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10/24/2014 — Happy Permutation Day!

Today we celebrate another Permutation Day!  I call days like today permutation days because the digits of the day and month can be rearranged to form the year.


This is the fourth permutation day of of 2014, and there’s one more on its way.

Celebrate Permutation Day by mixing things up!  Try doing things in a different order today.  Just remember, for some operations, order definitely matters!

Common Core and “Who Needs Algebra?”

Every so often, some variant of the question “Is Algebra Necessary?” comes to the fore in our national conversation on math education.

As I’ve written before, conversations like this don’t bother me.  I love math and I love teaching math, but I think the underlying questions here, “How much math, and what math, should everyone be required to know?” , are legitimate and worthy of serious consideration.  The mere fact that it keeps coming up suggests we have great answers to these questions, or even great explanations as to why things are the way they are.

So I’m always interested in pieces like NPR’s “Who Needs Algebra?”, which describes how colleges around the country are trying to address the problems created by algebra requirements.  According to NPR, nearly 50% of community college students fail to graduate because they can not pass a required algebra course.  For this reason, algebra is often called a gatekeeper course, as it prevents access to the credential of a college degree.

As the piece notes, colleges are doing some interesting and innovative things to try to get students around the algebra requirement.  One particular approach, developed by the Community College Pathways initiative, offers statistics and quantitative reasoning courses that “largely skip over abstract algebraic formulas and go directly to math concepts that students will use and find engaging”.  The piece speaks positively about this new approach, which I think has merit and deserves attention.

But I can’t help but wonder how this fits in with the Common Core standards initiative.  The Common Core state math standards mandate a substantial amount of algebra in junior high and high school.  In many cases, this is the same algebra that colleges are attempting to circumvent in order to increase graduation rates.  How can mandatory algebra in high school be reconciled with optional algebra in college?

I think about Common Core, too, when I read about the great work Cornell professor Steven Strogatz is doing in “teaching math to people who think they hate it“.  Strogatz, both a renowned mathematician and teacher, is implementing a curriculum based on Westfield State University’s Discovering the Art of Mathematics, and is finding great success reaching math-averse liberal arts students with its activity- and inquiry-based approach.  But can this type of course, that excites and engages students in authentic mathematics while eschewing the typical trappings of a traditional algebra curriculum, be reconciled with the mandatory algebra standards set forth in the Common Core?  [Strogatz shared some of his informed opinions about math education in his Math Horizons interview last year.]

I don’t believe these various positions are completely incompatible, but I do see a fundamental conflict here.  After all, if a reasonable argument can be made that “Not everyone needs algebra”, then mandating algebra for everyone seems likely to create as many problems as it attempts to solve.

Math Photo: Manhole Math Art

Manhole Math Art

Ever since I noticed this pothole pentagon, I’ve been looking down a lot more.

The lovely mathematical designs on this this manhole cover immediately put me in mind of the labyrinths of Robert Bosch.  And then later I realized this work resembled another piece from a Bridges artist:  Tim Locke’s Starburst.


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.

Math Photo: Pyramid Projection


Naturally, the geometry of this simple piece of playground equipment caught my eye, but the shadows really sparked my interest.

The shadows are the projections of the edges of this pyramid, and they form a set of angles on the ground.  Notice immediately that the largest angle (the shadow formed by the “back” face) is the sum of the other three angles.


There are many other interesting questions to ask, and relationships to explore.  What I was most curious about, however, is how accurately we could locate the sun in the sky based only on this information.