Precalculus Investigations: A Laboratory Manual, Preliminary Edition

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9780130109545: Precalculus Investigations: A Laboratory Manual, Preliminary Edition

Appropriate as a supplement to any text in the Precalculus Curriculum. College Algebra, Algebra and Trigonometry, Trigonometry or Precalculus. This three year NSF funded project integrates an applied approach to algebra/trigonometry/precalculus mathematics based on real engineering and design problems with mathematics curriculum reform principles and practice. The Investigations reflect the AMATC and NCTM Standards in both curriculum content and pedagogy. Each lab is based on a real-world application from another discipline, and involves interactive and collaborative learning. Students will use technology (primarily graphing calculators), employing multiple approaches (analytical, graphical, numerical, verbal) to model solutions to these problems, increasing their reasoning and problem-solving skills. Many mathematics instructors are eager to integrate realistic applications in their teaching, but lack the time and resources to develop the necessary connections on their own. These Investigations provide such applications by modeling workplace experiences of professionals in engineering, design and management occupations.

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From the Back Cover:

The laboratory investigations in this manual are an outgrowth of a campus-wide interdisciplinary collaboration at Wentworth Institute of Technology. With support from the National Science Foundation, mathematics faculty worked closely with colleagues in engineering, architecture, design, and management to identify field-specific problems that reveal rich connections to fundamental mathematics concepts in algebra, trigonometry, and precalculus.

The authors are full-time classroom mathematics instructors with many years of both college and high school teaching experience. In the spirit of the AMATYC and NCTM standards, they have incorporated a comprehensive "Rule of Four" pedagogy employing multiple representations in modeling real-world problems, interactive and collaborative learning, and regular use of technology. Many of the investigations require data collection in laboratory settings, and almost all involve some sort of hands-on activity. This manual is intended to provide students direct experience with mathematics as revealed in real applications, by modeling workplace experiences of professionals in business and industry. Students who have used these laboratory investigations have commented in course evaluations that they "make you think about the math topic in a whole new way," "keep you thinking of the math applications outside of class," and "helped give an understanding of how the math we are working on ties into everyday life." Other comments included "The labs we did were very realistic," and "I now try to look at a problem in more than one aspect."

Encouraged by these student responses, we believe Precalculus Investigations: A Laboratory Manual, will heighten students' interest in Precalculus. This manual exposes the student to lab projects that incorporate issues of daily life and today's careers such as, medical technology, weather, architecture, life cycles, natural resources, and noise pollution. These lab projects give students the ability to associate and extend the usefulness of mathematics in our ever-changing world.

From the Inside Flap:

Preface to the Student

The Mathematics Laboratory Investigations in this book are based on real workplace problems encountered by people in a variety of occupations. Some problems have been somewhat simplified or idealized in order to make the mathematical connections clearer, but the fundamental nature of each application has been preserved. In working through these labs you will see how thinking mathematically can help practicing professionals deal efficiently and effectively with problematical situations that arise in the course of their work. You'll be expected to work on each problem in a group with other students, similar to the way people typically collaborate in teams in their jobs.

Suggestions for Success

You'll probably find that thorough reading of the introductory material in each lab, as well as careful attention to the wording of the questions that are posed throughout, are keys to understanding and successfully completing the lab. In labs that involve experimentation, ask for assistance if you have any uncertainty about equipment setup and data collecting. Most labs assume that you have a graphing calculator available for your use. You'll be expected to be able to rely on mathematics skills you have previously learned. These are usually specified under "Prerequisites" at the beginning of each lab. Some of these laboratory activities will introduce you to new mathematics topics. Don't be surprised if you encounter an unfamiliar concept; the lab will help you learn and understand it. Many questions require written responses, in which you are asked to demonstrate your understanding of mathematical concepts. Discuss these among your group, and write in clear and complete sentences.

We hope that you will find these laboratory investigations challenging – they are designed to make you think, sometimes creatively, about mathematics : but that you will also get a great deal of satisfaction from using your mathematical knowledge to tackle these problems.

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