Chapter 2: Overview of Resources in Problem Solving
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Chapter 1 provided a four-part definition of a formal
problem:
- givens;
- goal;
- resources; and
- 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.
- 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?
- 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.
- 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?
- 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?
- 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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