## Tuesday, November 30, 2010

### The Agony of Math Review Games

My calculus classes took a quiz on the power rule and "reverse power rule" before Thanksgiving break. (The "reverse power rule" is my name for the elementary anti-derivatives they've been taking ... it's always funny to make up terminology on the spot, and then all of a sudden realize that the "reverse power rule" and the "freeloader rule" are now recorded in 50 calculus notebooks). The results of the quiz suggested that my kids needed more time to digest the material, so that's what we've been doing for the past couple of days. They have a re-quiz tomorrow, so I thought that a good way to practice in a relaxed, positive atmosphere would be to play a review game. Turns out, I was wrong.

I stole the game from one of my colleagues Ted. Students work in pairs to solve a problem on the mini white-boards. For the first problem, Partner A is the only one who can write on the board; Partner B can help and offer advice, but cannot touch the marker. The roles switch for each problem. When they are done, they hold up their board. The first team to hold up the correct answer gets to throw a hacky sack at a target I've drawn on the board, and depending on where the sack lands they either get 1, 2, or 3 points. The throwing of the hacky sack clearly has no purpose other than getting the students up and excited, which kind of reminds me of Solve Crumple Toss, except that they don't have to throw away their work when they finish a problem.

I'm not sure what it was -- maybe I made the problems too hard, maybe I should have given them time in between rounds to finish up their solution even if they weren't the winning team, or maybe I should've figured out a way to get rid of the time pressure. In any case, a couple of teams wound up dominating the game and many students expressed frustration after class that they weren't able to get any of the problems right and they didn't like the time pressure. I tend to agree about the time pressure - after all, it's not about how fast you can do a problem, but how well - but if there's one calculus skill that lends itself to this kind of a game, it has to be taking derivatives using the power rule. It's like the multiplication tables, but for calculus.

I'm really curious if anyone out there has developed the perfect math review game -- one that is fun and competitive, but encourages (or better yet, forces) everyone to participate and doesn't automatically favor the quickest kids in the in the class.

1. With calculus students, I've found that review games in general frustrate them for exactly the reasons you laid out. By the time students get to calculus you've cut down to the most serious (grade-) motivated kids, who all generally want to work the review problems independently. When we do hit rock bottom and it's time for just straight up circle-the-wagons time, I usually put up a basic problem, and intermediate quiz problem, and then a punishing one.

Although, as a teacher, review games are more fun for me. I used the partner white boards a few times, and would break the class into halves. Each half would then have a few partner teams, and each team would solve the problem on the white board. The white boards would come up to me, and then I'd add points to each half based on correct number of white boards.

Not as exciting, but everyone does the work and no one is embarrassed when they can't do it, because I check them anonymously at my desk (just glance at the answers.) Then, I work out the sticky part of the problem (invariably, the algebra >:| ) and we go to the next round.

There's a sense of anticipation as the scores go up, and I get dramatic about it. Alas, review games . . .

2. When I was student teaching in AB and BC Calculus I created a Jeopardy review game. The kids that got it right first got the most points, but everyone else had a chance to get half of the points and we didn't move on until everyone answered the questions.

Also I've done something called Math Mania where I take say 10 problems and cut them up so that only one problem is on a page. The kids can work in groups or on their own and their goal is to be accurate. If they get it right on the first try then they get 10 points, if they're wrong the 10 gets marked out and they can only get 9 points. The grade they get is what is on the score sheet at the end of class and they staple all of their work together. The part they seem to like the most is the ringing the bell when they get a question right.

3. Shawn, I think you hit the nail on the head. Review games with calculus students = square peg in a a round hole. Which doesn't mean we can't play a game once in a while because even "serious calculus" students need to let out their goofy/competitive sides, but it has to be done thoughtfully and in a way that doesn't alienate 75% of the students.

Sarah, I actually have a bell sitting around at home that I'll have to bring in next time I try a review game!

4. Whatever game you do, you can give a most improved prize. Use a multiplier of 1 over their current percentage score in the class. (Do you keep a score like that?) So someone with a perfect 100% has a multiplier of 1, and someone with 50% (= 1/2) has a multiplier of 2. If you have them write down their multiplier, most students will have 1.something (I used just one digit after the decimal), and it's harder for them to compare grades with it.

They can multiply their game score by the multiplier, and find out who got the best score that way.

5. I love to play a game I, by turns, call Bet Your Booty (which gets a laugh when I explain that the original meaning of booty is pirate treasure) or Math Poker. Students play against a partner. They each place a bet before they see the problem. I have a sheet prepared with a line for the bets and a space to show work. When they have finished their problem (no rush) we trade papers and if you got the problem right, you win your bet and add it to your starting amount (usually 500 and I tell them they can consider it billion dollars if they are in tune with the national debt or toothpicks if they want to stay simple). I also usually direct their bets (a number between 1 and 50 and then it escalates). Winner at the end gets 1 extra credit point on quiz/test. Kids seem to love this game and, as with all games, you can't play the same one more than twice a year.

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