As I lock picture on season six of this incoherent teevee drama called “Teaching,” I am very interested in articulating some general themes and principles around which I’ve tried to organize my instruction. Problem is: the more time I spend creating math problems, the more I detach myself from those interesting generalizations. I am grateful, then, to a couple of edubloggers who have done some of that heavy lifting for me.
1. The Skills Aren’t Arbitrary
The original Greek texts [of the New Testament] were written in all capital letters with no spacing and no punctuation. I wondered what would happen if I gave kids the note below on the first day of class?
It is exceptionally easy for me to treat the skills and structures of mathematics as holy writ. My default state is to assume that every student shares my reverence for the stone tablets onto which the math gods originally etched the quadratic formula. It is a matter of daily discipline to ask myself, instead:
- what problem was the quadratic formula originally intended to solve?
- why is the quadratic formula the best way to solve that problem?
- how can I put my students in a position to discover the answers to (a) and (b) on their own?
And the same mandate goes for any hapless ELA teacher reading this blog. Why spaces? Why apostrophes? Why different words for “happy” and “ecstatic?” Why hyphenated compound adjectives?
2. Great Problems Are The Coin Of The Realm.
Avery Pickford offers a five-bullet definition of great problems. It’s excellent and concise. Here is the first bullet:
The problem should be accessible. It should minimize vocabulary and notation, have multiple entry points, and include ways to collect data of some sort. It should have multiple methods that promote different learning styles and celebrate different ways of being smart.
Dr. Tom Sallee, math professor and president of College Preparatory Mathematics, gave two of the best conference sessions I have ever attended (recapped here and here) and said this in one of them about good problems:
A good problem seems natural. A good problem reveals its constraints quickly and clearly. Developing good problems is not at all an easy task. I have a lot of experience with it and I have failed many times.
The best part about this particular currency is that as I get richer, you do too. When you create and post a great problem about Applebee’s, that’s money in my pocket as well.
I find myself dazzled daily by the great problems y’all share. We’re just printing money lately.