Algebra, Jobs and Motivation

Algebra for the Technical Workforce Working Group

Proceedings of the Department of Education Algebra Initiative Colloquium, December 9--12, 1993, C. B. Lacampagne, W. Blair, J. Kaput (ed.), U. S. Department of Education, 1995, 159-160

Paul Davis

Mathematical Sciences Department
Worcester Polytechnic Institute
Worcester, MA 01609
Office: 508-831-5212 FAX: 508-831-5824

For all types of students, the first exposure to algebra is the beginning of a transition from numbers to letters, from concrete to abstract language. The importance of learning algebra as a language rather than as a set of memorized rituals will not be apparent until students recognize its power as a problem solving tool. Important questions of "Why?" and "What if?" can be posed and answered in this new language, a key feature too often concealed from students.

A core set of algebra skills can be defined by identifying the kinds of problems the target audience needs to solve. Besides defining the core, those problems must motivate the study of algebra. Indeed, one could argue that no concept of algebra should be taught unless it can be motivated by a problem that is likely to be part of the students' experience in the near future.

Unfortunately, the mathematics itself may be hiding in a spread sheet, for example. Or its real value may appear in the need for careful quantitative reasoning rather than in explicit manipulation of symbols. Ideally, students can be motivated both by the need to acquire quantitative thinking skills and by the demands of specific technical challenges. In any case, the problems of uncovering mathematics at use in the work place and conveying those experiences to students are formidable challenges that must be overcome. (The beginnings of one attempt at the graduate level in mathematics are described in [1].)

More simply, one can identify some specific skills students need at the pre-college level through widely available licensing examinations for many trades and professions. Students who aspire to become plumbers, electricians, or health care professionals, for example, will be asked to find areas of plane figures and volumes of common solids on their licensing examinations. They will have to manipulate relationships involving rates and slopes to pass those exams and to cope with their daily work.

Identifying these explicit challenges and conveying them to students can provide motivation of a very concrete sort. Of course, an algebra curriculum needs to go far beyond the need for formulas if it aims to develop flexible quantitative thinking skills.

Can algebra be presented as the key that unlocks those doors rather than the bar that blocks them? Can algebra become the language of the relationships among dimensions, areas, and volumes? Among rise, run, slope, and rate? Can it become the language of success, opportunity, and access?

Mastery of the language of algebra also lays a foundation for mathematical maturity. Familiarity with mathematical ideas enables an auto mechanic to manage comfortably the business affairs of an independent garage, to make informed decisions about loans and equipment depreciation. Good algebra skills set the stage for a trained secretary to undertake basic accounting and advance to a position as manager of a small business. Those same skills enhance the computer literacy of an electronic technician with the ability to implement spreadsheet calculations that speed and record a new procedure for testing equipment.

Necessity builds ownership, and genuine applications are evidence of the necessity of algebra in the professional life of the technical workforce. Students will take ownership if their algebra courses incorporate authentic applications like those they will encounter in their professions. The challenge is identifying those applications and using them as instructional vehicles.


1. P. W. Davis, Some views of mathematics in industry through focus groups, SIAM Mathematics in Industry Project, Report 1, Society for Industrial and Applied Mathematics, Philadelphia, PA (1-215-382-9800) 1991

Available electronically as siamrpt.dvi by anonymous ftp from /pub/forum on, from the SIAM Gopher server at, or by mail from the author. Alternate versions have appeared in:
SIAM News 26 (13): Mathematicians in Industry: Credentials and Skills (January 1993), page 16; Industrial Problems Sources and Solutions (March 1993), page 10; Industrial Mathematics, The Working Environment (May 1993), page 16
Notices of the American Mathematical Society, 40 (7) Some Glimpses of Mathematics in Industry, (September 1993), pages 800-802.

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