I’m on a quest to eliminate the boring, meaningless procedural practice from my curriculum and replace it with purposeful, meaningful, fun tasks that serve the same objective as what they are replacing. This is Post 3.

In this series, I’ve shown a few math problems that I believe prompt students to do purposeful practice. Here’s another task by Scott Farrand (via Henri Picciotto, via Dan Meyer):

Scott Farrand

In a comment on my previous post, Dan asked:

“Is (the task above) the same as what we’re talking about here, or something different?”

My response: The task does have students doing important practice, and the task does have a clear purpose. It’s a task I would certainly use, but not for the purpose of replacing boring, meaningless procedural practice. In other words, I don’t think it’s what I’m looking for. I’ll elaborate.

The purpose

So far, each task that I’ve described in this series has a purpose that is clear and simple: “Produce the highest number.” “Match this image.” “Use the least amount of packaging.” These purposes are perplexing and usually quite trivial (which is OK). They’re not intended to be driving towards deep conceptual understandings (though many can be extended to do so). In these tasks, “the purpose” is a vehicle to engage, to provide some urgency and motivation for students who find practicing dull, unsatisfying and tedious.

What is the purpose in Scott’s task above? What drives students to do it? What emerges from the task is a cool realization – once they compare a few rates of change, they see that each ROC is the same. But a realization is not the same as a purpose that drives engagement. In the directions, it’s the teacher who has prompted the practice work, not the perplexing nature of the task. It relies on students trusting that “If we do this seemingly pointless work, we’ll see something interesting.” If that trust exists in the culture of your classroom, then what’s driving this task is the mystery: “What will I see if I follow the teacher’s directions?”

If possible, though, I’d rather not bank on that trust because we know not every kid will buy it. Then again, Scott is talking about a really small task size. Yes, kids have to sip our Kool-Aid to see the purpose, but in this task, only for a couple minutes. And regardless of task size, assigning the tedium first with an unexpected payoff to follow is still an infinitely better formula than assigning tedium with no hope of a payoff.

So how useful is this task? For a conceptual understanding of rate of change, very useful. This is probably what Scott intended it for and what I will steal it for. For purposeful practice? Once students have the “OMG, the rates of change are all the same!” moment, the punchline is gone and the driving force of the task is gone with it – kids won’t find rate of change more than a couple times, because they know what they’ll find. Now we need a new driver, a new purpose to get them to practice this a bit.