“Well, No One’s Complained”

As I walk the halls during testing week I always peek into classrooms to make sure the lights are on. Far too often I’ve encountered teachers who leave the lights off while students are taking exams. I’m really not sure why; maybe their resentment at having to proctor an exam leads them to prioritize their own comfort over that of the students?

When I see that the lights are off, I’ll step in, flip all the lights on, make eye contact with the proctor, and loudly say “The lights need to be on during testing”. Most of the time the proctor quickly averts their eyes, knowing they were in the wrong and embarrassed they’ve been called out. But one time a teacher, seemingly offended, responded “Well, no one’s complained.” I’ve heard a similar defense from teachers flouting school-wide homework and testing policies: “I give tests on whatever day I want. The students don’t complain. It’s fine.”

But there are lots of reasons a student might not complain when a teacher doesn’t follow the rules. A student may not want to publicly confess to poor eyesight in demanding that a teacher turn the lights on; a student who already has two tests on Friday may not want to risk upsetting classmates who would be happy if the teacher breaks the rules and gives them a quiz that day; a student may not want to risk possible retribution from a teacher by pointing out they aren’t following school policy when it comes to assigning homework.

Students exist on the wrong side of a perpetual imbalance of power in the classroom. Challenging authority is especially difficult under such circumstances, and in cases like this, students shouldn’t have to. We adopt rules and policies to protect student interests precisely because we know that young students aren’t always able to advocate for themselves. It shouldn’t be a student’s responsibility to make sure teachers follow the rules. It’s our responsibility, and our job, to follow them, even if we think no one will complain if we don’t.

Books I Read in 2017

I read a lot of books in 2017, as part of a concerted effort to find healthier ways to spend time. I’d say it was a success! Here are some of the books that made an impact on me this past year.

Math

Genius at Play, by Siobhan Roberts

I enjoyed this biography of the mathematician John H. Conway, which includes so many lengthy quotations that it often feels like a dialogue between the subject and the author. At times, it even feels like an autobiographical soliloquy, which I gather is not uncommon for Conway. The book covers lots of great math, too, which Roberts presents in an engaging and inviting way.

How to Bake Pi, by Eugenia Cheng

A fun, general-audience book exploring the author’s parallel passions for cooking and mathematics. And a gentle introduction to category theory, to boot!

Teaching and Learning

Why Don’t Students Like School?, by Daniel Willingham

An overview of how some key results from cognitive science can inform effective teaching and learning. A book for practitioners, and a valuable read for teachers of any subject.

The Teacher Wars, by Dana Goldstein

A brief history of the teaching profession in the United States. I was surprised to learn that so many cornerstones of modern educational policy debate–tenure, training, curriculum, pay–have been argued about in much the same ways for over 100 years. An eye-opening read for teachers, and invaluable to those interested in framing current education policy in historical context.

Non-Fiction

The Girl with Seven Names, by Hyeonseo Lee

The fast-paced, harrowing tale of a young woman’s journey out of North Korea, full of twists, turns, and a good deal of sympathy for her homeland. An engaging and poignant look at a mysterious country through one person’s eyes.

China’s Second Continent, by Howard French

A journalist with deep connections to both lands explores the aggressive and strategic wave of Chinese immigration to Africa over the past 30 years. As someone who lived in China and wanted to learn more about modern Africa, it was a perfect fit for me.

Science Fiction

Old Man’s War, by John Scalzi

I ended up reading a lot of science fiction, and it started with this series from John Scalzi. Someone suggested that all the sci fi I read was a form of escapism, and it makes sense: these books were definitely a fun escape.

Foundation, by Isaac Asimov

Once I started with sci fi, I quickly gravitated here, and ended up reading quite a bit of Asimov in 2017. Having consumed so much sci fi in other forms (TV, movies), it’s fascinating going back to the source of so many of those themes, story lines, and even technical details. I was frequently taken aback at Asimov’s portrayal of the role of women in the distant future, which reminded me that stories about the future often tell us a lot about the present.

Thanks to these books, authors, and the Brooklyn Public Library, for making my 2017 healthier, happier, and better informed!

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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. * [See Update]

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.

UPDATE, 1/18/2018

In a comment, Brent pointed out that I undercounted the number of semiprimes adjacent to a prime. A recalculation is consistent with Brent’s numbers: among the 108,000 semiprimes up to 500,000, around 4,900 of them are adjacent to prime number. Thanks, Brent!

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