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Keynote: Making Our Mark

In November, I was honored to deliver the teacher keynote at Math for America’s annual Fall Function. Together with Giselle George-Gilkes, we spoke to over 1,600 teachers and guests about the many ways MfA has impacted us and our careers.

I’ve been a Math for America Master Teacher for the past 12 years, and it’s difficult to communicate the breadth and depth of the impact the organization and its community of 1,000 math and science teachers has had on me. I’ve had unique opportunities to learn, lead, and build relationships within New York City and across the country, all in the service of becoming a better teacher and leader.

Here is an excerpt from my speech:

I’ve dedicated myself to both leading and learning as a math teacher. And this community helps prepare me for those challenges every step of the way. This community makes me feel like a professional. A difference maker. And it makes me feel like I always have more to offer, both in and out of the classroom.

You can watch the video of the keynote at MfA’s YouTube page:

And you can find edited version of our speech, “Making Our Mark”, at MfA’s Teacher Voices blog.

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Math at the Deli Counter

The deli counter at the grocery store sometimes offers a poignant glimpse into how the public engages with mathematics.

Whenever I order a fractional quantity of meat or cheese, I prepare myself to manage confusion. When a blank stare lingers at “three-quarters of a pound of ham”, I’ll follow up with “point seven five”. I’ve heard “One-third… What is that?” more than a few times. And a deli employee once asked me if I wanted my two-thirds of a pound of cheese in two bags. Usually my deli experiences go smoothly, but there are some employees with whom I know to skip fractions and immediately go to decimals.

None of this bothers me; if anything, it reminds me that fractions really are one of the first walls people hit when learning mathematics. And it increases my empathy for those who obviously weren’t helped enough when they first hit that wall, and still struggle to get over it as adults.

I’ve also witnessed math-shaming in this situation. “Yes. Point seven five. Three-quarters is 0.75. You don’t know what three-quarters is?” As rude as this behavior is, I can’t help but sympathize a little with the shamers themselves: what mathematical experiences have they had that makes them feel the need to use math to belittle others? Sadly, I think I know at least part of the answer to that question.

It’s important for those who of us who see math as a source of pleasure and power to remember that, for many, it can be a source of confusion and, sometimes, shame.

The 2017-18 Conjecture

Like many mathematicians and teachers, I often enjoy thinking about the mathematical properties of dates, not because dates themselves are inherently meaningful numerically, but just because I enjoy thinking about numbers.

A new year means a new number to think about. And one interesting fact about our new year, 2018, is that it is semiprime.

A number is semiprime if it is the product of exactly two prime factors: for example, 15 = 3 * 5 is semiprime, as is 49 = 7 * 7, but neither 13 nor 30 are. Semiprime numbers are also referred to as biprime2-almost prime, or pqnumbers.

Semiprimes are very interesting in and of themselves, particularly in cryptography, but what caught my attention is that the previous year, 2017, is a prime number. That means we have a semiprime number, 2018, adjacent to a prime number, 2017. How unusual is this?

I played around a bit and ended up writing some simple programs to find and analyze semiprimes. Among the first 500,000 integers, there are roughly 108,000 semiprimes and 41,500 primes. Of the 108,000 semiprimes, only about 2,500 (or 2.3%) are adjacent to a prime number. This seems low to me: there are 83,000 prime-adjacent spots among the first 500,000 integers, representing 18% of the spots semiprimes could occupy. But only about 2.3% of the 108,000 semiprimes end up in those spots. That seems unusual.

In thinking about what happens further out along the number line, I couldn’t help but wonder if there are infinitely many prime-semiprime pairs like 2017 and 2018. I certainly don’t know the answer, but I thought I would start the new year boldly, with a conjecture:

The 2017-18 Conjecture

There are infinitely many pairs of consecutive integers one of which is prime and one of which is semiprime.

I think this problem’s resemblance to the Twin Prime Conjecture led me to both imagine this conjecture and also suspect it’s true. As with virtually everything in mathematics, I’m sure someone has thought of this before, and I would love a reference if anyone can provide it.

Thinking ahead, I was excited to notice that next year will also be a semiprime!

But it appears that the Twin Semiprime Conjecture is already an existing open question, which means I have less than a year to come up with a new conjecture for 2019.

Happy New Year! 2018 has already inspired to me to do some number theory, tackle some computing challenges, and think about some new ideas for the classroom. It’s a good mathematical start to the new year, and here’s hoping 2018 only gets better.

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2017 — My Year in Math

Dan Meyer recently shared a fun and telling graph describing his year in math. Inspired by Dan’s idea, and by a Math for America workshop with data visualization innovator Mona Chalabi, I created my own Year in Math entry. Though the real inspiration, I guess, came from the world events that made me want to read more books and less internet.

You can find more takes on the Year in Math theme on Twitter.

I think this could make for a fun student project. I hope the students agree!

The (Math) Problem with Pentagons — Quanta Magazine

My latest column for Quanta Magazine is about the recent classification of pentagonal tilings of the plane. Tilings involving triangles, quadrilaterals, and more have been well-understood for over a thousand years, but it wasn’t until 2017 that the question of which pentagons tile the plane was completely settled.

Here’s an excerpt.

People have been studying how to fit shapes together to make toys, floors, walls and art — and to understand the mathematics behind such patterns — for thousands of years. But it was only this year that we finally settled the question of how five-sided polygons “tile the plane.” Why did pentagons pose such a big problem for so long?

In my column I explore some of the reasons that certain kinds of pentagons might, or might not, tile the plane. It’s a fun exercise in elementary geometry, and a glimpse into a complex world of geometric relationships.

The full article is freely available here.