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Sources of Problems and Tasks

SUSAN FORMAN AND LYNN ARTHUR STEEN

Potential tasks for High School Mathematics at Work were solicited from many sources. Printed announcements of the project were distributed at national meetings of various professional societies; e-mail invitations were sent to many mathematicians, educators, and policy leaders; special invitations were extended to leaders of major high school curriculum and assessment projects, both academic and vocational; panel presentations were arranged to address the key question of what mathematics every high school graduate should know and be able to do; and visits were made to corporations to solicit examples of typical work tasks that require mathematical knowledge and insight.

From this enormous volume and variety of problems, the Task Force and its consultants shaped tasks for inclusion in the volume—by selection, by revision, by combination, and by creation. Virtually none of the tasks presented here are the same as originally proposed: each has been transformed to fit the context of this volume. Similarly, teachers who may wish to use these or other tasks will need to adapt them to their own contexts. The process of adaptation reinforces one of the key lessons of High School Mathematics at Work, namely, that context is important for mathematics.

That said, we list below the types of sources we found helpful in preparing High School Mathematics at Work. Though this list is intended to be illustrative



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--> A— Sources of Problems and Tasks SUSAN FORMAN AND LYNN ARTHUR STEEN Potential tasks for High School Mathematics at Work were solicited from many sources. Printed announcements of the project were distributed at national meetings of various professional societies; e-mail invitations were sent to many mathematicians, educators, and policy leaders; special invitations were extended to leaders of major high school curriculum and assessment projects, both academic and vocational; panel presentations were arranged to address the key question of what mathematics every high school graduate should know and be able to do; and visits were made to corporations to solicit examples of typical work tasks that require mathematical knowledge and insight. From this enormous volume and variety of problems, the Task Force and its consultants shaped tasks for inclusion in the volume—by selection, by revision, by combination, and by creation. Virtually none of the tasks presented here are the same as originally proposed: each has been transformed to fit the context of this volume. Similarly, teachers who may wish to use these or other tasks will need to adapt them to their own contexts. The process of adaptation reinforces one of the key lessons of High School Mathematics at Work, namely, that context is important for mathematics. That said, we list below the types of sources we found helpful in preparing High School Mathematics at Work. Though this list is intended to be illustrative

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--> rather than exhaustive, we apologize for omitting any particularly fruitful sources. Similar lists tied to regional contexts should be of help to teachers who want to offer their students more locally relevant but similar tasks. From Industry and Government Big companies and government agencies are awash in data, from the manufacturing floor to the sales office: effective companies expect all their employees to use these data for planning and quality control. For this project, we found interesting examples from different industrial and governmental sectors: transportation (Boeing), electronics (Motorola), entertainment (Disney), food (Starbucks), construction (Hilti), and health (Oregon Center for Health Statistics). From School-to-Work Programs Many organizations are working to develop effective school-business partnerships. These programs operate under titles such as "tech-prep" and "school-to-work." They include regional education consortia (e.g., the East San Gabriel Valley Regional Occupational Project or the Pennsylvania Youth Apprenticeship Program), regional corporate consortia (e.g., the Washington State Manufacturing Technology Advisory Group or Craftsmanship 2000 in Tulsa, Oklahoma); and curriculum development organizations (e.g., the Consortium on Occupational Research and Development [CORD] in Waco, Texas, or the School-to-Work project of the Learning Research and Development Center [LRDC] at the University of Pittsburgh). From High Schools Many districts have special high schools devoted to vocational or technological education. Some (e.g., Rindge School of Technical Arts in Cambridge, Massachusetts; Leander High School in Leander, Texas; the Williamson Free School of Mechanical Trades in Philadelphia) provide a comprehensive philosophy uniting vocational and academic education. Others (e.g., Franklin High School in Portland, Oregon, Brooklyn Technical High School in New York) have special projects (STELLA at Franklin, Design Challenge at Brooklyn Tech) that offer stimulating ideas for how mathematics relates to other subjects. From College Programs Although High School Mathematics at Work is about high school mathematics, many programs with similar tasks can be found at two- and four-year colleges. Some of these have been supported by federal grants, others with local funds. Among those that contributed to High School Mathematics at Work are the Mathematics in Industry project at Henry Ford Community College, Dearborn, Michigan (Barbara Near, Project Director), Snapshots of Applications in Mathematics at SUNY College of Technology in Delhi, New York (Dennis Callas,

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--> Project Director), and Interactive Mathematics at Mt. Hood Community College in Oregon (Penny Slingerland et al., project directors). More recent projects supported by the National Science Foundation's (NSF) Advanced Technological Initiative (ATE) program can be found at Wentworth Institute (Gary Simundza, Director) and Johns Hopkins University (Arnold Packer, Director). From Curriculum and Assessment Projects Many innovative tasks can be found in the material produced by the several nationally funded curriculum and assessment projects. High School Mathematics at Work benefited especially from ideas submitted by the Balanced Assessment Project, the Interactive Mathematics Project, the New Standards Project, and the Connecticut Academic Performance Test in Mathematics. From Individuals Many individuals contributed special ideas to High School Mathematics at Work—far more than can be named here or even recalled. We do mention, however, a few individuals who direct centers or projects that we found to be particularly rich sources of ideas: Dick Stanley, Charles A. Dana Center, University of California, Berkeley; Peter Costa, Center for Applied Mathematics, University of St. Thomas; Avner Friedman, Director of the Institute for Mathematics and Its Applications at the University of Minnesota; Cindy Hannon, Tech Prep Coordinator, Maryland State Department of Education; Thomas Hsu, Cambridge Physics Outlet, Woburn, Massachusetts; and Martin Nahemow, Director of School-to-Work Programs, LRDC, University of Pittsburgh, From Coordinating Organizations Several organizations serve as helpful sources of contacts for particular projects and programs. These include Schools that Work, a project directed by Gene Bottoms for the Southern Regional Education Board; the Advanced Technological Education (ATE) Program of the NSF (Elizabeth Teles and Gerhard Salinger, Program Directors); the National Center for Research in Vocational Education (NCRVE) at the University of California, Berkeley (Norton Grubb and David Stern, Directors); the Institute on Education and the Economy at Columbia University (Thomas Bailey, Director); and Jobs for the Future in Boston (Hilary Pennington, President and Susan Goldberger, Program Director). From Special Sources Ideas for tasks in High School Mathematics at Work also came from the National Security Agency's Summer Mathematics Teacher Institutes (Fort Meade, Maryland) and the TEAMS Competition of the Junior Engineering Technical Society (JETS). For similar problems from new sources, we suggest some of the NSF ATE projects, for example, the Sinclair Center and the Center for Image Processing in Education. Of course, some of the very best

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--> sources are the members of the Task Force for High School Mathematics at Work, who worked extensively with the many tasks that were reviewed in the process of preparing this volume. These diverse institutions and programs illustrate both the particular sources from which High School Mathematics at Work was developed, and also the enormous variety of places that educators should look to in their search for tasks that are mathematically rich and contextually relevant.