shifting gears, I was bummed. It was like the pizza was snatched from the fat kid and he wasn’t done eating.
Unfortunately there’s little research on elementary modeling. So as I collect my thoughts on virtual paper, I’m open to any suggestions as to what mathematical modeling is, and what should it look like through the eyes of an elementary teacher.
1.Without a context SMP #4 doesn’t exist: The use of manipulatives alone does not constitute modeling. This is the biggest misconception I repeatedly encounter when discussing this standard with teachers. There must be a context in order for mathematical modeling to take place. Modeling is everything that happens in-between the start and the finish.
2.The mathematics must be decontextualized: This means that students are looking at the initial problem and identifying key variables. Decontextualized mathematics means that variables have been extrapolated from problem and are now just numbers void of context. Once students have grappled with the numbers and determined a solution, they throw them back into context to assess the reasonableness of their solution. Does it fit? Does it make sense?
3.If you tell the students the information they need to solve the problem upfront…it’s not modeling. Students must identify the variables. I think if we start here as elementary teachers our students will be far better off. Joe Schwartz has one of the best posts I have read on this idea entitled What if we took the problem apart and put it back together again?
In Dan’s most recent article, he discusses the components of mathematical modeling:
- Identifying essential variables in a situation
- Formulating models from those variables
- Performing operations using those models
- Interpreting the results of those operations
- Validating the conclusions of those results
- Reporting the conclusion
Here’s how modeling flows in AND out of context.
Let’s not kid ourselves, it can be extremely difficult and frustrating at times to have 6 & 7 year olds engage in the modeling process. We might not get through the entire process in one or two classes…. and that’s ok. What I believe is most important is that we’re creating mathematical residue which is worth its weight in gold.
Exposure and opportunity to explore the components of modeling is what I’m personally after. Maybe not all of them every time…but definitely more than our track record shows. The bits and pieces of modeling should be woven into our everyday practice.
Bill McCallum and the wonderful people at Illustrative Mathematics do an excellent job laying out the SMPs in the K-5 Elaborations of the Practice Standards. Sure classroom posters are cute, but we need to ensure our own understanding isn’t watered down.
What’s your thoughts on modeling in the elementary grades? What’s worked? What hasn’t? Where did I miss the mark?