Did No One Care About Seth Godin?

In his typically direct style, Seth Godin’s “Good at Math” purports to rebuke the common belief that if you’re not a math person then you’re destined to never be good at math. This is indeed a destructive attitude, and one we should work to dispel.

Unfortunately, Godin’s piece takes an all too familiar turn. If not genetics, Godin wonders, then what has prevented you from learning math?

If you’re not good at math, it’s not because of your genes. It’s because you haven’t had a math teacher who cared enough to teach you math. They’ve probably been teaching you to memorize formulas and to be good at math tests instead.

To Seth Godin, the answer is simple: Bad teachers. And not just incompetent bad, but uncaring bad.

This claim is ridiculous.

First, most teachers care quite a lot about what they do, and whom they serve. Saying that students don’t learn because teachers don’t care is not only insulting, but it demonstrates a fundamental disconnect with the reality of who teachers are and what they do.

Second, there are many reasons why someone might not master math in school. Math is hard. Learning is hard. Teaching is hard. And even when teacher and student both care deeply, learning doesn’t always happen on schedule.

And if you want to criticize teachers for teaching students to be good at math tests, fine, but know that this is often exactly what teachers are told to do, directly or indirectly. This can be completely consistent with a teacher caring about their work and their students.

Lastly, there’s no point in telling people not to blame their genes if you’re just going to tell them to blame something else that’s largely out of their control. Blaming teachers won’t empower anyone to learn math; it just shifts the blame to a more convenient target. If anything, this argument reinforces the sense of powerlessness that struggling students often feel. At least Godin makes his attitude explicit: It’s far more common in today’s discourse to merely imply that teachers are an obstacle to improvement. Often, it’s simply an unstated assumption.

What would Seth Godin tell a struggling piano student who feels they simply aren’t a “music person”? Is this student not a good piano player because no teacher cared enough to really teach them piano? I suspect anyone who knows how hard it is to learn to play the piano would laugh at such a response. Is anyone laughing at this characterization of math teachers?

The work of a teacher is hard, and teachers work hard. And they care. Blaming teachers for all learning failures is simple-minded and impractical. No attempt to improve education will succeed if it is based on the premise that teachers are incompetent or uncaring, and that students are passive or powerless.

You can read Seth Godin’s piece here. And math educator David Coffey has written a nice response here.

Demonstration of Linear Independence

vectors spanning the plane

I’ve put together a simple Desmos interactive that demonstrates the basic ideas of linear independence.

If two plane vectors are linearly independent, then every vector in the plane can be written as a linear combination of those two vectors.  Those two vectors span the plane.

By playing around with the sliders in this interactive, you can see how every vector in the plane can be expressed as a linear combination of the two original vectors.

Moreover, if you make the two original vectors parallel, they no longer span the plane.  That’s because the two original vectors are now linearly dependent!  Each is a linear combination (in this case, a scalar multiple) of the other.

You can see this Desmos interactive here, and you can find more of my Desmos-based demonstrations here.

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.

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