Teaching

Next week I’ll be visiting Rutgers University to give a talk about communicating mathematics. I’ll be presenting “Math Outside the Bubble” to the Graduate Student Chapter of the American Mathematical Society on Monday, 3/2.

I’m excited to share some of what I’ve learned in my career communicating mathematics to students, parents, and educators through my work as a teacher, as well as to the public through my writing and mathematical outreach. It’s wonderful to know that math students at the beginning of their careers are thinking about the role communication plays in the field. It’s an undervalued, but increasingly critical component of the work.

Update: A recap of the event and some pictures are posted on the Rutgers AMS website here.

By MrHonner, 5 years5 years ago

Numbers Resources Teaching

Good Cube Hunting — Quanta Magazine

My latest column for Quanta Magazine is about the search for sums of cubes. While most integers are neither cubes nor the sum of two cubes, it is conjectured that most numbers can be written as the sum of three cubes. Finding those three cubes, however, can be a challenge.

For example, it was only this year we learned that the number 33 could be written as a sum of three cubes:

33 = 8,866,128,975,287,528³ + (−8,778,405,442,862,239)³ + (−2,736,111,468,807,040)³

What’s so hard about expressing numbers as a sum of three cubes?

It’s not hard to see that it combines the limited choices of the sum-of-squares problem with the infinite search space of the sum-of-integers problem. As with the squares, not every number is a cube. We can use numbers like 1 = 1³, 8 = 2³ and 125 = 5³, but we can never use 2, 3, 4, 10, 108 or most other numbers. But unlike squares, perfect cubes can be negative — for example, (-2)³ = -8, and (-4)³ = -64 — which means we can decrease our sum if we need to. This access to negative numbers gives us unlimited options for our sum, meaning that our search space, as in the sum-of-integers problem, is unbounded.

To learn more, read the full article, which is freely available here.

By MrHonner, 5 years5 years ago

Resources Teaching Technology

MfA Workshop — Computational Thinking

Tonight I’ll be running a workshop for teachers titled “Building Bridges Through Computational Thinking.”

In the workshop we’ll explore the mathematical and pedagogical benefits in taking a computational approach to mathematics. Through a variety of computational thinking tasks spanning different branches of math, we’ll see how these tasks offer alternate pathways into mathematical ideas, genuine engagement in applied mathematics and mathematical modeling, and opportunities for rich pedagogical variety.

This work is a natural continuation of the work I’ve been doing at the intersection of mathematics and computer science education for the past several years. As always, I’m grateful to be supported by Math for America and MfA’s teacher community in developing and trying out new ideas for students and teachers.

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By MrHonner, 5 years5 years ago

Resources Teaching

Global Math Department Webinar

On Tuesday, October 8th, I’ll be hosting a webinar for the Global Math Department, a volunteer organization run by math teachers for math teachers. The Global Math Department produces weekly webinars and newsletters that share what math teachers around the world are doing in and out of the classroom.

I’ll be hosting “A Computational Approach to Functions”, my latest talk at the intersection of mathematics and computer science education. Here’s the description:

Looking for a new approach to teaching domain and range? Or an opportunity for students to use their crossover computer science skills? Taking a computational approach to functions allows for the rigorous development of all the fundamental concepts in an active and creative way, while at the same time offering endless opportunities to extend deeper into both mathematics and computer science. If you teach about functions—and what math teacher doesn’t?—you will leave with something new to think about for your math classroom.

The webinar is free and will run from 9 – 10 pm, and a recording will be available after the fact for those unable to attend live. You can find out more information, and register, here.

UPDATE: The full video of the webinar has been posted here.

By MrHonner, 5 years5 years ago

Numbers Resources Teaching

On Your Mark, Get Set, Multiply — Quanta Magazine

Did you get caught up in the latest viral math problem, 8÷2(2+2)?

The problem here is simply how we interpret the division symbol. Does ÷ mean divide by the one number right after it or by everything after it? This isn’t much of a concern for most mathematicians, as they don’t use this symbol very often. Ask them to solve this problem and they’ll probably just make the whole thing into a multiplication problem: Once you choose to write it as either
$8 \times \frac{1}{2} \times (2 + 2)$ or $8 \times \frac{1}{2(2+2)}$ ,
the ambiguity is gone and the answer is clear. As a multiplication question, this isn’t particularly interesting.
But one multiplication question mathematicians do find interesting may surprise you: What is the best way to multiply?

And what is the best way to multiply? The answer may surprise you! Find out by reading my latest column for Quanta Magazine, freely available here.

By MrHonner, 5 years5 years ago

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