I’m still chewing on Dan Meyer’s talk at Asilomar. His premise was this: video game companies – in order to stay in business – design their products to rope people in and get them hooked. They’re widely successful at doing this; math class has a lot to learn.

No teacher is oblivious to the fact that their class is far less addicting than even the least popular video games, but there are always ways to rationalize. Especially early in my career, I found myself saying this: “Sure, I know how to make class engaging, but first I have to teach boring skill X. Kids, watch me do 1 of these, then you do 10 identical exercises for practice. Then we can do the fun stuff.”

It’s easy to fall back on the excuse that math class “has all these boring parts that we’re stuck with teaching.” Dan says this doesn’t hold water. *It’s all about the task design*.

In my previous post, I wrote how I brought in one of Dan’s examples to my math support class. I wanted the kids to practice multiplication, so I asked them a simple question:

*Find numbers that add to 25 and multiply them together. Make the result as large as possible.*

Every student got that practice I wanted them to, but I didn’t have to force it down their throats. The perplexing task demanded it, and no students pushed back (a rare day, in math support class).

In my Algebra 1 classes, I used this approach to address all the work these students needed on exponents. Here was our opening activity one day:

Kids were a little timid at first, but once the race began for the highest number, the urgency was palpable as kids eagerly practiced the exact rote exercises I would have otherwise placed on a worksheet. **This is practicing, but with a purpose.**

But this short activity turned into so much more. These students – like those in math support – were hooked. “1 times 4 to the 5th” said the boy who often gets things right. “What about 2 times (-6) to the 14th?” said the frequently-bored girl in 1st period, who I use as a barometer when I want to be hard on myself. “We can use negative numbers!?!? This changes everything.” And many rushed back to work before I could say “Go.”

**This task got harder, yes, but it also got more interesting – an essential element of video game design**. The class was hungry for any tips that would help them on this pursuit. I restrained myself for some time, letting kids experiment fitting negative numbers into this structure and listening to their audible noises when their mini-experiments about fitting in negative numbers either did or didn’t turn out how they planned. “Why did (-10) x (-5)^{15 }produce an enormous positive number, but (-10) x (-6)^{16} produce an enormous negative one?” “What the heck is going on here when I plug in (-15) x (10)^{15 }and I get *this*?”

Cue a review of scientific notation (so we can see what this number actually is and whether we’ve succeeded at the task!). Let’s also just nail down what negative numbers do when you put them in the blanks – who found something interesting? In some classes, I might fire up a conversation about number sets, and whether negative numbers are actually in the set of whole numbers. I chose not to, because we ended up getting perplexed and roped into a debate over the result when we typed in 10 x 200^{-200}:

**Keeping the momentum**

After seeing the purposeful practice that took place, with strong engagement and powerful mathematical inquiry to boot, I want to forgo Kuta Software worksheets for the rest of the year. But finding tasks that engage students in purposeful practice of important mathematical concepts is difficult; more difficult than it should be in 2014. I’ve been scouring the interwebs for other teachers’ work on this and have seen many libraries/banks of tasks that I love – too numerous to list – but I have yet to find a library of tasks specifically centered around tasks of this type. **So, to the Math Twitter Blog-o-Sphere: Help me out! I’ll keep looking for tasks like this, and you do the same.** Be in touch soon.

Wendy Menard

said:As I begin my holiday break, this post gives me a lot of food for thought. I am teaching Algebra 2, and there are a WHOLE LOT of boring practice skills we address in class. Maybe I can tweak them as you did yours. Thanks!

Ben Morris

said:Maybe we should start a website to share these “practice with a purpose” ideas… A wiki that anyone could add to, organized by subject and topic. Looking into it.

zackbmiller

said:I’m absolutely with you on that. I think that website would be a valuable resource to a lot of teachers. Dan’s comment below speaks to that too – a little more work is needed to define, specifically, what it is we’re talking about here.

danmeyer55351818

said:Really enjoying all these posts, Zack. Helpful to see what someone else pulls out of these talks.

I’m trying to figure out “what is the genre of task we’re talking about here?” Where are its edges? How do we travel throughout its territory? Because once those routes are mapped out, we can start making a lot of these tasks. (Maybe OpenMiddle.com has us covered, but I think there’s something more going on.)

Here’s a post about Scott Farrand’s talk at CMCN, which I’m retroactively wishing I attended.

http://blog.mathedpage.org/2014/12/asilomar-report.html

It describes a task. Is that task the same as what we’re talking about here, or something different?

The post has the same lament at the end, that we don’t have a collection. We DO need a collection, but first we need to know what we’re collecting.

zackbmiller

said:Somehow, this is the first I recall hearing about OpenMiddle.com. As I was reading your comment, I thought, “OpenMiddle.com sounds like a great thing that must be made ASAP” – and now I’ve just spent a good chunk of my morning mining it. So, thank you!

And I agree with you. What I’m talking about is tasks like Dandy Candies, which has overlap with OpenMiddle.com, but they’re not the same. So, this genre – let’s go with “purposeful practice,” as you called it – is about a perplexing task or challenge that can be broken up into much smaller exercises. It’s a desire to succeed at the larger task that motivates the practice, rather than oral or written directions that ask, specifically, to practice.

The Scott Farrand task you posted is an interesting one that I think borders on this genre, but isn’t quite in it. I just wrote a post elaborating on that.

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