Ii ..

Ii

Foundations of ,­P:rob·lem Solving Third Edition

Edited by Eric Myrvaagnes Suffolk University Boston, MA

Chapter Contributors: Eric Myrvaagnes Peter D. Smith Phanwadee Brooks Paula Wolf Sarah Carroll

Activity Contributors: Daniel K. Apple Marie Baehr Nancy Duffrin Karl Krumsieg Cy Leise Carol Zulauf

Cover photograph by Eric Myrvaagnes

Cover designed by Laurie Markus Pacific Crest

Frontispiece drawing by Laurie Markus

Pacific Crest

FOUNDATIONS OF PROBLEM SOLVING THIRD EDITION

By Eric Myrvaagnes, with

Phanwadee Brooks Sarah Carroll Peter D. Smith Paula Wolf

Editor and Production Designer Eric Myrvaagnes

General Editor Daniel K. Apple

Copyright © 1996-1999 by Pacific Crest Software and Eric Myrvaagnes, Phanwadee Brooks, and Paula Wolf 875 NW Grant Avenue Corvallis, Oregon 97330 (541) 754-1067

All rights reserved under international copyright conventions. No part of the contents of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without the written consent of the publisher.

Process Education nI and Skills for Life TN are trademarked terms for Pacific Crest Software. Use of these specifically defined terms is free but must include a citation to Krumsieg and Baehr, Foundations ofLearning (pacific Crest, 1996).

PC:SOLVB T", SOLVB TOI, and the Learning Assessment Joumal"" are trademarked terms for Pacific Crest Software.

ISBN 1-878437-42-9

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•

•••• PREFACE•• • The Need for This Book • ••

New demands are being placed on today's educators from employers and accreditation associations. Terms such as assessment. cri tical thinking, problem solving, and teamwork (to name a few) are now commonly used and

• discussed in many circles.

•• An increasingly competitive global economy calls for our schools to produce graduates capable of dealing with the challenge of today' s workplace. This includes workers who can think critically, learn quickly, solve problems,

• communicate, work in teams. and assess. The demand for more accountability on the part of education has led accreditation associations to require new measures for performance and assessment.

•• This book is intended for those faculty and institutions who are responding to these demands through improving teaching and redesigning curricula and core requirements. As more and more faculty implement "process education"

• techniques into their courses and institutions create courses centering on skill development. there is a growing need

• for the appropriate materials.

• What's New in This Edition

•• 1. .\ new chapter on Logic has been added .

.-\. new chapter on Programming has been added. using contexts ranging from Excel macros to the C language.

• 3. Several new problems have been added to the last chapter.

• 4. .-\.1: _om\." e examples now use standard spreadsheet software. such as Microsoft® Excel™.

11 e hapter on Graphical Analysis has been moved ahead of the chapter on Data Management Using

• Sprea ·sheets.

6. Se era! activities have been rewritten. and errors corrected.

• 7. . -ew cti\itie on estimating and on validating results have been added.

• Tne Communication Methodology in Chapter 2 has been shortened and simplified.

Overview of Foundations of Problem Solving

•• Fowu1aJions ofProblem Solving is very similar in spirit to the highly regarded Foundations ofLearning. in the same series. Both texts seek to help students develop the learning skills that will enable them to function effectively in our modem. rapidly changing world. While both texts use the techniques of Process Education. Foundations of Problem Solving places much more emphasis on quantitative methods and the computer as a tool for solving problems. Foundations ofProblem Solving is an activity-based book: the authors finnly believe that students learn problem sol ·ing better by doing it than by simply reading about it or listening to lectures. Nevertheless. critical reading. listening. and writing are considered essential skills for a good problem solver.

PREFACE ................... III

••

••

FOUNDATIONS OF PROBLEM SOLVING

Foundations ofProblem Solving grew out of numerous requests for a text that is more content-oriented than Foundations ofLearning. while retaining much of the innovative and successful process orientation of Foundations ofLearning and other Pacific Crest texts.

At Suffolk University. we have used Pacific Crest's Learning Through Problem Solving for a number of years . In preparing Foundations ofProblem Solving. we have tried to maintain and enhance the rich content of Learning Through Problem Solving while fitting it to the more accessible pedagogical style of Foundations ofLearning. We have also included a number of topics that did not appear in Learning Through Problem Solving .

The first two chapters introduce the philosophy of Process Education and principal methodologies of the book. The next three chapters present the essential foundation skills in three areas that are necessary for effective problem solving: learning to use tools. using computers and software. and doing basic mathematics. We feel that every course using Foundations ofProblem Solving should cover these five chapters. unless the students are known to have unusually high mathematical or communication skills when entering the course.

Later chapters cover a variety of problem-solving tools and topics ranging from tables and graphing to logic and probability, with application in business, finance, statistics, and everyday life. We encourage students to develop their own specialized algorithms and methodologies and to express them clearly using flow charts, pseudo-code. or outlines. Throughout the course. students work in teams, use guided discovery, learn critical thinking. and frequently self-assess in the form of written journals and reports. The final chapter, Research Problems, is a rich compendium of thought-provoking and challenging problems from a wide variety of contexts. While a few are short. individual exercises. the majority are larger-scale or open-ended problems, suitable for term projects and in­class team presentations. •A key feature of the text is the presence of five major themes of problem solving that permeate every chapter. These are: (1) Problem Solving

We refer to problem solving in a very broad and general sense. • (2) Assessment •

In particular, assessment of growth in problem solving performance and specific supporting problem solving skills. •

(3) Mathematical Thinking Thinking in terms of mathematical structures, measures, reasoning. language. and modeling.

(4) Communication Writing with technical precision, reading with perception, and clear presentation of results with supporting arguments.

(5) Teamwork • In particular, team-based problem solving. •

Every chapter contains activities stressing all or most of the five themes. These are highlighted in the table on the • next page and at the start of each activity. • This scheme permits considerable flexibility in the design of courses to suit students' needs. For a class of • especially mathematically mature students, one might downplay or touch lightly (as review reading) the activities relating to mathematical thinking and modeling. while in a school with a strong mandate for "writing across the curriculum", the writing, reading, and presentation activities could be given special emphasis. It is also possible (with a careful eye on the Prerequisites for each chapter and activity) to follow one or two themes through several chapters, and then come back to pick up others.

We strongly recommend accompanying this text with Pacific Crest's Learning Assessment Journal and A Fresh Look at Math and Graphing, both of which greatly enhance the effectiveness of the activities in this text at our college.

IV ............ PREFACE

FOUNDATIONS OF PROBLEM SOLVING

Table ofMajor Themes for Each Activity:

•••••••••••••••••••••• =

Theme ~ Chapter I

Problem Solving Assessment Mathematical Thinking

Communication Teamwork

1: Profiles 1.2 1.1,1.3 1.4 1.5 1.6

2: Theme Area Methodologies

2.1 2.3 2.2 2.4 2.5

3: Tools 3.1 3.2 3.3 3.4 3.5

4: Computer Tools

4.5 4.6 4.4 4.1 4.2

4.3

5: Mathematics Fundamentals

- 5.4,5.5 5.1,5.3, 5.6 5.2 5.8

6: Graphical Analysis

6.6 6.2 6.1,6.5 6.3 6.4

7: Data Management Using Spreadsheets

f . 7.3 7.4 7.1 7.2

8: Logic 8.4 8.1 8.2 8.3 8.5

9: Probability 9.5. 9.7 9.1 9.2,9.3 9.6 9.4

10: Statistics 10. ­ 10.3 10.1 10.2 10.4

11: ~1athematics of Finance

11.6, 11.7 11.4 11.1, 11.2 ll.5 11.3

1~: PrVel ,no 1-. 12.3 12.2, 12.4, 12.5, 12.6

12.8 12.1

13: R.ese2rch Problems

AlI problems Most problems Most problems Most problems Most problems

Who Can Benefit?

n --;: .....""Se!.s esigned to benefit all students by developing and improving their skills in the following areas: .e!"':- -g: .earn. problem solving, assessment, teamwork, communication, mathematical thinking, using computers, -~ :i" - -g about one' s education.

T.- =--ereq...Jsl<es for this course include a willingness to exercise and expand your mental processes, a desire to ez..- ~:: _ ;easonable background in high school mathematics. Familiarity with computers can help, but none is

.::. T.., - course was designed to serve as a starting point for skill development, providing a foundation to ~ ' '':::' ~ n -e most ideal settings for the use of this book are courses where "process" skills are emphasized and

F'"e5 -~'l Foun ations Course. Fres·-.. ~n Quantitative Reasoning Course. COIqJ_ler an Reasoning Skills Course.

.! . Learn'ig. Thinking, and Problem Solving Course . Llbed Am ~lath Course.

PREFACE .................. . . V

FOUNDATIONS OF PROBLEM SOLVING

Expected Student Outcomes

Key Outcomes from this course:

A student successfully completing this course should be able to:

1. Read instructions, process problems, construct and modify work products, document with quality, and present final efforts for official publication and review.

2. Read, process, construct, modify, transform, document, and present models representing relationships between variables in a system.

3. Read, process, construct, modify, transform, document, and present tables and graphical representations of data.

4. Learn how to learn new mathematical or technological concepts, tools, and processes so that they can acquire their own learning of material not covered in this course.

5. Act as a mentor or consultant to others in a variety of problem solving situations.

Students engaged in process education can expect to benefit in the following ways:

1. To increase the chances for success in, college by building a positive relationship with other students, faculty, staff, and the college community through a challenging, intense, and rewarding experience early in the college career.

2. To create more student ownership for individual learning through a course design that puts students at the •center of the learning process with faculty as facilitators. •

3. To improve their critical thinking skills through a course design that incorporates a discovery learning approach •with critical thinking questions in addition to strong course emphasis on self-assessment. •

4. To develop and improve "process" skills through study, application, and self-assessment of problem solving •techniques. •

5. Students will build foundations for future growth through the use of methodologies in the following skill areas: • a. Assessment. The ability to set up guidelines and criteria to assess products, performances, and situations •

involving other people and especially oneself. •b. Writing. The ability to express oneself and one's thoughts through answers to critical thinking questions,

reports, learning journals, and portfolio entries. • c. Critical Reading. The ability to interpret or acquire desired knowledge enhancing one's ability to learn on

one's own. d. Communication. The ability to provide information to others through various forms and media including

team and class interactions, reports, presentations, portfolios, and computer work. e. Teamwork. The ability to develop interpersonal skills as part of a group of people actively cooperating in

an organized way to achieve a goal. f. Problem Solving. The ability to resolve difficulties and find solutions to problems.

6. To improve one's mathematical reasoning skills and the ability to make effective use of current and new technologies as tools for the solution of problems.

V I ... . ........ PREFACE

•••••••••••••••••••••••••

FOUNDATIONS OF PROBLEM SOLVING

We look forward to hearing about the experiences of teachers and students who use this book. You can write to us at:

Pacific Crest Software 875 NW Grant A venue Corvallis, Oregon 97330

or via email at:

eric@cas.suffolk.edu or at: dan@pcrest.com

Acknowledgments

The editors would like to thank the many writers and teachers who helped make this edition possible. The team of authors have tackled a subject both important and timely and have done it with skill and imagination.

Parts of this book are adaptations of previous Pacific Crest books and workbooks. We would particularly like to thank Karl Krurnsieg and Marie Baehr, authors of Foundations ofLearning. Peter Smith made very substantial contributions to this edition. Phanwadee Brooks and Paula Wolf were both significant contributors to previous editions , and much of their work is retained here. Sarah Carroll was very helpful as we were getting this project started. Also, several faculty looked over early drafts of this book and gave quality feedback on materials as they were compiled or contributed activities or problems to the present edition. They include:

Karen Anderson Madison Area Technical College

Richard Armstrong Madison Area Technical College

Grady Batchelor Bellevue University

Steve Beyerlein University of Idaho

Greg Bole SUNY Stony Brook

Rufus Brey SUNY Stony Brook

Phanwadee Brooks Suffolk University

Sarah Carroll Suffolk University

Corinne M. Darvennes T nnessee Technological Cni\'e~iry

Jeanne Dodge Suffolk University

Nancy Duffrin SUNY Stony Brook

David L. Ferguson SUNY Stony Brook

David C. Johanson Uniformed Services University of the Health Sciences

David Kaplan York College

Celia Knapp Jamestown Community College

Paul Kramer SUNY Farmingdale

Joel Lehmann Valparaiso University

CyLeise Bellevue University

Charlotte Rakich Purdue University Calumet

Barbara Reed Framingham High School

Peter D. Smith St. Mary's College

Merriline Smith California State Polytechnic University

Robert Van Foote St. Augustine's College

Kathy Wendling Kirkwood Community College

Eric Wignall Pacific Crest

Paula Wolf Suffolk University

Carol Zulauf Suffolk University

PREFACE ......... . ......... VII

FOUNDATIONS OF PROBLEM SOLVING

•••

••

Table of Contents

Preface . ......................................... . . .... . .. .......... .. ......... iii The Need for This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ill

What's New in This Edition .. ... ....... .... ................. . ......... .. ....... . .. . .... . . ..... ill Overview of Foundations of Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. iii Who Can Benefit? ............................................................................ v Expected Student Outcomes .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. vi Acknowledgments ........................................................................... vii

Chapter One - Getting Started: Profiles and Cultures ................................. 1 Activity 1.1: Introduction to the Course .. .................................................. 5 Activity 1.2: What is a Good Problem Solver? ....... . . ............. ..... . .... ..... ... .. .... 9 Activity 1.3: Becoming a Self-grower ..... ...... ........ . ... ... ...................... ... . 12 Activity 1.4: What is a Mathematical Thinker? ... .......... . . .............................. 16 Activity 1.5: What is a Systems Thinker? ................................................. 19 Activity 1.6: What is a Good Team Player? ................................................ 23

Chapter Two - Theme Area Methodologies ......................................... 26 Methodology 2.1: The Problem Solving Methodology ............. . ............. . . . ... . ......... 28 Methodology 2.2: The Learning Process Methodology ......... ..... ......... . ... ......... ....... 34 Methodology 2.3: The Assessment Methodology ....... . .. ........ .. ... ........... ..... ........ 38 Methodology 2.4: The Communication Methodology ............................................ 42 Methodology 2.5: The Teamwork Methodology ................................................ 46 Activity 2.1: The Problem Solving Methodology .. .... . ........ ................. ..... ..... . 50 Activity 2.2: The Learning Process Methodology ............................... . ........... 53 Activity 2.3: The Assessment Methodology ............... .. .................... .. . . . . .... 57 Activity 2.4: The Communication Methodology . ... . ... ........ ....... . . ........... ... ... . . 59 • Activity 2.5: The Teamwork Methodology ................................................ 61 ••

Chapter Three - Tools .......................................................... 63 •Activity 3.1: Learning a Tool .............................................. .. ........... 65 Activity 3.2: The Learning Assessment Journal ...... .............. ........... ......... ... .. 70 • Activity 3.3: Algorithms and Flow Charts ............................. .. .................. 73 •Activity 3.4: Learning a Help System ..... ...... . ...... .. ........... ... ...... . ........... 80 Activity 3.5: Team Roles ... .. ..... ....... .......................... .... .. ...... .. ..... 83

Chapter Four - Computer Tools .................................................. 87 Activity 4.1: Email ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 89 Activity 4.2: The World Wide Web ...................................................... 94 Activity 4.3: A Methodology for Learning New Software ... ................................. 99 Activity 4.4: Exploring Spreadsheets ..... . ..................... .. . . ..................... 103 Activity 4.5: A Spreadsheet Problem ............................. .... . ... .... . ..... ... .. 106 Activity 4.6: Math Skills .... ..... ................... . .................. ... ........... 109

VIII .. . ......... PREFACE

• • FOUNDATIONS OF PROBLEM SOLVING•

• Activity 5.2: Order of Operations ... ................. . .... . .................. .. . . ....... 11 7 •

••

Chapter Five - Mathematics Fundamentals ....... ... . .. .......... . ... . . .. ...... ... 11_ Activity 5.1 : Variables and Functions . . ... . .. .. . . ..... .. .. ......... . . ..... . .. .. ...... .... 114 • Activity 5.3: Activity 5.4: Computing a Grade Point Average .... . ...... . .... ... . .. .......... ... .. .... .. 126 Activity 5.5: Validating Results ... ...... .. .... ... . . ...... ..... . . .. . ......... .. ..... .. . . 131

•• Activity 5.6: Estimating . ........ ...... . ... . ..... . ... .... .... . ... . . .. . . . . . .... . . . .... . 135

.. ......... ..... ..... ... ........ ..... . .. ........ .. 139 .. . . . . ....... . .... . ... . ... .. ....... . . . ..... . .. .. .... ... . 143

Activity 5.7: Solving a Word Problem . Activity 5.8: The Rent Problem

•• Activity 6.3: Graphing Table Data ... . . ... . . ............ ... .. .. ......... . . .. .. ... . . . .. .. 157

• Activity 6.4 : Linear Regression ...... ... .. . .. . ........ .. .. . . . .. . ..... . .. .... . . . . . ... . . . 160

• Activity 6.5 : Polynomial Curve Fitting .. . . . . .. .... ....... . ... ... ........ . ....... .... .. .. . 163

.. ..... . ..... . ... .. .. ...... . . ...... . ......... . 166Activity 6.6: A Numerical Integration Tool .

•

•• Activity 6.1: Activity 6.2:

Chapter Six - Graphical Analysis .... . .......... . . . ....................... .. .... . 146 Common Functions ............ .. .. . ........ . .. .... .. . .... .. .. . . .. . .... . .. 148 Functional Graphing .. ...... ............ ..... .. . . ...... .. . .. . . . ... .... . . .. 154

•• Chapter Seven - Data Management Using Spreadsheets ............................. 169

Activit 7.1 : Introduction to Tables . .. .. .. . .......... . . . ........... . ... . .. ... . . .... . .... 171

• Activity 7._: Moving and Sorting Data . . . ... . . .. . ........ . ... .. .... . ...... .. .... .... .... 174 Activity 7. 3: Searching and Selecting Data ...... ..... . . ... ... . . . .. ... .. . . .. . ... .. . . . . .. . .. 177

• Activity 7.4: Database Functions In Spreadsheets .. ... .. ..... .. . ................... . ....... 180 Activi ty 7. - : A Database Problem . .. . .. . ...... .. . . .. . . . ....... .. . .. . ... .. . .... . ......... 183

••• Chapter Eight - Logic

Activit)' 8.2:

.... . ...... . ..... .. . . ...... . .. . .. .. .. ... .......... .... .. . . 186 Activity .1: Using Venn Diagrams to Test Conclusions .. . ....... . . .. ........ ... ... . ... . ... . 188

•• A ti\;ty 8.3: Determining When Arguments are Valid ...... . . ... . . . . . . . . . . .. . . . . .. . ..... . ... 201

........ . ... .. ...... . . .. . .... . .... ..... . . .. . 205Acti\'ity 8.4 : Circuits: An Application of Logic

• A ti\ity 8.5: Solving Logic Puzzles . .. .. .. . ..................................... . ..... .. 210

• ••

A ti\'iry 9._: Counting Event Elements . .... ..... ...... . . ....... . . ............. . . . ........ 233 .. ... . ............ .... . .. .... . .. . . .... ...... . . . 239A tiviry 9.3 : Generating Random Numbers

• Activi .

• :\ u\ity 9.5 : Using a Continuous Normal Distribution Function to Compute Probability .... . .. ..... 246

• A uvity 9.6: Generating a Set of Sample Values for a Variable . .. ...... .... . .. ..... . .. . .... . . 250 A :hity 9.7: Using Simulation to Study and Make Decisions about Systems .... . . . ..... . . . . .. . . . 254

•• A tivity 10.2: Visual Displays of Statistical Data ............ . .... . .... . . .... . . .... .... . . . . .. 263

• :\ ti\'ity 10.3: Averages: Mean, Median, and Mode . .. . . ... . .. . ... ..... . ... . . .. .. . ... ..... . .. 269

... . . ... . ..... . . . .. .. . ..... . .... ..... ... . .... ... 272 Acti\iry 10.4: The Normal Distribution . . .

• Activity 10.5: Statistics and Software Functions .. ... ... . . .... . ... . . .. . . ... . .. ... . .. . . . . . . .. 275

Recognizing Patterns - Sequences and Series . . ... . . . . .. ............... .. .. .. .. . 122

Using Truth Tables to Test Equivalence ... ...... . . . ...... . ......... . ....... . . . 195

Probability ..... . . . ......... . .... . ............ .. . . ......... ... .. . 215• Chapter ~ine ­A thity 9.1 Constructing Sampling Distributions . . .... . . . ....... . .. ..... . . . ... .. .. .. . ..... 223

' 9.4: Using Discrete Uniform and Binomial Probability and Cumulative Distributions Functions to Compute Probability . . ... .......... . ... .. . .. .. ... ... . .. ............... .. . . 242

•• :\ctivity 10.1: Chapter Ten - Statistics .... . .......... . ...................... . .......... . ... .. . 258

Fundamentals of Statistics .... ..... . ..... .. .. ........ . . . ........ . ..... . ..... 260

PREFACE . . . .. . .. .. .... . .... IX

••• ••

FOUNDATIONS OF PROBLEM SOLVING

Chapter Eleven - Mathematics of Finance . .. .. .. ... . . .. ........... . ...... .. .. . .. .. 278 Activity 11.1: Present and Future Value with Simple Interest . . . . .. . .... . .. .. ... ...... . .. ..... . 280 Activity 11.2: Present and Future Value with Compound Interest .. . ..... . . .. . .. .. ... .. .. . .. . . . . 283 Activity 11.3: Cash Flow . . .... ... . .... . . ... ... ... ... . ... .......... ... .. . . ........ .. . .. 285 Activity 11.4: Net Present Value .. .. .... .... ...... . .. ..... . . . . .... ....... . ...... . . .. .... 288 Activity 11.5: Amortization . . .... ..... .. ... .. . . .. . ... .. . . ........ ..... .. ... . .. ... .. . ... 290 Activity 11.6: Managing a Personal Budget .. . . . ..... ... .. ...... ... ..... ... .... ..... . ...... 293

Chapter Twelve - Programming . . ........... . ... . .... .... ..... .. ........... . .... 297 Activity 12.1: Reusable Code ... .......... . ... . ... . . ... ....... .. . ........... . . . ... .. . ... 309 Activity 12.2: Creating Functions .. . .. ....... . . . . . ..... ...... . .. . . .... ... . . ... . ..... ... . 312 Activity 12.3: Testing and Debugging .. ... ......... ........ ....... . . . ... ... . . .. . . . .. ... . . 315 Activity 12.4: Data Structures ... ..... . .. . .. .... . ...... ...... .. .. .......... .. ..... ... .. . 321 Activity 12.5: Conditional Branching ... . .. .... .... ....... . .. . .. ... ..... .. . . ....... ...... 325 Activity 12.6: Iteration ... . .... . .... .. .... . .. . .... . . .. ......... ... ....... ... . . .. . . ..... 329 Activity 12.7: User Control Techniques ..... . ........... ... . .... .. . .. .. . . . ... .... ... . . .... 333 Activity 12.8: Documenting a Program .... ...... .... .. .. ... ..... .... . . ..... . ... .. . . . .... . 337

Chapter Thirteen - Research Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 342 Problems .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

Appendices ............... . ....... . . . ........ . .......... . .. .. .... .. ........... 361 Appendix 1: A Taxonomy ofPerformance Skills . .. . . . ......... .. . . ... . . ...... ...... . . . .. . . 362 Appendix 2: Final Growth Report . .. . ......... . ...... . ........ .. . .... . . .... . .. . ........ 364 Appendix 3: Personal Reflecting Journal ... ...... .... ... . ...... .. . .... . . . ....... ... . .... 365 Appendix 4: A Glossary for Process Education .... . .... . . . ..... .. .. .. ..... . . . . .. ... . . .. . . 366 Appendix 5: A Glossary ofProblem Solving Terms .. . .. . . .. ... . . . ...... .......... . .. . .. . . . 370 •Index of Research Problems .. . ... . ....... .. ........ . .. . ............ ... .......... 380

Index of Activities, Appendices, and Methodologies . . ..... .. .... . ....... . . ... . . ..... 382 •••••

x .. ... ....... PREFACE