In the forward to this monograph. Kevin Devlin of Stanford University, a well renowned mathematician, tells the story of how Paul Lockhart, someone who had given up his career as a research mathematician to devote himself to the mission of improving K-12 mathematical education, turned an earnest but obscure essay into a resounding statement.
The first genesis of this book is as a 25-page document that
was passed around in the mathematical education circles. It became a sensation
because many felt that Paul Lockhart had hit the nail on the head with his
observations; observations and beliefs that resonated with mathematics educators;
indeed, he struck a very sensitive nerve. As this document was passed around,
it became a clarion call to mathematicians, mathematics teachers, and anyone
who has a passion for how mathematics is taught.
A Mathematicians Lament is short and compact. Paul
Lockhart had a lot to say, and he says it with urgency and alarm. Part I of the book is the lamentation, he goes into everything
that he feels is wrong with mathematical education. He makes his argument
progressively starting with a discussion on mathematics and culture, then a discussion on mathematics in the
school, a dive into the national mathematics curriculum — a chapter in which he
was unsparing in his criticism. In the last chapter in Part I, Lockhart zeroes
in on a well-known and well reviled target: high school geometry. Lockhart gave it a subtitle: Instrument of the
Devil. This is his coup de grรขce,
his pronouncement on the abysmal state of mathematics education in the United
States.
He expounds on the insidious practice of limiting
mathematics education to just computation, while emphasizing the mechanical and
uninspiring practice of training skills without giving the students a vision of
what true mathematics is. We don’t give the students enough credit for being perspicacious
enough to sense the immutable and deep beauty of mathematics. We don’t give the
allure of the mathematical abstraction enough credit for being able to inspire
and elicit passion from the students; we
think that the average student could not fathom the depths of meaning of
mathematics; and that the student can only appreciate mathematics in its most utilitarian
and unimaginative incarnation. It is an insult to the students and to
mathematics.
As an engineer by training, I managed to survive my formal mathematics
training with my love of mathematics intact, even though I knew my talent for
theoretical math is limited. I recognize
all the stated pitfalls and shortcomings of how mathematics is taught because I
had experienced it firsthand.
Although I appreciate
the beauty of mathematics, as I had aspired to be an applied mathematician; unfortunately,
I had made a mess of the higher math that I took as a grad student in
engineering, I didn’t have the patience nor the curiosity to sustain my
interest because I was studying to gain a degree rather than studying for the
love of a discipline. I was resigned to take enough applied math to help me become
an engineer even though I was always curious about doing pure mathematics. Even
as I have resigned myself to the fact
that I won't ever be a pure mathematician nor even be a good applied mathematician, I have
come to appreciate and love the subject.
In the second part of A Mathematician’s Lament —
titled Exultation — Paul Lockhart made his elevator speech to anyone
and everyone reading about the beauty of mathematics. He assiduously avoided
the equations, a smart decision in my estimate. He dealt with mathematics as a
holistic entity. He is much more eloquent in stating his case than I will ever
be, so I will let the reader read the
book rather than dilute his passion and his narrative.
He discusses the common sensical instinctive aspect of mathematics. There are crude but effective
sketches about the points that he wanted to make, adding to the intuitive charm
of the narrative. He refrains from delving
into the dreaded and unwelcoming geometry that he wrote about in Part I; he uses simple sketches to ease the reader into
mathematical thinking.
When he hit his stride talking about mathematics, it is a beauteous
expression of passion he speaks of the raw beauty of mathematics that makes it
so attractive, intoxicating, and habit
forming for so many. It is as if mathematics is some kind of addiction. And to
mathematicians that I know, and to a much lesser degree to me, that addiction
is very real.
The second part of the monograph reminds me of the passion
exuded by another book written by a mathematician. Francis Su wrote Mathematics
for Human Flourishing,
The monograph is an extended essay identifying the problems
with the way we have taught mathematics, how the math that is taught is contrary
to what the mathematics lovers love about mathematics; what mathematics is in
the eyes of those that are knowledgeable in the art; while proposing in broad strokes what need to be
done to change that paradigm. It is a timely and necessary clarion call to our
society and our educators that we are irresponsibly squandering our opportunity
to educate our society in the art of thinking, questioning, and creating. It is
an attempt to reverse the trend, and more broadly, it is a valiant attempt to
convince a math deficient public that they are missing the boat, and our
society will suffer.
I hope that this is not just preaching to the choir, but the
obstacles to universal understanding of the importance of the subject is quite
high. I hope that Paul Lockhart is not too late.
Works Cited
Su, Francis. Mathematics for Human Flourishing.
Yale: Yale University Press, 2020.
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