Executive Summary
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.
Beyond Eighth Grade:
Functional Mathematics
for Life and Work
For most of this century, schools have been organized to prepare some students for college and others for work. But the world of work is changing, much of it requiring increased use of data and computers, measurements and graphs. In the twenty-first century, most jobs and all careers will require some form of postsecondary education. Thus, all students, regardless of career goals, will benefit from a curriculum that prepares them for both work and higher education. Instead of either/or, schools must now focus on both/and.
In this paper, we propose a three-year high school program based on functional mathematicsthat prepares students for life and work. Typically, classroom applications are designed to serve mathematics--to offer context, to illustrate use, to motivate new concepts, or to integrate topics. In functional mathematics, the priorities are reversed. Instead of applications being introduced to help students learn a predefined body of knowledge, the mathematical topics are selected to prepare students to cope with common problems they will face in life and work. Examples of such real-life problems appear throughout this paper to illustrate in a concrete way the nature of functional mathematics.
Functional mathematics, if thoughtfully and rigorously developed, can provide a strong background both for students entering the workforce and for those moving directly into postsecondary education. Indeed, for most students, functional mathematics will provide better preparation than the current high school curricula. Functional mathematics stresses an in-depth understanding of fundamental topics that are most likely to be used by large numbers of people. By employing concrete tools in settings that are both complex and realistic, functional mathematics pushes students to draw on the full breadth of mathematics. In short, focusing on useful mathematics increases total learning.