Teaching

2015 — Year in Review

I always enjoy taking time at the end of the year to review my blog. It’s a great way to reflect on what I did and what I was thinking about, and it always reminds me how busy the year was! And 2015 was definitely a busy year.

The Presidential Award

Without a doubt, the highlight of my professional year was being named a recipient of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST).

I traveled to Washington, DC with other awardees to meet with representatives of the National Science Foundation, the National Academies of Science, and the Office of Science and Technology Policy. And the highlight of trip was meeting President Obama at the White House!

The trip to DC was part of an active professional summer. I presented my paper “Monte Carlo Art” at this year’s Bridges Math and Art conference, and the following week I ran a fun workshop called “Games on Graphs” at the MOVES conference at the Museum of Mathematics. At the end of a very busy few weeks, I was surprised to find myself in this terrific New Yorker piece, “Cogito, Ergo, Summer” by Siobhan Roberts!

Speaking

In addition to presenting at Bridges and MOVES this summer, I traveled to Washington, DC earlier this year to speak at a policy briefing hosted by the Mathematical Sciences Research Institute (MSRI) during the first ever National Math Festival. I spoke about building the profession of math teachers, and was a bit intimidated to follow Nancy Pelosi, Harry Reid, and Al Franken! I also ran a variety of workshops on math and technology for teachers, and hosted Math for America’s 4th annual Master Teachers on Teaching, a great evening of talks from MfA Master Teachers.

Teaching

I always try to do new things in my classroom and my school, and 2015 was no exception. I’ve been having fun playing around with 3D-printing in a variety of classes, building demonstrations for geometric ideas, printing hard-to-imagine surfaces, and getting students creating with mathematics. I continue to develop and teach an integrated mathematics and computer science course, and I have taken on a part-time role as our department’s instructional coach.

Writing

For a variety of reasons I write less frequently than I used to, but I did surpass 1,000 total blog posts this past year! My work critiquing the New York State Regents exams continues to get attention, and I was informally consulted for an excellent report by the Center for New York City Affairs about the serious issues facing New York state’s algebra exams that eventually caught the attention of the New York Times. And I continued my work with the New York Times Learning Network, contributing math lessons on evaluating compulsory retirement savings plans and asking students “Why Do Americans Stink at Math?”

So a great year comes to an end, but here’s hoping 2016 is just as challenging, productive, and rewarding!

MT^2 2015

I am excited to be hosting Math for America’s Master Teachers on Teaching (MT^2) event this December 10th at the Gerald D. Fischbaum auditorium.

MT^2 is an evening of short talks from MfA Master Teachers that are meant to inspire and challenge the MfA community. And it is a showcase of the passion and talent of that community, which now numbers nearly 1,000 teachers of math and science in New York City.

This will be the 4th annual MT^2, and the theme is Equality / Inequality. The evening’s lineup features eight talks from middle and high school math and science teachers offering a variety of different interpretations on the theme.

I have given talks in each of the first three MT^2’s: first, on the bad habits students learn from standardized tests; then on my relationship with change; and last year, about how to turn technology’s failures into teachable moments. While I enjoy the challenge of presenting, I am honored to be hosting this year’s event, and I look forward to an evening of great ideas.

And Math for America hopes to live-stream the event, so stay tuned!

By MrHonner, 10 yearsNovember 29, 2015 ago

Teaching Testing

Regents Recap — January 2015: Gravity on the Moon

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

There is something of a history with Regents exams and the force of gravity.

An infamous problem years ago modeled a falling object with the quadratic function

$y = 2x^2 -12x + 10$ .

This would imply that the acceleration due to gravity, or g, would be equal to 4 f/s², not the -32 f/s² we are accustomed to. This amusing error inspired my talk “g = 4, and Other Lies the Test Told Me“.

So, it was interesting to see projectile motion appear twice in the most recent round of math Regents exams. This is from the Integrated Algebra exam.

I was pleasantly surprised to see the proper coefficient!

And then I noticed a second appearance of gravity. This is from the Common Core Algebra exam.

Of course, I had to check. Kudos to the exam writers for looking up the actual force of gravity on the moon. If we’re going to go to the trouble of trying to establish “real world” contexts for these problems, we should make sure physical forces are accurately represented.

By MrHonner, 10 yearsNovember 21, 2015 ago

Resources Student Work Teaching Technology

Student Desmos Projects

Desmos, the free, browser-based graphing utility, has quickly become an indispensable tool in the mathematics classroom. It provides easy, intuitive access to graphs of functions and relations, and creates unique opportunities to understand mathematical relationships dynamically.

But to me, its greatest virtue may be that Desmos provides opportunities to use mathematics to create. I like to think of Desmos as a mathematical makerspace, where the tools at our disposal are exactly the tools of mathematics.

To that end, when I introduce students to Desmos, we always work toward the creation of something mathematical. Below are some beautiful examples of student work from our latest round of Desmos projects.


Varignon’s Theorem	Vector Projections


Angle Bisector Theorem	Three Lines Intersecting

You can find more of my work with Desmos here.

By MrHonner, 10 yearsNovember 10, 2015 ago

Statistics Teaching Testing

Regents Recap — August 2015: Modeling Data

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

Data and statistics play a much bigger role in algebra courses now, due in part to their increased emphasis in the Common Core standards. I am generally supportive of this, but I do worry about how statistical concepts are presented and assessed in these courses and on their exams.

For example, here is question 27 from the August, 2015 Common Core Algebra exam.

Evaluating mathematical models is an extremely important skill in many aspects of life. But properly evaluating mathematical models is subtle and complex.

The following sample response, provided by New York state as an example of an answer deserving of full credit, does not respect that complexity. And it makes me worry about what we are teaching our students about this important topic.

It’s true that the given data does not grow at a constant rate. But that isn’t a good reason to reject a linear model for this set of data. Models are used to approximate data, not represent them perfectly. It would be unusual if a linear model fit a real set of data perfectly.

The weakness of this argument becomes even more apparent when we notice that the data isn’t perfectly fit by an exponential model, either. Therefore, how could it be wrong for a student to say “We should use a linear model, because the data doesn’t grow at a linear rate and thus isn’t exponential”?

This is another example of the problems we are seeing with how statistics concepts are being handled on these high stakes exams, which is a consequence of both the rushed implementation of new standards and an ever-increasing emphasis on high-stakes testing in education. It is also an example of how high-stakes tests often encourage terrible mathematical habits in students, something I address in my talk “g = 4, and Other Lies the Test Told Me“.