Tag Archives: relevance

What I believe now

Turns out, things are simpler than I thought.

I used to think that education and schooling was an unimaginably complex system.  I used to think that because no two people and no two brains and no two circumstances are alike, education, which is a fundamentally human endeavor, was essentially un-replicable.  You couldn’t do it the same way twice.  And you couldn’t predict outcomes (because the starting conditions were so varied).  And you couldn’t plan for it with any real surety because the fact that learning ever happened at all, was a miracle, so unlikely as to be unexplainable and totally unique.  Like magic.

I think I used to think that teaching was magic in some way.  Like prestidigitation.  Conjuring.  Alchemy.

Don’t get me wrong, learning still impresses the hell out of me.  Sometimes, I will be watching something simple happening – my son learning to juggle, my daughter taking free throws – and I still find myself in awe.  She misses the first 3, makes 2 of the next 4, and then makes 3 in a row – and I find myself in total disbelief.  What the hell just happened?  I mean, actually.  Literally, what changed?

Learning makes things different now than they were before.  And that is like magic.

So I am still impressed with what learning is and how fast it happens, but the conditions necessary for learning no longer seem unknowable or mysterious.  Whereas once, I thought what conjured learning in each individual was unique, I now believe that there are only a handful of design principles that set the conditions under which learning happens:

  • Relevance
  • Utility
  • Connectedness
  • Competence
  • Autonomy

Each has subtlety and nuance, and I will try to break it down for you.

Is Math Relevant?

Math is coming under attack recently at education conferences, in the literature, and in conversations about school reform.  Fully half of the subject-specific workshops at a recent California Association of Independent Schools conference were about math.  Relevance, engagement, projects – all of the presentations in one way or another sought to justify the teaching of math at the high school level.  In question is whether high school students really need all the math they get in the typical high school curriculum.  Is trigonometry useful for the average high school student?  Maybe.  What about calculus?  That one is a little harder, testing even dyed-in-the-wool math teachers, most of whom concede eventually that calculus in high school is more about the challenge than its usefulness to life.

How much math is enough math and what is its value beyond a facility with numbers and quantities?  If you had the resources to offer either a calculus class or a statistics class but not both, how would you choose?  And just under the surface is a deeper question, is a subject’s connection to the real world, what we are calling real-world application, the highest value in school curriculum?

It seems it is.  Or is becoming so.  There are strong calls lately for a new three R’s – Rigor, Relevance, and Relationships.  There are high school programs emerging all over that incorporate job skills, internships, and real-world learning.  Linked Learning, which has its origins in what used to be known as Vocational Training (i.e.: shop class), is a wonderful and long overdue evolution of Career Technical Education.  Linked Learning is a comprehensive, pathways-based approach to learning in the world that creates a meaningful and mutually educative partnership between school and career by involving students in internships and working with schools to create programming that supports their experiences.  One of their mottos is, “Life comes to school.”

So relevance is playing a larger role in high school education.  And that makes math teachers nervous.

For many educators, many of whom are now in positions to affect high school curricula, math in high school was an interminable series of puzzles that neither had nor claimed to have relevance in the world outside of math class.  At best it was amusing.  At worst, dehumanizing.   But regardless of whether one liked it or not, it was unapologetically divested from the world outside.

“Solve for x,” we were told.

“X what?  What is x?” we all thought and some of us asked.

“No, no,” we were told.  “X isn’t something.  It isn’t anything.  Its a quantity of whatever.”

And I need to solve for it?  Even though it isn’t anything, doesn’t intend to be anything, has no basis in life or reality?  We aren’t talking about apples or oranges, not slices of pie or distances between stars.  We are not talking about anything identifiable or recognizable.  It is a pure abstraction.  Do I have that right?

For many that is a hard truth.  Add to that the fact that for most students the advanced topics in math will never be used and you can see the argument for math’s irrelevance in high school.

What do math teachers say?  I recently sat with a great group of inspired and inspiring colleagues, most of them math teachers, in a workshop that touched on these topics.  What is mathematics?  What is mathematical thinking?  What is the argument for math in high school?  The workshop put us into the shoes of students and walked us through a lesson designed to help us identify and recognize mathematical thinking in ourselves and our students.  The math challenge – or puzzle – was to figure out how many squares can be made with twelve straight lines.  And from there we went on to wonder and explore what we could understand about lines and squares.  Was there a relationship between the number of lines and the number of squares?  Could we generate an equation?

It was an engaging lesson, no question.  We enjoyed the challenge and it felt fun to do the math, work creatively in a small group of interested folks, and feel like we were figuring something out.  And when the question came up, “So, beyond the fun, what is the application for this in the world outside of math class?” things got a little dicey.

“Why isn’t fun enough of a justification?” was one response.

“Not everything in math has a real-world application,” came another.

“They are learning how to think.”

There was some genuine defensiveness in the room.  Also a great deal of compassion.  And I did feel some pity for the poor, recovering, misunderstanding English teacher for whom the deeper relevance of finding squares with lines remained elusive.  But we had been encouraged at this conference to “go hard on the content, easy on the people” so I persisted in spite of my better judgement and strong internal messaging that to back away slowly.

In the end, the workshop ended and I had the familiar feeling of being pitied for my ignorance.  As I began to scratch some feedback for the presenter on the back of a handout, I felt one of my table mates lean in.  I stopped writing and scanned my peripheral vision.  What was about to happen?  My eyes wandered up and met hers.  She was grinning at me.

What ensued was a wonderful and very helpful 45-minute conversation that went from real world utility of math to conferences to education to what we believe most about students and learning – and finally to three of the biggest concepts out there: truth, beauty, and goodness – three things that need no further justification.

The study of math, she proposed, has a grander relevance than simply utility.  We do math, she said, like we play piano.  Because it is beautiful.  Not because it is useful.  A simple, elegant solution to a problem is beautiful.  A relationship between numbers that proves true in all cases is beautiful.  Math, she said, is much more like art than tooth brushing.

And truly, for the first time, I got it.  Beauty, truth, and goodness – these are things I get and I look for them in all worthy endeavors.

So, what I understand now is that math does have a real-world relevance – it is beauty (and truth, maybe not goodness).  Beauty is relevant, in and of itself.  Like art.  And that, I think, is that much stronger argument in favor of math than the somethings-just-don’t-connect line.  Math teachers should stop saying that fun is enough of a justification for math.  It isn’t.  There is no other subject in high school or education at any level that is comfortable relying solely on fun as its reason for being.  Fun is wonderful – anyone who knows me knows that I go for fun at the expense of productivity too often.  But it is not enough to justify a high school curriculum.  And math teachers should stop saying that not all math needs a real world application.  It does.  To spend time doing it, it has to have relevance.  No question.

The challenge then is to recast math as relevant in grander and more subtle ways.  It is relevant not because you use it all the time.  Most people don’t.  Math is relevant because it is elegant truth.  Math is beautiful.