All posts by Kathleen Offenholley

Math Games

Bizz Buzz for Base Systems

numbers

A simple game for learning base systems illustrates many of the connections between game based learning and other pedagogies. This game can be played in a liberal arts or mathematics for elementary education class. The game is a variant of Bizz Buzz, often played as a drinking game.

Students sit in a circle and count off – one, two three, four. The fifth person, instead of saying five, says “bizz.” The count continues – one, two, three, four, bizz-bizz, one, two, three, four, bizz-bizz-bizz, one, two, three, four, bizz-bizz-bizz-bizz. After this (four bizzes), the count changes — one, two, three, four, buzz.

This is a base 5 counting game, with 105, or 5, represented by bizz, and 1005, or 25, represented by buzz. The game typically engenders much laughter as students who are not quite paying attention say 5 instead of bizz, or bizz instead of buzz. Students help each other to say the right word, “Say bizz!” they call out to the confused fifth person. But the game is not too hard, and soon everyone gets the hang of it.

Explicit connections can then be made between the game and the notation for base 5. For example, the seventh person is bizz + two = 125 in base 5. The connection can also be made to base 5 manipulatives — units, 5-unit rods, and 25-unit squares.

The game can later be played in a different base, to extend the difficulty level and to deepen understanding. I like to ask my students “how would you play this in base 7?” and they can quickly come up with the new rules.

Math Games

The Spread of a Rumor or Virus

rumor

This game introduces students to the concept of exponential growth. It can be played as the spread of a rumor, or the spread of a virus, and works well in an algebra or modeling course, in a quantitative reasoning course, or a liberal arts mathematics class.

Each student gets a card, labeled “Round 0 ____, Round 1 ____, etc.” On one student’s card, there is a yes next to round 0, while on the rest of the cards, there is a no. The student with a yes is the student who “knows” the rumor or who has the virus.

Students are instructed to stand up and mill around. In each round, they must look at one other person’s card. If that person’s card has a yes, the student who did not have a yes now has one, while everyone else writes no – without saying anything about which they have on their card. After enough rounds so that everyone has a yes (for a class of 35, this is usually about 6 rounds), students sit down and a chart is made of how many had a yes at each round. Connections are then made to doubling, and to powers of 2, which then leads to a discussion of exponential growth.

Note that the growth modeled here is actually logistic, since there is a limit to the number who will have the rumor or virus, but if the game is played only up to a certain number of rounds, it mimics plain exponential growth nicely – as does the spread of a rumor or virus in a large population. The game can later be played with different growth factors, such as introducing some amount of immunity (a person only gets the virus after being exposed twice, or three times) or increased virulence (each person shows two or three people their card, on each round).

The Spread of a Rumor can be seen as a simulation, rather than a game, although the distinction between a simulation and a game is often only a matter of semantics. However, for serious 18-year olds, it can be problematic to be seen “playing” – whereas older students and future teachers do not seem to mind as much.  I usually introduce this one without saying the word “game.”

Math Games

NIU-Torcs for Numerical Methods

car

See the game video: https://www.youtube.com/watch?v=LYGwaI-haOM

NIU-Torcs is an example of a college-level mathematics game that allows for deeper learning within the game. Brianno Coller and colleagues developed the game through an NSF grant to help their mechanical engineering students learn numerical methods (Coller & Scott 2009). Students begin the game by learning how to code acceleration and steering using the programming language C++.  They then move to making the car move fast without skidding off the road, by calculating numerical roots, solving systems of linear equations, and doing curve fitting and simple optimization. The authors report that students are motivated to keep trying far more than when given these types of problems as meaningless homework exercises. Concept maps produced by the students in both the game-based and traditional classes showed that although measures of low-level knowledge were statistically identical, students in the game-based class had much greater levels of deep thinking, which included being able to compare and contrast methods and link concepts together.  In addition, student attitudes about the class had changed – they were more engaged, and more able to recognize the value of the mathematics they were doing.