Beyond Eighth Grade: Functional Mathematics for Life and Work
Mathematics is the key to many of the most secure and financially
rewarding careers in every sector of the economy. The impact of
computers and information technology can be seen not just in
engineering and science, but in such diverse areas as
manufacturing, agriculture, health care, and advertising. To be
prepared for careers in virtually any industry, and especially
for changing careers during a lifetime, secondary school students
need to learn a substantial core of mathematics. However, this
core is not like either the abstract pre-engineering mathematics
of the academic curriculum or the restricted topics of the
discredited “vocational math.” New approaches are needed to meet
today’s challenges.
For most of this century, schools have been organized to prepare
some students for college and others for work. In the future,
most jobs and all careers will require some form of postsecondary
education. Thus, all students, regardless of career goals, can
benefit from a mathematics curriculum that prepares them for both
work and higher education. A three-year high school program based
on “functional” mathematics can do just that: provide a strong
background for students entering the workforce as well as for
those moving directly into postsecondary education.
A high school curriculum that helps all students master
functional mathematics would effectively address issues of both
equity and competitiveness. All students would have equal
opportunity to master the mathematics required for the new world
of work. Moreover, a three-year core of functional mathematics
would give students a strong foundation from which to enter the
workplace or pursue advanced education.
Most of the elements of functional mathematics are unsurprising.
Percentages and ratios; linear and quadratic equations; areas,
angles, and volumes; and exponential growth and trigonometric
relations are included in any strong high school mathematics
program. Although some topics in functional mathematics are
uncommon (e.g., index numbers, tolerances, three-dimensional
geometry, indirect measurement, financial mathematics), most are
taught in any high-quality high school mathematics program. To
achieve its goal of preparing students both for work and for
further education, functional mathematics respects the many parts
of the traditional curriculum that are broadly useful, even while
including topics such as spreadsheets, data analysis, and
statistical quality control that are hardly ever part of high
school mathematics. In functional mathematics, utility is center
stage.
The elements of functional mathematics can be embedded in many
different curricula. However, any mathematics curriculum designed
on functional grounds–whether organized around external contexts
or mathematical themes–will emphasize authentic applications
from everyday life and work. In such a curriculum, students will
gain considerable experience with mathematical tasks that are
concrete yet sophisticated, conceptually simple yet cognitively
complex. By highlighting the rich mathematics embedded in
everyday tasks, this approach (in contrast to traditional
“vocational math”) can dispel both minimalist views about the
mathematics required for work and elitist views of academic
mathematics as an area with little to learn from work-based
problems.
A curriculum based on functional mathematics requires appropriate
content, authentic contexts, engaging tasks, and active learning.
By featuring mathematics in common contexts, a functional
curriculum can motivate students to link meaning with
mathematics. Such contexts invite variations that can propel
students to deep understanding and stimulate mathematical habits
of mind.
Functional mathematics channels the much-criticized “mile-wide,
inch-deep” curricular river into a narrower stream of ideas and
procedures that reinforce each other as students progress through
school and college and on into careers. It provides a rich
foundation of experience and examples on which students can build
subsequent abstractions and generalizations. Indeed, to fulfill
its goals, a functional curriculum must leave students well
prepared not only for work but also for subsequent courses in
more abstract mathematics.
Functional mathematics addresses many needs that are otherwise
often neglected. Neither traditional college-preparatory
mathematics curricula nor the newer standards-inspired curricula
were designed specifically to meet either the technical and
problem-solving needs of the contemporary workforce or the modern
demands of active citizenship. Although each includes much that
is of value for employment and citizenship, neither provides the
context, motivation, or balance of mathematical topics necessary
for employees or citizens in a data-drenched world.
Indeed, for most students, functional mathematics will provide
better preparation than current high school curricula. Functional
mathematics stresses an in-depth understanding of topics that are
most likely to be used by large numbers of people. By employing
concrete methods in settings that are both complex and realistic,
functional mathematics pushes all students to draw on the full
breadth of mathematics. In short, by focusing on what is useful,
functional mathematics increases both student interest and
student learning.
Forman, S. L., & Steen, L. A. (1999, May). Beyond eighth grade: Functional mathematics for life and work. Berkeley, CA: National Center for Research in Vocational Education.