Math Forum Discussions

Jonathan Groves

Posts: 2,068
From: Kaplan University, Argosy University, Florida Institute of Technology
Registered: 8/18/05

More Reflections on Peter Hilton's Comments
Posted: Sep 1, 2010 7:23 PM

Plain Text

Dear All,

In the post

http://mathforum.org/kb/thread.jspa?threadID=2111343&tstart=0

I had quoted what the mathematician Peter Hilton had said about skills and
education versus training. And Peter Hilton makes a valid point because what
skills are necessary are constantly changing, and what skills are necessary
will also depend on what students will do later in their lives; thus, any mathematics
classroom consists of students whose skills they will need for the future we
cannot predict except those skills that we call "soft skills." Soft skills are
the ability to think critically and creativity, the ability to think
mathematically, the ability to read and write and communicate effectively, the
ability to work and learn independently, the ability to work with others, and so
on. So-called "hard skills" cannot be predicted. Hard skills are the
ability to use particular technology and other highly specific skills that work
only for a narrow range of tasks. Hard skills, especially those related to
technology, tend to go out of date quickly.

Education is not career training but preparation for life and for society.
Education is about helping us learn to think for themselves, to learn for
ourselves, to learn to be creative, to learn about the world, to learn about our
society--in short, education is about giving us all the tools we will need to
succeed in our lives and careers but those tools that we all need, regardless of
what our futures will be. None of our teachers can predict all the career
skills we will need though some pretend that they can do so. In fact, none of
us can say with certainty what our own futures will be. For instance, can I say
for myself that I will continue teaching college mathematics the rest of my
life? I cannot.

What about mathematics education? What should that give us? For one thing, a
good mathematics education should give us the ability to think mathematically
and the ability to make sense of numerical data all around us. Good number
sense goes along with this. These abilities will serve us regardless of how
mathematics plays a role in our lives later on. It does no good to have all
these so-called "skills" in mathematics if one does not have good number
sense and if one has no clue as to the meaning of what they are doing beyond
merely scratching symbols onto a piece of paper.

Good mathematics education should help us to learn to mature mathematically so
that we can learn whatever mathematics later on we are interested in learning or
need to learn. Low mathematical maturity accounts for many of the struggles
with mathematics that I see among students, and low mathematical maturity causes
crippling math anxiety in students, which in turn makes them falsely believe
that they are no good at mathematics. College mathematics will make no sense to
anybody with low mathematical maturity. But focusing on teaching all these
so-called "skills" and procedures and formulas does not contribute to students
learning to develop mathematical maturity. What contributes to them learning
mathematical maturity is being encouraged to think about the mathematics they
are learning and working on by asking themselves questions that mathematicians
often ask themselves: Why is this result true? Why does this procedure work?
Can I find an alternate way to do this problem? Can I find another algorithm
for carrying out such-and-such a computation? Why is this result important?
Where does this definition come from? And so on. In short, for students to
learn mathematical maturity, they must actively engage with the mathematics
itself by seeking meaning behind the mathematics. Learning mathematical
maturity will serve them more in their mathematics education than anything else
mathematics education can offer them.

And a good mathematics education should give us a view of what mathematics
is really like and why mathematicians find it fascinating. And a good
mathematics education should help us learn to see where mathematics has come
from, how it has impacted culture, how culture has impacted mathematics (these
last two ideas are ideas I wish I knew a lot more about)--in short, to learn to
see the human side to mathematics. Without seeing the human side to
mathematics, students end up falsely believing that mathematics is purely
mechanical, uncreative, and disconnected from people's lives (except from the
lives of some "weirdos" or "nerds" or "geeks" called mathematicians) and end up
seeing math as simply one of those things we have to learn to get through
school. What a waste! No wonder that mathematics suffers from a low status in
our culture: Many schools and teachers so badly distort mathematics in the
classroom that it ends up looking like nothing like the mathematics we
mathematicians have fallen in love with. In short, school mathematics is often
boring and an extreme drudgery to students.

And it irritates me that so many of these mathematicians who support MC/HOLD see
no problem with their beloved subject so badly maligned in the classrooms. How
can those fools refuse to see that most of the problems with mathematics
education are simply because mathematics is taught so that it becomes forbidding
to students--even when you mention that to them?

What I had learned in mathematics that serves me best is the ability to think
mathematically, the ability to learn mathematics for myself, and the reasons
that mathematicians find mathematics fascinating. These things have served me
much more than any specific content knowledge I have learned because any
specific knowledge would not help me in the least bit without these other skills
(in other words, without these skills, all I could do is quote mathematical
facts but not be able to use them in any meaningful way).

Jonathan Groves