Beware Of Fake Math Modeling Problems

Here’s a question to think about: if you can completely remove a problem’s context and still solve it, can it really be mathematical modeling?

Consider the math problem below from a middle school math textbook. It uses the context of a baseball diamond to discuss rational numbers. It is listed as a “Real-World Link” and demonstrating Math Practice 4 (notice the box in the upper right).

I was watching students work on this page and wondered how important the context was to solving these problems. Then it made me wonder, “What if there was no context? What would change?” This is what the problem might look like it the context was completely removed.

What’s the Difference Between Honors and Regular Math Classes?

Consider this thought experiment:

What if we eliminated separate Honors and regular math classes? For example, instead of there being an Honors Geometry course and a regular Geometry course, we mixed all students together so there was just one type of Geometry course that every Geometry student took.

There’s a catch though: any of these Geometry students may earn Honors credit for the course, as long as the student does X, Y, and Z. What would X, Y, and Z need to be for this to be fair?

We’ll come back to that question later on.

A Common Professional Development Mistake

I think that professional development providers, certainly including myself, often miss the mark and commit a common mistake when they tell attendees what they need to do but don’t leave them equipped to implement it. To explain this, consider how we teach students what to do during a fire.

The two most common options are providing a map (like you see in hotel rooms) or by simulating the experience through a fire drill (like you see in schools). Giving students a map is certainly less time consuming than running a fire drill, so why don’t we just give students a map?

Lessons Learned from Lesson Study

From 2010 to 2013, I had the opportunity to facilitate approximately 70 lesson study days with third grade through high school math teachers in my district. It was one of the best experiences of my career as my job was focused on learning about how students learn. So, I thought it would be worthwhile to share some of the lessons learned (many the hard way) as I believe that other educators may find them useful.

First, let me describe the lesson study process we used:

Troubleshooting #ObserveMe

If you’ve put up your #ObserveMe sign but things aren’t going the way you hoped, then this post’s for you. I’m using this as a running list of solutions for problems that educators are encountering so we can have them in a central location. Here’s how you can help:

Are you encountering issues that aren’t listed?
Do you have solutions that aren’t listed?
If so, please mention them in the comments and I will add them.