How People Learn:
Brain, Mind,
Experience, and School
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Part II: Learners and Learning
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2
How Experts Differ from Novices
People who have
developed expertise in particular areas are, by definition, able to
think effectively about problems in those areas. Understanding
expertise is important because it provides insights into the nature of
thinking and problem solving. Research shows that it is not simply
general abilities, such as memory or intelligence, nor the use of
general strategies that differentiate experts from novices. Instead,
experts have acquired extensive knowledge that affects what they notice
and how they organize, represent, and interpret information in their
environment. This, in turn, affects their abilities to remember,
reason, and solve problems.
This chapter
illustrates key scientific findings that have come from the study of
people who have developed expertise in areas such as chess, physics,
mathematics, electronics, and history. We discuss these examples not
because all school children are expected to become experts in these
or any other areas, but because the study of expertise shows what the
results of successful learning look like. In later chapters we explore
what is known about processes of learning that can eventually lead to
the development of expertise.
We consider several key
principles of experts' knowledge and their potential implications for
learning and instruction:
1. Experts notice features and meaningful patterns of information
that are not noticed by novices.
2. Experts have acquired a great deal of content knowledge that is
organized in ways that reflect a deep understanding of their subject
matter.
3. Experts' knowledge cannot be reduced to sets of isolated facts or
propositions but, instead, reflects contexts of applicability: that is,
the knowledge is "conditionalized" on a set of circumstances.
4. Experts are able to flexibly retrieve important aspects of their
knowledge with little attentional effort.
5. Though experts know their disciplines thoroughly, this does not
guarantee that they are able to teach others.
6. Experts have varying levels of flexibility in their approach to
new situations.
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MEANINGFUL PATTERNS OF INFORMATION |
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One of the earliest
studies of expertise demonstrated that the same stimulus is perceived
and understood differently, depending on the knowledge that a person
brings to the situation. DeGroot (1965) was interested in understanding
how world-class chess masters are consistently able to out-think their
opponents. Chess masters and less experienced but still extremely good
players were shown examples of chess games and asked to think aloud as
they decided on the move they would make if they were one of the
players; see Box 2.1. DeGroot's
hypothesis was that the chess masters would be more likely than the
nonmasters to (a) think through all the possibilities before making a
move (greater breadth of search) and (b) think through all the possible
countermoves of the opponent for every move considered (greater depth of
search). In this pioneering research, the chess masters did exhibit
considerable breadth and depth to their searches, but so did the lesser
ranked chess players. And none of them conducted searches that covered
all the possibilities. Somehow, the chess masters considered
possibilities for moves that were of higher quality than those
considered by the lesser experienced players. Something other than
differences in general strategies seemed to be responsible for
differences in expertise.
DeGroot concluded that
the knowledge acquired over tens of thousands of hours of chess playing
enabled chess masters to out-play their opponents. Specifically,
masters were more likely to recognize meaningful chess configurations
and realize the strategic implications of these situations; this
recognition allowed them to consider sets of possible moves that were
superior to others. The meaningful patterns seemed readily apparent to
the masters, leading deGroot (1965:33-34) to note:
We know that increasing experience and knowledge in a
specific field (chess, for instance) has the effect that things
(properties, etc.) which, at earlier stages, had to be abstracted, or
even inferred are apt to be immediately perceived at later stages. To a
rather large extent, abstraction is replaced by perception, but we do
not know much about how this works, nor where the borderline lies. As
an effect of this replacement, a so-called 'given' problem situation is
not really given since it is seen differently by an expert than it is
perceived by an inexperienced person. . . .
DeGroot's
think-aloud method provided for a very careful analysis of the
conditions of specialized learning and the kinds of conclusions one can
draw from them (see Ericsson and Simon, 1993). Hypotheses generated
from think-aloud protocols are usually cross-validated through the use
of other methodologies.
The superior recall
ability of experts, illustrated in the example in the box, has been
explained in terms of how they "chunk" various elements of a
configuration that are related by an underlying function or strategy.
Since there are limits on the amount of information that people can hold
in short-term memory, short-term memory is enhanced when people are able
to chunk information into familiar patterns (Miller, 1956). Chess
masters perceive chunks of meaningful information, which affects their
memory for what they see. Chess masters are able to chunk together
several chess pieces in a configuration that is governed by some
strategic component of the game. Lacking a hierarchical, highly
organized structure for the domain, novices cannot use this chunking
strategy. It is noteworthy that people do not have to be world-class
experts to benefit from their abilities to encode meaningful chunks of
information: 10- and 11-year-olds who are experienced in chess are able
to remember more chess pieces than college students who are not chess
players. In contrast, when the college students were presented with
other stimuli, such as strings of numbers, they were able to remember
more (Chi, 1978; Schneider et al., 1993); see Figure 2.3.
Skills similar to those
of master chess players have been demonstrated for experts in other
domains, including electronic circuitry (Egan and Schwartz, 1979),
radiology (Lesgold, 1988), and computer programming (Ehrlich and
Soloway, 1984). In each case, expertise in a domain helps people
develop a sensitivity to patterns of meaningful information that are not
available to novices. For example, electronics technicians were able to
reproduce large portions of complex circuit diagrams after only a few
seconds of viewing; novices could not. The expert circuit technicians
chunked several individual circuit elements (e.g., resistors and
capacitors) that performed the function of an amplifier. By remembering
the structure and function of a typical amplifier, experts were able to
recall the arrangement of many of the individual circuit elements
comprising the "amplifier chunk."
Mathematics experts are
also able to quickly recognize patterns of information, such as
particular problem types that involve specific classes of mathematical
solutions (Hinsley et al., 1977; Robinson and Hayes, 1978). For
example, physicists recognize problems of river currents and problems of
headwinds and tailwinds in airplanes as involving similar mathematical
principles, such as relative velocities. The expert knowledge that
underlies the ability to recognize problem types has been characterized
as involving the development of organized conceptual structures, or
schemas, that guide how problems are represented and understood (e.g.,
Glaser and Chi, 1988).
Expert teachers, too,
have been shown to have schemas similar to those found in chess and
mathematics. Expert and novice teachers were shown a videotaped
classroom lesson (Sabers et al., 1991). The experimental set-up
involved three screens that showed simultaneous events occurring
throughout the classroom (the left, center, and right). During part of
the session, the expert and novice teachers were asked to talk aloud
about what they were seeing. Later, they were asked questions about
classroom events. Overall, the expert teachers had very different
understandings of the events they were watching than did the novice
teachers; see examples in Box
2.2.
The idea that experts
recognize features and patterns that are not noticed by novices is
potentially important for improving instruction. When viewing
instructional texts, slides, and videotapes, for example, the
information noticed by novices can be quite different from what is
noticed by experts (e.g., Sabers et al., 1991; Bransford et al., 1988).
One dimension of acquiring greater competence appears to be the
increased ability to segment the perceptual field (learning how to see).
Research on expertise suggests the importance of providing students
with learning experiences that specifically enhance their abilities to
recognize meaningful patterns of information (e.g., Simon, 1980;
Bransford et al., 1989).
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ORGANIZATION OF KNOWLEDGE |
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We turn now
to the question of how experts' knowledge is organized and how this
affects their abilities to understand and represent problems. Their
knowledge is not simply a list of facts and formulas that are relevant
to their domain; instead, their knowledge is organized around core
concepts or "big ideas" that guide their thinking about their domains.
In an example from
physics, experts and competent beginners (college students) were asked
to describe verbally the approach they would use to solve physics
problems. Experts usually mentioned the major principle(s) or law(s)
that were applicable to the problem, together with a rationale for why
those laws applied to the problem and how one could apply them (Chi et
al., 1981). In contrast, competent beginners rarely referred to major
principles and laws in physics; instead, they typically described which
equations they would use and how those equations would be manipulated
(Larkin, 1981, 1983).
Experts' thinking seems
to be organized around big ideas in physics, such as Newton's second law
and how it would apply, while novices tend to perceive problem solving
in physics as memorizing, recalling, and manipulating equations to get
answers. When solving problems, experts in physics often pause to draw
a simple qualitative diagram--they do not simply attempt to plug numbers
into a formula. The diagram is often elaborated as the expert seeks to
find a workable solution path (e.g., see Larkin et al., 1980; Larkin and
Simon, 1987; Simon and Simon, 1978).
Differences in how
physics experts and novices approach problems can also be seen when they
are asked to sort problems, written on index cards, according to the
approach that could be used to solve them (Chi et al., 1981). Experts'
problem piles are arranged on the basis of the principles that can be
applied to solve the problems; novices' piles are arranged on the basis
of the problems' surface attributes. For example, in the physics
subfield of mechanics, an expert's pile might consist of problems that
can be solved by conservation of energy, while a novice's pile might
consist of problems that contain inclined planes; see Figure 2.4. Responding to the
surface characteristics of problems is not very useful, since two
problems that share the same objects and look very similar may actually
be solved by entirely different approaches.
Some studies of experts
and novices in physics have explored the organization of the knowledge
structures that are available to these different groups of individuals
(Chi et al., 1982); see Figure
2.5. In representing a schema for an incline plane, the novice's
schema contains primarily surface features of the incline plane. In
contrast, the expert's schema immediately connects the notion of an
incline plane with the laws of physics and the conditions under which
laws are applicable.
Pause times have also
been used to infer the structure of expert knowledge in domains such as
chess and physics. Physics experts appear to evoke sets of related
equations, with the recall of one equation activating related equations
that are retrieved rapidly (Larkin, 1979). Novices, in contrast,
retrieve equations more equally spaced in time, suggesting a sequential
search in memory. Experts appear to possess an efficient organization
of knowledge with meaningful relations among related elements clustered
into related units that are governed by underlying concepts and
principles; see Box 2.3. Within
this picture of expertise, "knowing more" means having more conceptual
chunks in memory, more relations or features defining each chunk, more
interrelations among the chunks, and efficient methods for retrieving
related chunks and procedures for applying these informational units in
problem-solving contexts (Chi et al., 1981).
Differences between how
experts and nonexperts organize knowledge has also been demonstrated in
such fields as history (Wineburg, 1991). A group of history experts and
a group of gifted, high-achieving high school seniors enrolled in an
advanced placement course in history were first given a test of facts
about the American Revolution. The historians with backgrounds in
American history knew most of the items. However, many of the
historians had specialties that lay elsewhere and they knew only
one-third of the facts on the tests. Several of the students outscored
several of the historians on the factual test. The study then compared
how the historians and students made sense of historical documents; the
result revealed dramatic differences on virtually any criterion. The
historians excelled in the elaborateness of understandings they
developed in their ability to pose alternative explanations for events
and in their use of corroborating evidence. This depth of understanding
was as true for the Asian specialists and the medievalists as it was for
the Americanists.
When the two groups
were asked to select one of three pictures that best reflect their
understanding of the battle of Lexington, historians and students
displayed the greatest differences. Historians carefully navigated back
and forth between the corpus of written documents and the three images
of the battlefield. For them, the picture selection task was the
quintessential epistemological exercise, a task that explored the limits
of historical knowledge. They knew that no single document or picture
could tell the story of history; hence, they thought very hard about
their choices. In contrast, the students generally just looked at the
pictures and made a selection without regard or qualification. For
students, the process was similar to finding the correct answer on a
multiple choice test.
In sum, although the
students scored very well on facts about history, they were largely
unacquainted with modes of inquiry with real historical thinking. They
had no systematic way of making sense of contradictory claims. Thrust
into a set of historical documents that demanded that they sort out
competing claims and formulate a reasoned interpretation, the students,
on the whole, were stymied. They lacked the experts' deep understanding
of how to formulate reasoned interpretations of sets of historical
documents. Experts in other social sciences also organize their problem
solving around big ideas (see, e.g., Voss et al., 1984).
The fact that experts'
knowledge is organized around important ideas or concepts suggests that
curricula should also be organized in ways that lead to conceptual
understanding. Many approaches to curriculum design make it difficult
for students to organize knowledge meaningfully. Often there is only
superficial coverage of facts before moving on to the next topic; there
is little time to develop important, organizing ideas. History texts
sometimes emphasize facts without providing support for understanding
(e.g., Beck et al., 1989, 1991). Many ways of teaching science also
overemphasize facts (American Association for the Advancement of
Science, 1989; National Research Council, 1996).
The Third International
Mathematics and Science Survey (TIMSS) (Schmidt et al., 1997) criticized
curricula that were "a mile wide and an inch deep" and argued that this
is much more of a problem in America than in most other countries.
Research on expertise suggests that a superficial coverage of many
topics in the domain may be a poor way to help students develop the
competencies that will prepare them for future learning and work. The
idea of helping students organize their knowledge also suggests that
novices might benefit from models of how experts approach problem
solving--especially if they then receive coaching in using similar
strategies (e.g., Brown et al., 1989; we discuss this more fully in Chapters 3 and 7).
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CONTEXT AND ACCESS TO KNOWLEDGE |
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Experts have a vast
repertoire of knowledge that is relevant to their domain or discipline,
but only a subset of that knowledge is relevant to any particular
problem. Experts do not have to search through everything they know in
order to find what is relevant; such an approach would overwhelm their
working memory (Miller, 1956). For example, the chess masters described
above considered only a subset of possible chess moves, but those moves
were generally superior to the ones considered by the lesser ranked
players. Experts have not only acquired knowledge, but are also good at
retrieving the knowledge that is relevant to a particular task. In the
language of cognitive scientists, experts' knowledge is
"conditionalized"--it includes a specification of the contexts in which
it is useful (Simon, 1980; Glaser, 1992). Knowledge that is not
conditionalized is often "inert" because it is not activated, even
though it is relevant (Whitehead, 1929).
The concept of
conditionalized knowledge has implications for the design of curriculum,
instruction, and assessment practices that promote effective learning.
Many forms of curricula and instruction do not help students
conditionalize their knowledge: "Textbooks are much more explicit in
enunciating the laws of mathematics or of nature than in saying anything
about when these laws may be useful in solving problems" (Simon,
1980:92). It is left largely to students to generate the
condition-action pairs required for solving novel problems.
One way to help
students learn about conditions of applicability is to assign word
problems that require students to use appropriate concepts and formulas
(Lesgold, 1984, 1988; Simon, 1980). If well designed, these problems
can help students learn when, where, and why to use the knowledge they
are learning. Sometimes, however, students can solve sets of practice
problems but fail to conditionalize their knowledge because they know
which chapter the problems came from and so automatically use this
information to decide which concepts and formulas are relevant.
Practice problems that are organized into very structured worksheets can
also cause this problem. Sometimes students who have done well on such
assignments--and believe that they are learning--are unpleasantly
surprised when they take tests in which problems from the entire course
are randomly presented so there are no clues about where they appeared
in a text (Bransford, 1979).
The concept of
conditionalized knowledge also has important implications for assessment
practices that provide feedback about learning. Many types of tests
fail to help teachers and students assess the degree to which the
students' knowledge is conditionalized. For example, students might be
asked whether the formula that quantifies the relationship between mass
and energy is E = MC, E = MC2, or
E = MC3. A correct answer requires no
knowledge of the conditions under which it is appropriate to use the
formula. Similarly, students in a literature class might be asked to
explain the meaning of familiar proverbs, such as "he who hesitates is
lost" or "too many cooks spoil the broth." The ability to explain the
meaning of each proverb provides no guarantee that students will know
the conditions under which either proverb is useful. Such knowledge is
important because, when viewed solely as propositions, proverbs often
contradict one another. To use them effectively, people need to know
when and why it is appropriate to apply the maxim "too many cooks spoil
the broth" versus "many hands make light work" or "he who hesitates is
lost" versus "haste makes waste" (see Bransford and Stein, 1993).
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FLUENT RETRIEVAL |
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People's abilities to
retrieve relevant knowledge can vary from being "effortful" to
"relatively effortless" (fluent) to "automatic" (Schneider and
Shiffrin, 1977). Automatic and fluent retrieval are important
characteristics of expertise.
Fluent retrieval does
not mean that experts always perform a task faster than novices.
Because experts attempt to understand problems rather than to jump
immediately to solution strategies, they sometimes take more time than
novices (e.g., Getzels and Csikszentmihalyi, 1976). But within the
overall process of problem solving there are a number of subprocesses
that, for experts, vary from fluent to automatic. Fluency is important
because effortless processing places fewer demands on conscious
attention. Since the amount of information a person can attend to at
any one time is limited (Miller, 1956), ease of processing some aspects
of a task gives a person more capacity to attend to other aspects of the
task (LaBerge and Samuels, 1974; Schneider and Shiffrin, 1985; Anderson,
1981, 1982; Lesgold et al., 1988).
Learning to drive a car
provides a good example of fluency and automaticity. When first
learning, novices cannot drive and simultaneously carry on a
conversation. With experience, it becomes easy to do so. Similarly,
novice readers whose ability to decode words is not yet fluent are
unable to devote attention to the task of understanding what they are
reading (LaBerge and Samuels, 1974). Issues of fluency are very
important for understanding learning and instruction. Many
instructional environments stop short of helping all students develop
the fluency needed to successfully perform cognitive tasks (Beck et al.,
1989; Case, 1978; Hasselbring et al., 1987; LaBerge and Samuels, 1974).
An important aspect of
learning is to become fluent at recognizing problem types in particular
domains--such as problems involving Newton's second law or concepts of
rate and functions--so that appropriate solutions can be easily
retrieved from memory. The use of instructional procedures that speed
pattern recognition are promising in this regard (e.g., Simon, 1980).
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EXPERTS AND TEACHING |
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Expertise in a
particular domain does not guarantee that one is good at helping others
learn it. In fact, expertise can sometimes hurt teaching because many
experts forget what is easy and what is difficult for students.
Recognizing this fact, some groups who design educational materials pair
content area experts with "accomplished novices" whose area of expertise
lies elsewhere: their task is to continually challenge the experts
until the experts' ideas for instruction begin to make sense to them
(Cognition and Technology Group at Vanderbilt, 1997).
The content knowledge
necessary for expertise in a discipline needs to be differentiated from
the pedagogical content knowledge that underlies effective teaching
(Redish, 1996; Shulman, 1986, 1987). The latter includes information
about typical difficulties that students encounter as they attempt to
learn about a set of topics; typical paths students must traverse in
order to achieve understanding; and sets of potential strategies for
helping students overcome the difficulties that they encounter. Shulman
(1986, 1987) argues that pedagogical content knowledge is not equivalent
to knowledge of a content domain plus a generic set of teaching
strategies; instead, teaching strategies differ across disciplines.
Expert teachers know the kinds of difficulties that students are likely
to face; they know how to tap into students' existing knowledge in order
to make new information meaningful; and they know how to assess their
students' progress. Expert teachers have acquired pedagogical content
knowledge as well as content knowledge; see Box 2.4. In the absence of pedagogical content
knowledge, teachers often rely on textbook publishers for decisions
about how to best organize subjects for students. They are therefore
forced to rely on the "prescriptions of absentee curriculum developers"
(Brophy, 1983), who know nothing about the particular students in each
teacher's classroom. Pedagogical content knowledge is an extremely
important part of what teachers need to learn to be more effective.
(This topic is discussed more fully in Chapter
7.)
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ADAPTIVE EXPERTISE |
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An important question
for educators is whether some ways of organizing knowledge are better at
helping people remain flexible and adaptive to new situations than
others. For example, contrast two types of Japanese sushi experts
(Hatano and Ignaki, 1986): one excels at following a fixed recipe; the other has
"adaptive expertise" and is able to prepare sushi quite creatively.
These appear to be examples of two very different types of expertise,
one that is relatively routinized and one that is flexible and more
adaptable to external demands: experts have been characterized as being
"merely skilled" versus "highly competent" or more colorfully as
"artisans" versus "virtuosos" (Miller, 1978). These differences
apparently exist across a wide range of jobs.
One analysis looked at
these differences in terms of information systems design (Miller, 1978).
Information systems designers typically work with clients who specify
what they want. The goal of the designer is to construct systems that
allow people to efficiently store and access relevant information
(usually through computers). Artisan experts seek to identify the
functions that their clients want automated; they tend to accept the
problem and its limits as stated by the clients. They approach new
problems as opportunities to use their existing expertise to do familiar
tasks more efficiently. It is important to emphasize that artisans'
skills are often extensive and should not be underestimated. In
contrast, however, the virtuoso experts treat the client's statement of
the problem with respect, but consider it "a point for departure and
exploration" (Miller, 1978). They view assignments as opportunities to
explore and expand their current levels of expertise. Miller also
observes that, in his experience, virtuosos exhibit their positive
characteristics despite their training, which is usually
restricted solely to technical skills.
The concept of adaptive
expertise has also been explored in a study of history experts
(Wineburg, 1998). Two history experts and a group of future teachers
were asked to read and interpret a set of documents about Abraham
Lincoln and his view of slavery. This is a complex issue that, for
Lincoln, involved conflicts between enacted law (the Constitution),
natural law (as encoded in the Declaration of Independence), and divine
law (assumptions about basic rights). One of the historians was an
expert on Lincoln; the second historian's expertise lay elsewhere. The
Lincoln expert brought detailed content knowledge to the documents and
easily interpreted them; the other historian was familiar with some of
the broad themes in the documents but quickly became confused in the
details. In fact, at the beginning of the task, the second historian
reacted no differently than a group of future high school teachers who
were faced with the same task (Wineburg and Fournier, 1994): attempting
to harmonize discrepant information about Lincoln's position, they both
appealed to an array of present social forms and institutions--such as
speech writers, press conferences, and "spin doctors"--to explain why
things seemed discrepant. Unlike the future teachers, however, the
second historian did not stop with his initial analysis. He instead
adopted a working hypothesis that assumed that the apparent
contradictions might be rooted less in Lincoln's duplicity than in his
own ignorance of the nineteenth century. The expert stepped back from
his own initial interpretation and searched for a deeper understanding
of the issues. As he read texts from this perspective, his
understanding deepened, and he learned from the experience. After
considerable work, the second historian was able to piece together an
interpretive structure that brought him by the task's end to where his
more knowledgeable colleague had begun. The future history teachers, in
contrast, never moved beyond their initial interpretations of events.
An important
characteristic exhibited by the history expert involves what is known as
"metacognition"--the ability to monitor one's current level of
understanding and decide when it is not adequate. The concept of
metacognition was originally introduced in the context of studying young
children (e.g., Brown, 1980; Flavell, 1985, 1991). For example, young
children often erroneously believe that they can remember information
and hence fail to use effective strategies, such as rehearsal. The
ability to recognize the limits of one's current knowledge, then take
steps to remedy the situation, is extremely important for learners at
all ages. The history expert who was not a specialist in Lincoln was
metacognitive in the sense that he successfully recognized the
insufficiency of his initial attempts to explain Lincoln's position. As
a consequence, he adopted the working hypothesis that he needed to learn
more about the context of Lincoln's times before coming to a reasoned
conclusion.
Beliefs about what it
means to be an expert can affect the degree to which people explicitly
search for what they don't know and take steps to improve the situation.
In a study of researchers and veteran teachers, a common assumption was
that "an expert is someone who knows all the answers" (Cognition and
Technology Group at Vanderbilt, 1997). This assumption had been
implicit rather than explicit and had never been questioned and
discussed. But when the researchers and teachers discussed this
concept, they discovered that it placed severe constraints on new
learning because the tendency was to worry about looking competent
rather than publicly acknowledging the need for help in certain areas
(see Dweck, 1989, for similar findings with students). The researchers
and the teachers found it useful to replace their previous model of
"answer-filled experts" with the model of "accomplished novices."
Accomplished novices are skilled in many areas and proud of their
accomplishments, but they realize that what they know is minuscule
compared to all that is potentially knowable. This model helps free
people to continue to learn even though they may have spent 10 to 20
years as an "expert" in their field.
The concept of adaptive
expertise (Hatano and Ignaki, 1986) provides an important model of successful
learning. Adaptive experts are able to approach new situations flexibly
and to learn throughout their lifetimes. They not only use what they
have learned, they are metacognitive and continually question their
current levels of expertise and attempt to move beyond them. They don't
simply attempt to do the same things more efficiently; they attempt to
do things better. A major challenge for theories of learning is to
understand how particular kinds of learning experiences develop adaptive
expertise or "virtuosos."
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CONCLUSION |
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Experts' abilities to
reason and solve problems depend on well-organized knowledge that
affects what they notice and how they represent problems. Experts are
not simply "general problem solvers" who have learned a set of
strategies that operate across all domains. The fact that experts are
more likely than novices to recognize meaningful patterns of information
applies in all domains, whether chess, electronics, mathematics, or
classroom teaching. In deGroot's (1965) words, a "given" problem
situation is not really a given. Because of their ability to see
patterns of meaningful information, experts begin problem solving at "a
higher place" (deGroot, 1965). An emphasis on the patterns perceived by
experts suggests that pattern recognition is an important strategy for
helping students develop confidence and competence. These patterns
provide triggering conditions for accessing knowledge that is relevant
to a task.
Studies in areas such
as physics, mathematics, and history also demonstrate that experts first
seek to develop an understanding of problems, and this often involves
thinking in terms of core concepts or big ideas, such as Newton's second
law in physics. Novices' knowledge is much less likely to be organized
around big ideas; they are more likely to approach problems by searching
for correct formulas and pat answers that fit their everyday intuitions.
Curricula that
emphasize breadth of knowledge may prevent effective organization of
knowledge because there is not enough time to learn anything in depth.
Instruction that enables students to see models of how experts organize
and solve problems may be helpful. However, as discussed in more detail
in later chapters, the level of complexity of the models must be
tailored to the learners' current levels of knowledge and skills.
While experts possess a
vast repertoire of knowledge, only a subset of it is relevant to any
particular problem. Experts do not conduct an exhaustive search of
everything they know; this would overwhelm their working memory (Miller,
1956). Instead, information that is relevant to a task tends to be
selectively retrieved (e.g., Ericsson and Staszewski, 1989; deGroot,
1965).
The issue of retrieving
relevant information provides clues about the nature of usable
knowledge. Knowledge must be "conditionalized" in order to be retrieved
when it is needed; otherwise, it remains inert (Whitehead, 1929). Many
designs for curriculum instruction and assessment practices fail to
emphasize the importance of conditionalized knowledge. For example,
texts often present facts and formulas with little attention to helping
students learn the conditions under which they are most useful. Many
assessments measure only propositional (factual) knowledge and never ask
whether students know when, where, and why to use that knowledge.
Another important
characteristic of expertise is the ability to retrieve relevant
knowledge in a manner that is relatively "effortless." This fluent
retrieval does not mean that experts always accomplish tasks in less
time than novices; often they take more time in order to fully
understand a problem. But their ability to retrieve information
effortlessly is extremely important because fluency places fewer demands
on conscious attention, which is limited in capacity (Schneider and
Shiffrin, 1977, 1985). Effortful retrieval, by contrast, places many
demands on a learner's attention: attentional effort is being expended
on remembering instead of learning. Instruction that focuses solely on
accuracy does not necessarily help students develop fluency (e.g., Beck
et al., 1989; Hasselbring et al., 1987; LaBerge and Samuels, 1974).
Expertise in an area
does not guarantee that one can effectively teach others about that
area. Expert teachers know the kinds of difficulties that students are
likely to face, and they know how to tap into their students' existing
knowledge in order to make new information meaningful plus assess their
students' progress. In Shulman's (1986, 1987) terms, expert teachers
have acquired pedagogical content knowledge and not just content
knowledge. (This concept is explored more fully in Chapter 7.)
The concept of adaptive
expertise raises the question of whether some ways of organizing
knowledge lead to greater flexibility in problem solving than others
(Hatano and Ignaki, 1986; Spiro et al., 1991). Differences between the "merely
skilled" (artisans) and the "highly competent" (virtuosos) can be seen
in fields as disparate as sushi making and information design.
Virtuosos not only apply expertise to a given problem, they also
consider whether the problem as presented is the best way to begin.
The ability to monitor
one's approach to problem solving--to be metacognitive--is an important
aspect of the expert's competence. Experts step back from their first,
oversimplistic interpretation of a problem or situation and question
their own knowledge that is relevant. People's mental models of what it
means to be an expert can affect the degree to which they learn
throughout their lifetimes. A model that assumes that experts know all
the answers is very different from a model of the accomplished novice,
who is proud of his or her achievements and yet also realizes that there
is much more to learn.
We close this chapter
with two important cautionary notes. First, the six principles of
expertise need to be considered simultaneously, as parts of an overall
system. We divided our discussion into six points in order to
facilitate explanation, but each point interacts with the others; this
interrelationship has important educational implications. For example,
the idea of promoting fluent access to knowledge (principle 4) must be
approached with an eye toward helping students develop an understanding
of the subject matter (principle 2), learn when, where and why to use
information (principle 3), and learn to recognize meaningful patterns of
information (principle 1). Furthermore, all these need to be approached
from the perspective of helping students develop adaptive expertise
(principle 6), which includes helping them become metacognitive about
their learning so that they can assess their own progress and
continually identify and pursue new learning goals. An example in
mathematics is getting students to recognize when a proof is needed.
Metacognition can help students develop personally relevant pedagogical
content knowledge, analogous to the pedagogical content knowledge
available to effective teachers (principle 5). In short, students need
to develop the ability to teach themselves.
The second cautionary
note is that although the study of experts provides important
information about learning and instruction, it can be misleading if
applied inappropriately. For example, it would be a mistake simply to
expose novices to expert models and assume that the novices will learn
effectively; what they will learn depends on how much they know already.
Discussions in the next chapters (3 and 4) show that effective
instruction begins with the knowledge and skills that learners bring to
the learning task.
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