Habitat for Humanity uses volunteer labor to build inexpensive homes, which it sells for the cost of materials. Using information on standard building supplies obtained from a local lumberyard, design a simple home whose building materials can be obtained for $15,000.

High School Mathematics

            Traditionally, high school mathematics has served two different purposes--to prepare college-intending students for calculus (and other mathematics-based courses) and to equip other students with necessary skills, mostly arithmetic, so that they can function as employees, homemakers, and citizens. Although most traditionalists--and most parents and grandparents--still support these dual goals, reformers argue for a common curriculum for allstudents which emphasizes problem solving, communication, reasoning, and connections with other disciplines.

            Proposed goals for school mathematics can be found in many sources. Some focus directly on K-12, others on the needs of postsecondary education or employers. NCTM (1989) provides a comprehensive set of standards for grade levels K-4, 5-8, and 9-12 that represents the "reform" perspective. In contrast, California recently adopted mathematics standards that represent a more traditional perspective (California Academic Standards Commission, 1997). The American Mathematical Association of Two-Year Colleges (1995) articulated standards for college mathematics before calculus that include expectations for the mathematical foundation that students need to succeed in college. In addition, in the influential report What Work Requires of Schools(Secretary's Commission on Achieving Necessary Skills [SCANS], 1991), the U.S. Department of Labor outlined both foundation skills and broad employability competencies for mathematics and other subjects.

            These standards differ greatly in both mathematical content and rhetorical style (see Appendix A), although most have overlapping goals. Indeed, to succeed in the real world of teachers and parents, schools and school boards, a mathematics curriculum must

            (1) meet society's expectations of what all high school graduates should know and be able to do.

            (2) reflect priorities common to state and national guidelines.

            (3) increase the number of students who successfully persist in advanced mathematics-based courses, including calculus.

            (4) enable students to see and use mathematics in everyday aspects of life and work.

            (5) help students understand and use correct mathematical language.

            Functional mathematics must also meet these objectives. The first two objectives establish priorities: to focus early and often on what everyone agrees must be learned, leaving to later (or to optional strands) those topics that only some students will find interesting or important. The third objective establishes a standard of quality: to increase the number of students who persist in further mathematics-based courses (including calculus, the traditional hallmark of mathematical success). The fourth objective conveys a commitment to utility--to ensure that students see mathematics as something real in their lives rather than as an alien subject encountered only in school. Finally, the fifth objective stresses command of the language of mathematics, a skill at least as important for success as a command of English.

            By meeting these objectives, functional mathematics will satisfy the general public's expectations of school mathematics. In addition, these objectives also enhance functional mathematics' primary goal of preparing students for life and work. Consistent quality and high standards are essential in today's high-performance industries. Persistence in mathematics is not just of academic importance; it is also one of the best predictors of success in careers (Commission on the Skills of the American Workforce, 1990). Moreover, the language of mathematics provides the power to analyze and express complex issues in all aspects of life and work. Fluency in this language is important not only for productive employees but also for careful consumers and critical citizens.

            In functional mathematics, utility is center stage. Other objectives play important but supporting roles. Unfortunately, many mathematicians and mathematics teachers find utility at best a bleak justification (Howe, 1998) for a subject that they chose for its beauty and elegance. For them, the power of mathematics--in Eugene Wigner's famous phrase, its "unreasonable effectiveness"--is not its primary virtue, but merely a consequence of its elegance and internal structure. Thus, mathematicians are wont to stage their subject with theory and abstraction at the center, employing applications, technology, and practice as needed to help promote understanding.

            To engage mathematicians and mathematics teachers, functional mathematics needs to be seen in terms of both utility and beauty. For many students, utility can be a path to beauty, while for others, mathematics by itself provides sufficient internal motivation to sustain interest and accomplishment. For any mathematics curriculum to succeed with all students, it must build on the twin foundations of utility and elegance.