Let's Abolish General Math!

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.

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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.


Words! Mere Words! Was there anything so real as words? - Dorian Gray