May 23rd, 2013 by Dan Meyer
If you and I have had a conversation about math education in the last month, it's likely I've taken you by the collar, stared straight at you, and said, "Can I tell you about the math lesson that has me most excited right now?"
There was probably some spittle involved.
Evan Weinberg posted "(Students) Thinking Like Computer Scientists" a month ago and the lesson idea haunted me since. It realizes the promise of digital, networked math curricula as well as anything else I can point to. If math textbooks have a digital future, you're looking at a piece of it in Evan's post.
Evan's idea basically demanded a full-scale Internetization so I spent the next month conspiring with Evan and Dave Major to put the lesson online where anybody could use it.
That's Do You Know Blue?
Five Reasons To Love This Lesson
It's so easy to start. While most modeling lessons begin by throwing information and formulas and dense blocks of text at students, Evan's task begins with the concise, enticing, intuitive question "Is this blue?" That's the power of a digital math curriculum. The abstraction can just wait a minute. We'll eventually arrive at all those equations and tables and data but we don't have to start with them.
Students embed their own data in the problem. By judging ten colors at the start of the task, students are supplying the data they'll try to model later. That's fun.
It's a bridge from math to computer science. Students get a chance to write algorithms in a language understood by both mathematicians and the computer scientists. It's analogous to the Netflix Prize for grown-up computer scientists.
It's scaffolded. I won't say we got the scaffolds exactly right, but we asked students to try two tasks in between voting on "blueness" and constructing a rule.
- They try to create a target color from RGB values. We didn't want to assume students were all familiar with the decomposition of colors into red, green, and blue values. So we gave them something to play with.
- They guess, based on RGB values, if a color will be blue. This was instructive for me. It was obvious to me that a big number for blue and and little numbers for red and green would result in a blue color. I learned some other, more subtle combinations on this particular scaffold.
This is the modeling cycle. Modeling is often a cycle. You take the world, turn it into math, then you check the math against the world. In that validation step, if the world disagrees with your model, you cycle back and formulate a new model.
My three-act tasks rarely invoke the cycle, in contrast to Evan's task. You model once, you see the answer, and then you discuss sources of error. But Evan's activity requires the full cycle. You submit your first rule and it matches only 40% of the test data, so you cycle back, peer harder at the data, make a sharper observation, and then try a new model.
The contest is running for another five days. The top-ranked student, Rebecca Christainsen, has a rule that correctly predicts the blueness of 2,309 out of 2,594 colors for an overall accuracy of 89%. That's awesome but not untouchable. Get on it. Get your students on it.