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
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.