Mr Honner

Roundtable Discussion on Math Education in the US

This Thursday I’ll be participating in a roundtable discussion on math education in the U.S hosted by the National Museum of Mathematics. Panelists include Sol Friedberg (chair of the National Academy of Science’s Commission on Math Instruction), Lorraine Howard (President of Women and Mathematics Education), Edna Jones (Math PhD student and MS math educator) and John Staley (part president of NASM and former chair of the U.S. National Commission on Math Instruction).

This on-line event is happening Thursday, July 29th at 6:30 PM. More information, including registration details, can be found here.

By MrHonner, 5 yearsJuly 27, 2021 ago

How to Find Rational Points Like Your Job Depends On It — Quanta Magazine

My latest column for Quanta Magazine begins with a story from my past.

You’re sitting at the end of a long conference table, interviewing for your dream job. You’ve made it this far, but there’s just one more question you have to answer.
“Is it possible for a line that passes through the origin to pass through no other rational points?”
Five pairs of intense eyes watch you, waiting for your response. Do you get the job?

The simple challenge of finding rational points on lines leads to a more interesting property of rational points on circles, which ultimately lands us in the fascinating world of elliptic curves, which are essential in modern cryptography and were instrumental in proving Fermat’s Last Theorem.

The entire article is freely available here.

By MrHonner, 5 yearsJuly 25, 2021 ago

Teaching Writing

Essay on MAA’s MathValues.org

“It’s October, and I have no idea what I’m doing.“

So begins my essay “Let’s Remember the Year Everyone Wants to Forget”, which appears on the Mathematical Association of America‘s website MathValues.org. It’s a reflection on our shared year of pandemic teaching and learning, and it offers something to think about as we look to return to normal.

The essay draws heavily from my weekly reflections on remote and hybrid learning, and I’m happy to have to opportunity to share it with the MAA. You can read the piece here.

Art Photography

Math Photo: Spherical Garden

Here’s a lovely art installation at the top of Prospect Park in Brooklyn. This is Public Water from Mary Mattingly, and you can learn more here. I wonder what kind of relationship this artist has with mathematics.

Teaching Testing

Regents Recap, January 2020: Isn’t the Quadratic Formula Completing the Square?

Completing the square is one of those mathematical techniques that should be taught but probably shouldn’t be assessed on state exams.

First, when you insist that a student use a specific technique to solve a problem, you penalize flexible and creative thinking. Second, completing the square probably isn’t important enough a problem solving technique to warrant its yearly appearance on the New York State Algebra 1 exam.

Of course, the one situation in which completing the square is absolutely indispensable is in deriving the quadratic formula. Which makes this sample student response from the exam’s official scoring materials a bit puzzling.

The student lost a point because, instead of completing the square, they used the quadratic formula to solve this equation. But the whole point of the quadratic formula is that it completes the square for every trinomial. The quadratic formula is completing the square.

As I clarified in comments on Twitter, I find this more amusing than objectionable. But these little windows into the testing process often tell us more about what is valued and understood than test scores themselves.

Roundtable Discussion on Math Education in the US

How to Find Rational Points Like Your Job Depends On It — Quanta Magazine

Essay on MAA’s MathValues.org

Math Photo: Spherical Garden

Regents Recap, January 2020: Isn’t the Quadratic Formula Completing the Square?

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