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.

 

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Varignon’s Theorem Vector Projections
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Angle Bisector Theorem Three Lines Intersecting

You can find more of my work with Desmos here.

3D Printing in Math Class

We were fortunate to receive a 3D printer for use in our math class midway through the last school year.  Figuring out how it best worked was fun, and often frustrating.

We enjoyed a variety of successes throughout the spring, printing simple surfaces and some complicated ones, too.  It was fascinating to uncover how the printer, and its software and hardware, tackled certain engineering obstacles, like how to print in mid-air!

Ultimately I got comfortable enough to start producing some lesson-specific mathematical objects.  This trio of solids I designed worked perfectly as an introduction to Cavalieri’s principle:  seeing and holding the objects immediately initiated the conversations I wanted students to have.

By the end of the school year, I felt comfortable enough with the process to run our first official student project.  It was fairly open-ended, with options for students, but essentially the idea was to design an object for printing using equations and inequalities.

The project was a success, and here are some of the student designs.
Student 3d Prints

I’m looking forward to exploring some new ideas and projects this year.  It’s clear to me that this technology, which is fundamentally mathematical in concept and design, can play a valuable and meaningful role in math class.

MOVES 2015

MOVES 2015I’m excited to once again be participating in the MOVES conference at the Museum of Mathematics!

MOVES, the Mathematics of Various Entertaining Subjects, is a biennial event run by MoMath that celebrates recreational mathematics.  This year, the conference will be headlined by John Conway, Elwyn Berlekamp, and Richard Guy, co-authors of Winning Ways for Your Mathematical Plays, a classic book on mathematical games.

I’ll be running a session on the Activity Track called Games on Graphs”, where we will explore some elementary graph theory through a few simple graph-based games.   Most importantly, we’ll talk about how to create new games that can further our mathematical investigations!

You can learn more about the conference here, and see the full program here.

Math Photo: Hexagonal Rabbits

Hexagonal Rabbits

The tilling station is one of my favorite exhibits at the Museum of Mathematics.  These rabbit tiles create a hexagonal tiling of the plane.  Pick any rabbit, and you’ll notice six rabbits all around it; this is exactly how hexagons fit together to tile the plane.

What I really like about this tiling is the the various levels of triangles that emerge.  Triangles of rabbits, one of each color, mutually intersect at ears and paws.  And I can’t help but seeing the monochromatic rabbit triangles!

 

Bridges Math and Art 2015

Bridges 2015I am excited to once again be participating in the Bridges Math and Art conference this summer!

The Bridges organization has been hosting this international conference highlighting the connections between art, mathematics, and computer science since 1994.

I have participated in several Bridges conferences, and my experiences there have greatly influenced me as a mathematician and a teacher.

This year, I’ll be presenting a short paper, “Monte Carlo Art Using Scratch“, chairing a short paper session, and exhibiting a photograph in the Bridges Mathematical Art Gallery.

You can view the Bridges 2015 program here, see the entire 2015 Art Exhibit here, and learn more about the conference and the Bridges organization here.

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