obvious. I couldn’t see, and then all of a sudden I could. Somehow, I was able to create a
profound simple beauty out of nothing, and change myself in the process. Isn’t that what art is
all about?
This is why it is so heartbreaking to see what is being done to mathematics in school. This
rich and fascinating adventure of the imagination has been reduced to a sterile set of “facts” to be
memorized and procedures to be followed. In place of a simple and natural question about
shapes, and a creative and rewarding process of invention and discovery, students are treated to
this:
Triangle Area Formula:
A = 1/2 b h h
b
“The area of a triangle is equal to one-half its base times its height.” Students are asked to
memorize this formula and then “apply” it over and over in the “exercises.” Gone is the thrill,
the joy, even the pain and frustration of the creative act. There is not even a problem anymore.
The question has been asked and answered at the same time— there is nothing left for the
student to do.
Now let me be clear about what I’m objecting to. It’s not about formulas, or memorizing
interesting facts. That’s fine in context, and has its place just as learning a vocabulary does— it
helps you to create richer, more nuanced works of art. But it’s not the fact that triangles take up
half their box that matters. What matters is the beautiful idea of chopping it with the line, and
how that might inspire other beautiful ideas and lead to creative breakthroughs in other
problems— something a mere statement of fact can never give you.
By removing the creative process and leaving only the results of that process, you virtually
guarantee that no one will have any real engagement with the subject. It is like saying that
Michelangelo created a beautiful sculpture, without letting me see it. How am I supposed to be
inspired by that? (And of course it’s actually much worse than this— at least it’s understood that
there is an art of sculpture that I am being prevented from appreciating).
By concentrating on what, and leaving out why, mathematics is reduced to an empty shell.
The art is not in the “truth” but in the explanation, the argument. It is the argument itself which
gives the truth its context, and determines what is really being said and meant. Mathematics is
the art of explanation. If you deny students the opportunity to engage in this activity— to pose
their own problems, make their own conjectures and discoveries, to be wrong, to be creatively
frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you
deny them mathematics itself. So no, I’m not complaining about the presence of facts and
formulas in our mathematics classes, I’m complaining about the lack of mathematics in our
mathematics classes.
f your art teacher were to tell you that painting is all about filling in numbered regions, you
would know that something was wrong. The culture informs you— there are museums and
galleries, as well as the art in your own home. Painting is well understood by society as a