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Links to the chapters of the book. You are currently reading Chapter 3.

Title Page

Preface

Chapter 1: Introduction

Chapter 2: Inventing Your Future

Chapter 3: Expertise and Problem Solving

Chapter 4: Human and Artificial Intelligence

Chapter 5: Computer-Assisted and Distance Learning

Chapter 6: Learning and Learning Theory

Chapter 7: Increasing Your Expertise in ICT

Chapter 8: Brief Introductions to A number of Key Ideas

Chapter 9: On the Lighter Side

References

Links to Sections of Chapter 3

Beginning of Chapter 3: Expertise and Problem Solving

“In short, learning is the process by which novices become experts.“ (John T. Bruer. Schools for Thought, 1999, page 13.)

“Through learning we re-create ourselves. Through learning we become able to do something we never were able to do. Through learning we re-perceive the world and our relationship to it. Through learning we extend our capacity to create, to be part of the generative process of life. There is within each of us a deep hunger for this type of learning.” (Peter Senge, 1990)

The history of formal schooling designed to teach reading, writing, and arithmetic goes back more than 5,000 years, to the time of the invention of writing. The 3Rs are mind tools—aids to the human brain. It takes considerable time and effort to develop a level of expertise in these disciplines that meets contemporary standards.

Your current level of expertise in these areas is useful to you in your everyday life and in your academic pursuits. You routinely use this expertise in representing and solving problems that you encounter in your everyday life.

Problem solving is part of every discipline, and it is a discipline of study in its own right. Computers are a powerful aid to solving problems in every academic discipline. This chapter includes an introduction to roles of ICT in problem solving.

There is a field of study called the Scholarship of Teaching and Learning, or the Science of Teaching and Learning (SoTL). This discipline contains considerable information that is useful both to students and to teachers. Since you routinely help yourself and others to learn, SoTL is doubly useful to you.

Expertise

Figure 3-1 is a general-purpose expertise scale. At the left end of the scale, a person’s knowledge and skills in an area may be so limited that some unlearning needs to occur to move up the scale. For example, this situation exists in some parts of science and medicine, where a person’s initial learning is wrong and does not serve as a useful foundation for future learning.

Figure 3-1. General-purpose expertise scale.

Consider a limited subdiscipline you have not previously encountered. Then think about the level of expertise you might achieve in this subdiscipline in 1 hour, 10 hours, 100 hours, 1,000 hours, and 10,000 hours of study and practice. (See Figure 3-2.) The level of expertise you will achieve depends on a number of things, such as your current level of expertise in closely related areas, your innate ability in the area, the quality of instruction and coaching you receive, and your dedication and perseverance. This simple set of observations lies at the very heart of education. A well-designed and well-implemented educational system helps students gain expertise faster than they would gain it without any outside help.

Figure 3-2. Time to develop expertise.

“Be all you can be” lies in the 10,000 to 100,000 hours range, combined with 10 years or more of concerted and guided effort. The level you reach depends on many things, such as quality of instruction and coaching, natural abilities, intrinsic motivation and drive, and extrinsic motivation. However, you can develop an island of expertise (a narrow pocket of expertise) in much less time and with much less effort.

In gaining an increased level of expertise in any area, both nature and nurture are important. It is not clear whether the extent to which your final level of expertise in an area depends more strongly on your innate abilities (nature, genetic disposition) or on the nurture you receive (Ericsson, n.d.). Moreover, there is the issue of intrinsic motivation and drive versus extrinsic motivation, or being coerced to do the studying and practice. The following quote from Jonah Lehrer (2006) helps capture the basic elements of nature-versus-nurture arguments:

Two obvious rebuttals to the argument that talent is just a matter of learning by doing are Mozart and Tiger Woods. Mozart famously began composing symphonies as an eight-year-old, and Woods was the world’s best golfer at 21. But do they really contradict the “learning by doing” principle?

Not so much. Mozart began playing at two, and if he averaged 35 hours of practice a week—his father was known as a stern taskmaster—he would, by the age of eight, have accumulated Ericsson’s golden number of 10,000 hours of practice. In addition, Mozart’s early symphonies are not nearly as accomplished as his later works.

Lehrer goes on to say:

Thanks to an encouraging father who happened to be a golf fanatic, Tiger [Woods] took his first golf swing before he took his first steps. When he was 18 months old, his dad started taking him to the driving range. By the age of three, Tiger was better than most weekend amateurs.

This allowed Woods to get a head start on his current competitors, but what really made him great is how he practices. For starters, his routine is merciless. Rain or shine, Woods sets out. More importantly, he always makes sure his practice sessions revolve around learning by doing. He analyzes sequential snapshots of himself playing, relentlessly scrutinizes the elements of his swing, then drills these subtle alterations into his nervous system through thousands of repetitions. Of course, more practice leads to more new ideas, which leads to more practice.

The quantity 10,000 hours is frequently mentioned as the amount of time it takes to achieve one’s potential or come close to achieving one’s potential. (The figure 10 years is also often used as an estimate, instead of 10,000 hours.) Thus, for example, suppose you have never played a game of chess. In 1 hour, you can learn the rudiments of what constitutes a legal move and what constitutes winning a game. In 10,000 hours, you will have made considerable progress toward being as good as you can be.

In chess, however, additional hours of study and practice will likely continue to move you up the expertise scale. For example, the current average age of the world’s top-ranked human chess players is about 30. These people have put in 30,000 to 40,000 hours or more in gaining their current level of chess expertise.

While there are some young prodigies in music performance, world-class instrumentalists typically have put in 20,000 to 30,000 hours to achieve their current level of expertise.

High Level of Expertise in an Academic Discipline

Consider a faculty member with a doctorate who has just been promoted to an associate professorship in a research university. This person has probably put in well over 20,000 hours to achieve his or her current level of discipline-specific expertise. Most of these hours of time were spent during upper division undergraduate specialization, four to six years of graduate school, and five to six years serving as an assistant professor.

This figure of more than 20,000 hours can be contrasted with the time invested by a student before beginning serious work in a college major. For example, consider a student who begins to receive some formal instruction in math while in kindergarten, and then takes math every year up through his or her freshman year in college. I would estimate that this student has invested about 2,000 hours of time at school and home in developing the level of expertise that he or she has attained.

Research on Expertise

There has been substantial research on expertise and gaining expertise in various disciplines. Some of this is summarized in Ericsson (n.d.), who discusses ideas highly relevant to higher education in any discipline:

The difference between experts and less skilled subjects is not merely a matter of the amount and complexity of the accumulated knowledge; it also reflects qualitative differences in the organization of knowledge and its representation (Chi, Glaser & Rees, 1982). Experts’ knowledge is encoded around key domain-related concepts and solution procedures that allow rapid and reliable retrieval whenever stored information is relevant. Less skilled subjects’ knowledge, in contrast, is encoded using everyday concepts that make the retrieval of even their limited relevant knowledge difficult and unreliable. Furthermore, experts have acquired domain-specific memory skills that allow them to rely on long-term memory (Long-Term Working Memory, Ericsson & Kintsch, 1995) to dramatically expand the amount of information that can be kept accessible during planning and during reasoning about alternative courses of action. The superior quality of the experts’ mental representations allow them to adapt rapidly to changing circumstances and anticipate future events in advance. The same acquired representations appear to be essential for experts’ ability to monitor and evaluate their own performance (Ericsson, 1996; Glaser, 1996) so they can keep improving their own performance by designing their own training and assimilating new knowledge. [Italics added for emphasis]

The quoted paragraph is a good example scholarly writing that is dense with important ideas. One of the key ideas is that experts learn how to learn in their area of expertise, and they learn how to self-assess. This suggests that we might want to place more emphasis on these two general ideas in all of our teaching.

A nice summary of some of the research on expertise—with a special emphasis on research on chess experts—is available in Phillip Ross’s (2006) work. In talking about long-term working memory, Ross says:

The one thing that all expertise theorists agree on is that it takes enormous effort to build these structures in the mind. Simon coined a psychological law of his own, the 10-year rule, which states that it takes approximately a decade of heavy labor to master any field. Even child prodigies, such as Gauss in mathematics, Mozart in music and Bobby Fischer in chess, must have made an equivalent effort, perhaps by starting earlier and working harder than others.

…

Ericsson argues that what matters is not experience per se but “effortful study,” which entails continually tackling challenges that lie just beyond one’s competence. That is why it is possible for enthusiasts to spend tens of thousands of hours playing chess or golf or a musical instrument without ever advancing beyond the amateur level and why a properly trained student can overtake them in a relatively short time. [Italics added for emphasis]

I find the educational implications of these statements quite interesting. Experts in a discipline have learned to do the effortful study that advances expertise, and they put in the thousands of hours of effort needed to move to a high level of expertise. A good teacher or a good coach helps students learn to do this type of effortful study.

Ross also gives a brief summary of studies that attempt to get at the issue of nature versus nurture in achieving a high level of expertise. He concludes that, “the preponderance of psychological evidence indicates that experts are made, not born. What is more, the demonstrated ability to turn a child quickly into an expert—in chess, music and a host of other subjects—sets a clear challenge before the schools.”

Problem Solving

In discussing problem solving situations, I include the following:

Question situations: recognizing, posing, clarifying, and answering questions.

Problem situations: recognizing, posing, clarifying, and then solving problems.

Task situations: recognizing, posing, clarifying, and accomplishing tasks.

Decision situations: recognizing, posing, clarifying, and making good decisions.

All situations: using higher-order critical, creative, wise, and foresightful thinking to do all of the above. Often the results are shared, demonstrated, or used as a product, performance, or presentation.

You have been solving problems and accomplishing tasks all of your life. My goal here is to broaden your internal model of the terms problem and problem solving. I want you to have a mental model that fits with developing a high level of expertise in any discipline you decide to study in depth.

It may surprise you that the list places so much emphasis on posing questions, problems, and tasks. Gaining skill in such posing is an important part of increasing expertise in a discipline. Think about this when you are taking a course. From time to time as you listen to a lecture or participate in a discussion, think about what deep, penetrating questions you might raise and/or that you are learning to answer.

Here is a definition of problem that I have found useful in my teaching and writing:

You (personally) have a problem if the following four conditions are satisfied:

You have a clearly defined given initial situation.
You have a clearly defined goal (a desired end situation). Some writers talk about having multiple goals in a problem. However, such a multiple goal situation can be broken down into a number of single-goal problems.
You have a clearly defined set of resources that may be applicable in helping you move from the given initial situation to the desired goal situation. These typically include some of your time, knowledge, and skills. Resources might include money, the Web, and the telecommunication system. There may be specified limitations on resources, such as rules, regulations, guidelines, and timelines for what you are allowed to do in attempting to solve a particular problem.
You have some ownership—you are committed to using some of your own resources, such as your knowledge, skills, time, and energy, to achieve the desired final goal.

In many problem-solving situations, ICT and computerized tools are resources of the type mentioned in the third part of the definition. These resources have grown more powerful over the years. That is one reason why it is so important to integrate the use of computers in problem solving thoroughly into the basic fabric of the courses you are taking and the areas you are studying.

The fourth part of the definition of a problem is particularly important. Unless you have ownership—through an appropriate combination of intrinsic and extrinsic motivation—you do not have a problem. Motivation, especially intrinsic motivation, is a huge topic in its own right, and I will not attempt to explore it in detail in this book. Edward Vockell (n.d) maintains an online book, Educational Psychology: A Practical Workbook. The fifth chapter provides a nice discussion of motivation.

George Polya

George Polya was one of the leading mathematicians of the 20th century, and he wrote extensively about problem solving. His 1945 book, How to Solve It: A New Aspect of Mathematical Method, is well known in math education circles (Polya, 1957).

In a talk to elementary school teachers, Polya said:

To understand mathematics means to be able to do mathematics. And what does it mean doing mathematics? In the first place it means to be able to solve mathematical problems. For the higher aims about which I am now talking are some general tactics of problems—to have the right attitude for problems and to be able to attack all kinds of problems, not only very simple problems, which can be solved with the skills of the primary school, but more complicated problems of engineering, physics and so on, which will be further developed in the high school. But the foundations should be started in the primary school. And so I think an essential point in the primary school is to introduce the children to the tactics of problem solving. Not to solve this or that kind of problem, not to make just long divisions or some such thing, but to develop a general attitude for the solution of problems. (Polya, 1969)

Polya’s statements about mathematics apply to any academic discipline. A student who takes one or more college courses in a discipline should gain an understanding of the general nature of the types of problems it addresses. The student should make some progress in thinking like an expert in the discipline.

Polya (1957) provides a general heuristic strategy for attempting to solve any math problem. I have reworded his strategy so that it is applicable to a wide range of problems in a wide range of disciplines—not just in math. This six-step strategy can be called the Polya Strategy or the Six Step Strategy.

It is a heuristic strategy. There is no guarantee that use of the Six Step Strategy will lead to success in solving a particular problem. You may lack the knowledge, skills, time, and other resources needed to solve a particular problem, or the problem might not be solvable.

1. Understand the problem. Among other things, this includes working toward having a well-defined (clearly defined) problem. You need an initial understanding of the Givens, Resources, and Goal. This requires knowledge of the domain(s) of the problem, which could well be interdisciplinary. You need to make a personal commitment—have ownership—to solving the problem.

2. Determine a plan of action. This is a thinking activity. What strategies will you apply? What resources will you use, how will you use them, in what order will you use them? Are the resources adequate to the task? On hard problems, it is often difficult to develop a plan of action. Research into this situation suggests that many good problem solvers “sleep on the problem.” That is, after working on a problem for quite a while with little or no success, they put the problem out of their minds and do something else for days or even weeks. What may well happen is that at subconscious level the mind continues to work on the problem. Eventually, an “ah-ha” experience sometimes occurs.

3. Think carefully about possible consequences of carrying out your plan of action. Focus major emphasis on trying to anticipate undesirable outcomes. What new problems will be created? You may decide to stop working on the problem or return to step 1 because of this thinking.

4. Carry out your plan of action. Make appropriate use of physical and cognitive tools in this activity. Do reflective thinking as you carry out your plan. This thinking may lead you to the conclusion that you need to return to one of the earlier steps. Note also that this reflective thinking contributes to increased expertise.

5. Analyze the results achieved by carrying out your plan of action. Then do one of the following:

A.If the problem has been solved, go to step 6.

B.If the problem has not been solved and you are willing to devote more time and energy to it, make use of the knowledge and experience you have gained as you return to step 1 or step 2.

C. Make a decision to stop working on the problem. This might be a temporary or a permanent decision. Keep in mind that the problem you are working on may not be solvable, or it may be beyond your current capabilities and resources.

6. Do a reflective analysis of the steps you have carried out and the results you have achieved to see if you have created new, additional problems that need to be addressed. Reflect on (do metacognition on) what you have learned by solving the problem. Think about how your increased knowledge and skills can be used in other problem-solving situations. Work to increase your reflective intelligence!

Many of the steps in this Six Step Strategy require careful thinking. However, there are a steadily growing number of situations in which much of the work of Step 4 can be carried out by a computer. The person who is skilled at using a computer for this purpose may gain a significant advantage in problem solving over a person who lacks computer knowledge and skill. This type of knowledge and skill in using computers is a way to build on the previous work of others.

Step 6 emphasizes metacognition. There is considerable research to support the contention that metacognition is a key to building expertise and getting better at problem solving. It is a process in which you think about what you already know and how what you are doing ties in with what you already know.

Every problem-solving activity that you do during your everyday life provides an opportunity for metacognition.

You make a decision. How and why did you make that decision? How do you know it is a good decision?

You pose a question. What led you to pose this particular question? In the process of thinking about the question, did you also posit the answer you expect to get or find? Did you think about the usefulness of possible answers? Was the question carefully constructed so that an answer can be found and will prove useful?

You solved a relatively challenging problem. What knowledge and skills did you draw on? What did you learn during the problem solving process that will likely be useful when you encounter other somewhat similar problems in the future?

Building on Previous Work

One of the most important ideas in problem solving is to build on your own previous work and on the previous work of others. That is, one way to solve a problem is to retrieve from your own memory either a solution to the problem or a method for solving the problem. Another way is to retrieve this information from another person, from a physical library, or from a virtual library such as the Web.

The human race’s accumulated knowledge is stored in tens of millions of books, monographs, journals, Web publications, and other forms of publication written in many different languages. Much of the accumulated knowledge in a discipline is only accessible to those who have studied the discipline at a graduate school level. While it is easy to talk about the importance of building on the knowledge of others, it can take many years of hard work to develop the knowledge needed to read and understand the accumulated research knowledge in a discipline.

Moreover, most of the accumulated knowledge in any specific academic discipline is not readily available or easily retrievable. It is scattered throughout the libraries of the world, it is written in many different languages, and much is stored in people’s heads. Over time, such difficulties of accessing materials will decrease as the materials are digitized and become accessible through the Web. Progress in the computer translation of languages will help, as will the development of better expert systems (a type of Artificially Intelligent computer system that has a relatively high level of expertise in a narrow field).

Perhaps you don’t know much about expert systems. This topic is covered in Chapter 4. For now, it suffices for you to know that thousands of artificially intelligent expert systems are in use. Each has a very narrow range of capability. For example, nowadays if you apply for a loan at a bank, the decision as to whether to grant you the loan will likely be made mainly by a computer system. Because of progress in this small area, there are far fewer human loan officers working in banks.

To summarize, one goal in the study of an academic discipline should be to learn to access the accumulated, discipline-specific knowledge that is appropriate to their educational level and needs and to learn to use this accumulated knowledge to solve problems and accomplish tasks. Certainly you will want to learn what aspects of jobs in your chosen area of study are likely to change significantly or even disappear because of the increasing capability of computer systems.

To Memorize or Not to Memorize: That Is the Question

Researchers in the area of expertise distinguish between rote memory (which involves little understanding) and the type of memorization being done by experts in a discipline. Rote memory is useful in problem solving. However, a focus on rote memory tends to be a poor approach to building a useful level of expertise in any discipline.

As Ericsson (n.d., in press) notes:

The primary goal for all experts is to excel at the representative tasks in their domains. For example, chess experts need to find the best moves to win chess matches and medical experts have to diagnose sick patients in order to give them the best treatment. … As part of performing the representative task of selecting the best move, the experts encode the important features of the presented information and store them in accessible form in memory. In contrast, when subjects, after training based on mnemonics and knowledge unrelated to chess, attain a recall performance comparable with that of the chess experts, they still lack the ability to extract the information important for selecting the best move.

The ideas in Ericsson’s quote have deep educational implications. Many students resort to rote memory with only modest understanding in order to pass tests and the course. The long-term retention of such memorized information tends to be quite low and this approach to learning does not contribute much to building a useful level of expertise.

Academic Disciplines

The terms discipline and academic discipline have been used repeatedly in earlier parts of this book. I did not define the terms, since I am sure that you already know what I am talking about.

However, in this section I want us to take a deeper look into academic disciplines. I use the term discipline when I am talking about a large and inclusive discipline of study, a sub discipline, an interdisciplinary discipline, and so on. Each academic discipline or area of study can be defined by a combination of general things such as:

The types of problems, tasks, and activities it addresses.

Its accumulated accomplishments such as results, achievements, products, performances, scope, power, uses, impact on the societies of the world, and so on.

Its history, culture, and language, including notation and special vocabulary.

Its methods of teaching, learning, assessment, and thinking. What it does to preserve and sustain its work and pass it on to future generations.

Its tools, methodologies, and types of evidence and arguments used in solving problems, accomplishing tasks, and recording and sharing accumulated results.

The knowledge and skills that separate and distinguish among: a) a novice; b) a person who has a personally useful level of competence; c) a reasonably competent person, employable in the discipline; d) an expert; and e) a world-class expert.

Notice the emphasis on solving problems, accomplishing tasks, producing products, doing performances, accumulating knowledge and skills, and sharing knowledge and skills. Suppose that you are taking a course in which the book you are currently reading is part of the required readings. You are browsing along, perhaps even enjoying the reading, and you come to a list such as the one given above.

“Hmm,” you think. “What should I do now? I wonder if the teacher expects me to memorize this bulleted list. What are the chances it will be on a test? Maybe all I need to do is understand the general idea that an academic discipline tends to be broad and deep, and it takes a person many years to achieve a high level of expertise in such a discipline.”

One of the challenges in taking a college course is to decide what you want to learn versus what the teacher wants you to learn. You know yourself, and you can look into your own mind as an aid to deciding what you want to learn. However, it is difficult to read the teacher’s mind, even if the teacher provides a clear syllabus, assignments, and lectures.

Let me help you read my mind in this particular instance. I am writing a book to help you and other students who are taking college courses. I want you to learn to take increased responsibility for your own learning, and I want you to increase your expertise as a learner.

I, personally, have not memorized my bulleted list that helps to define a discipline. I developed the list over a considerable time, I have used it in several books, and I have revised it a number of times. What I actually carry around in my head is roughly, “the general idea that an academic discipline tends to be broad and deep, and it takes a person many years to achieve a high level of expertise in such a discipline.”

However, I have though about the details in the list. I have used them to examine various disciplines that interest me. When I am talking and writing, the word discipline has a relatively broad and deep meaning and is an important part of how I view my work. The word is part of me. It is stored in my brain’s neurons and I have grown many neural connections that help tie the word in with my other knowledge.

Thus, as an author and teacher, I want the word discipline to become part of your working vocabulary—part of you and your worldviews. I want you to have a rich set of neural connections that give meaning to the word in your brain. Memorizing the bulleted list in order to pass a test, and then soon forgetting what you have memorized, contributes very little to your education.

Suppose instead that you select a discipline that interests you and where you have some knowledge and skills. Examine each bulleted item from the point of view of your insights into the discipline. Where are your strengths, weaknesses, interests, and disintersts? What have you done to achieve your current level of expertise in various aspects of the discipline? What helps and encourages you to learn and to increase your expertise in various aspects of the discipline?

Next, do some of the same thinking over again, but now think specifically about how ICT is affecting the discipline and what you know about the discipline. Do you have knowledge of how computers have changed and are changing the discipline? Have any of the courses you have taken in your precollege and college education included a modern discussion of roles of computers in the discipline? Are you skilled in using the Web and other electronic resources to retrieve up to date information in this discipline? What other pieces of software do you know how to use that are relevant to the discipline?

Notice that these are thinking exercises, and you are in charge of doing the thinking. This thinking builds neural connections; it changes your brain! As you think about the questions I have provided, you will likely develop other questions that you feel are more important and more appropriate to you. If that happens and you indeed spend time thinking about a discipline of interest to you, the learning that I want to occur will occur. I cannot guarantee that this will lead to you getting a good grade in a test over this part of the chapter, but likely it will help. I can guarantee if you routinely practice the line of thinking I am encouraging, it will help you to become a more self-responsible and better learner!

Summary and Self-Assessment

One of your goals in school is to increase your level of expertise in solving problems and accomplishing tasks. You now realize that computer technology is a useful aid to solving problems and accomplishing tasks in every discipline. Thus, as you take courses in various disciplines you will want to increase your ICT knowledge and skills that are relevant to these disciplines. You might think of this in terms of building an island of ICT expertise that is quite specific to a discipline you are studying or a course you are taking.

You are used to the difference between a generalist and a specialist. A generalist tends to have a useful but limited level of knowledge over a very broad range of areas, while a specialist has a very high level of expertise in one specific area. The generalist versus specialist idea even holds within a specific discipline, such as medicine. A general practitioner can handle a wide range of medical problems, but will often refer patients to a specialist. Of course, the specialist has a broad general background, but has far greater depth and experience in one narrow area than does the general practitioner.

As you plan your higher education, think about this idea of generalist versus specialist. What seems to fit best with your insights into yourself and your goals for the future? This type of thinking is useful in any discipline, including ICT. You may want to be a computer science major, perhaps going on to graduate work in this field. Alternatively, you may want to just develop the functional level of ICT knowledge and skills that are or will be useful to you in the various other areas in which you are developing expertise.

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