I Shall Never Play a Review Game Again!

Update 8/3/15: I've decided that you probably shouldn't use this game in class and I blogged about that here. I could just delete this post, but I figure there's always the chance that someone will think of a way to improve it.

This is the second part of my ramblings about exponents. You should probably go read the first part before you read this!

I don't think there was ever a moment in my life where I said, "Hey! That review game worked really well today. It really helped to prepare my students for that big test tomorrow. Everyone was fully engaged and asking questions about the problems they didn't understand. They had so much fun and I was really impressed by their good sportsmanship! I can't wait to do it again."

Here's why it never worked for me.... The kids who struggle don't want others to notice, so they make some excuse about how they don't want to play the game. The game is "stupid". So I have to give them a worksheet to do instead. Then somebody notices somebody cheating and demands that points be taken away. Then I have to explain that I didn't catch them, but I will certainly be watching to see if anyone is cheating from now on. Then someone will get caught, and I take points away from that team, and then that team gets mad, and then the other team says something nasty to them, and then they say something nasty back, and then I explain that it's just a game, but that doesn't help, because after a few questions they're arguing again, and then I threaten to give them all boring worksheets to do, and so on and so forth.

I don't know. Maybe I'm doing something wrong, but my kids can't seem to handle competition.

So after one horrible day, I declared, "I shall never play another review game again!" That sounds overly dramatic, but that's how it went down.

So today, after seven months of not allowing any games, I decided to play a game.

It was very spontaneous. Someone asked if we could "do something fun", which annoys me to no end, but after practicing solving systems for the last couple of days, I agreed that something fun was in order. I also ran out of Oreos from a task we did the other day, so bribing them to do work was out of the question.

I remembered reading a post a few months back by Kara Wilkins called Grudgeball. It was some sort of game where everybody gets so many X's and you want to be the last student/group with an X. Kids take turns answering questions, and if the question is right, they toss a basketball into a hoop, and if they make a shot, they can erase one of their opponent's X's. I basically did the same thing, minus the basketball. (I decided to name it "Grudge"...but there has to be a better name for it.)

I wrote everyone's names on the Smartboard and everybody got three X's. It looked something like this:

(I know what you're thinking...does he really have kids named Fawn? Hedge? Timon? Bowman??? No. They're completely made up. No one would actually name their kids that.)

I then explained the rules of the game to my students. An expression with exponents would be written on the board. Everyone would write an answer on their little whiteboards, and then anyone with a right answer would erase one X from the board. The last student with an X under their name wins.

First problem:

This isn't tough. In fact, they just learned how to expand these expressions and rewrite them yesterday. So everybody got it right. Awesome. And everybody got to remove an X. Our board looked like this:

Monya, Kishi and Andrew took Fawn out pretty quickly. Fawn took a little bit of revenge on Andrew, but it didn't do much good.

I gave the students another problem, but this time it was something a little different.

Several of my students point out that they've never seen a problem like this before. With the utmost seriousness, I said, "No. You've never seen this. But you're smart enough to figure it out. Just think about what's going on here." It was just one of those moments where you tell the kids that they're on their own and they need to believe in themselves. Maybe a little corny, but it works.

A little over half of the class got the right answer. We talked about what people did to simplify the expression, and for the most part, everyone was engaged because they wanted to make sure they were good at playing the game. And if that's the carrot that I have to dangle to get my students to think algebraically with 11 days left in the school year, so be it.

Note on game play: Although Fawn, Hedge, and Nathan were out of the game, they could play a zombie role and "attack" other players by erasing their X's. This motivated them to keep playing, even though they could no longer win.

Another problem was given that was similar to the last one. That time just about everybody got it. Then we tried dividing powers. Only two or three students figured it out. Then we did another, then half the class figured it out. You see where I'm going with this?

I kept introducing something new. Some students got it right away. For some, it took a couple tries. But eventually, everybody learned how to do it.

The game was finished when all of the X's were gone except for one. Usually the kid that wins is the one you least expect.

If you remember, I said I'd never play a review game again. And technically, I didn't. This wasn't a review. This was mostly new material. I wasn't using a game to trick my students into practicing something one last time before a test. I was using a game to encourage them to learn something new.

Caution: This game seems to work differently for different groups of kids. If there's a lot of animosity in the room, it's probably not a good idea.

Exponents Rules are Lame.

I originally wrote one long post about teaching exponents and incorporating a game. It got to be so long that I split it up into two posts. So bear with me.

Admit it. For most students, exponent rules can seem really lame. It's easy to confuse them and there's not much real-world application for these things. Textbooks try really hard to make it sound like there is...but they're a bunch of liars. The only applications I could find in my textbook (that weren't related to scientific notation) looked this like:

I don't think this is a bad problem. In fact, I like that it makes you think about area. But this isn't a real-world application because you'd never actually need to find the length of a rectangle like this. (Trust me. I was an engineer for six years. I never had to do anything like this.)

And kids pick up on that lameness. This is one of those lessons, up there with factoring polynomials and simplifying radicals, where students will at some point ask, "When will I ever use this?" This question usually comes up when a particular student is getting frustrated with the lesson and suddenly says to himself, "I don't get this. This is stupid and not worth my time. I'll probably never use this outside of school anyway."

And then we, the teachers, come up with a myriad of excuses: you need it for Algebra 2, you'll need it for the test, you'll need it when you're doing sciencey-kinds of things some day, you'll need it when you're flipping burgers at a rate of 2x^6/x^6 per minute, etc.  None of these answers are satisfying to the students.

On top of all of this lameness, we make things worse by explicitly teaching students the rules for exponents. We don't give them the chance to figure them out on their own. I think there is a huge danger in just teaching students rules (or procedures or tricks). If you don't let students develop the meaning behind those rules and procedures, they are subject to error...like when a student tries to multiply two fractions, but for some reason he or she cross-multiplies. Or when they get really good with rise over run, and when you ask them to plot (4, 3), they move 4 up from the origin, and then over 3. Without meaning, rules and procedures become confused and are applied in the wrong situations.

Now, I always thought that I did a good job with teaching exponents. I always explained everything. I showed them how to expand expressions and put them back together.

The logic was there. The kids who were carefully listening "got it". But there were a lot of kids who only got the rule...just add the exponents.

As time went on, and I explained more and more of these rules, students became confused. They didn't really understand what was going on. They didn't know when to add or multiply exponents. They forgot that powers had to have the same base to combine them. They started to think that 2 times 3 was 5!

Here's a nice little graphic that shows how I feel when I teach exponents. You can see what happens as more and more rules get piled on. Students get confused and I'm left wondering, what happened? It was all going so well.

Some teachers are using a different approach. They're allowing students to discover the rules on their own. Just read these sweet posts by Andrew Stadel and Timon Piccini. (It's worth mentioning that both of these posts were inspired by Michael Pershan, who is doing a lot of awesome stuff himself.) I believe that exponents, like many things we teach, are a lot easier to understand if we de-emphasize the rules. And when students understand, they are less likely to ask, "When are we going to use this?", and they might actually enjoy mastering this concept.

Many times, we think we have to show our students every little step before they can do it on their own. Over the last few years, I've discovered that this really isn't the case. Don't believe me? Next time you teach something new, ask yourself if any of your students can figure it out without you explaining it to them. If you believe that at least one of your students can solve it without your help, let them try it. Just shut up, and let them work. Let them come to terms with what you're asking them to do. Let them wrestle with it a bit. Even if they don't get it, at least they're invested in the problem and they have some motivation to learn about its solution.

When you allow students to find their own solutions, they're going to appreciate it much more than you telling them how to do it...if only you'd shut up for once.

Here's the sequel to this post...."I Shall Never Play a Review Game Again!"