How much blue do you see? One-fourteenth is certainly an odd number to see around town.
Appreciation Geometry
9/12/15 — Happy Right Triangle Day!
Happy Right Triangle Day! Today, on 9/12/15, we celebrate a favorite triangle: the 9-12-15 right triangle.
We know this triangle is right because the side lengths satisfy the Pythagorean Theorem.
It’s actually been less than a month since we last celebrated a Right Triangle Day, but they are rare, so enjoy being right today!
Appreciation Teaching
Cogito, Ergo, Summer
I was quite surprised to find myself prominently featured in the New Yorker essay, “Cogito Ergo Summer“, by Siobhan Roberts.
The piece begins ominously:
Patrick Honner, a math teacher at Brooklyn Technical High School, arrived at a recent class seemingly unprepared. This was surprising, given that, days before, he had received a Presidential Award for Excellence in Mathematics and Science Teaching.
“Cogito, Ergo, Summer” is about the important role recreation plays in studying mathematics and science. Summer is a time to relax and have fun, far from the responsibilities of the classroom and lab. But for mathematicians and scientists, it is also a time for serious play.
Roberts experienced this firsthand this summer at both the Bridges Math and Art conference and the MOVES conference at the Museum of Mathematics, where she spoke about her new book “Genius at Play: The Curious Mind of John Horton Conway“. Few know the value of mathematical play as well as Conway, which Roberts clearly captured in her work.
As summer comes to an end, it’s nice to reflect on a busy summer of serious play. And here’s hoping those experiences can fuel us through another busy academic year!
Teaching Testing
Regents Recap — June 2015: Are They Reading?
Here is another installment in my series reviewing the NY State Regents exams in mathematics.
I have been reviewing New York State Math Regents exams for several years now, and I occasionally wonder if anyone involved in the production of the exams pays attention to what I say.
Earlier this year I wrote about a terrible question asking students to justify why the sum of a rational number and an irrational number is irrational. (Answer: because the sum of a rational number and an irrational number is always irrational.)
So I was pleasantly surprised to see this question in the June 2015 Common Core Algebra exam.
This multiple choice question assesses the same concept, but doesn’t ask the student to write a circular explanation as justification. The less these tests ask students to do mathematically meaningless things, the better.
I also had serious complaints about how certain 3D geometry concepts were handled on the June, 2015 Common Core Geometry exam. In particular, a solid of revolution problem was very poorly stated. This question from the August, 2015 Common Core Geometry Regents exam shows some improvement.
It’s also true that recent locus questions have not suffered from the imprecise language I complained about some time ago: in the last few iterations, problems have been more carefully worded to ask students explicitly to sketch individual loci and then indicate their intersection.
In the vastness of these flawed tests, it’s nice to occasionally see some progress.
Appreciation Geometry Teaching
Is Steven Strogatz Writing Regents Exam Questions?
When I saw this question on the 2015 Common Core Geometry Regents exam, I couldn’t help but think of mathematician and author Steven Strogatz.
Strogatz wrote a popular series on math in the New York Times, and in his piece “Take it to the Limit“, he shares a beautiful and intuitive derivation of the formula for the area of a circle. That technique involves slicing the circle up into sectors and re-arranging them into a shape that approximates a rectangle.
I’m certain his piece inspired this question (which I like), just as it inspired me when I was cutting up my homemade pizza!
Maybe we can add test prep to the long list of reasons to be reading Steve’s work!