I gave a short course at a local high school recently. Three days in a row, two hours a day, to fifteen students. To my mind, it was a huge success. By the end of the course, the students had successfully reverse-engineered UPS’s core routing/scheduling algorithm. In fact, they spent the last half hour brainstorming how UPS might improve their efficiency. (My guess is the company had long ago implemented, or at least considered, the ideas the kids came up with, but that simply serves to illustrate how far they had come in just six hours of class-time.)
To be sure, it was not an average class in an average high school. Nueva School, located in the
northern reaches of Silicon Valley, is private and expensive (tuition runs at $36,750 for an 8th gader), and caters to students who have already shown themselves to be high achievers.
Many Silicon Valley tech luminaries send their children there, and some serve on the board.
They have an excellent faculty. Moreover, the fifteen students in my class had elected to be
there, as part of their rich, January, electives learning experience called “Intersession”.
I was familiar with the school, having been invited to speak at their annual education
conference on a couple of occasions, but this was the first time I had taught a class.
Surprisingly, the experience reminded me of my own high school education, back in the UK in
the early 1960s. My high school was a state run, selective school in the working class city of
Hull, a major industrial city and large ocean fishing and shipping port. Socially and financially, it
was about as far away as you could get from Nueva School on the San Francisco Peninsula, and
my fellow students came from very different backgrounds than the students at Nueva.
What made my education so good was a highly unusual set of historical circumstances. Back
then, Hull was a fiercely socialist city that, along with the rest of the UK, was clawing its way out
of the ravages of the Second World War. For a few short years, the crippling English class
system broke down, and an entire generation of baby boomers entered the school system
determined to make better lives for themselves—and everyone else. (“Me first” came a
We had teachers who had either just returned from fighting the war (the men on the
battlefields, the women in the factories or in military support jobs), or were young men and
women just starting out on their teaching careers, having received their own school education
while the nation was at war. There was a newly established, free National Health Service, an
emerging new broadcasting technology (television) run by a public entity, a rapidly growing
communications systems (a publicly funded telephone service), and free education, including
government-paid- for university education for the 3 percent or so able to pass the challenging
We were the generation that the nation was dependent on to rebuild, making our way through
the education system in a social and political environment where the class divisions that had
been a part of British life for centuries had been (temporarily, it turned out) cast aside by the need to fight a common enemy across the English Channel. The result was that, starting in the middle of the 1960s, a “British Explosion” of creative scientific, engineering, and artistic talent
burst forth onto the world. Within our individual chosen domains, we all felt we could do
anything we set our minds to. And a great many of us did just that. About half my high school
class became highly successful people. That from a financially impoverished, working class
It was short lived, lasting but a single generation. I was simply lucky to be part of it.
What brought it all back to me was finding myself in a very similar educational environment in
my three days at Nueva School. The circumstances could hardly be more different, of course.
But talking and working with those students, I sensed the same thirst to learn, the same drive
to succeed (in terms they set for themselves), and the same readiness to keep trying I had
experienced two generations earlier. It felt comfortingly—and encouragingly—familiar.
But I digress. In fact, I’ve done more than digress. I’ve wandered far from my intended path. Or
have I? The point I want to get across is that when it comes to learning, success is about 5
percent talent, 35 percent the teachers and students around you, and 60 percent desire and
commitment. (I just made up those figures, but they represent more or less how I see the
landscape, having been an education professional for half a century.)
It turns out that, in today’s world, given those ingredients, in roughly those proportions, it is
possible for a small group of people, in the space of just a few days, to make significant
progress in solving a major problem of massive societal importance. (If you can figure out how
UPS performs its magic, you can do the same thing with many other large organizations,
Walmart, Amazon, United Airlines, and so on.)
How can it be possible to take a small group of students, still in high school, and make solid
progress on a major mathematical problem like that? It would not have been possible in my
school days. The answer is, in today’s world, everyone has access to the same rich toolset the
professionals use. Moreover, most of those tools—or at least, enough of them—are free to
anyone with access to a smartphone or a personal computer. You just have to know how to
make effective use of them.
Next month, I will describe how my Nueva class went about the UPS project. (I had done it once
before, with a non-science majors undergraduate class at Princeton University. Doing it with
high school students confirmed my belief that a group with less academic background could
achieve the same result, in the process providing me with some major-league ammunition to
back up my oft-repeated—and oft-ignored or disputed—claim that K-12 mathematics
education is in need of a major (and I mean MAJOR) makeover. (After the invention of the
automobile, it made more sense to teach people how to drive than how to look after a horse. I
feel the math ed argument should end with that razor-sharp analogy, but it rarely does.)
As I say, that discussion is for next month. But let me leave you with a teaser. Actually, two
teasers. One is my January 1, 2017 opinion piece in the Huffington Post, "All The MathematicalMethods I Learned In My University Math Degree Became Obsolete In My Lifetime." The
other teaser is the diagram I will end with. It summarizes some of the most useful tools that
a professional mathematician today uses when starting to work on a new problem. (Note: I’m
talking about using math to solve real-world problems here. Pure mathematics is very different,
although all the tools I will mention can be of use to a pure mathematician.)
This is my set of “most useful tools,” I should note, and reading the diagram left-to- right, top to
bottom, the tools I list are roughly in the order I have used them in working on various projects
over the past fifteen years. Other mathematicians might produce different collections and
different orders. But they won’t be that much different, and I’ll bet they all begin with the same
If you find this diagram in any way surprising, you likely have not worked in today’s world of
mathematical problem solving. If you find it surprising and are in mathematics education, I
respectfully point out that this is the mathematical toolset that your students will need to
master in order to make use of math in the world they will inhabit after graduation. You may or
may not like that. If you don’t like it, then that is unfortunate. Mathematical problem solving is
simply done differently today. It just is.
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