PREFACE

Approximately seventy-five percent of the U.S. work force comprises people who do not hold bachelor's degrees. Yet the work force of the future will require a high level of technical skills—using computers for tasks ranging from word-processing to controlling machines, analyzing complicated sets of data, and ensuring quality control in production processes. The academic preparation of this work force must incorporate skills for life-long learning, strategies for problem-solving, practice in working collaboratively, and experience reading and interpreting technical documents.

Mathematics is fundamental to achieving these goals because of the key role it plays in subjects vital to the education of the technical work force. The study of mathematics helps people learn to represent and reason about quantities and complex relations in ways that many believe are crucial for success in the workplace. For this reason, mathematics is often used as a “gatekeeper” for admission into special programs; for example, many vocational education programs require that applicants have successfully completed a course in algebra.

Mathematics in the workplace is quite different from mathematics in school. It is more concrete and more intuitive, yet at the same time more exacting and more unpredictable. It is rich in data and inextricably linked with technology. Technicians and other workers are routinely expected to carry out multi-step applications of simple mathematics—especially three-dimensional geometry, triangle trigonometry, and elementary data analysis. School mathematics needs to reflect this reality, even as it also builds a base for students who will go on to more advanced mathematics in college courses.

Many members of the mathematics community, including both researchers and educators (kindergarten through graduate school), are actively involved in implementing mathematics education reform at all levels. At the same time, much of the development of technical curricula for grades 10-14 has been taking place outside mathematics departments. Programs such as “youth apprenticeships” and “tech-prep” that address school-to-work issues are growing in number and importance. However, even in the same building there is virtually no communication between teachers of mathematics in academic programs and teachers of mathematics in vocational education programs. Moreover, the professional networking necessary to make those connections has not been put in place. Collaborative efforts between these communities are needed to create programs that provide the flexibility to allow students to transfer between college-preparatory and technical education programs. Such undertakings also would begin to change the second-class status of technical education programs (vividly illustrated by the fact that they are often located in high school basements).

MATHEMATICS IN THE WORKPLACE IS QUITE DIFFERENT FROM MATHEMATICS IN SCHOOL. IT IS MORE CONCRETE AND MORE INTUITIVE, YET MORE EXACTING AND MORE UNPREDICTABLE. IT IS RICH IN DATA AND INEXTRICABLY LINKED WITH TECHNOLOGY.



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MATHEMATICAL PREPARATION OF THE TECHNICAL WORK FORCE: REPORT OF A WORKSHOP PREFACE Approximately seventy-five percent of the U.S. work force comprises people who do not hold bachelor's degrees. Yet the work force of the future will require a high level of technical skills—using computers for tasks ranging from word-processing to controlling machines, analyzing complicated sets of data, and ensuring quality control in production processes. The academic preparation of this work force must incorporate skills for life-long learning, strategies for problem-solving, practice in working collaboratively, and experience reading and interpreting technical documents. Mathematics is fundamental to achieving these goals because of the key role it plays in subjects vital to the education of the technical work force. The study of mathematics helps people learn to represent and reason about quantities and complex relations in ways that many believe are crucial for success in the workplace. For this reason, mathematics is often used as a “gatekeeper” for admission into special programs; for example, many vocational education programs require that applicants have successfully completed a course in algebra. Mathematics in the workplace is quite different from mathematics in school. It is more concrete and more intuitive, yet at the same time more exacting and more unpredictable. It is rich in data and inextricably linked with technology. Technicians and other workers are routinely expected to carry out multi-step applications of simple mathematics—especially three-dimensional geometry, triangle trigonometry, and elementary data analysis. School mathematics needs to reflect this reality, even as it also builds a base for students who will go on to more advanced mathematics in college courses. Many members of the mathematics community, including both researchers and educators (kindergarten through graduate school), are actively involved in implementing mathematics education reform at all levels. At the same time, much of the development of technical curricula for grades 10-14 has been taking place outside mathematics departments. Programs such as “youth apprenticeships” and “tech-prep” that address school-to-work issues are growing in number and importance. However, even in the same building there is virtually no communication between teachers of mathematics in academic programs and teachers of mathematics in vocational education programs. Moreover, the professional networking necessary to make those connections has not been put in place. Collaborative efforts between these communities are needed to create programs that provide the flexibility to allow students to transfer between college-preparatory and technical education programs. Such undertakings also would begin to change the second-class status of technical education programs (vividly illustrated by the fact that they are often located in high school basements). MATHEMATICS IN THE WORKPLACE IS QUITE DIFFERENT FROM MATHEMATICS IN SCHOOL. IT IS MORE CONCRETE AND MORE INTUITIVE, YET MORE EXACTING AND MORE UNPREDICTABLE. IT IS RICH IN DATA AND INEXTRICABLY LINKED WITH TECHNOLOGY.

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MATHEMATICAL PREPARATION OF THE TECHNICAL WORK FORCE: REPORT OF A WORKSHOP IS THE MATHEMATICS INCLUDED IN TECHNICAL EDUCATION PROGRAMS CONSISTENT WITH EMERGING EDUCATIONAL AND OCCUPATIONAL SKILLS STANDARDS? Other issues that require attention by these two communities include: How can mathematics content and technical applications of mathematics be integrated into educational programs? Who should be responsible for the mathematics component of technical education 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? At what grade level, if any, is it appropriate to “track” students into technical education programs? How are skills such as reading technical materials and working cooperatively in groups—skills that are necessary for independent life-long learning and success in the workplace—being incorporated into the mathematics curriculum? On November 18, 1994 the Mathematical Sciences Education Board (MSEB) hosted a workshop as a first step in linking the communities that need to jointly address the challenges of alignment between occupational and educational expectations. The workshop, supported by a grant from the Alfred P. Sloan Foundation, brought together mathematicians, mathematics educators, vocational educators, business leaders, and representatives from federal and private funding agencies to open dialogue about issues and stimulate activity in those communities. Workshop participants had opportunities to work in small-group sessions on issues related to: (1) tracking, (2) core curriculum, (3) students ' needs, and (4) articulation. This report describes the Workshop and the outcomes of the working groups. It also contains brief position papers by some participants who were asked to address questions such as: What is the purpose of high school mathematics? How can you tell if a tech-prep program is effective? Is tracking students ever appropriate? Is workplace-based mathematics good mathematics for everyone? Can all students benefit from a tech-prep program?

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MATHEMATICAL PREPARATION OF THE TECHNICAL WORK FORCE: REPORT OF A WORKSHOP The Workshop was intended as just a first step in examining ways in which our schools and colleges can better integrate academic and vocational education. The issues raised need continual scrutiny by groups that offer the combined wisdom of mathematicians, engineers, scientists, policy makers, members of the business community, and educators drawn from different disciplines and perspectives. Although the major focus of schools has tradeitionally been to prepare a select group of students for college, it is clear that this mission must be broadened to better educate all future workers for the challenges they will face. That goal can be accomplished only through the concerted efforts of responsible, caring professionals who commit themselves to improving the education of every student. These are the voices that speak in this volume. SUSAN L. FORMAN Director of Postsecondary Programs Mathematical Sciences Education Board June 1995

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