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Getting Smarter
At Solving Problems:
Teacher's Manual

Moursund, D.G. (Copyright © ICCE 1990; Copyright © David Moursund December 2004). Getting Smarter At Solving Problems Teacher's Manual.

The "Getting Smarter at Solving Problems" book is written at a 6th grade reading level and intended mainly for junior high and middle school students. Click here to access the book.

Click here for PDF file of the book.

Click here for Microsoft Word file of this book. Note that this may download the document to your desktop so that you need to open it from there. The file name is Getting_Smarter.doc.

Click here for Table of Contents.

Click here for Preface to the 2004 Reprint

Click here for Preface for Students.

Click here for Preface for Teachers.

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Table of Contents

Preface to 2004 Reprint 4
Preface for Teachers 6
Preface for Students 10
Chapter 1: Introduction to This Book 13
Chapter 2: You Are A Smart Person 25
Chapter 3: What Is A Problem? 34
Chapter 4: A Four-Step Plan for Solving a Problem 47
Chapter 5: Problem-Solving Strategies 58
Chapter 6: Getting Better At Thinking 69
Chapter 7: Transfer of Learning 82
Chapter 8: Modeling 94
Chapter 9: General Purpose Computer Tools 107
Chapter 10: Computer Systems 119
Glossary 131

Preface to the 2004 Reprint

I read the “old” manuscript and cleaned up its desktop publication at the end of fall term, 2004. During fall term I taught a one-credit graduate course for preservice and inservice teachers on the topic of roles of Information and Communication Technology in problem solving. A detailed syllabus for this course and no-cost access to my book used in the course are available at http://darkwing.uoregon.edu/~moursund/SPSB/Short-course.htm. Thus, I had the details of that course in mind as I read the old book.

Interestingly, I found only three areas in which the content of the old book was significantly different from the ideas I taught this fall. They are:

  1. The old book does not reflect the existence of the Web. It talks about communication via the Internet and about information retrieval from CD-ROM. Thus, it has a focus on use of retrieved information as an aid to problem solving.
  2. The old book talks about transfer of learning, but it only covers the “near transfer, far transfer theory.” My more recent books, and the course I taught this fall, stressed the “high-road, low-road” theory of transfer of learning. This is a better theory, in that it provides a better foundation for teaching to improve transfer.
  3. The old book contains some brain theory, including a statement that the human brain contains 30 to 100 billion neurons and a picture of a neuron. Now, this figure is usually stated as 100 billion neurons. The brain scanning equipment available in the early 1990s looks rather quaint relative to what is now available. Brain science has certainly made a huge amount of progress over the past decade.

As I read the old book, I thought about how educators are faced by the problem of educating children for their future life in a very rapidly changing world. In many fields of science and technology we are seeing a doubling of knowledge in as little as 5 to 10 years. In ICT, we have been seeing a doubling of cost effectiveness in under two years.

However, most of the ideas from the old book are still quite good—indeed, quite up to date. A student who learned these ideas a dozen years ago would still be well served by the knowledge. That is because the focus is on general ideas, rather than on specific details.

For example, consider the idea of learning lower-order knowledge and skills versus learning high-order knowledge and skills. Both are important to a person’s education. However, the book has a focus on higher-order—because it is a book about dealing with novel, challenging problems. Students at the middle school and junior high school levels are quite capable of understanding lower-order versus higher-order. This empowers them as they gradually assume more responsibility for their own education.

The idea of a strategy that might problem helpful in solving a problem is fundamental to problem solving. By and large, students are not taught very many strategies that will have long-term value. The book teaches various problem-solving strategies that are apt to last a lifetime.

Problem posing and converting ill-defined problems into clearly defined problems are taught in the book. Again, knowledge and skills gained in this area are apt to last a lifetime.

The book is about problem solving and the increasing roles of ICT in problem solving. The ideas of developing a mental model or a written model of a problem are stressed. But then, these ideas are expanded into a discussion of computer modeling. What does one gain by having an electronic (a word processed) version of a written document versus a hard copy of the document. What are the advantages and disadvantages of each as an aid to representing and solving problems?

This discussion then moves into the issue of what aspects of problem solving can be automated through appropriate use of a computer. One of the advantages of computer modeling is that it fits in well with computer-based automation of a wide variety of problem-solving activities. Today’s spelling checker in a word processor is better than what was available in the early 1990s. However, the underlying concept that a word processor can incorporate a spell checker that can help to detect and correct spelling errors has not changed between then and now.

In summary, the “old” book demonstrates that in the early 1990s we knew enough about computers and problem solving to develop and teach a course of enduring value for middle school and junior high school students. By and large, however, few schools have implemented such a course.

David Moursund

December 2004

Preface for Students

ORGANIZE YOUR THINKING

There is a box like this at the beginning of each chapter. It contains some of the highlights of the chapter. Spend a minute or two reading and thinking about these highlights. Research says that this time will be well spent. It will help you to learn the chapter material much better.

The Preface is about:

  • Aids to the human mind.
  • Thinking about how you learn.
  • Using computers to help you solve problems.

The Computer is an Aid to the Human Mind

This is a book about how computers can help you to solve problems. However, a computer is merely a tool to help your mind. Your mind still has to do most of the thinking!

Thus, this book talks a lot about how your mind works. It talks about how to help your mind get better at solving problems. If you practice the ideas in this book, you will get a lot better at solving problems in school and outside of school.

Other Aids to the Human Mind

There are many aids to the human mind. Reading, writing, and arithmetic are all very important mind aids. They help you to solve problems that you could not solve just using your mind all by itself.

Reading is especially important. If you can read this book, you can read well enough so that you can learn new things by reading. Being able to read opens up a whole new world. It allows you to solve problems by reading about how others have solved the problems.

Another important mind aid is learning to learn. There are lots of ways to learn new things. As you know, different people learn in different ways. Some people learn best by "seeing"—by receiving information through their eyes. Others learn best by "hearing"—by receiving information through their ears. Still others learn best by "physically doing"—by being physically engaged in carrying out the processes to be learned.

These differences in how people learn make it difficult for a teacher to teach only in the way that seems best for you. This means that it is important for you to learn how you best learn. You must become responsible for your own learning.

Also, the way you learn best may vary with different things that you want to learn. Think about sports, and how you get better at sports. Think about how you learned to make friends and how you get better at making friends. Think about how you learned how to read, and how you get better at reading. Think about math classes, and how you get better at solving math problems.

Now be aware of what you just did. You were thinking about how you learn. You are a unique person. You are different from every other person. You are the only person who can really know yourself. You are the only person who can really learn how you learn best.

One of the most important learning things that you can learn is how to learn. How does your mind work as it learns new things? What helps it to learn rapidly and well? What helps it to remember important new ideas? What helps it to get better at solving problems?

You learn many new things everyday. This means that you get a lot of practice in learning. Some of this learning occurs without much effort on your part. For example, you see and hear a television ad, and you learn a little about the product being advertised. You hear a friend using a new word, and you automatically start using that new word.

But other learning takes more effort. Over the centuries, humans have accumulated a great deal of knowledge and wisdom. Many brilliant thinkers, such as Marie Curie and Albert Einstein, have contributed. There is lots to learn.

One reason we have schools is to make it easier for people to learn. One goal of this book is to help you get better at learning. There is a simple way to get better at learning. As you learn, think about learning. Examine your own personal learning processes. Figure out what works best for you. Experiment. Try different approaches. Gradually you will get better at learning.

You Will Need a Journal

Early explorers kept journals or diaries in which they wrote about their travels. As you read this book, think of yourself as an explorer. You are exploring the content of this book. You are exploring your mind and how it reacts to the book. You are exploring computers and how they can help you solve problems.

Many of the activities in this book ask you to write in a journal. You will need a bound book, such as a spiral bound notebook, to use as a journal. Please get yourself a journal book before starting to read the first chapter. Keep it with this book, so that you will have it when you need it.

Educational researchers have thought a lot about how to help students learn better. They have decided that writing in a journal helps most students learn better. This seems to be true in every school subject. And it works well for both young people and adults. Don't be surprised if you see your teacher doing journaling!

What This Book is About

This is a book about human problem solving. It places a major emphasis on roles of computers as an aid in problem solving. Computers are a very powerful aid. Computers are especially useful in solving the types of problems that you study in school. You can get much better at solving many types of problems by learning to use computers as an aid to problem solving.

This book will help you get better at problem solving. However, don't expect any magic. It has taken your entire life to get as good at problem solving as you are now. This book will help you get better. But getting better at problem solving takes time and effort.

PREFACE SUMMARY

There is a box like this at the end of each chapter. It contains a summary of a few of the key ideas in the chapter.

The purpose of the Preface is to get you started in thinking about what this book is about. Some key ideas include:

  1. A computer is a powerful aid to the human mind. Reading, writing, and arithmetic are also powerful mind aids.
  2. It is important for you to learn how you best learn.
  3. By studying and practice, you can get better at problem solving.

Preface for Teachers

Specific Intended Audience

Getting Smarter at Solving Problems is specifically designed to be used as a supplemental text in a secondary school Computer Literacy course. When used in that format, the book contains sufficient materials to be used two days a week or part of each day in a semester-length course.

However, Getting Smarter at Solving Problems can also be used in a wide variety of other settings. It can be used in a "Modern Problems" class in the social studies; it can be used in a course on problem solving; it can be used in a math course. In all cases the emphasis is on problem solving in general, and roles of computers as an aid to problem solving.

This book is based on the following two premises. The premises are strongly supported by the research literature.

  1. Through the appropriate study of the discipline of problem solving, a student can get better at solving both school problems and non-school problems
  2. Computers are a powerful aid to problem solving. A student can get better at solving certain types of problems by learning to make appropriate use of computers as an aid to solving the problems.

Computer Literacy Courses

There are many different versions of Computer Literacy courses. A typical Computer Literacy course may focus on just one of the following themes, or it may draw from several of them.

  1. Generic tool approaches that focus on use of one or more of the general-purpose tools database, graphics, spreadsheet, telecommunications, and word processor. These tools are interdisciplinary, useful in all levels of schools, and useful both in school and outside of school.
    An alternative is to build a Computer Literacy course around applications software that fits the needs of people in a specific applications area. Music software provides a good example, as does software for use in the fine arts. A Computer Literacy course could be build around a specific piece of desktop publication software or a specific piece of hypermedia software.
  2. Computer programming, making use of languages such as BASIC and Logo.
  3. A reading, talking, and critical analysis approach. Here the emphasis is on understanding and analyzing the history and current applications of computers, and how computers are affecting our society.

There are many definitions of computer literacy. Generally speaking, computer literacy is a blend of computer science (including computer programming), computer applications, and computers in society (including reading, writing, and talking about computers and their impact on our society). However, there should be one unifying theme: computers are a new and powerful aid to problem solving; they extend the capability of the human mind. Computers can be used to help solve problems in every area of human intellectual endeavor. The capabilities of computers are having a major impact on our world.

Getting Smarter at Solving Problems is designed to provide a unifying and underlying theme of problem solving in a computer literacy course. There is a lengthy Teacher's Manual that accompanies this book. It contains detailed lesson plans and specific suggestions on how to integrate problem solving into each of the general types of computer literacy courses listed above.

Guided Discovery-Based Learning

Getting Smarter at Solving Problems contains an underlying philosophy of discovery-based learning. One reason for this is the general nature of the computer field. The computer field is changing very rapidly. The computers your students will have available in their homes and on their jobs 20 years from now will be a hundred or a thousand times as powerful as the computers they now have available in school. This means that there must be a strong focus on learning to learn and on transfer of learning. A guided discovery-based learning environment contributes greatly to learning to learn, and it facilitates transfer of learning.

Puzzle Problems

Most books on problem solving are full of "puzzle problems." Here is an example.

TWO
+ TWO
----------
FOUR

In this puzzle, each letter stands for one of the digits 0, 1, 2,..., 9. The letter F stands for a digit that is larger than 0. The goal is to find one or more solutions. (Typically, a puzzle problem always has at least one solution. Of course, in the real world there are lots of problems that have no solution.)

For many students, puzzle problems are challenging and fun. Unfortunately, there are two distinct drawbacks to making extensive use of them in instruction.

  1. The research suggests that there is relatively little transfer of learning from puzzle problems to other problem-solving tasks. That is, practice in solving puzzle problems helps a student to get better at solving the specific types of puzzle problems being studied. It does not help a student to get better at solving real world problems or even the other types of problems they encounter in school.
  2. Many students are turned off by puzzle problems.

Getting Smarter at Solving Problems is quite different from the puzzle problem books. It focuses on the underlying theory and practice of the discipline of problem solving. It focuses on methodologies such as journaling, learning to learn, metacognition, and modeling that cut across all disciplines. It lays foundations that will serve students throughout their lives.

Problem-Solving Software

There are two major categories of problem-solving software that are not discussed in this book. The first type is software specifically designed to help teach problem solving. A number of the educational software publishers make available a wide range of such software. The second type is software specifically designed to help solve certain types of problems, such as math problems. This type of software is of growing importance in each academic discipline. The inclusion of either of both types of software in a course on computers and problem solving is quite appropriate. However, the author of this book decided to write the book to be independent of any specific piece of software or hardware.

Computer and Non-Computer Aids to Problem Solving

The computer is but one of many different powerful aids to problem solving. Reading, writing, arithmetic, speaking, and listening are certainly powerful aids to problem solving.

Most students in your class will have had little or no previous formal instruction in problem solving. Thus, you will be faced by two interrelated tasks.

  1. To help your students learn about the general discipline of problem solving. This instruction is oriented toward helping your students get better at dealing with all sorts of problems and using all sorts of aids to problem solving.
  2. To help your students learn the capabilities and limitations of computers as an aid to problem solving.

It should be clear that the first task is more general. It does relatively little good to teach the specifics of problem solving in a computer environment if students have no knowledge of general ideas of problem solving. However, it does make sense to use a computer environment as a motivation to study problem solving in general, and then to focus specifically on how computers affect this discipline. That is the design philosophy of this book.

The student text, Getting Smarter at Solving Problems , contains only a modest amount of specific focus on computers. However, each topic has been carefully selected to fill a dual role. First, it has been selected because it is foundational within the discipline of problem solving in general. Second, it has been selected because it easily ties in with studying the roles of computers in problem solving.

To a great extent, the Teacher's Manual, rather than the student text, provides the bridge between these two areas. This is because the student text is designed to be used in a wide variety of instructional settings. Thus, it is important that you, the course instructor, focus on bridging between problem solving in general, and problem solving within the context of the specific course that you are teaching. The Teacher's Manual provides a number of quite specific suggestions in how to do this in a variety of instructional situations.

Don't Expect Miracles

Every student in your class is a smart, problem-solving person. Your students have been developing their problem-solving skills throughout their lives. Your course, and the specific instruction on problem solving based on this book, will be a very modest-sized intervention in the lives of your students. It can make a significant contribution. However, it is a small intervention relative to the total amount of time each student has already spent on learning to solve problems. Getting smarter at solving problems is a life-long task.