Kent City — Sixth-grader Ella Browe solemnly studied the game board on the desk in front of her, eyes darting between the resource cards in her hand and the wooden pieces on the colorful board. Then, she made a decision.
“I’ll give you a brick for a wood,” she told one of her opponents, Colton Wray. “That’s the only offer I’m making.”
Colton agreed to the offer, and they traded cards. As Ella reorganized the cards in her hand, she smiled to herself.
“This is a way more fun game than I thought it would be, because it’s math,” she said to no one in particular, mostly to herself, as if the revelation was something she couldn’t keep inside. “Yeah, I pretty much have the best cards ever!”
Ella and her fellow sixth-graders learned to play the popular board game Settlers of Catan this fall in their Math Investigations class, a new elective dreamed up by teacher Erik West. The goal of the class, West said, is to demonstrate how math can be applied to everyday actions, even those you might not expect.
“We talk about wanting to make math more meaningful in terms of application — I wanted (Math Investigations) to give (students) a chance to do stuff that didn’t feel like math, but they’d be learning it without even realizing,” West said. “It’s more hands-on math — more fun, everyday usage.”
The Game of Math Concepts
West also happens to be a Settlers of Catan aficionado. The strategy game challenges players to develop settlements, roads and cities on the fictional island of Catan, using resources they earn either by rolling a pair of dice or by trading with another player. Because the board that represents the “island” is made up of individual tiles, no two games are ever the same.
The math used in Catan gameplay is “so unbelievably complex, you only scratch the surface of it in sixth grade,” West said. His class focuses on three math concepts as they’re playing: probability, expected values and map theory.
Probability: How many different number combinations can be rolled between the two dice, and what’s the probability of rolling a certain number? If you want a brick resource card, what is the probability that your opponent may have one, based on their settlements or number of cards?
Expected values: If you build a settlement in this location, how many resources can you expect to gain on each turn?
Map theory: How can you get to your intended destination with these obstacles in your path, or by using the fewest number of resources?
Learning as They Play
West doesn’t teach any of these concepts to his students before they begin playing, however. Part of the fun in learning is discovering the math as they go along.
“I only teach them the game rules at the start, no other instruction,” he said. “So you see them make really poor choices. … You watch it happen and think, ‘Gosh, that’s terrible, they’re going to learn quick.’ But I want them to experience that.
“After we get done playing a full game, we’ll talk about some of the things we learned, and then discuss the math behind those observations. And then we play again, and hopefully they see the difference.”
A revelation like that is what got Ella smiling during her resource trade with Colton.
“Basically, the whole idea of the game and the strategy and the math concepts is really fun,” the sixth-grader said. “Say you roll a certain number of dice, you have to use math to figure out how many cards you need and what you can do (in that turn). … We’re also learning how to work together as a team to make sure you get the right amount of cards.”
Ultimately with Math Investigations, West said he didn’t want to create “just another math class.”
“Hopefully it opens some doors for them,” he said. “Number one, I hope they want to play (Catan) on their own sometime — or any board game, that would be great. But number two, they’re getting a lot of learning about math in a more meaningful way — versus just doing more practice (math) problems — and hopefully they’ll want to keep doing it.”
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