Games, Games, Games

Children at PDS play a lot of games in math class. If you're the parent of a PDS child, you may have heard your child talk about Bears in a Cave, Addition Bingo, Tens Go Fish, Negative One and Out, Digit Place, Uncover, Cross Out Singles, and many more. (You may also have heard them talk vaguely about "the adding game" or "the game with the pattern blocks where you roll the dice--you know, that one." We teachers are not always as consistent with the names of games as we should be.)

Sometimes I'm asked why we have kids play so many games. The questioners, generally speaking, like the idea of games--but they just aren't sure. They wonder whether--and how--the games help develop mathematical skills and mathematical thinking. They worry that games might take away from "real" work, which mostly means computational work with paper and pencil. And while parents are usually pleased that their children have fun playing these games, they often don't have fond memories of math from their own elementary school days. That makes sense. Throughout American history we have looked at school as a nose-to-the-grindstone institution with a heaping helping of drill and perhaps even drudgery. Traditionally, school has been a place where fun goes to die. We are, as a result, naturally a bit suspicious when children seem to be enjoying themselves. It isn't supposed to be that way.

So, why do we play games?

First, precisely because they are fun. While it's certainly true that some children enjoy filling in worksheets, most don't--or enjoy it only in small doses. There's a place for worksheets, of course, but as a rule children are much more motivated to play games. And a motivated student is generally a student who is more likely to learn.

Second, math games are almost always focused on developing a particular math skill. Negative One and Out, for instance, involves rolling dice to form two-digit numbers, which are then progressively subtracted from a starting three-digit number; the object is to get as close to 0 as possible without passing it. This game provides plenty of practice in subtracting, especially in subtracting with regrouping. The game 3-Digit requires children to compare three-digit numbers. Forceout and other geometry games offer practice in visual thinking. Double Compare gives young children experience in adding small numbers. Cover Up develops children's understanding of fractions. As long as games are reasonably fast-paced, children get essentially the same practice by playing them as they would if they did a couple of worksheets--and, as mentioned, the games are typically more compelling.

Third, because games are an excellent way to bridge the gap between concrete and abstract reasoning. First and second grade children, for example, often play a game we call Subtraction Nim. In this version of a (very) old game, pairs of children place 15 counters on the table. They take turns removing 1, 2, 3, or 4 counters (their choice) from the table and recording the subtraction sentence (such as 15 - 2 = 13). The winner is the player who removes the last counter. After children play a few rounds with the counters, we'll have them put the counters away and try it with the numbers alone. In this way, the game helps move children from the concrete to the more strictly numerical.

Fourth, because games involve strategic mathematical thinking. Our fourth graders often play a multiplication game known as Midas Dice. In its most basic form (there are more complex variations too), they roll a die three times and fill the results one at a time into an empty multiplication grid, resulting in a two-digit number multiplied by a one-digit number. The winner is the player who forms the greatest product--or the one with the least product--or the one who's able to predict whether he or she has the greatest or the least...or whatever the teacher decides.

Midas Dice obviously provides practice in multidigit multiplication, just as a worksheet of multiplication examples would do. But Midas Dice adds a twist. Say you roll a 5 on your first turn. Where should you put it to improve your chances of getting the greatest product? Most children realize quickly that a 5 will probably be wasted as the ones digit in the two-digit number. But is it better to have a relatively large number in the tens place of that number--or as the standalone one-digit number? And what if you get a 6 on your next roll? As children play the game, they find that it's very much worthwhile to determine which is greater, 43 x 5 or 53 x 4, and to apply what they learned to the next series of rolls; similarly, they find their chances of winning improve as they think through questions of what is and what is not likely to happen. It's harder to develop this kind of thinking through worksheets alone.

Of course, games aren't perfect. Though we emphasize (and usually get) good sportsmanship, sometimes feelings do get hurt when children become overly competitive, and arguments do break out over whose turn it is or whether someone cheated. Dice fall on the floor, fraction bars get knocked askew, children can become silly. Occasionally players don't try very hard, or cede decision-making to their partners, and even the most interesting game begins to pale after a while. Accordingly, we mix up games with pencil-and-paper practice and other activities as well.

Still, games are very much at the heart of what we do in math. They provide an enjoyable way for students to practice math concepts and skills; they offer a built-in way to challenge players to think more deeply about the topics we're teaching; they help with the transition between concrete thinking and more abstract reasoning. We think of games as being about winning AND losing...but in my book at least, using games is a win for everyone.

Photo credits to Gretchen Lytle.