By Dan Teague, posted November 9, 2015 —
It was early
September 1963. At John Hanson Junior High, I was part of a new program in
which a small group of eighth graders were taking Algebra 1. Mr. Green was my
teacher, explaining the difference between a number and the numeral
representing the number and why x = 3
wasn’t the solution to the equation 2x
= 6; rather, it should be {x ∈ ℜ |
x = 3}. (New Math—those were the
days). As far as we knew, we were the first kids in the history of the world
allowed to take Algebra 1 in eighth grade. We thought we were hot stuff.
Then Mr. Green,
in an effort to contain our youthful arrogance, said something equivalent to,
“You guys are good, and math is easy for you. But always remember this: Everyone
has their Green’s theorem.” Probably this stuck with me because of Mr. Green
talking about Green’s theorem (no relation), but I’d like to think I would have
remembered it anyway. He went on to explain what he meant. When he was a
student, mathematics was easy. Algebra, Geometry, Trigonometry, and Calculus—all
were all very easy for him. But then he got to Green’s theorem in Multivariable
Calculus. From then on, in every mathematics course, although he was just as
good as he had always been, he had to work really hard to master the content. His
meaning for us was that, at some point, mathematics becomes difficult—for
everyone. And when we hit our personal Green’s theorem, as we all eventually
will, we need to learn to work at it like everyone else.
Fast forward fifty-two
years, and I’m talking with a student about courses she wants to take next term.
She tells me, “I really like mathematics, but I’m not very good at it.” Her
proof? “I have to work really hard to be successful.” In the world of students,
if you can do something easily, you are good at it, and if something is not
easy for you (no matter how successful you are and no matter how much you enjoy
it), you are not very good at it. Moreover (and this is the dangerous part of
this thought), if a subject isn’t easy for you, then you just aren’t cut out
for it. My student could not imagine mathematics as a major and certainly not
as a career option.
But Mr. Green
would tell her that she is using the wrong metric. For everyone, mathematics becomes challenging. Mathematics is one of
the greatest intellectual achievements of humankind. Of course, it will be
challenging. Everyone has to work at it—some earlier than others and some later
than others. But everyone has a personal Green’s theorem.
It is important
for students to understand that, whatever their area of interest, the subject
will eventually become challenging. So what? Hard isn’t bad. The real question isn’t
whether a student finds a subject easy or hard; all subjects will all be hard
eventually. The real question is, Do you enjoy that challenge? That’s how to decide
what career path to pursue. You actually don’t want an “easy” job. You want to
be challenged by your work and to draw joy and contentment from accepting the
challenges it offers and working hard to meet them.
Mathematics is
the hardest thing I know, with the possible exception of teaching mathematics. I
do them both not because they are easy. Like you, I do them both because I love
the challenges they offer and because each day I have to work really hard to be
successful. Thank you, Mr. Green.
DAN TEAGUE,
teague@ncssm.edu, teaches at the North Carolina School of Science and
Mathematics in Durham. He is interested in mathematical modeling and finding
problems that connect concepts from different areas of mathematics.