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2018 National STEM Teacher Ambassador

I’m proud to announce that I am a 2018-19 National STEM Teacher Ambassador!

Through a National Science Foundation grant, the National Science Teachers Association (NSTA) and the National Council of Teachers of Mathematics (NCTM) jointly created a National STEM Teacher Ambassador program that brings together accomplished teachers from across the country for intensive training in policy, media, and advocacy. The goal is to create a network of teachers equipped to advocate for STEM education and related issues at the district, state, and national level.

The program is only open to teachers who have received the Presidential Award for Excellence in Mathematics and Science Teaching, and admission is very competitive. I’m honored to have been chosen, and I have already benefited greatly from meeting and working with the other nine teachers in my cohort.

You can find out more about the 2018 Teacher Ambassadors here, and learn more about the program at the NSTA website. You can also find NCTM’s press release here.

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By MrHonner, ago

Remembering Alexander Bogomolny

Like so many in the mathematical community, I was deeply saddened by the sudden passing of Alexander Bogomolny.

Alex built and curated an incredible website, Cut-the-Knot.org, that showcased the playfulness, creativity, beauty, and rigor of mathematics. When I was studying to become a high school teacher, I remember listing Cut the Knot as one of my favorite mathematical resources. Twenty years later, there still isn’t anything quite like what he created.

I learned a tremendous amount of geometry and trigonometry thanks to Alex. His resources opened up new worlds to me, helped shape my thinking, and directly impacted my classroom practice. After I started a math research course at my school, his website inspired dozens of student projects. And his work often inspired me to do and to write about math.

I was excited to find him on Twitter many years ago, where he continued to share resources, pose puzzles, and engage our community in problem solving and reflection. It was a privilege to cross paths with him so often.

Alex did what so many of us aspire to do: He made a tremendous impact spreading the joy, wonder, and challenge of mathematics. The world of mathematics is poorer for his passing, but so much richer for his life and work. Thank you, Alex.

Photo Credit: Nassim Taleb

Thanks to Nassim Taleb for sharing the news of Alex’s passing, as well as his lovely tribute. Please read the other moving tributes to Alex by Jim Wilder and Gary Davis.

By MrHonner, ago

Four Is Not Enough — Quanta Magazine

My latest column for Quanta Magazine explores the elementary geometry underlying an open problem in mathematics that has been given new life thanks to a recent, surprising discovery.

The Hadwiger-Nelson problem, also known as finding the chromatic number of the plane, involves determining the minimum number of colors necessary to color every point of the plane subject to a specific restriction.

Consider the standard geometric plane, an infinite expanse of points in two dimensions. Your task is to color each of the infinitely many points in the plane. You might wish to color the entire plane red, or maybe half red and half blue, or maybe you’d splatter the color like in a Jackson Pollack painting. But there’s one rule in our plane coloring problem: If two points are exactly 1 unit apart, they cannot be the same color. Can you color every point in the plane without violating this rule?

“Of course!” you might say, “I’ll just use infinitely many colors.” There is a certain elegance to this sneaky approach (setting aside the philosophical question of whether infinitely many colors exist), but can you do it with finitely many colors? And if so, how many different colors would you need? 

Though studied for nearly 70 years, the Hadwiger-Nelson problem remains unsolved, but an unexpected discovery earlier this year has narrowed the possibilities. In my column, I explore elementary approaches to establishing both upper and lower bounds on the chromatic number of the plane, and discuss the exciting discovery that has re-energized the mathematical community around this problem. You can read my full article here.

By MrHonner, ago

Teaching With the Data of Economic Mobility

My latest piece for the New York Times Learning Network was inspired by some amazing data visualizations from The Upshot.

These animations show trends in economic mobility gathered from a landmark study of 20 million Americans. In my lesson, students use the Upshot’s customizable tools to collect and analyze data from the study to determine which groups of Americans have the best chance of improving their economic standing.

Here’s the introduction:

America is often referred to as the land of opportunity. But are all opportunities created equal? Do all Americans have the same chance of achieving the American dream?

A groundbreaking study of United States census data examined how the economic status of 20 million Americans changed from childhood to adulthood, and while the data has a lot to tell us about economic opportunity in the United States, it is likely to raise more questions than it answers.

In this lesson, students use tools created by The New York Times to explore data from the study on economic mobility. They will analyze and categorize economic outcomes, compare and contrast statistics for different demographic groups, and pose and explore their own questions about what this data has to say about economic opportunity.

Does everyone in America have the same chance at success? Let’s see what the data says.

The full lesson is freely available here.

By MrHonner, ago

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.

By MrHonner, ago
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