Introduction to Problem Solving in the Information Age Introduction to Problem Solving in the Information Age David Moursund College of Education, University of Oregon Email: [email protected] Website: http://uoregon.edu/~moursund/dave/index.htm Website: http://i-a-e.org/ Brief Abstract of Book “Never doubt that a small group of thoughtful committed citizens can change the world: indeed; it's the only thing that ever has.” (Margaret Mead) In this book, the term problem solving includes posing and solving problems, posing and accomplishing tasks, posing and answering questions, and posing and making decisions. Problem solving is an integral component of every academic discipline. The Information Age officially began in the United States in 1956 when the number of “white collar” workers first exceeded the number of “blue collar” workers. The primary audience of this book is preservice and inservice teachers, and others who help students to learn. The goal of this book is to help K-12 students get better at problem solving in the various disciplines they study. We get better at problem solving through informal and formal education, and through reflective practice. We also get better at problem solving through learning to make effective use of tools. In some sense, a tool incorporates the problem-solving insights of the inventor of the tool. When you learn to make effective use of a tool, you are building upon the knowledge and skills inherent to the tool. This is true whether the tool is designed to aid your physical capabilities or your mental capabilities. A bicycle, motorbike, and a piece of factory machinery are aids to one’s physical capabilities. Reading, writing, and a library are aids to one’s mental capabilities. This book explores how Information and Communication Technology (including calculators and computers) aid both your physical capabilities and your mental capabilities. By learning to make effective use of ICT tools, you can improve your problem-solving capabilities. Copyright and Right to Copy This book is Copyright © David Moursund 2007. However, it can be accessed free on the Web in both PDF and Microsoft Word formats and given to students and others for non- commercial purposes. This is done under the Creative Commons Attribution-NonCommercial 3.0 License. More detail is available at http://creativecommons.org/licenses/by-nc/3.0/. Page 1 Introduction to Problem Solving in the Information Age About Dave Moursund, the Author “The wisest mind has something yet to learn.” (George Santayana) • Bachelor’s degree in mathematics, University of Oregon. • Master’s degree and doctorate in mathematics (specializing in numerical analysis) from the University of Wisconsin-Madison. • Instructor, Department of Mathematics, University of Wisconsin-Madison. • Assistant Professor and then Associate Professor, Department of Mathematics and Computing Center (School of Engineering), Michigan State University. • Associate Professor, Department of Mathematics and Computing Center, University of Oregon. • Associate and then Full Professor, Department of Computer Science, University of Oregon. • Served six years as the first Head of the Computer Science Department at the University of Oregon, 1969-1975. • Full Professor in the College of Education at the University of Oregon for more than 20 years. Currently retired with rank Emeritus Professor. • In 1974, started the publication that eventually became Learning and Leading with Technology, the flagship publication of the International Society for Technology in Education (ISTE). • In 1979, founded the International Society for Technology in Education ). Headed this organization for 19 years. • Author or co-author of about 50 books and several hundred articles in the field of computers in education. • Presented about 200 workshops in the field of computers in education. • Served as a major professor for about 50 doctoral students (six in math, the rest in education). Served on the doctoral committees of about 25 other students. • Founding member of the Math Learning Center. Served on the MLC Board of Directors since its inception in 1976, and chaired the board for several years. • For more information about Dave Moursund and for free online, no cost access to 20 of his books and a number of articles, go to http://uoregon.edu/~moursund/dave/. Page 2 Introduction to Problem Solving in the Information Age Contents "The strongest memory is not as strong as the weakest ink." (Confucius, 551-479 B.C.) About Dave Moursund, the Author ...............................................2 Contents .......................................................................................3 Preface..........................................................................................6 Chapter 1: Introduction and Overview ..........................................8 Improving Education...................................................................8 Academic Disciplines..................................................................9 Subconscious Thinking and Problem Solving.........................10 Our Formal Educational System...............................................11 What is Problem Solving? ........................................................12 Critical Thinking........................................................................12 Higher-Order Thinking .............................................................12 Some Important Aspects of Problem Solving .........................13 Chapter 2: What is a Formal Problem?........................................17 Definition of a Formal Problem................................................17 More Detail About the Four-Component Definition...............18 Dealing With Problem Situations.............................................19 Immediate Actions for Chapter 2 .............................................21 Chapter 3: Information and Problem Overload............................ 23 Problem Overload......................................................................23 Who or What Should Do the Solving of a Problem? ..............25 A Story About Building on Work of Others............................25 Should We Drop Some Content from the School Curriculum?26 Summary ....................................................................................27 Chapter 4: Problem and Task Team ............................................ 30 Introduction................................................................................30 Project-Based Learning.............................................................32 Problem-Based Learning...........................................................33 Problem Solving as a Process ...................................................33 Chapter 5: Transfer of Learning.................................................. 36 We All Do Transfer of Our Learning.......................................36 Transfer of Learning Theories ..................................................37 Page 3 Introduction to Problem Solving in the Information Age High-road and Low-Road Transfer of Learning......................38 Final Remarks............................................................................40 Chapter 6: Expertise and Domain Specificity.............................. 42 Expertise and being an Expertise..............................................42 Domain-Specific Knowledge in a Productivity Tool..............43 Chapter 7: Some Problem-Solving Strategies.............................. 46 Introduction................................................................................46 Information Retrieval as a General-Purpose Strategy.............47 Other General-Purpose Strategies ............................................47 Still More Strategies..................................................................53 Chapter 8: Representations of a Problem..................................... 55 Introduction................................................................................55 Non-Mental Models ..................................................................55 Special Vocabulary and Notation in Various Disciplines.......58 Chapter 9: Representing & Solving Problems Using Computers . 60 Computational Thinking ...........................................................60 Computer Models ......................................................................61 Spreadsheet Models...................................................................62 Some Applications of Computer Models.................................62 Artificial Intelligence (Machine Intelligence) .........................63 Highly Interactive intelligent CAL...........................................64 Virtual Reality ...........................................................................65 Chapter 10: Computer Programming........................................... 68 Procedural Thinking ..................................................................68 Types of Computer Programming ............................................69 Using a General-purpose Programming Language .................70 Testing and Debugging .............................................................71 Some History of Programming Languages..............................72 Data Structures and Control Structures....................................73 Object Oriented Programming..................................................74 Transfer of Problem-Solving Skills From Programming........75 Final Remarks............................................................................75