Calculus: Art on the Wall Game (Teena Carroll, Saint Norbert College)

This is a great calculus game that I saw demonstrated at the MAA/AMS joint conference in Boston in January. It was created by Teena Carroll of Saint Norbert College.

Students are in groups of 4, each with a post-it note. On the post it note, each student draws an arc that goes from one corner of the post-it to the opposite corner:

Student 1 is then asked to position their post it so that is is concave up and increasing, student 2 so it is concave down and decreasing, student three so that it is concave up and decreasing, and student 4 so that it is concrete down and decreasing.

The group then links their post-its together on the wall, in any order, and identifies points of discontinuity and inflection points.

I’m not teaching calculus this semester, so I played this game with a student I am tutoring. I was wowed at the way the game teases out the difference between concave up (positive second derivative) and increasing (positive first derivative). I’m looking forward to playing it with a whole calculus class!

Finally, I wonder if this is a game, really, or is it art? Or is it not art, but just great math? Whatever it is, it’s certainly a lot of fun and a great learning tool.

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.

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.”

Educators coming together to explore how the principles of games promote learning

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