A Soccer Masterclass

Over the past few years I’ve attended around 100 youth soccer classes. Apart from the joy (and occasional frustration) of watching my children learn the game, it’s been interesting observing the classes from a teacher’s perspective.

I’ve seen lots of ineffective instruction. Too much teacher talking. Too much student sitting. Confusing directions. Meaningless metaphors. Wildly inaccurate assessment of prior knowledge. A lack of context for skill development. To be fair, the instructors are almost always warm, well-intentioned, and passionate; they simply aren’t properly trained as teachers. Observing them has been an enlightening professional experience.

But when the head of the program’s curriculum development led a recent class, the difference was dramatic. I watched with another parent, also a teacher, who described it as a masterclass on youth sport instruction. She was right.

Here were some of the most noticeable features:

  • The teacher simultaneously conveyed warmth, invitation, and authority
  • Routines were immediately established to capture students’ attention
  • Though only teaching the class for a single day, the teacher learned and used students’ names
  • Students had freedom to make choices, like poses to strike when freezing the ball, or names for each side of the practice field
  • The teacher masterfully blended seriousness and silliness

The students were moving for most of the class, and they were clearly having fun. It was an obviously successful lesson.

What was more subtle, and perhaps more impressive to me given my previous observations, was the instructional content. The students were engaged in activities that served a fundamental and developmentally-appropriate soccer skill: finding and moving into open space. And this goal was clearly communicated, both explicitly and through the instructional design of the activities.

It may seem funny that a group of five-year-olds running around in the park prompted some deep reflection on high school math instruction. But good teaching is good teaching. And regardless of the context, it’s a pleasure to behold.

Why Winning in Rock-Paper-Scissors (and in Life) Isn’t Everything — Quanta Magazine

My latest column for Quanta Magazine explores the concept of a Nash equilibrium in the simple game of Rock-Paper-Scissors.

A Nash equilibrium occurs in a game when each player employs a strategy that can’t be improved upon. That is, in a Nash equilibrium, no player can improve their individual outcome by changing their strategies. John Nash proved that in all games involving a finite number of players and a finite number of options, a Nash equilibrium must exist. This result revolutionized game theory and economics, and earned Nash the Nobel Prize in 1994.

My column explores the nature of Nash equlibria in the context of a game everyone is familiar with: Rock-Paper-Scissors.

So, what does a Nash equilibrium look like in Rock-Paper-Scissors? Let’s model the situation with you (Player A) and your opponent (Player B) playing the game over and over. Each round, the winner earns a point, the loser loses a point, and ties count as zero.

Now, suppose Player B adopts the (silly) strategy of choosing Paper every turn. After a few rounds of winning, losing, and tying, you are likely to notice the pattern and adopt a winning counterstrategy by choosing Scissors every turn. Let’s call this strategy profile (Scissors, Paper). If every round unfolds as Scissors vs. Paper, you’ll slice your way to a perfect record.

The guaranteed existence of Nash equilibria dramatically impacts the way we study economic incentives, treaty negotiations, network analysis, and many other things. However, a recent paper suggests that even though Nash equilibria must exist, it may be unwise to assume players will always find them! You can learn more by reading the full article at Quanta Magazine.

Quantized Academy Columns Now Featured in WIRED

I’m excited to announce that my column for Quanta Magazine, Quantized Academy, is also being featured in WIRED magazine.

You can find my pieces on pentagonal tilings, symmetry and group theory, and gerrymandering there. And there was actually a brief window where my column on the efficiency gap was among the most popular articles on WIRED, which was a cool surprise!

 

You can find all my Quantized Academy articles at Quanta Magazine, and those that appear on WIRED can be found here.

MfA and Story Collider

I am excited to be taking part in a Story Collider event this April!

The Story Collider’s mission is to bring true, personal stories about science to life through their live storytelling shows, and Math for America is partnering with the Story Collider to create an evening of teacher storytelling.

I’ll be joining five other MfA teachers to tell our stories about our classrooms, professional lives, and journeys through teaching. This is yet another example of the incredible professional opportunities that Math for America creates for its teachers to learn, to lead, and to be heard.

You can find out more about the Story Collider here, including links to their podcasts and a schedule of upcoming events.

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