Introduction

Society's technological, economic, and cultural changes of the last 50 years have made many important mathematical ideas more relevant and accessible in work and in everyday life. As examples of mathematics proliferate, the mathematics education community is provided with both a responsibility and an opportunity. Educators have a responsibility to provide a high-quality mathematics education for all of our students. A recent report of the National Academy of Sciences (NAS) entitled Preparing for the 21st Century: The Education Imperative (National Research Council [NRC], 1997) neatly summarizes this point:

… today, an understanding of science, mathematics, and technology is very important in the workplace. As routine mechanical and clerical tasks become computerized, more and more jobs require high-level skills that involve critical thinking, problem solving, communicating ideas to others and collaborating effectively. Many of these jobs build on skills developed through high-quality science, mathematics, and technology education. Our nation is unlikely to remain a world leader without a better-educated workforce. (p. 1)

These economic and technological changes also present an opportunity for providing that high-quality education. Specifically, there is rich mathematics in workplace applications and in everyday life that can contribute to the school curriculum. Thus, today's world not only calls for increasing connection



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--> Introduction Society's technological, economic, and cultural changes of the last 50 years have made many important mathematical ideas more relevant and accessible in work and in everyday life. As examples of mathematics proliferate, the mathematics education community is provided with both a responsibility and an opportunity. Educators have a responsibility to provide a high-quality mathematics education for all of our students. A recent report of the National Academy of Sciences (NAS) entitled Preparing for the 21st Century: The Education Imperative (National Research Council [NRC], 1997) neatly summarizes this point: … today, an understanding of science, mathematics, and technology is very important in the workplace. As routine mechanical and clerical tasks become computerized, more and more jobs require high-level skills that involve critical thinking, problem solving, communicating ideas to others and collaborating effectively. Many of these jobs build on skills developed through high-quality science, mathematics, and technology education. Our nation is unlikely to remain a world leader without a better-educated workforce. (p. 1) These economic and technological changes also present an opportunity for providing that high-quality education. Specifically, there is rich mathematics in workplace applications and in everyday life that can contribute to the school curriculum. Thus, today's world not only calls for increasing connection

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--> between mathematics and its applications, but also provides compelling examples of mathematical ideas in everyday and workplace settings. These examples can serve to broaden the nation's mathematics education programs to encompass the dual objectives of preparing students for the worlds of work and of higher education. Furthermore, such programs can provide students with the flexibility to return to higher education whenever appropriate in their career paths. By illustrating the commonalities among the mathematical expectations for college, for work, and for everyday life, and by illustrating sophisticated uses of mathematics taught in high schools as well as in community colleges, this document aims to offer an expanded vision of mathematics. Mathematics based in the workplace and in everyday life can be good mathematics for everyone. High School Mathematics at Work is a collection of essays and illustrative tasks from workplace and everyday contexts that suggest ways to strengthen the mathematical education of all students. The essays are written by a wide range of individuals who have thought deeply about mathematics education and about the futures of today's students, from mathematics educators to business leaders, from mathematicians to educational researchers, from curriculum developers to policy makers. The essays and tasks in High School Mathematics at Work not only underscore the points made in The Education Imperative (NRC, 1997), but also begin to explore connections between academic mathematics and mathematics for work and life. As a step toward examining ways in which our schools and colleges can better serve the needs of both academic and vocational education, the National Research Council (NRC) of the National Academy of Sciences hosted a workshop in 1994 that resulted in a report entitled Mathematical Preparation of the Technical Work Force (NRC, 1995). Participants discussed questions such as How can mathematics content and technical applications of mathematics be integrated into educational programs? Should algebra continue to be the ''critical filter" used to determine whether or not students will be admitted into youth apprenticeship programs? Is the mathematics included in technical education programs consistent with emerging educational and occupational skills standards? Is it possible (or desirable) to design a core mathematics curriculum for the high school and community college levels that prepares students both for further formal education and for immediate employment in the technical work force? (p. 6) High School Mathematics at Work continues discussion of these questions, and considers in particular how workplace and everyday mathematics can enrich mathematics teaching and learning.

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--> Though the nominal mathematical content of this volume is high school mathematics, consideration of the above issues will lead to implications for colleges as well. For example, some two-year colleges have moved toward programs that include contextual learning and work-based experiences to enhance academic learning, often through articulated 2+2 partnerships that combine two years of course-work in high school with two years at a community college. The movement toward work-based learning has gained momentum in recent years through the School-to-Work Opportunities Act of 1994, administered jointly by the Departments of Education and Labor, and through the Advanced Technological Education program at the National Science Foundation. Both programs emphasize high academic expectations and require strong connections among schools, two-year colleges, businesses, and industry. By bringing these issues to the attention of the broader college and school communities, and by promoting higher mathematical expectations for all students, this document might provide an opportunity for schools and colleges to reconsider the mathematics courses before calculus, perhaps leading to new conceptualizations of their remedial, developmental, and "liberal arts" courses. Fundamentally, High School Mathematics at Work is about mathematics. Its view of mathematics and mathematics learning recognizes a potential symbiotic relationship between concrete and abstract mathematics, each contributing to the other, enhancing their joint richness and power. This view is not new. Historically, much mathematics originated from attempts to solve problems from science and engineering. On the other hand, solutions to many problems from science and engineering have been based on creative ways of applying some mathematics that until then had no known applications. Mathematics can help solve problems, and complex workplace problems can help stimulate the creation of new mathematics. Embracing this connected view of mathematics requires more than addressing content issues. In this document, the essays and tasks are organized according to four themes, each considering a different aspect of the many challenges involved in creating an enriched mathematics education for students. Each theme is introduced by an overview that provides a context for and a summary of the essays and tasks that follow. The first theme, Connecting Mathematics with Work and Life, sets the stage for the document as a whole, examining why and how "real world problems" can be used to enhance the learning of mathematics. With that premise, the remaining themes emphasize implications for various components of the educational system. The Roles of Standards and Assessments highlights the roles of standards and assessments in maintaining and also changing a vision of mathematics education. Curricular Considerations explores ways of designing curricula that attend to the needs of a diverse citizenry. Finally, Implications for Teaching and Teacher Education underscores the background and support teachers must have to respond to the needs of today's students.

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--> Many of the issues raised by these essays are quite complex; no single essay provides a definitive resolution for any of these issues, and in fact, on some matters, some of the essayists disagree. Collectively, these essays point toward a vision of mathematics education that simultaneously considers the needs of all students. High School Mathematics at Work, however, unlike many documents produced by the National Research Council, is not a consensus document. The intent of this document is to point out some mathematical possibilities that are provided by today's world and to discuss some of the issues involved—not to resolve the issues, but to put forward some individual and personal perspectives that may contribute to the discussion. Under each theme, the essays are accompanied by several tasks that illustrate some of the points raised in those essays, though many of the tasks could appropriately fit under several of the themes. The tasks serve as examples of where today's world can provide good contexts for good mathematics. They never were intended to represent, or even suggest, a full menu of high school mathematics. They provide possibilities for teaching. They exemplify central mathematical ideas and simultaneously convey the explanatory power of mathematics to help us make sense of the world around us. This book offers an existence proof: one can make connections between typical high school mathematics content and important problems from our everyday lives. And, it makes an important point: that the mathematics we learn in the classroom can and should help us to deal with the situations we encounter in our everyday lives. But High School Mathematics at Work is not only about relevance and utility. The mathematics involved is often generalizable; it often has aesthetic value, too. Mathematics can be beautiful, powerful, and useful. We hope you will discover all three of these virtues in some of the examples. At a time when analysts of the Third International Mathematics and Science Study (TIMSS) have characterized the K-12 mathematics curriculum as "a mile wide and an inch deep" (Schmidt, McKnight & Raizen, 1996) this report does not advocate that tasks like the ones in this volume merely augment the curriculum. Rather, it suggests that tasks like these can provide meaningful contexts for important mathematics we already teach, including both well-established topics such as exponential growth and proportional reasoning, as well as more recent additions to the curriculum, such as data analysis and statistics. Collectively, these essays and tasks explore how mathematics supports careers that are both high in stature and widely in demand. By suggesting ways that mathematics education can be structured to serve the needs of all students, the Mathematical Sciences Education Board (MSEB) hopes to initiate, inform, and invigorate discussions of how and what might be taught to whom. To this end, High School Mathematics at Work is appropriate for a broad audience, including teachers, teacher educators, college faculty, parents, mathematicians, curriculum designers, superintendents, school board members, and policy makers—in short, anyone interested in mathematics education.

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--> For those who teach mathematics, the essays might provide new ways of thinking about teaching and learning; the tasks might provide ideas for the classroom. For parents, this book can give a sense of how mathematics can be powerful, useful, beautiful, meaningful, and relevant for students. And for those who influence educational policy, this book might motivate a search for curricula with these virtues. As with all of the recent published work of the MSEB, High School Mathematics at Work is meant to be shared by all who care about the future of mathematics education, to serve as a stimulus for further discussion, planning, and action. All those who contributed to this report would be delighted if teachers gave copies to school board members, college faculty gave copies to deans, curriculum developers gave copies to publishers, employers gave copies to policy makers, and so on. Only through continued, broad-based discussion of curricular issues can we implement change and raise our expectations of what students know and are able to do. References National Research Council. (1995). Mathematical preparation of the technical work force. Washington, DC: National Academy Press. National Research Council. (1997). Preparing for the 21st century: The education imperative. Washington, DC: National Academy Press. Schmidt, W. H., McKnight, C. C., & Raizen, S. A. (1996). A splintered vision: An investigation of U.S. science and mathematics education . Dordrecht, The Netherlands: Kluwer Academic Publishers.

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