Mathematical play, but, like, for older kids

Chris and Melissa gave a great talk on the importance of mathematical play at NCTM-Seattle last week. You can see their Math-on-a-Stick work on their website. There you can see pictures and examples and of children enjoying and playing with math in interesting and delightful ways. One of my many takeaways from their keynote was that play is math and math is play. In their talk, they referenced research that lays out seven attributes of play. Play (a) is purposeless, (b) is voluntary, (c) is inherently attracting, (d) involves freedom from time, (e) involves a diminished consciousness of self, (f) has possibility for improvisation, and (g) produces the desire to continue.

When I saw the mics set up I A) assumed there were going to be questions and B) just knew one of the questions was going to be “but what about older kids?” Sure enough, there was a question about how adolescents might play with math. The premise – which I kind of (but not entirely) disagree with – was that older kids wouldn’t be engaged by things like pattern machines, tiling turtles, and Truchet tiles. Chris and Melissa gave good answers about the age band of the kids of math-on-a-stick and spoke to the non-zero amount of older kids, but I’d like to offer a few examples of older kids playing with math. Unfortunately, I didn’t take as much time playing with math as I should have as a teacher. So I’ll share a few ways I and my kids play with math as regular ol’ humans.

Me: Baseball Prospectus and Sabermetrics

I was trying to think of the first time I played with math post-pubescence. I was such a baseball fan in high school, partially because the Cleveland Baseball Team was quite excellent at the time (despite not having any rings to show for it), but also because of stats. I began reading the great baseball writer and sabermetrician, Rob Neyer. I began organizing various baseball reference spreadsheets. I felt like I was finding out secrets of baseball that most managers (and fewer commentators) knew. Things like “on-base percentage is more important than batting average” and “home runs yielded are a better predictor of future pitching success than other categories.” This secret information yielded by mathematics helped me understand the game while also helping me win my fantasy league to boot. (Note: I’ve written a bit about this before.)

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My daughter (age 13): Animation

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My daughter is a phenomenal artist. She draws all day, every day. If there is a Gladwell-ian 10,000 hours rule, she eclipsed that at least year ago. She likes to create animations, frame-by-frame. Moreover, she likes to animate to music. She plays with math by timing out the different scenes in a potential song and crafts them into a music video.

My son (age 11): Scorigami

Scorigami is a concept created by Jon Bois, a content creator for SB Nation. A scorigami is a final score of an NFL game that has never occurred before. For instance, the score of seven to eight has never occurred before. Were two teams to end up with that final score, that would be a scorigami. Because of the interesting numbers and combinations of numbers that occur in a football game, many scores have not been achieved in an NFL game. Scores in football come in 6 (touchdowns), 3 (field goals), 2 (safety or two-point conversion after a touchdown), or 1 (extra point, but that has to come after a touchdown, 6).

For instance, there has never been an 18 to 9 final score. There has been an 18-10 final score, but never 18-9.

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Every Sunday we watch football and keep an eye out for potential scorigamis. Once it gets to the fourth quarter and we’re looking at, say, a team with 11 points, we’re in scorigami red alert mode. My son plays with math by keeping an eye on the scorigami grid, including the density map, to identify how scores could occur throughout the Sunday games.

Here are a few more rapid fire examples of mathematical play I’ve seen or experienced from adolescents:

  • Google Sketch up
  • Messing around with pascal’s triangle
  • Fantasy sports
  • Games of chance
  • Des-man

What about you? What have you seen or done that might constitute as mathematical play that secondary kids might be interested in?

Update (12/6): Within hours of publishing this post, my son had an idea for mathematical play (he did not call it that).

Mario Party is a video game for the Nintendo Switch. It acts essentially as a board game with little mini-games throughout. Characters roll dice and move around the board collecting things. What’s interesting and made this ripe for mathematical play is that each playable character has a different die. They all have six sides, but have non-standard values.

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For example, the six values for the Luigi die are 1️⃣1️⃣1️⃣5️⃣6️⃣7️⃣. The six values for the Peach die are 0️⃣2️⃣4️⃣4️⃣4️⃣6️⃣. You can also have dice that give you coins instead of moves for some rolls. The goomba dice yields +2 coins, +2 coins, 3️⃣4️⃣5️⃣6️⃣.

For seemingly no reason at all, my son decided last night he wanted to tabulate the average (mean) values to determine the best character die. He also assigned commentary (“high risk, high reward”) to the dice. I do not know how he factored in the coin values.

He then sorted the dice into tiers – really good, okay, and bad based on the mean rolled value.

Why did he do this activity? Well, he’s not allowed to have screen-time during the school week, so this might have been his way of coping. But regardless, it was generally pointless, which, when it comes to mathematical play, is essentially the point.

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3 Responses to Mathematical play, but, like, for older kids

  1. Mary says:

    I attended the presentation also and wondered if they would discuss “play” for the older student. A topic my students have “played” with is mathematical applications of coloring.

  2. @jstevens009 says:

    What about having kids create some Islamic Geometry Art, Geoboards, or designing a Rube Goldberg machine?

    I had the same feeling as you during the keynote. Loved it, and wanted more as it related to the kids/classrooms I support. Even seeing those pattern machines get used by a middle schooler (or high schooler, which yes, is possible), would have been helpful.

    I feel/worry that there is this stigma around play for our middle/high school students. Play becomes more rigid, more competition-based, more everything *except* fun, especially when we are the ones defining the constraints. Personally, I love fantasy sports (except for when my players suck or get hurt… thanks, 2018), yet I know that many students have no interest in it. Your example of Scorigami is spot-on.

    I’d love to hear other ways people are getting their teenagers to engage in genuine play that has mathematical value as well.

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