I’ve thought about “modeling” more than I’ve thought about any other specialization in mathematics. I’m learning less and less about it each year so I’m hopping onto a different track for awhile, moving onto other questions. First, I wanted to collect these links in one location:
- Missing the Promise of Mathematical Modeling. My Spring 2015 article in Mathematics Teacher analyzes the meager opportunities for modeling in school mathematics and recommends some solutions.
- The Checkout Line Is A Scam. (Or Is It? [Yes, It Is.]) My blog post illustrating modeling through the lens of grocery express lines, which are a scam.
- Math Class Needs a Makeover. A 11-minute talk I gave for TEDxNYED in 2010. Couple million views.
- Fake-World Math: When Mathematical Modeling Goes Wrong and How to Get it Right My TEDxNYED talk + five more years of study + 50 extra minutes.
Summarizing all of the above in a single paragraph:
Modeling asks students a) to take the world and turn it into mathematical structures, then b) to operate on those mathematical structures, and then c) to take the results of those operations and turn them back into the world. That entire cycle is some of the most challenging, exhilarating, democratic work your students will ever do in mathematics, requiring the best from all of your students, even the ones who dislike mathematics. If traditional textbooks have failed modeling in any one way, it’s that they perform the first and last acts for students, leaving only the most mathematical, most abstract act behind.