Trying to find math inside everything else

Posts tagged ‘games’

Set Building Game

(For Explore MTBoS Mission #1)

So I came up with this semi-game last year, based on Frank Noschese’s Subversive Lab Grouping activity. My students had already done that activity at the beginning of the year, so they were familiar with the cards and the idea that the groups were not always what they appeared.

This time, I gave each student a badge that had two words on it: one word on the front, and one word on the back. I asked the students to create groups of 3-4 students using either of their two words. After they formed a group, they had to come up with a description of their group that applied to ALL of their members but ONLY to their members.

This was tricky because of the set of words that I chose, which I had displayed at the front of the room. Set Game List.007

Almost any group of 4 you could create would have some errant fifth member that would fit. And I was VERY adamant that they could not have more than 4 people in a group, no matter how much they asked. So the students needed to use set operations to include or exclude other words. For example, if the students were {Arizona, Brooklyn, Georgia, Virginia} they might say “Our group is the set of x such that x is a girl’s name AND x is a location AND x is NOT Asian.”

Often students would give sentences that weren’t quite precise enough, so I (and later other students in the class) would push back. “Wait! China is a girl’s name and a location.” “Okay, so we’ll add ‘AND x is not Asian.” This caused them to think deeply about what the actual definitions of their group were, and to be careful with being precise. If they weren’t precise enough, they would let other words into their group.

After we got the gist, the groups would then either come up with a description and see if the other students could guess their members OR list their members and see if the other students could figure our their description.

Each round, I had the groups write down on an accompanying sheet their group in Roster Notation, Set Builder Notation, and draw a Venn Diagram where they shaded in where their group lies. So through this I introduce the different notation we use, intersections, and complements. (That left only unions and interval notation for the next day.) I also included pictures of 4-way and 5-way Venn diagrams, in case they needed it.

Stuff

Set Cards (pdf – formatted for name-tag size)

Set Game Worksheet (pdf)

Set Game Worksheet (pages)

Math Games

Back in January I participated in a panel on Math Games over at the Global Math. I meant to write this follow-up post shortly after, but January was a hell of a month for me and it slipped to the wayside. See my talk here, at the 2:55 mark.

I sorta hit the same point over and over, using six different games as examples, but that’s because I truly believe it is the most important point in both designing math games as well as choosing which games to use in your classroom. If the math action required is separate from the game action performed, then it will seem forced and lead students to believe that math is useless.

Global Math - Math Games.003This can be fine if you want. Maybe you want to play a trivia game, where the knowledge action is separate from the game action. But if you pretend that they are the same, then you have problems.

This is the same essential argument as the one against psuedocontext. It may seem like you could say “It’s just a game,” but students see it as a shallow way to spice something up that can’t stand on its own. (I’m not saying review games and trivia games don’t have their place, but they can’t expand beyond their place.)

Below are the six examples I gave, with the breakdown of their game action and math action. I hope to use what I learned in this process to have us make a new, better math game in the summer, during Twitter Math Camp.

Example 1 – Math Man

A Pac-Man game where you can only eat a certain ghost, depending on the solution to an equation.

Global Math - Math Games.005

If we apply the metric above and think about what is the math action and what is the game action? Here, the math actions are simplifying expressions and adding/subtracting, but the game actions are navigating the maze and avoiding ghosts. If I’m a student playing this game, I want to play Pac-Man. The math here is preventing me from playing the game, not aiding me, which makes me resentful towards that math.

Verdict: Bad

Example 2: Ice Ice Maybe

Global Math - Math Games.008In this game, you help penguins cross a shark filled expanse by placing a platform for them to bounce over. Because of a time limit, you can’t calculate precisely where the platform needs to go, so you need to estimate. That skill is both the math action and the game action, so that alignment means that this game accomplishes its goal.

Verdict: Good

Example 3: Penguin Jump

Global Math - Math Games.011Here you pick a penguin, color them, and then race other people online jumping from iceberg to iceberg. The problem is that the math action is multiplying, which is not at all the same. The game gets worse, though, because AS the multiplying is preventing you from getting to the next iceberg, because maybe you are not good at it yet, you visibly see the other players pulling ahead, solidifying in your mind that you are bad at math, at exactly the point when you need the most support. A good math game should be easing you into the learning, not penalizing you when you are at your most vulnerable point, the beginning of your learning.

Verdict: Terrible

Example 4: FactortrisGlobal Math - Math Games.014

This is a game that seems like it has potential: given a number, factor that number into a rectangle (shout-out to Fawn Nguyen here in my talk), then drop the block you created by factoring to play Tetris.

Again, the math action is factoring whole numbers and creating visual representations, which are good actions. But the game action is dropping blocks into a space to fill up lines. As Megan called it, though, we have a carrot and stick layout here, and often in many games. Do the math, and you get to play a game afterwards. (Also, the Tetris part doesn’t really pan out, because all the blocks are rectangles, which is the most boring game of Tetris ever.)

Verdict: Bad

Example 5: DragonboxGlobal Math - Math Games.017

I’ve written about Dragonbox before, so I won’t write about it too much here. The goal of Dragonbox is to isolate the Dragon Box by removing extraneous monsters and cards. The math actions include combining inverses to zero-out or one-out, or to isolate variables. The game action is to combine day/night cards to swirl them out, or isolate the dragon box. The game action is in perfect alignment with the math action, which makes the game very engaging and very instructive.

Verdict: Good

Example 6: Totally RadicalPlaying the Root

The board game I created last year (and you can also make your own free following instructions here, or buy at the above link). In this game, the game actions were designed to match up with math actions. Simplifying a radical by moving a root outside the radical sign, as in the picture above, is done by playing the root card outside and removing the square from the inside (and keeping it as points).Global Math - Math Games.021 You also need to identify when a radical is fully simplified, which you do in game actions by slapping the board (because everything is better with slapping) and keeping the cards there as points.

Verdict: Good

Final Note

One of the real challenges of finding good math games, as a teacher, is curriculum. Most math teachers know of several good math games, like Set or Blokus. While these games are great and very mathematical, they’re not the math content that we usually need to teach in our classes. So the challenge falls on us to create our own games, but making good math games is hard. (Making bad ones is pretty easy.) On that note, if you know of some good math games (that meet the criteria mentioned in this post), drop a line in the comments!