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Cogito, Ergo, Summer

cogito ergo summerI 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!

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.

2015 CC ALG 8

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.

2015 August CC GEO 3

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.

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.

2015 CC GEO 23

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.

Circle with many slices

I’m certain his piece inspired this question (which I like), just as it inspired me when I was cutting up my homemade pizza!

Pizza Rectangle

Maybe we can add test prep to the long list of reasons to be reading Steve’s work!

8/17/15: Happy Right Triangle Day!

It’s 8/17/15, or as I like to think of it, Right Triangle Day!

8-15-17 Triangle


8^2 + 15^2 = 17^2

we know that 8, 15, and 17 are the lengths of the sides of a right triangle.  Informally, we say this is true because of the Pythagorean Theorem, but technically it’s true because of the converse of the Pythagorean Theorem.

It’s been a while since we’ve celebrated a Right Triangle day, and it won’t be long before we get to celebrate another.  To commemorate this numerical novelty, the Museum of Mathematics is teaming up with the Pacific Science Center to pythagorize Seattle’s Triangle Pub.  They certainly had fun pythagorizing the Flatiron building in NYC on 5/12/13!

Enjoy being right today!

Regents Recap — June 2015: Pointless Questions

Here is another installment in my series reviewing the NY State Regents exams in mathematics.

I really do not understand the point of questions like this, from the June 2015 Geometry Regents exam.

2015 GEO 12Why do we manufacture artificial multiple choice questions to assess whether or not students understands geometric constructions?  Why not just ask them to construct something?

Moreover, the construction aspect of this question is essentially irrelevant:  the question might as well be, “Which diagram shows an altitude?”.

The Regents exam writers have been using this approach in testing geometric constructions for some time.  It just seems pointless to me.  And it is often the case that the exam also includes a free-response question that asks the student to actually construct something with a compass, which makes this multiple choice question both pointless and redundant.

Much is made about the importance of testing when it comes to student learning and teacher accountability.  But such arguments seem less reasonable the more closely we look at what we test and how we test it.