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Mashable: In Defense of Math

mashable artI had fun contributing to this Mashable piece, “In Defense of Math:  7 Reasons Numbers Rule“.

I, and a few other Math for America master teachers, were asked to pitch some ideas for a light-hearted refutation of the all-too-common “I hate Math!” refrain.

A couple of my ideas made it in, and I doubt it’s hard to figure out which were mine.  In any event, it should be easy to identify a couple that definitely weren’t mine.

A bit goofy, but all in good fun!

Writing in Math Class: Favorite Shape

favorite shapesI love giving short writing assignments to my math classes.  It’s a great way to get students engaged in mathematics in a different way, and it gives me a different window into how my students think and who they are.

Here’s a prompt I gave them recently.

Draw a shape that you like.  Write 1-2 complete sentences explaining what this shape is and why it appeals to you.

This simple prompt was something of an afterthought on a recent assignment, but as usual, the students surprised me with their responses.  Here are some of my favorites.

I like the square because of how organized it is.

The triangle appeals to me because it is the shape of things I love to eat, like a slice of pizza or a piece of cake or pie.

A rhombus is different from other shapes, but so alike.  It shows how a little change can make a new shape.

Circles appeal to me because they have infinite lines of symmetry.

This is a circle.  It has no corners and is symmetrical.  This shape is appealing because it feels open, and since there are no corners, there are no sharp edges to hurt you.

This shape is a circle.  It appeals to me because, as weird as it sounds, I want my life to be as perfect and as well-rounded as a circle.

A triangle is simple.  It has the least number of sides a polygon needs.

I like the square because I like things to be equal, not different.

I’m always smiling, laughing, and thinking after reading what students have to write.  There are lots of great reasons to get students writing in math class, so give it a try!  You can find more resources here.

3D Printing in Calculus Class

I’m looking forward to exploring 3D printing in Calculus class this year.  We don’t have a printer in our classroom (yet!), but some students have enough experience and access to work on modest projects outside of class.

Here’s a print of an interesting surface in xyz-coordinate space.

Beautiful Surface and Printed SurfaceIt’s always exciting to find a new way to represent or experience a mathematical idea, and physical representations can be especially powerful.

And perhaps more importantly, 3D printing gives students an opportunity to use mathematics to create.  Mathematics is a creative endeavor, and whatever helps promote this idea will ultimately help change attitudes about math.


George Hart Workshop on Symmetry

Through Math for America, I had the pleasure of participating in a one-day workshop on symmetry led by well-known mathematician/computer scientist/sculptor George Hart.  The workshop featured some great math and some excellent hands-on projects that really had us exploring some deep mathematical ideas.

We began the day by talking a bit about what symmetry is and the types of symmetries we’re accustomed to thinking about.  Then we explored how the symmetries of a given object, when thought of as actions (like reflections or rotations), form a group, which creates an interesting mathematical structure to work with.

After the introductory mathematics, George led us through three hands-on activities meant to explore different symmetry groups.

The first project was building a Tunnel Cube from a set of pre-cut playing cards.  The 12 cards were notched in such a way that the piece could be assembled without any glue or tape.

Tunnel Cube

It did, however, require a great deal of dexterity and patience!  You can see George’s explanation of the Tunnel Cube here, and watch a video in which he assembles it here.

The second project was building a ruled hyperboloid using kebab skewers and rubber bands.

Ruled Hyperboloid

The last project was a group build, where we assembled a George Hart original sculpture.  This was a bit harder than I imagined, but the process was full of the small frustrations and successes that good collaborative work entails.

George Hart Sculpture

In addition to the fun project ideas, the big takeaway for me was using symmetry as a design parameter.  While we assembled, and then admired, the final sculpture, George talked a little bit about his creative process.  By thinking first of symmetries, and symmetry groups in particular, he outlines a design space for a particular piece, and then starts playing around in that space until he finds what he’s looking for.  Each of the projects emphasized that idea with a different symmetry group.

Many thanks to George Hart, and Math for America, for an enriching day!  You can see more pictures from the workshop here.

Math Photo: Concentric Octagons

Concentric Octagons

There’s something especially appealing, and uncommon, about these concentric octagons.  I like the isosceles triangles radiating outward, and the pairs of perpendicular lines that meet at the center.