**LET’S ABOLISH GENERAL MATH!**

by Thomas E. Seddon

Recently I taught “general math” in eleventh grade
for the first time in almost twenty years of teaching. I was as unprepared as anyone for the
general-math challenge.

It didn’t take long for me to see that something was very wrong. By body language and other more direct
forms of communication, students were shouting at me that I was wasting their
time, and when I thought about it, I realized that they were right!

As I plodded through the venerable text, I discovered that several
sections were clearly obsolete.
Does *anyone* need to learn and
eleven-step arithmetic algorithm for approximating the square root of a
number? Such a process was
anachronistic even in the days of slide rules. Some sections were too abstract for the general student, who
really couldn’t care less about the distinction between rational and irrational
numbers. Most selections, however,
were simply presented in topical order with no context. When does one need to be able to
construct a regular hexagon geometrically?

In a desperate search for resources, I picked up a paperback study guide
for the armed forces qualifying test (Steinberg 1986). Unlike my text, it was loaded with
practical word problems based on real-life situations. Furthermore, many problems required
surprisingly abstract thinking skills and multiple steps to arrive at a
solution.

The contrast between what the armed services were expecting from the
average student and what I was teaching prompted me to take a sabbatical
research year funded by the Christa McAuliffe Fellowship Program. The design of that project is described
elsewhere (Seddon 1988).

**But let’s not abandon the general-math student.**

As part of my research into alternatives for our present programs, I
reached some specific conclusions for the general-mathematics class in grades
11 and 12:

1.
*Get rid of the arithmetic!* Stop trying to pound away at those
whole-number algorithms or put the remedial work on a machine—let the computer
drill them. Pass out the calculators
and work on real problems.

2.
*Individualize!* A must. Find a way to help those hoping to go on to college to
prepare for the ACT or SAT mathematics sections. Find a way to help those special-education kids in their
first mainstreamed class to master basic skills and household or consumer
mathematics. But don’t try to give
everybody a little of everything.
No one likes to be forced to take a tiny helping of every dish in a
cafeteria.

3.
*Context is everything!* Consider the arbitrary rules involving
numbers and numerical relationships that young people learn to get their
driver’s license or their hunter-safety card. Students’ brains are not mathematically dysfunctional, but
they won’t exercise their brains without good reason. To get students to learn what they need, we must teach all
mathematics in relation to a real-world setting. No more sets of computational practice! Deviate from a strictly topical content
approach! Use multifaceted
problems. Have students make
contact with people who must do mathematics in their daily work or get
fired! Use laboratory or field
work to solve problems as they occur in some interesting project.

One major national curriculum-development project that has addressed some
of these issues of general mathematics is *Applied Mathematics* by the Center for Occupational Research and
Development (1988). They use
exclusively word problems drawn from real-life occupations, and they have made
an excellent series of videotapes.
Mathematics laboratories focus on integrating skills in measurement and
computation, and every student starts the year with a scientific
calculator. But the content is
still introduced topically in a basically artificial setting.

Can we salvage general mathematics with problems and laboratory
experiences rooted in reality?
Maybe we can in the ninth and tenth grades, the target grades of Applied
Mathematics, but at the eleventh and twelfth grades, I’m afraid, more radical
approaches are necessary. We
simply must stop trying to teach mathematics in a traditional classroom from
just another textbook. Let’s
abolish this traditional general math!

**Can we work with the vocational teachers?**

Alternatively, consider that industrial and vocational educators have
been calling for greater “articulation” between academic and vocational courses
for years (National Commission on Secondary Vocational Education 1984). They have urged hands-on projects that
emphasize solving practical problems using a learning-by-doing approach
(Silberman 1988). So why don’t we
get the mathematics teachers together with the vocational teachers, sit down,
and talk up a plan? With a little
ingenuity we can devise courses, or even minicourses, that involve the building
trades, auto mechanics, and cooperative-education programs in industry and
business. Let’s have these courses
taught by a certified mathematics instructor but on vocational turf. Let’s allow the mathematics to emerge
from the context, not force the context onto the mathematics.

Keep focused on the possibilities; don’t get hung up on the admittedly
imposing difficulties. The key is
to “laterally articulate” programs that are in place right now. Let’s face facts; almost anything would
improve on what we’re doing now.

### References

Center for Occupational Research and Development
(CORD). *Applied Mathematics*. Waco, Tex.: CORD, 1988.

The National Commission on Secondary Vocational
Education. *The Unfinished
Agenda: The Role of Vocational Education in the High School*.
Columbus, Ohio: The National Center for Research in Vocational
Education, 1984.

Seddon, Thomas E. “An Innovative Curriculum
Development in Applied Technical Mathematics.” *Journal of the New Mexico Council of Teachers of
Mathematics* 88-89 (Fall 1988): 1-5.

Silberman, Harry F. “The Unfinished Agenda Revisited.” Vocational Education Journal 63 (October 1988): 38-40.

Steinberg, Eve P. *Practice for Army Placement
Tests.* New York: Simon &
Schuster, ARCO Publishing, 1986.

____________________

The support of the U.S. Office of Education through the Christa McAuliffe Fellowship Program and the Alamogordo, New Mexico, Public School District is gratefully acknowledged. The views and opinions contained in this paper are those of the author, who is solely responsible for its content.