MfA Workshop – A Crash Course in Geogebra

Today I’ll be facilitating “A Crash Course in Geogebra” as part of Math for America‘s summer professional development series.

In response to the challenges and uncertainty of the upcoming school year, MfA teachers have been sharing ideas and expertise with the community this summer. My experiences using Geogebra during NYC’s emergency remote learning led me to develop this workshop.

Geogebra is an invaluable tool for doing mathematics under normal circumstances, but its versatility as a mathematics environment, a demonstration tool, and an assessment platform is even more important in this era of remote and hybrid learning. In addition to reviewing the basics of Geogebra in the webinar, I’ll also share specific classroom strategies and student project ideas for implementation in either face-to-face or remote/hybrid learning.

As I said recently, I can’t imagine teaching geometry remotely without Geogebra. And while I can imagine teaching geometry face-to-face without it, I wouldn’t want to!

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Coding Math at a Distance — #NCTM100

I’m excited to be co-presenting “Coding Math at a Distance” this week as part of NCTM’s 100 Days of Professional Learning webinar series.

I’ll be working with Mike Larson and Ashley Goetz, the teachers who co-founded CSandMath.org, and our webinar focuses on simple ways teachers can use computer science to enrich math learning. Mike, Ashley, and I have all been involved in this work for many years, and we’re excited to share both big ideas and classroom-ready resources for teachers.

We’ll pay particular attention to the ways in which integrating CS and math makes sense for remote and hybrid learning environments. We know teachers are looking for new approaches to engagement, assessment, and collaboration in this era of remote learning, and integrated math and CS projects offer lots of exciting opportunities, for both teachers and students.

The webinar is free and part of NCTM’s centennial celebration. You can find out more, and register, here. You can also access resources from our session: Our takeaway document; a Scratch studio that includes code examples; and a set of function-based extension projects.

UPDATE: The full webinar has been posted on the NCTM website.

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AMS Math in the Media — Interview

I was recently interviewed for the American Mathematical Society’s Math in the Media column, in which I answer some questions my Quanta Magazine column and about writing about math for the public. I was asked specifically about my column on the universal covering problem.

Why did you recently choose to write about the universal covering problem?
It’s such a fun mathematical story to tell, with meaningful connections to high school geometry. And there’s something uniquely mathematical about studying a shape for a hundred years and still not knowing exactly what it looks like. I enjoy bringing those experiences to others.

The rest of the short interview can be found here.

The Math of Social Distancing is a Lesson in Geometry — Quanta Magazine

My latest column for Quanta Magazine connects the geometry of social distancing, a topic on everyone’s mind right now, with sphere packing, a problem mathematicians have been working on for hundreds of years.

Determining how to safely reopen buildings and public spaces under social distancing is in part an exercise in geometry: If each person must keep six feet away from everyone else, then figuring out how many people can sit in a classroom or a dining room is a question about packing non-overlapping circles into floor plans.

In two dimensions, the sphere packing problem is really the circle packing problem, and the best way to pack circles in the plane is known. But it was only recently that mathematicians settled the question about how to most efficiently pack spheres in dimensions 8 and 24. And there are still many open questions in other dimensions!

You can read the entire article here.

To Win This Numbers Game, Learn to Avoid Making Math Patterns — Quanta Magazine

My latest column for Quanta Magazine starts with a simple game of numbers and ends with some unsolved problems in mathematics.

For example, let’s change the rules to make the loser the first person to complete three in a row of any step size. This means you lose if you make 2-3-4, as in the original game, but also if you make 1-3-5 (three in a row of step size 2) or 1-4-7 (step size 3). These patterns are “arithmetic progressions”: sequences of numbers with a common step size, called the common difference.
Let’s return to our first game board and use the new rules. It’s still your turn. And you’ve lost.

This simple game, where each player tries to avoid completing an arithmetic progression, leads to some complicated math, involving open questions about Salem-Spencer sets and a new result about polynomial sequences.

The full article is available here and includes several exercises to test your game play!

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