Prealgebra: Journey Into a Mathematical World, Preliminary Edition / Edition 1

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Overview

Ideal for adult learners who have been away from mathematics for awhile or who never really understood the first time around, this book offers an alternative to the traditional prealgebra or basic mathematics books that focus on drill and practice problems. Instead, it takes a discovery approach to learning concepts by using interesting and real-life problems from the world around us -- enjoyable problems that will simultaneously challenge, interest and entertain, and guide readers toward active problem solving in the context of real and thought provoking situations. Covers: Number Sense and Integers. Number Sense with Rational and Irrational Numbers. Percents, Ratio, and Proportion. Geometry and Measurement. Variable and Function Concepts. Probability and Statistics. Symbol Sense and Algebraic Problem Solving. For those needing a math review or a "fresh start" to math.
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Product Details

  • ISBN-13: 9780139586460
  • Publisher: Pearson Education
  • Publication date: 11/28/2001
  • Edition description: PRELMNRY
  • Edition number: 1
  • Pages: 695
  • Product dimensions: 8.52 (w) x 10.89 (h) x 1.01 (d)

Table of Contents

Preface to Instructors.
Preface to Students.
1. Problem Solving and Number Sense.
Problem Solving in the Real World. Estimation, Numerical Reasoning, and Mental Arithmetic. Exponents, Factors, and the Order of Operations.

2. Sets of Numbers and Integer Operations.
Numbers and Their Properties. Addition and Subtraction of Integers. Multiplication and Division of Integers.

3. Rational and Irrational Numbers.
Rational Numbers in Fractional and Decimal Form. Adding and Subtracting Rational Numbers. Multiplying and Dividing Rational Numbers. Numbers That Are Not Rational.

4. Percent, Rate, and Proportion.
Connections Between Fraction, Decimal, and Percent. Use and Misuse of Percent. Rates and Percent Change. Ratio and Proportion.

5. Geometry and Measurement.
Estimation, Measurement, and Unit Analysis. Plane Geometry: Area and Perimeter. Solid Geometry: Volume and Surface Area. Large Numbers, Small Numbers, and Scientific Notation.

6. Functional Relationships and Symbol Sense.
Numerical Relationships in Tables of Data. Graphical Relationships in the Rectangular Coordinate System. Symbolic Relationships in Equations.

7. Basic Concepts of Descriptive Statistics.
Organizing and Representing Data. Summarizing Data by Measures of Center. Summarizing Data by Measures of Spread.

8. Basic Concepts of Probability.
Probability Act I: A Classical Approach. Probability Act II: An Empirical Approach.
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Preface

To Instructors

Success is a Journey, not a Destination
– Ben Sweetland

This book was written as an alternative to the traditional Prealgebra or Basic Mathematics book and to help students begin building the mathematical foundation needed to function in the 21 S` century. In today's world, students must achieve a minimum level of mathematical literacy if they hope to succeed in other college courses, have a variety of career choices, and develop the critical-thinking skills necessary for effective citizenship.

In the spirit of the NCTM and AMATYC standards, and the MAA's report on Quantitative Reasoning for College Graduates, this book addresses the need for students to:

  • Develop problem-solving strategies while working on meaningful problems of interest.
  • Become involved in building simple mathematical models of real world problems.
  • Support their mathematical work with logical reasoning.
  • Make connections with how mathematics is used in other disciplines.
  • Read, write, and speak the language of mathematics with understanding.
  • Use technology as a tool to help understand mathematical ideas and solve real life problems.
  • Develop confidence in their ability to do and understand any mathematics that they may encounter at school, home, or work.

The core of the material includes basic ideas of number sense, symbolism and algebra, geometry, function, discrete mathematics, probability, and statistics. The material is intended for adult students who place into either a course in Prealgebra or Basic Mathematics.

This book is a startingpoint for underprepared students to begin their journey into a mathematical world. It is only a beginning, but beginnings are important times. The student will have the opportunity to learn all the topics traditionally taught at this developmental level. However, much of the learning will occur through guided activities called Discovery Adventures. These adventures put the student into real and thought-provoking situations where mathematical ideas naturally arise. The student is guided through these adventures with many questions that lead to active involvement in constructing their own learning. The student is then given feedback on the concepts and procedures present in the activity. The explanations provide a balance between understanding the ideas and learning the procedures.

All the concepts and skills needed to move on to a course in Introductory Algebra will be covered, and more. The coverage will be such that students will get lots of practice mastering each topic by working on in-depth, context-driven activities. These activities are constructed so that the student gains an intuitive understanding of how mathematics works and how it can be applied to the world around them.

While it is assumed that all students will have access to a scientific calculator, some activities will ask the student to put their calculator aside. Some exercises will require them to use it, but most will not mention it at all. The problems are designed to give the student a conceptual understanding of basic mathematics, practice learning routine procedures, and the ability to apply the concepts and procedures to everyday life. The calculator is just a tool, like pencil and paper that is used in the problem solving process. Part of the learning is deciding which tool is most appropriate for different tasks.

On a more personal note, teaching our Basic Math Studies course at Massachusetts Bay Community College has always been a challenge because I could never find any published material that presented Basic Mathematics or Prealgebra as an interesting and useful subject to study. I wanted a text that allowed the student to discover the beauty and power of math in an environment that was comfortable and challenging. It was time to stop complaining about the lack of material and instead dive into creating a book that would motivate students by putting them into real life situations that involve active hands-on learning.

The material has been developed, written, and class tested by the author while teaching numerous sections of Basic Math Studies to a very diverse group of students including many ESL students. There has been constant feedback from the students that has prompted many changes to allow the text to be as user friendly as possible.

I deeply believe in this work and I am committed to seeing positive change occur. I have the confidence to promote this material because I have seen it work! All my students were interviewed at midterm and during the last week of classes. The main purpose of the interview was to review a portfolio of the student's work and to let them do some self-assessment on what they felt they had learned. The interviews validated what I had observed in and out of the classroom. The students were working hard, learning mathematics, and enjoying the experience.

In concluding this preface, let me say that this book was written for the student to enjoy. The idea being that, one can work hard, think creatively, and have fun, all at the same time. It is hoped that the students and instructors will find the material rich in flavor, challenging in content, and fun to use.

I would like to thank the many developmental math instructors who reviewed this book: James Barr, Laramie County Community College; Celeste Carter, Richland College; Elizabeth Chu, Suffolk Community College; Margaret Crider, Tomball College; Irene Doo, Austin Community College; Rebecca Easley, Rose State College; Sharon Edgrnon, Bakersfield College; Grace Foster, Beaufort County Community College; Terry Fung,, Kean University; Roberta Lacefield, Waycross College; Rowan Lindley, Westchester Community College; Debra Pharo, Northwestern Michigan College; Barbara Sausen, Fresno City College; Michael Scroggins, Lewis & Clark Community College; Gwen Terwilliger, University of Toledo; Sam Tinsley, Richland College; Elaine M. Werner, University of the Pacific; and Tom Williams, RowanCabarrus Community College.

James Sullivan
Massachusetts Bay Community College

To Students

Tell me and I'll forget. Show me and I may not remember. Involve me, and I'll understand.
– Native American saying

While this text will tell you about mathematics and show you the process of doing mathematics, its main purpose is to involve you in doing mathematics. To tell and show must be part of any learning materials, but a student of mathematics does not take ownership of knowledge until he/she is actively involved in creating their own learning. This text will put you into different problem situations and guide you to discover the concepts that will help build your mathematical power. As you gain math power, you will have the confidence to face a world where more and more jobs require mathematical thinking. Thoughtful use of this power will give you the ability to solve math-related problems at home, school, and work. You will gain a vision that allows you to see that mathematics is everywhere and the more mathematical power you develop, the better you will understand and function in the real world.

Many students are apprehensive about starting a mathematics class. Perhaps it has been many years since you have taken any formal mathematics, or maybe you have never seen the reason or relevancy of studying math, or possibly you just never really understood it the first time around. This material was written for you, the student, to be actively involved with in a comfortable environment. You will be challenged to think critically about solving real problems and be asked to express your ideas and results in writing.

The text will take you on a journey into a mathematical world through different discovery adventures. These adventures are intended to be enjoyable problems that will simultaneously challenge, interest and entertain you. While not all problems will meet this expectation for each individual student, it is hoped that the overall effect will be an experience that is useful and fun to take part in. Learning mathematics does not have to be a dreadful chore that students endure to graduate. It can be an exciting exploration that all students look forward to.

Try to start these materials with an open mind and positive outlook. This is an experience that might be different from what you're used to seeing in a mathematics class. Regardless, you need to be actively involved with each problem situation to learn, through discovery, the concepts and procedures of basic mathematics.

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