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Why We Should Reduce Skills Teaching in the Math Class

## by Keith Devlin

In an ideal world -- at least, a world that most
mathematics educators would probably see as
ideal -- almost everyone would see the need to
have some mathematical skills, and would make
the effort to acquire them. Moreover, in that
same ideal world, everyone would, at some stage
in their education, get a good overall sense of
mathematics and its importance, either by
attending a "broad brush stroke" survey course on
mathematics or by reading one of a small but
growing number of excellent expository books on
mathematics.

Unfortunately, the world we live in is far from
being that mathematician's ideal. Rather, the
real world is one in which there is math phobia
among a sizeable minority, some level of math
anxiety among many more, a general antipathy
toward mathematics in the majority, and
ignorance about the true nature of mathematics
on the part of practically everyone but the
professional mathematician.

Surely, none of these observations comes as a
surprise to anyone. But to judge by much of the
current national debate about "math standards",
you would think that my remarks constitute the
discovery of the century.

At the risk of spoiling an enjoyable tussle, let
me try to relocate the Great Math Education
Debate from the ideal world of the students we
would like to have -- i.e., copies of our younger
selves as we remember that long lost golden age
of our youth -- to the real world of the students
who actually populate our classrooms.

I'll start with two observations concerning that
ideal world I described in my opening
paragraph:

Fact 1: Acquiring mathematical skills involves
dedication and hard work. As such, it requires
motivation. That is already problematic, since
for most people the payoff comes later in life.

Fact 2: Getting a general sense of mathematics
requires nothing more than interest.

At present, we put immense effort into trying to
develop mathematical skills in our students, and
we wring our hands endlessly when, for the
majority of our students, we fail. At the same
time, we rarely try to provide our students with
a good, overall picture of the mathematical
enterprise.

The paradox in this state of affairs is that Fact 2
probably provides the key to overcoming the
obstacles stated in Fact 1. By providing our
students with a good overall sense of mathematics,
including the many major roles it plays in all our
lives, we might well be able to provide the
motivation the students need to spend some time
acquiring basic skills.

By persisting with a largely unmotivated
attempt to force feed the population with a set
of perceived essential mathematical skills, we
simply turn (what I think is) the majority of
people off mathematics altogether and produce
significant math anxiety in far too large a
minority. As a result, even when people do
subsequently find themselves in need of some
mathematics, they are often too math phobic to
acquire that knowledge.

I believe we need to reduce drastically the time
we spend teaching basic skills in middle and high
school mathematics classes. I do not see this as
a great loss. The plain fact is, few citizens in
modern society need or make real use of any
appreciable knowledge of, or skill in,
mathematics. What mathematics they need and
use they have probably already met by the time
they are twelve years old.

On the other hand, the continuance of modern
society requires a steady supply of a relatively
small number of individuals having considerable
training in mathematics. In order that the
critical future supply of mathematicians does
not dry up, we must ensure that all high school
and university students are made aware of the
nature and importance of mathematics, so that
those who find they have an interest in and
aptitude for the subject can choose to study it in
depth.

For the middle and high school grades, the main
goal in the math class should be to create an
awareness of the nature of mathematics and the
role it plays in contemporary society. To do this,
mathematics should be taught in much the same
way as history or geography or English literature
-- not as a utilitarian toolbox but as a part of
human culture.

In my view, an educated citizen should be able to
answer the two questions:

- What is mathematics?
- Where and how is mathematics used?

At present, few people can answer either
question correctly.

Existing methods turn off students in droves and
produce math anxiety in many, and this is
counterproductive. Teach mathematics as a part
of our culture and the result will be many more
students who are motivated to want to learn
mathematics. Surely, the aim of a mathematics
education should be to produce an educated
citizen, not a poor imitation of a $30 calculator.

I should stress that I am not saying that basic
numerical skills are not important. On the
contrary, I would put quantitative literacy on the
same crucial footing as ordinary literacy: both
are so fundamental in today's society that they
are *everybody's* responsibility. The
development of basic quantitative skills are as
much the responsibility of, say, the social
studies or the English teacher as language and
presentation skills are the responsibility of the
math and science teachers. To leave the
development of quantitative skills to the
mathematics teacher sends quite the wrong
message to the student.

By changing our present education system
radically so that, for the vast majority of
students, the primary goal in the mathematics
class is to create an awareness of the what, the
how, and the why of mathematics, rather than
the development of skills that, apart from a tiny
majority, none of them will ever make use of, we
will achieve two important goals:

- Tomorrow's citizens will appreciate the
pervasive role played by one of the main formers
of the culture in which they live their lives. As
such, if and when they find that they do have
explicit need of some mathematics, they will not
start with the disadvantage of having to
overcome math anxiety, as is so often the case
today.
- Those individuals who turn out to have an
interest in and a talent for advanced
mathematics will be exposed to the true nature
and the full extent of the subject at an early age,
and as a result will have an opportunity to
pursue that interest to the eventual benefit of
both themselves and society as a whole.

Leaving aside the payoff for those people who
eventually encounter a need for mathematical
skills, the major justification for goal 1 is
simply this: A human life is the richer for having
greater understanding of the nature of that life.
The more ways we have to know our world and
ourselves, the richer are our lives.

Turning to goal 2, any university mathematics
instructor will tell you that the present high
school mathematics curriculum does not prepare
students well for university level mathematics.
Nor is success at high school mathematics a good
predictor of later success in mathematics. The
reason is simple. School mathematics is largely
algorithmic: To succeed, the student needs only
to learn various rules and procedures and know
when and how to apply them. In contrast,
university level mathematics is highly creative,
requiring original thought and the ability to see
things in novel ways. Since the creative
mathematician does often need to apply rules and
use algorithmic thinking, many successful
mathematicians did indeed excel in the high
school mathematics class. But many university
mathematics students who shone in high school
find they struggle with and eventually give up
the subject at university when they discover
that algorithmic ability on its own is not enough.
And the fact that some of the very best
professional mathematicians did poorly at high
school mathematics, but by some fluke were
drawn to the discipline later in life, suggests
that our present system of school mathematics
education probably turns off a significant
number of students who have the talent for later
mathematical greatness.

So there you have it. Reduce skills teaching and
concentrate on the big picture. And, please, don't
pay so much attention to those international
comparisons of math skills attainment. Parents
and educators have been berating declining
educational standards since the time of Euclid.
There is surely something vaguely comical about
the nation that leads the world in science and
technology, and which virtually dominates the
world in the development of computer hardware
and software, constantly lamenting the poor
math skills of its population. Sure the USA has to
import a great deal of mathematical talent. That
is because there are plenty of Americans with
the talent, mathematical ability, and drive to
generate a large demand for such people, a far
greater demand than in any other country in the
world. The time to worry would be when there is
a major outflux of American mathematicians to
one of those competitor countries we keep
worrying about. Frankly, I don't see that
happening any time soon.

That's not a "complacent, self-satisfied
American" talking, by the way. Hey, I'm a Green
Card carrying immigrant with the stamp on my
entry visa barely a decade old. Now, if you want
to know about the poor state of math education
in my native Britain . . . but that's another story.

**See also:** "Is Mathematics Necessary?" by Underwood Dudley, *College Mathematics Journal*, vol. 28,
November 1997, pp. 360--364.

Dr. Keith Devlin ([email protected]) is Dean of Science at Saint Mary's
College of California and a Senior Researcher at Stanford University's
Center for the Study of Language and Information. A shorter version of the
above article first appeared in an editorial by Devlin in the December 1997
issue of the MAA newsletter FOCUS, which Devlin edited from 1991 to 1997.

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