Discrete Mathematics and Theoretical Computer Science

TITLE: "Discrete Mathematics in the Schools"

EDITORS: Joseph G. Rosenstein, Deborah S. Franzblau and Fred S. Roberts. Published by the American Mathematical Society and the National Council of Teachers of Mathematics

A PostScript version of this document

A major reform effort is now underway in mathematics education. The goals of this reform are to enable us to educate informed citizens who are better able to function in our increasingly technological society; have better reasoning power and problem-solving skills; are aware of the importance of mathematics in our society; and are prepared for future careers which will require new and more sophisticated analytical and technical tools.

We feel that *discrete mathematics is an exciting and
appropriate vehicle for working toward and achieving these goals.* It
is an excellent tool for improving reasoning and problem-solving
skills. It lends itself well to the evolving consensus on effective
instructional strategies expressed in the *Curriculum and Evaluation
Standards for School Mathematics* of the National Council of Teachers
of Mathematics (NCTM). Discrete mathematics has many practical
applications that are useful for solving some of the problems of our
society and that are meaningful to our students. Its problems make
mathematics come alive for students, and help them see the relevance
of mathematics to the real world. Discrete mathematics does not have
extensive prerequisites, yet poses challenges to all students. It is
fun to do, is often geometrically based, and stimulates an interest in
mathematics on the part of students at all levels and of all
abilities.

At the same time, we feel that *discrete mathematics needs
to be introduced into the K-12 curriculum for its own sake.* During
the past 30 years, discrete mathematics has grown rapidly and has
become a significant area of mathematics. Increasingly, discrete
mathematics is the mathematics that is being used by decision-makers
in business and government; by workers in fields such as
telecommunications and computing that depend upon information
transmission; and by those in many rapidly changing professions
involving health care, biology, chemistry, automated manufacturing,
transportation, etc. Increasingly, discrete mathematics is the
language of a large body of science and underlies decisions that
individuals will have to make
in their own lives, in their professions, and as citizens.

It should be stressed, however, that *we are not advocating
any specific set of topics in discrete mathematics that should be
taught*; discrete mathematics includes many different areas, each of
which is valuable. Rather, we feel it is important that students be
able to speak the language of discrete mathematics and be exposed to
the ways of thinking and reasoning that are inherent in modern
discrete mathematics; all students should know and be able to apply
discrete mathematics concepts and skills in a variety of contexts.
And it is * especially* important for teachers to become excited about
their own experiences with discrete mathematics and to share that
excitement with their students.