Home Page of Problem Solving Book

Introduction to the Book

Chapter 1: Introduction to Problem Solving

Chapter 2

Some General Categories of Problems

Five General Categories of Resources

A Rising Level of Expectation

Computer as a Broad-Based Resource

Activities and Self-Assessment

Chapter 3: Intelligence as Resource

Chapter 4: Tools as Resource

Chapter 5: Accumulated Knowledge as Resource

Chapter 6: Education and Training as Resource

Chapter 7: A Computer System

Chapter 8: Personal Productivity Tools

Chapter 9: Computer Programming

Chapter 10: Final Remarks

References and Resources

Search Engine in Lieu of Index

Chapter 2: Overview of Resources in Problem Solving

Chapter 1 provided a four-part definition of a formal problem:

  1. givens;
  2. goal;
  3. resources; and
  4. ownership.

This chapter provides a general overview of resources. It lays the groundwork for specific consideration of the computer as a resource.

Some General Categories of Problems

If every problem that you encountered were completely unique and novel, problem solving would be really difficult. Fortunately, this is not the case. Many of the problems that you encounter are problems that you have seen in the past, [[or quite similar to such problems.]] Even many of the "new" problems that you encounter are problems that lots of other people have addressed before.

The single most important idea in problem solving is building on the previous work that has been done by yourself and others. To help in this approach, problems are divided into categories. For example, there are accounting problems, music problems, personal relationship problems, and political problems. The problems in a particular category are somewhat related to each other. Thus, you can take an accounting course and learn quite a bit about a huge range of different accounting problems. You can learn the types of problems the field of accounting addresses and what aids exist to help solve these types of problems.

It is also possible to classify problems on the basis of general techniques or tools needed to solve them. For example, there are a large number of problems that fall into the database category. Examples of databases include a telephone book, a dictionary, and a personal address book. Many problems can be solved by "looking up" needed [[data or]] information. This has led to the development of database software. Computers are particularly useful in helping to solve database problems. [[The Web can be thought of as a database. Thus, you should not think of a database as being just a fixed field and quite limited set of data, as one finds in a telephone book.]]

With database software and telecommunications, some problems that used to be quite complex are now quite simple. For example, an airline has hundreds of flights each day. It must sell tickets for each flight, perhaps for a year into the future. Agencies selling airline tickets are located throughout the world. This ticket sales problem is solved by use of computers, database software, and telecommunications.

Many different problems fall into a bookkeeping and accounting category. They range from simple personal budgeting to handling the payroll and fiscal planning of a multi billion-dollar enterprise. Spreadsheet software has proven to be a powerful tool in dealing with such problems.

A spreadsheet can be thought of as an automated accounting sheet that can contain both numbers and formulas. The computer can automatically apply the formulas to the numbers. For example, suppose that you have a spreadsheet model of the payroll for a company. A few changes occur, such as an increase in social security taxes and a cost of living wage increase for all workers. A few quick changes in the spreadsheet and the computer produces the new payroll.

Both database and spreadsheet software are sufficiently general so that they facilitate the modeling (representation) of a wide range of problems. Database and spreadsheet representations of problems are very powerful aids to solving certain kinds of problems. If you need to solve problems that fall into these categories, it is well worth your time and effort to learn how to make use of these computer applications. We will explore these applications more in a later chapter.

[[This section discusses classification of problems by the subject matter domains in which they lie. This approach to teaching, research, and learning helps people to gain expertise within a specific domain. However, most "real world" problems are interdisciplinary. This means that people are faced by the need to transfer learning from a number of different domains, and bring all of this learning together, to address a typical real world problem.

Such transfer of learning is difficult. Our educational system does a relatively poor job of teaching interdisciplinary problem solving. One might argue that each teacher is responsible for teaching transfer from the specific domain (subject areas) the teacher teaches. But, because the responsibility is divided among all teachers, most teachers do not feel individual responsibility.

There are some interdisciplinary tools and there are some interdisciplinary problem-solving strategies. For example, reading and writing are interdisciplinary tools. Somewhat similarly, math, science, computing, and the Internet are interdisciplinary tools, useful in many different domains.

The interdisciplinary nature of reading, writing, and arithmetic help to explain why they are considered to be "basics" in education. The same type of analysis leads to classifying science, computing, and the Internet as basics.

Project-based learning tends to provide environments in which students encounter interdisciplinary problems. There is a close parallel between project-based learning and the overall field of problem solving. Indeed, problem-based learning (which is closely related to project-based learning) is a commonly used teaching method.]]

Five General Categories of Resources

This book focuses on five general categories of resources: creative intelligence of people; tools; accumulated knowledge; education and training; and time. Each of the first four can be enhanced or improved. Roles of computers in enhancing these resources are discussed in the next four chapters of this book.

The fifth resource--time--is somewhat different. Your time is limited. Once time has passed, it cannot be regained or replaced. Thus, time is a resource that needs to be used carefully. There are many situations in which appropriate use of a computer can save you a lot of time. This is a unifying theme in the next four chapters.

Creative Intelligence

You are intelligent, and you are creative. That is, you can use your intelligence in novel (creative) ways to solve problems. In this book, we will use the term creative intelligence to represent the combination of creativity and intelligence.

It is possible to differentiate between intelligence and creativity. Thus, a person may score really well on a standard measure of intelligence (an intelligence quotient test) yet have a relatively low level of creativity. [[The opposite is also true. Some highly creative people perform quite poorly on IQ tests. They may do poorly in school, because their talents do not align well with school curriculum and assessment.]] There has been a lot of research on creativity and how to increase creativity. Courses on creative problem solving are offered at many universities. Workshops on creative problem solving are readily available. They tend to be particularly popular in business and industry. Edward de Bono (1973&endash;75, 1985, 1992) has written a number of books on this subject and is a popular workshop presenter. One of the key ideas stressed in the de Bono books is that if you are actively engaged in creative problem solving, you will get better at it. Another key idea is that creativity can be taught.

When you work to solve a problem, you bring your creative intelligence to the task. This intelligence is used: to understand the problem; to help reformulate a problem situation so it is a clearly defined problem; to modify the problem (pose a modified problem) based on information gained during the solution process; and to provide guidance in making effective use of other resources. The book (Perkins, 1995) contains an analysis of a number of ways that you can get better at such tasks.

Tools

In this book, we divide tools into two categories--physical artifacts (tools to supplement physical resources of a person) and cognitive artifacts (tools to supplement mental resources of a person). Some tools, such as computerized machinery, fall into both categories. A modern car contains a large number of microprocessors. An electron microscope can be thought of as a computerized microscope that makes use of a beam of electrons instead of light to illuminate the object being viewed.

It is evident that tools contribute to cumulative progress in helping people get better at problem solving. Once a useful tool is invented, it is relatively easy for other people to learn to use the tool. For example, you probably have made use of a microscope and a telescope. These tools have contributed greatly to a number of different fields of scientific knowledge.

We remember Alexander Graham Bell for his invention of the telephone. This invention has greatly changed the societies of the world. Nowadays, we think nothing of the fact that children learn to use a telephone even before they are old enough to go to school.

[[Increasingly, we also think nothing of a student walking across campus while talking on a cell phone. The cell telephone is a tool that helps to solve communications problems. It is very useful and relatively inexpensive. Thus, its use has quickly spread throughout the world.

It is worth pointing out that it takes most people very little time and effort to learn to use a cell telephone. Many powerful aids to problem solving are easily and quickly mastered. For many others (such as the three Rs) such is not the case.

The telephone represents a very important idea in human tool-making progress. It took the genius of just one person (Bell) to create a tool that has spread to the entire world. However, often an invention occurs when the underlying technology needed has developed to a level that readily supports the invention. Thus, a second inventor simultaneously developed the telephone, but arrived at the US Patent Office a few minutes later that did Alexander Graham Bell.]]

Some tools are general purpose, while others are designed to help solve a very narrow range of problems. As part of a general education, you learn to use a number of general-purpose cognitive and physical artifacts. These become so commonplace to you that you don't even think about them. Thus, you may not even think of reading, writing, and arithmetic as cognitive artifacts--useful across every area of human intellectual endeavor.

A person who is working to develop a high level of expertise in a narrow area of specialization is apt to be learning to use some tools that are specific to that area. For example, the tools of a professional welder are quite a bit different than the tools of an eye surgeon.

Accumulated Knowledge

The amount of accumulated knowledge of the human race is huge and is continuing to grow rapidly. Various people have made estimates on how rapidly the accumulated knowledge is growing. Estimates range from a doubling every three years to a doubling every 10 years.

However, it is not clear what people mean when they say that the amount of accumulated knowledge is doubling every few years. Some people like to talk about a continuum that runs from data to information to knowledge.

Figure 2.1 The knowledge continuum.

For example, the instruments on a space ship that travels to Mars collect a great deal of data (often referred to as raw data) and transmit it back to Earth stations. This raw data is analyzed to give us information about temperature, wind velocity, size and location of hills and gullies, and so on. People analyze and synthesize this information to produce detailed knowledge about weather patterns on Mars and how they have shaped the planet's surface.

It is clear that the amount of accumulated data, information, and knowledge is all growing rapidly. It is increasing so rapidly that even experts in narrow specialization areas are hard pressed to remain at the forefront of their specialty areas. This information explosion contributes both to the number and nature of problems that people want to solve and to their ability to solve the problems that they pose.

There are many ways to store data, information, and knowledge. People carry a lot of it around in their heads. It may be in written form and stored on stone or clay tablets, or on paper. It may be stored on audio- and videotapes. It may be in photographs, paintings, or drawings.

And, of course, data, information, and knowledge can be stored in a computer. Computers are a key tool of the Information Age. A computer is both a storage and a processing device. It is the combination of storage and processing that make computers such powerful aids to problem solving.

[[This section talks about the accumulated knowledge of the human race, and it makes a somewhat glib statement about storing knowledge in a computer. Many people think of knowledge as something that can only be stored in a person's head. They balk at the idea that a machine might have intelligence--be able to accumulate, store, process, and act on knowledge.

Perhaps the key idea is that there are various ways to represent data, information, and knowledge. Knowledge stored or represented in a person's head is certainly in a different form than knowledge stored in a book, knowledge integrated into the design and workings of a piece of machinery, or knowledge stored in a computer. If one insists on a definition that "knowledge" is something that can only be stored and represented in a person's head, than that certainly precludes the idea of storing knowledge in a computer system. However, most people use a broader definition of the term.

I enjoy discussing such ideas with my students and other colleagues. My point of view is that it doesn't make any difference whether we agree or disagree that machines (such as computers) can have knowledge. We have many and a growing number of examples of computer systems that can help humans to solve problems. Within narrowly defied domains, we have a steadily increasing number of examples of computer systems whose problem-solving expertise meets or exceeds those of human experts in the domain. Chess playing is often cited as an example. A computer beat the reigning world chess champion in 1997.]]

Education and Training

Education and training are needed to learn to make use of tools. Some education and training is quite general, cutting across many disciplines. Other education and training is highly specific to a narrow area.

[[We must not forget that we have both formal and informal education and training. The chances are that you have used a cell phone (a wireless phone). You learned to do this by transfer of learning from use of a wire-connected phone, by trial and error, by observing a colleague using a cell phone, and so on. Most likely you did not enroll in a course on how to use a cell phone.]]

The basics of education that are emphasized in the early grades of school, such as reading, writing, arithmetic, speaking, and listening, tend to be quite general purpose. These basics of education are useful in addressing a wide range of problems. As one progresses further along in school, education and training begin to become more specialized. Through formal education, extending even to the postdoctoral level and through apprenticeship training that may take many years, one can gain a great deal of expertise in a specialized area.

The human mind is always learning. Information flows into the mind from the senses. It is processed--mostly at a subconscious level. Thus, it is appropriate to say that we are all lifelong learners. Much of this lifelong learning is informal, incidental, and non-directed. However, some of this learning is consciously directed. This consciously directed learning may occur at work, play, or school. Conscious, directed learning is essential to developing expertise and to increasing one's overall abilities as a problem solver. We will discuss this in more detail in later chapters.

Time

We have now listed four major types of resources that can be used in problem solving. Figure 2.2 shows each of these resources inside a circle. The diagram is designed to suggest the interaction of the various resources that are available to support a person doing problem solving. You might visualize yourself sitting at the top of a pyramid of resources that are available to support you in problem solving.

Figure 2.2 Four major resources in problem solving.

Finally, it is time to talk about time. The ownership component in the definition of a problem indicates that you are willing to devote some of your personal resources to accomplishing the goal. This may include putting in time thinking about the problem and time actually carrying out steps to solve the problem.

It is useful to think about two different uses of time. First, there is the time spent before the problem is encountered. This time is spent in gaining general and specific knowledge and skills. It is time spent developing your mind and body. It is time spent honing an essential resource--namely, you!

Then there is the time actually devoted to solving a particular problem or accomplishing a particular task. This may be a few seconds, or it may be many years. It is important to remember that time spent solving a problem contributes to your overall knowledge, skills, and experience. It helps prepare you for the next time you encounter a somewhat similar problem.

Both the preparation time and the problem-solving time vary with the problem to be solved or task to be accomplished. However, the time needed can be decreased through using appropriate tools, education and training, access to accumulated knowledge, and so on. There are ways to save time when preparing yourself to solve problems and when actually solving problems.

[[We spend many years going to school. Relatively little of this time is spent in learning to learn and in learning to learn faster. One of the results from careful studies of computer-assisted learning (CAL) is that on average, students learn 30% faster through this approach. Since time is such a limited resource, this might lead you to wonder why our schools do not make more use of CAL.]]

A Rising Level of Expectation

In recent years, people in our society have come to expect continuing major breakthroughs in medicine, telecommunications, electronics, and other areas.

What has fueled this sustained pace of change? There is no evidence to suggest that people are inherently more creatively intelligent nowadays than they were 1,000 or 2,000 years ago. So, improvements in the resource that we have named creative intelligence do not explain what has transpired.

[[One of the things that fuels the sustained pace of change is that powerful tools are developed, and their use quickly spreads. We have previously mentioned the development of the three Rs, which occurred approximately 5,000 years ago. About 3,700 years ago a small group of scholars developed the idea of using an alphabet for written language. This was a very powerful idea (invention) that eventually spread to much of the world.

Over the years, communication and transportation has improved. This fuels change in other areas, as it facilitates more rapid dissemination of the successful inventions of individuals or small groups.]]

The next three categories of resources listed in the previous section have improved significantly over the years. More and better tools have been developed. The quantity, quality, and accessibility of stored information has improved. Education and training have responded to the changes in tools and in stored information. They have also responded to the changing needs of society and to the progress in the fields of learning and teaching.

All of these changes can be thought of as people building on the previous work of other people. The net result is a rising level of expectation. The problems that people are expected to routinely solve become more complex. The expected level of expertise or performance rises. As a simple example, it took the genius of Isaac Newton and Gottfried Leibniz--two of the greatest mathematicians of their time--to invent calculus a little more than 300 years ago. Now, many students learn calculus while still in high school.

Of course, one can go back still further in time. Two thousand years ago, only a small percentage of the population could do simple arithmetic. A problem involving working with fractions could challenge a professional mathematician. Now, middle school and junior high school students routinely deal with such problems.

This rising tide of expectation is a challenge, especially to adults. You go to school, get a good education, and get a good job. Over the years, you improve in your expertise at handling the job. The question is, do you improve fast enough to keep up with the rising tide of expectation? If not, your overall level of expertise may actually be declining relative to contemporary standards.

[[Moreover, tools may be developed that greatly decrease the number of workers needed in your particular area of expertise. At the time of the American Revolution, about 90% of the population of the 13 colonies lived and worked on farms. Now, less that three percent of the workforce in the US is needed to feed the country and produce a surplus for export. There has been a somewhat similar trend in industrial manufacturing.]]

Computer as a Broad-Based Resource

A computer is a versatile resource in problem solving. [[In this book, I have been somewhat sloppy in use of the term computer. It would be better to use the term Information and Communications Technology.]] It is a resource that cuts across all academic disciplines. Moreover, it is a resource that is continuing to improve rapidly. Today's computers are a lot faster than computers of a few years ago. The cost-effectiveness of computers is growing rapidly. More and better software is being developed. The human-machine interface is being improved, making it easier for people to use computers. The term human-machine interface refers to the design and implementation of the way humans input information to the machine and the way humans receive information from the machine. The development of the mouse as a pointing and selecting device was a major improvement in the human-machine interface.

The first four main categories of problem-related resources listed in this chapter are each affected by computers. The next four chapters of this book explore these four categories of resources from a computer-oriented point of view. One of the underlying themes is time. Appropriate use of computers may save time as you prepare yourself to solve problems and may save time in the actual process of solving problems.

Activities and Self-Assessment

Have you been writing in your journal while working through the material in this chapter? Some of the following questions may help guide your journal-writing activities.

  1. Do some introspection about your creative intelligence. What are some of your greatest strengths? What are some of your relative weaknesses? Have your strengths and weaknesses changed over time? How have your relative strengths and weaknesses affected you at work, at play, and at school?
  2. Name some of the tools that you routinely use in solving the problems that you encounter. Analyze these tools from several points of view. For example, you might compare them in terms of how useful they are, how long it took you to learn to use the tools, their cost, their versatility, and so on.
  3. Humans have accumulated a great deal of knowledge. Much of this knowledge is stored in libraries. Many of the problems that people encounter have already been successfully solved by other people. Discuss the capabilities and limitations of information retrieval--for example, accessing the accumulated knowledge in libraries--as an aid to problem solving. How is this being affected by the rapid trend toward computerization of libraries?
  4. Analyze the quality of education that you have received in the past and are currently receiving. What are its strengths and weaknesses in terms of preparing you to effectively deal with the types of problems that people face in our Information Age society? Have you used your school time efficiently and effectively?
  5. The business world is familiar with the idea of "just in time" delivery of materials to a manufacturing site. The idea is to avoid unnecessary costs of warehousing a large supply of parts. The idea of "just in time" education is new and interesting. It leads to a discussion of what you should learn well in advance of attempting to solve certain categories of problems, and what you should learn "just in time" when you encounter the problems. Discuss "just in time" education.

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