Thanks, James

I was recently surprised by a visit from a student I hadn’t seen in eight years. Though he had often come to mind, I never expected to see him again.

Eight school years ago, James and I got off to a good start. But in the spring term, expectations were not being met. On a bad day, I communicated this to James in a way that negatively impacted our relationship. He stopped coming to class.

I didn’t see him for a week or so. When I tracked him down, he told me he had lost respect for me because of the way I had treated him. It was hard to hear; the truth often is. I apologized. He resumed coming to class and finished the year, but our relationship was never quite right again.

The falling out was on both our minds when he visited. “I still think about it,” I said. “Yeah, I wanted to apologize for that,” James replied. I told him no apology was necessary. In fact, I appreciated his courage and maturity in calling me out. I had good intentions, but my actions made the situation worse. It happens sometimes: Often enough, in my career, that I feel like I’ve finally learned my lesson.

Unfortunately I won’t get the opportunity to resolve all those issues from the past. But I’m glad I got that chance here. James is doing well, figuring out who he is, finding success. I’m not sure exactly why, but there was some comfort in knowing that our falling out affected him, too. I was grateful that we could find some positive resolution, even after eight years.

Teaching is an incredibly challenging job. It is a constant struggle to find balance: the balance between expectations and patience; between being tough and being understanding; between pushing a young person and letting them be. As teachers, we are challenged to find that balance a hundred times a day. Somedays we come up short, and we have to live with the consequences. This is the emotional toll of the job.

But that emotional investment also means a brief, unexpected visit years later can make a world of difference. Thanks, James.

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.

What Will They Be Doing?

When planning a lesson, start with the question “What will the students be doing?”

I received this piece of advice as a pre-service teacher and it has stuck with me my entire career.

Before you get too excited, my answer to this question is usually pretty straightforward; most often, it’s “Working on a problem I’ve shared” or “Thinking about a question I’ve asked“. But making this activity explicit in the planning process reminds me to focus on those things that matter most in my lesson: the specific questions I want to ask and the specific problems I want students to engage with.

Asking myself this simple question also helps keep the focus of my planning where it belongs. Instead of starting from “How do I understand this?”, I start from “How will my students come to understand this?” This is a small shift that makes a big difference.

 

NCTM Annual — 2018

I’m excited to be heading to Washington, DC in April for the 2018 NCTM Annual Meeting!

NCTM’s annual meeting brings together thousands of educators from across the country to discuss mathematics, pedagogy, technology, and more. I presented at the 2017 Annual Meeting in San Antonio and had a great time, so I’m looking forward to this year in DC.

I’ll be presenting Statistics and Simulation in Scratch, a 60-minute session about using simple computer programming tools to make the study of probability and statistics more experimental and exploratory. We’ll look at ways teachers and students can use Scratch, the free, web-based programming environment designed by the MIT Media Lab, to model simple probability experiments, collect and analyze data, and create mathematically compelling projects. The technology tools we’ll be using are free and intuitive, and they open up a new pathway to probability and statistics for students and teachers. In addition, it creates opportunities to learn and apply fundamental computer programming skills in a meaningful context.

My talk is scheduled for Thursday, 4/26/18, at 3:00 pm, so if you’re planning on attending the NCTM Annual, please keep my session in mind!

Conferences like this are great opportunities for professional growth, but the logistics are often complicated for classroom teachers.  I’m fortunate to have received support from Math for America, which makes attending NCTM’s Annual Meeting in Washington DC possible. And I’m proud to be one of several MfA teachers presenting at NCTM! You can find a complete list of MfA presenters here.

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