My May post is more than a little late. The initial delay was caused by a mountain of other deadlines. When I did finally start to come up for air, there just did not seem to be any suitable math stories floating around to riff off, but I did not have enough time to dig around for one. That this has happened so rarely in the twenty years I have been writing Devlin’s Angle (and various other outlets going back to the early 1980s in the UK), that it speaks volumes against the claim you sometimes hear that nothing much happens in the world of mathematics. There is always stuff going on.
Be that as it may, when I woke up this morning and went online, two fascinating stories were
waiting for me. What’s more, they are connected – at least, that’s how I saw them.
First, my Stanford colleague Professor Jo Boaler sent out a group email pointing to a New York
Times article that quoted her, and which, she noted, she helped the author to write. Titled "No
Such Thing as a Math Person," it summarizes the consensus among informed math educators
that mathematical ability is a spectrum. Just like any other human ability. What is more, the
basic math of the K-8 system is well within the capacity of the vast majority of people. Not easy
to master, to be sure; but definitely within most people’s ability. It may be defensible to apply
terms such as “gifted and talented” to higher mathematics (though I will come back to that
momentarily), but basic math is almost entirely a matter of wanting to master it and being
willing to put in the effort. People who say otherwise are either (1) education suppliers trying to
sell products, (2) children who for whatever reason simply do not want to learn and find it
reassuring to convince themselves they just don’t have the gift, or (3) mums and dads who
want to use the term as a parental boast or an excuse.
Unfortunately, the belief that mathematical ability is a “gift” (that you either have or you don’t)
is so well established it is hard to get rid of. Part of the problem is the way it is often taught, as
a collection of rules and procedures, rather than a way of thinking (and a very simplistic one at
that). Today, this is compounded by the rapid changes in society over the past few decades,
that have revolutionized the way mathematics needs to be taught to prepare the new
generation for life in today’s – and tomorrow’s – world. (See my January 1 article in The
Huffington Post, "All The Mathematical Methods I Learned In My University Math Degree
Became Obsolete In My Lifetime," and its follow up article (same date), "Number Sense: the
most important mathematical concept in 21st Century K-12 education.")
With many parents, and not a few teachers, having convinced themselves of the “Math Gift
Myth,” attempts over the past several decades to change that mindset have met with
considerable resistance. If you have such a mindset, it is easy to see what happens in the
educational world around you as confirming it. For instance, one teacher commented on The
New York Times article:
“Excuse me? I'm a teacher and I refute your assertion. I have seen countless individuals who
have problems with math – and some never get it. The same goes for English. But, unless
you've spent years in the classroom, it takes years to fully accept that observation. The article's
writer is a doctor, not a teacher; accomplishment in one field does not necessarily translate
readily to another.”
Others were quick to push back against that comment, with one pointing out that her final
remark surely argues in favor of everyone in the education world keeping up with the latest
scientific research in learning. We are all liable to seek confirmation of our initial biases. And
both teachers and parents are in powerful positions to pass on those biases to a new
generation of math learners.
In her most recent book, Mathematical Mindsets: Unleashing Students' Potential through
Creative Math, Inspiring Messages and Innovative Teaching, Prof Boaler lays out some of the
considerable evidence against the Math Gift Myth, and provides pointers to how to overcome it
in the classroom. The sellout audiences Boaler draws for her talks at teachers conferences
around the world indicates the hunger there is to provide math learning that does not produce
the math-averse, and even math-phobic, citizens we have grown accustomed to.
And so to that second story I came across. Hemant Mehta is a former National Board Certified
high school math teacher in the suburbs of Chicago, where he taught for seven years, who is
arguably best known for his blog The Friendly Atheist. His post on May 22 was titled "Years Later,
the Mother Who 'Audited' an Evolution Exhibit Reflects on the Viral Response." Knowing
Mehta’s work (for the record, I have also been interviewed by him on his education-related
podcast), that title hooked me at first glance. I could not resist diving in.
As with The New York Times article I led off with, Mehta’s post is brief and to the point, so I
won’t attempt to summarize it here. Like Mehta, as an experienced educator I know that it
requires real effort, and courage, to take apart ones beliefs and assumptions, when faced with
contrary evidence, and then to reason oneself to a new understanding. So I side with him in not
in any way trying to diminish the individual who made the two videos he comments on. What
we can do, is use her videos to observe how difficult it can be to make that leap from
interpreting seemingly nonsensical and mutually contradictory evidence from within our
(current!) belief system, to seeing it from a new viewpoint from which it all makes perfect
sense – to rise above the trees to view the forest, if you will. The video lady cannot do that, and
assumes no one else can either.
Finally, what about my claim that post K-12 mathematics may be beyond the reach of many
individuals’ innate capacity for progression along that spectrum I referred to? Of course, it
depends on what you mean by “many”. Leaving that aside, however, if someone, for whatever
reason, develops a passionate interest in mathematics, how far can they go? I don’t know.
Based on a sample size of one, me, we can go further than we think. I look at the achievement
of mathematicians such as Andrew Wiles or Terrence Tao and experience the same degree of
their being from a different species as the keen-amateur- cyclist-me feels when I see the likes of
Tour de France winner Chris Froome or World Champion Peter Sagan climb mountains at twice
the speed I can sustain.
Yet, on a number of occasions where I failed to solve a mathematics problem I had been
working on for months and sometimes years, when someone else did solve it, my first reaction
was, “Oh no, I was so close. If only I had tried just a tiny bit harder!” Not always, to be sure. Not
infrequently, I was convinced I would never have found the solution. But I got within a
hairsbreadth on enough occasions to realize that with more effort I could have done better
than I did. (I have the same experience with cycling, but there I do not have a particular desire
to aim for the top.)
In other words, all my experience in mathematics tells me I do not have an absolute ability
limit. Nor, I am sure, do you. Mathematical proficiency is indeed a spectrum. We can all do
better – if we want to. That, surely is the message we educators should be telling our students,
be they in the K-8 classroom or the postgraduate seminar room.
Gifted and talented? Time to recognize that as an educational equivalent of the Flat Earth
Belief. Sure, we are surrounded by seemingly overwhelming daily experience that the world is
flat. But it isn’t. And once you accept that, guess what? From a new perspective, you start to
see supporting evidence for the Earth being spherical.