Teaching

Full Interview with Steven Strogatz Freely Available

My complete interview with Steven Strogatz in the February 2014 issue of Math Horizons is now freely available.

Math Horizons makes one article from each issue freely available online, and I’m thrilled that for the February 2014 issue they chose my piece. Professor Strogatz is an acclaimed mathematician, writer, and teacher, and I think this interview captures a small amount of his enthusiasm, insight, and brilliance in all these fields.

The full interview is available as a PDF here. You can also find our conversation about math education in the Aftermath section of the magazine (posted online here), as well as some bonus material from our conversation here.

By MrHonner, 12 yearsApril 18, 2014 ago

Balancing Act

We’ve been discussing center of mass in class recently. While this powerful idea extends well beyond its physical interpretation, it’s good to frame the conversation around the idea of balancing objects on their centroids.

One student was inspired by the claim that all physical objects have centroids, and that they can be found fairly easily. So he took a small plate of aluminum, drilled a bunch of random holes in it, and tried to find its center of mass.

He claimed he had done it. But how could we test his hypothesis? It seemed like there was only one way!

It took us a while, and a few attempts, but we were able to do it! It created a nice little challenge for us, and a nice physical experience with the center of mass.

By MrHonner, 12 yearsApril 7, 2014 ago

Teaching Testing

This is Not an Exponential Function

A question from the January 2014 Integrated Algebra Regents exam asks students to identify a graph showing exponential decay. This graph was the correct choice.

We regularly see terrible graphs on these exams: non-trigonmetric trig functions, functions intersecting their vertical asymptotes, and unscaled coordinate systems. So it comes as no surprise that this graph is not actually the graph of an exponential function!

First, note that all exponential functions have the form $y = C a ^{kx}$ . Since this graph passes through the point (0,4), we immediately see that $C = 4$ .

Note also that the graph passes through the point (2,1). Thus, $y(2) = 4 a ^{2k} = 1$ . We can now use this information to compute $y(1)$ .

Since $4 a ^{2k} = 1$ , we see $a^{2k} = \frac{1}{4}$ . But $a^{2k} = (a^{k})^{2}$ , and so $(a^{k} )^{2} = \frac{1}{4}$ .

Taking the square root of both sides, we see that $a^{k} = \pm \frac{1}{2}$ . Assuming $a > 0$ , we have $a^{k} = \frac{1}{2}$ , and so $4a^{k} = 2$ . But $y(1) = 4 a ^{k}$ , so we now know that $y(1) = 2$ .

Notice, however, that the graph does not pass through the point (1,2)! Thus, this is not the graph of an exponential function.

NYT Probability Resources Teaching

Teaching Math Through March Madness

My latest piece for the New York Times Learning Network leverages March Madness to explore some basic ideas in counting and probability.

Begin by having students explore how to count the number of possible brackets. Start by analyzing a four-team bracket, say, with Team A playing Team B and Team C playing Team D in the first round. Have the students directly list the eight possible tournament outcomes: For example, A beats B, D beats C, and then D beats A is one such outcome. The use of tree diagrams may be helpful in representing the possible brackets.

Then ask students to predict and explore how many brackets are possible with an eight-team tournament. There are 2 raised to the 7th power, or 128, such brackets. One way to see this is first by noting that eight teams in a single-elimination tournament will end up playing seven total games: Seven of the eight teams must be eliminated, which requires that they lose a game.

I’m glad I could make a small contribution to the Math Madness surrounding March Madness! You can find the entire lesson here.

By MrHonner, 12 yearsMarch 20, 2014 ago

Teaching

Speaking at NYSMATYC

I’m excited to be speaking at the upcoming conference of the New York State Mathematics Association of Two-Year Colleges (NYSMATYC) .

The NYSMATYC is the country’s oldest professional organization devoted to mathematics and two-year colleges. The NYSMATYC focuses on supporting mathematics teachers and students at two-year colleges across New York state through publications, awards, scholarships, and regional conferences.

The theme of this year’s conference is “The Career Journey” and runs April 4th-6th. I’ll be giving the banquet keynote address on Saturday night, where I’ll be talking about my own career journey and offering my thoughts on the rapidly evolving landscape of of mathematics education.

You can find out more about the organization and the conference at the NYSMATYC website.

By MrHonner, 12 yearsMarch 18, 2014 ago

Full Interview with Steven Strogatz Freely Available

Balancing Act

This is Not an Exponential Function

Teaching Math Through March Madness

Speaking at NYSMATYC

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