How People Learn:
Brain, Mind,
Experience, and School
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Part II: Learners and Learning
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3
Learning and Transfer
Processes of learning
and the transfer of learning are central to understanding how people
develop important competencies. Learning is important because no one is
born with the ability to function competently as an adult in society.
It is especially important to understand the kinds of learning
experiences that lead to transfer, defined as the ability to extend what
has been learned in one context to new contexts (e.g., Byrnes, 1996:74).
Educators hope that students will transfer learning from one problem to
another within a course, from one year in school to another, between
school and home, and from school to workplace. Assumptions about
transfer accompany the belief that it is better to broadly "educate"
people than simply "train" them to perform particular tasks (e.g.,
Broudy, 1977).
Measures of transfer
play an important role in assessing the quality of people's learning
experiences. Different kinds of learning experiences can look
equivalent when tests of learning focus solely on remembering (e.g., on
the ability to repeat previously taught facts or procedures), but they
can look quite different when tests of transfer are used. Some kinds of
learning experiences result in effective memory but poor transfer;
others produce effective memory plus positive transfer.
Thorndike and his
colleagues were among the first to use transfer tests to examine
assumptions about learning (e.g., Thorndike and Woodworth, 1901). One
of their goals was to test the doctrine of "formal discipline" that was
prevalent at the turn of the century. According to this doctrine,
practice by learning Latin and other difficult subjects had broad-based
effects, such as developing general skills of learning and attention.
But these studies raised serious questions about the fruitfulness of
designing educational experiences based on the assumption of formal
discipline. Rather than developing some kind of "general skill" or
"mental muscle" that affected a wide range of performances, people
seemed to learn things that were more specific; see Box 3.1.
Early research on the
transfer of learning was guided by theories that emphasized the
similarity between conditions of learning and conditions of transfer.
Thorndike (1913), for example, hypothesized that the degree of transfer
between initial and later learning depends upon the match between
elements across the two events. The essential elements were
presumed to be specific facts and skills. By such an account, skills of
writing letters of the alphabet are useful to writing words (vertical
transfer). The theory posited that transfer from one school task and a
highly similar task (near transfer), and from school subjects to
nonschool settings (far transfer), could be facilitated by teaching
knowledge and skills in school subjects that have elements
identical to activities encountered in the transfer context
(Klausmeier, 1985). Transfer could also be negative in the sense that
experience with one set of events could hurt performance on related
tasks (Luchins and Luchins, 1970); see Box 3.2.
The emphasis on
identical elements of tasks excluded consideration of any learner
characteristics, including when attention was directed, whether relevant
principles were extrapolated, problem solving, or creativity and
motivation. The primary emphasis was on drill and practice. Modern
theories of learning and transfer retain the emphasis on practice, but
they specify the kinds of practice that are important and take learner
characteristics (e.g., existing knowledge and strategies) into account
(e.g., Singley and Anderson, 1989).
In the discussion below
we explore key characteristics of learning and transfer that have
important implications for education:
- Initial learning is necessary for transfer, and a considerable
amount is known about the kinds of learning experiences that support
transfer.
- Knowledge that is overly contextualized can reduce transfer;
abstract representations of knowledge can help promote transfer.
- Transfer is best viewed as an active, dynamic process rather
than a passive end-product of a particular set of learning experiences.
- All new learning involves transfer based on previous learning,
and this fact has important implications for the design of instruction
that helps students learn.
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ELEMENTS THAT PROMOTE INITIAL LEARNING |
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The first factor that
influences successful transfer is degree of mastery of the original
subject. Without an adequate level of initial learning, transfer cannot
be expected. This point seems obvious, but it is often overlooked.
The importance of
initial learning is illustrated by a series of studies designed to
assess the effects of learning to program in the computer language LOGO.
The hypothesis was that students who learned LOGO would transfer this
knowledge to other areas that required thinking and problem solving
(Papert, 1980). Yet in many cases, the studies found no differences on
transfer tests between students who had been taught LOGO and those who
had not (see Cognition and Technology Group at Vanderbilt, 1996; Mayer,
1988). However, many of these studies failed to assess the degree to
which LOGO was learned in the first place (see Klahr and Carver, 1988;
Littlefield et al., 1988). When initial learning was assessed, it was
found that students often had not learned enough about LOGO to provide a
basis for transfer. Subsequent studies began to pay more attention to
student learning, and they did find transfer to related tasks (Klahr and
Carver, 1988; Littlefield et al., 1988). Other research studies have
shown that additional qualities of initial learning affect transfer and
are reviewed next.
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Understanding Versus Memorizing |
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Transfer is affected by
the degree to which people learn with understanding rather than merely
memorize sets of facts or follow a fixed set of procedures; see Boxes 3.3 and 3.4.
In Chapter 1, the advantages of learning with
understanding were illustrated with an example from biology that
involved learning about the physical properties of veins and arteries.
We noted that the ability to remember properties of veins and arteries
(e.g., that arteries are thicker than veins, more elastic, and carry
blood from the heart) is not the same as understanding why they have
particular properties. The ability to understand becomes important for
transfer problems, such as: "Imagine trying to design an artificial
artery. Would it have to be elastic? Why or why not?" Students who
only memorize facts have little basis for approaching this kind of
problem-solving task (Bransford and Stein, 1993; Bransford et al.,
1983). The act of organizing facts about veins and arteries around more
general principles such as "how structure is related to function" is
consistent with the knowledge organization of experts discussed in Chapter 2.
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Time to Learn |
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It is important to be
realistic about the amount of time it takes to learn complex subject
matter. It has been estimated that world-class chess masters require
from 50,000 to 100,000 hours of practice to reach that level of
expertise; they rely on a knowledge base containing some 50,000 familiar
chess patterns to guide their selection of moves (Chase and Simon, 1973;
Simon and Chase, 1973). Much of this time involves the development of
pattern recognition skills that support the fluent identification of
meaningful patterns of information plus knowledge of their implications
for future outcomes (see Chapter 2). In all
domains of learning, the development of expertise occurs only with major
investments of time, and the amount of time it takes to learn material
is roughly proportional to the amount of material being learned (Singley
and Anderson, 1989); see Box 3.5.
Although many people believe that "talent" plays a role in who becomes
an expert in a particular area, even seemingly talented individuals
require a great deal of practice in order to develop their expertise
(Ericsson et al., 1993).
Learners, especially in
school settings, are often faced with tasks that do not have apparent
meaning or logic (Klausmeier, 1985). It can be difficult for them to
learn with understanding at the start; they may need to take time to
explore underlying concepts and to generate connections to other
information they possess. Attempts to cover too many topics too quickly
may hinder learning and subsequent transfer because students (a) learn
only isolated sets of facts that are not organized and connected or (b)
are introduced to organizing principles that they cannot grasp because
they lack enough specific knowledge to make them meaningful. Providing
students with opportunities to first grapple with specific information
relevant to a topic has been shown to create a "time for telling" that
enables them to learn much more from an organizing lecture (as measured
by subsequent abilities to transfer) than students who did not first
have these specific opportunities; see Box 3.6.
Providing students with
time to learn also includes providing enough time for them to process
information. Pezdek and Miceli (1982) found that on one particular
task, it took 3rd graders 15 seconds to integrate pictorial and verbal
information; when given only 8 seconds, they couldn't mentally integrate
the information, probably due to short-term memory limitations. The
implication is that learning cannot be rushed; the complex cognitive
activity of information integration requires time.
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Beyond "Time on Task" |
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It is clear that
different ways of using one's time have different effects on learning
and transfer. A considerable amount is known about variables that
affect learning. For example, learning is most effective when people
engage in "deliberate practice" that includes active monitoring of one's
learning experiences (Ericsson et al., 1993). Monitoring involves
attempts to seek and use feedback about one's progress. Feedback has
long been identified as important for successful learning (see, e.g.,
Thorndike, 1913), but it should not be regarded as a unidimensional
concept. For example, feedback that signals progress in memorizing
facts and formulas is different from feedback that signals the state of
the students' understanding (Chi et al., 1989, 1994). In addition, as
noted in Chapter 2, students need feedback about
the degree to which they know when, where, and how to use the knowledge
they are learning. By inadvertently relying on clues--such as which
chapter in a text the practice problems came from--students can
erroneously think they have conditionalized their knowledge when, in
fact, they have not (Bransford, 1979).
Understanding when,
where, and why to use new knowledge can be enhanced through the use of
"contrasting cases," a concept from the field of perceptual learning
(see, e.g., Gagné and Gibson, 1947; Garner, 1974; Gibson and
Gibson, 1955). Appropriately arranged contrasts can help people notice
new features that previously escaped their attention and learn which
features are relevant or irrelevant to a particular concept. The
benefits of appropriately arranged contrasting cases apply not only to
perceptual learning, but also to conceptual learning (Bransford et al.,
1989; Schwartz et al., in press). For example, the concept of linear
function becomes clearer when contrasted with nonlinear functions; the
concept of recognition memory becomes clearer when contrasted with
measures such as free recall and cued recall.
A number of studies
converge on the conclusion that transfer is enhanced by helping students
see potential transfer implications of what they are learning (Anderson
et al., 1996). In one of the studies on learning LOGO programming
(Klahr and Carver, 1988), the goal was to help students learn to
generate "bug-free" instructions for others to follow. The researchers
first conducted a careful task analysis of the important skills
underlying the ability to program in LOGO and focused especially on LOGO
debugging skills--the process by which children find and correct errors
in their programs. Part of the researchers' success in teaching LOGO
depended on this task analysis. The researchers identified the four key
aspects of debugging a program as identifying the buggy behavior,
representing the program, locating the bug in the program, and then
correcting the bug. They highlighted these key abstract steps and
signaled to the students that the steps would be relevant to the
transfer task of writing debugging directions. Students who had LOGO
training increased from 33 percent correct instructions to 55 percent
correct instructions. They could have approached this task by
memorizing the procedures for programming LOGO routines to "make a
house," "make a polygon," and so forth. Simply memorizing the
procedures, however, would not be expected to help students accomplish
the transfer task of generating clear, bug-free instructions.
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Motivation to Learn |
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Motivation affects the
amount of time that people are willing to devote to learning. Humans
are motivated to develop competence and to solve problems; they have, as
White (1959) put it, "competence motivation." Although extrinsic
rewards and punishments clearly affect behavior (see Chapter 1), people work hard for intrinsic reasons,
as well.
Challenges, however,
must be at the proper level of difficulty in order to be and to remain
motivating: tasks that are too easy become boring; tasks that are too
difficult cause frustration. In addition, learners' tendencies to
persist in the face of difficulty are strongly affected by whether they
are "performance oriented" or "learning oriented" (Dweck, 1989).
Students who are learning oriented like new challenges; those who are
performance oriented are more worried about making errors than about
learning. Being learning oriented is similar to the concept of adaptive
expertise discussed in Chapter 2. It is
probable, but needs to be verified experimentally, that being "learning
oriented" or "performance oriented" is not a stable trait of an
individual but, instead, varies across disciplines (e.g., a person may
be performance oriented in mathematics but learning oriented in science
and social studies or vice versa).
Social opportunities
also affect motivation. Feeling that one is contributing something to
others appears to be especially motivating (Schwartz et al., in press).
For example, young learners are highly motivated to write stories
and draw pictures that they can share with others. First graders in an
inner-city school were so highly motivated to write books to be shared
with others that the teachers had to make a rule: "No leaving recess
early to go back to class to work on your book" (Cognition and
Technology Group at Vanderbilt, 1998).
Learners of all ages
are more motivated when they can see the usefulness of what they are
learning and when they can use that information to do something that has
an impact on others--especially their local community (McCombs, 1996;
Pintrich and Schunk, 1996). Sixth graders in an inner-city school were
asked to explain the highlights of their previous year in fifth grade to
an anonymous interviewer, who asked them to describe anything that made
them feel proud, successful, or creative (Barron et al., 1998).
Students frequently mentioned projects that had strong social
consequences, such as tutoring younger children, learning to make
presentations to outside audiences, designing blueprints for playhouses
that were to be built by professionals and then donated to preschool
programs, and learning to work effectively in groups. Many of the
activities mentioned by the students had involved a great deal of hard
work on their part: for example, they had had to learn about geometry
and architecture in order to get the chance to create blueprints for the
playhouses, and they had had to explain their blueprints to a group of
outside experts who held them to very high standards. (For other
examples and discussions of highly motivating activities, see Pintrich
and Schunk, 1996.)
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OTHER FACTORS THAT INFLUENCE TRANSFER |
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Context |
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Transfer is also
affected by the context of original learning; people can learn in one
context, yet fail to transfer to other contexts. For example, a group
of Orange County homemakers did very well at making supermarket best-buy
calculations despite doing poorly on equivalent school-like
paper-and-pencil mathematics problems (Lave, 1988). Similarly, some
Brazilian street children could perform mathematics when making sales in
the street but were unable to answer similar problems presented in a
school context (Carraher, 1986; Carraher et al., 1985).
How tightly learning is
tied to contexts depends on how the knowledge is acquired (Eich, 1985).
Research has indicated that transfer across contexts is especially
difficult when a subject is taught only in a single context rather than
in multiple contexts (Bjork and Richardson-Klavhen, 1989). One
frequently used teaching technique is to get learners to elaborate on
the examples used during learning in order to facilitate retrieval at a
later time. The practice, however, has the potential of actually making
it more difficult to retrieve the lesson material in other contexts,
because knowledge tends to be especially context-bound when learners
elaborate the new material with details of the context in which the
material is learned (Eich, 1985). When a subject is taught in multiple
contexts, however, and includes examples that demonstrate wide
application of what is being taught, people are more likely to abstract
the relevant features of concepts and to develop a flexible
representation of knowledge (Gick and Holyoak, 1983).
The problem of overly
contextualized knowledge has been studied in instructional programs that
use case-based and problem-based learning. In these programs,
information is presented in a context of attempting to solve complex,
realistic problems (e.g., Barrows, 1985; Cognition and Technology Group
at Vanderbilt, 1997; Gragg, 1940; Hmelo, 1995; Williams, 1992). For
example, fifth- and sixth-grade students may learn mathematical concepts
of distance-rate-time in the context of solving a complex case involving
planning for a boat trip. The findings indicate that if students learn
only in this context, they often fail to transfer flexibly to new
situations (Cognition and Technology Group at Vanderbilt, 1997). The
issue is how to promote wide transfer of the learning.
One way to deal with
lack of flexibility is to ask learners to solve a specific case and then
provide them with an additional, similar case; the goal is to help them
abstract general principles that lead to more flexible transfer (Gick
and Holyoak, 1983); see Box 3.7.
A second way to improve flexibility is to let students learn in a
specific context and then help them engage in "what-if" problem solving
designed to increase the flexibility of their understanding. They might
be asked: "What if this part of the problem were changed, or this
part?" (Cognition and Technology Group at Vanderbilt, 1997). A third
way is to generalize the case so that learners are asked to create a
solution that applies not simply to a single problem, but to a whole
class of related problems. For example, instead of planning a single
boat trip, students might run a trip planning company that has to advise
people on travel times for different regions of the country. Learners
are asked to adopt the goal of learning to "work smart" by creating
mathematical models that characterize a variety of travel problems and
using these models to create tools, ranging from simple tables and
graphs to computer programs. Under these conditions, transfer to novel
problems is enhanced (e.g., Bransford et al., 1998).
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Problem Representations |
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Transfer is also
enhanced by instruction that helps students represent problems at higher
levels of abstraction. For example, students who create a specific
business plan for a complex problem may not initially realize that their
plan works well for "fixed-cost" situations but not for others. Helping
students represent their solution strategies at a more general level can
help them increase the probability of positive transfer and decrease
the degree to which a previous solution strategy is used inappropriately
(negative transfer).
Advantages of abstract
problem representations have been studied in the context of algebra word
problems involving mixtures. Some students were trained with pictures
of the mixtures and other students were trained with abstract tabular
representations that highlighted the underlying mathematical
relationships (Singley and Anderson, 1989). Students who were trained
on specific task components without being provided with the principles
underlying the problems could do the specific tasks well, but they could
not apply their learning to new problems. By contrast, the students who
received abstract training showed transfer to new problems that involved
analogous mathematical relations. Research has also shown that
developing a suite of representations enables learners to think flexibly
about complex domains (Spiro et al., 1991).
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Relationships Between Learning and Transfer
Conditions |
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Transfer is always a
function of relationships between what is learned and what is tested.
Many theorists argue that the amount of transfer will be a function of
the overlap between the original domain of learning and the novel one.
Measuring overlap requires a theory of how knowledge is represented and
conceptually mapped across domains. Examples of research studies on
conceptual representation include Brown (1986), Bassok and Holyoak
(1989a, b), and Singley and Anderson (1989). Whether students will
transfer across domains--such as distance formulas from physics to
formally equivalent biological growth problems, for example--depends on
whether they conceive of the growth as occurring continuously
(successful transfer) or in discrete steps (unsuccessful transfer)
(Bassok and Olseth, 1995).
Singley and Anderson
(1989) argue that transfer between tasks is a function of the degree to
which the tasks share cognitive elements. This hypothesis was
also put forth very early in the development of research on transfer of
identical elements, mentioned previously (Thorndike and Woodworth, 1901;
Woodworth, 1938), but it was hard to test experimentally until there was
a way to identify task components. In addition, modern theorists
include cognitive representations and strategies as "elements" that
vary across tasks (Singley and Anderson, 1989).
Singley and Anderson
taught students several text editors, one after another, and sought to
predict transfer, defined as the savings in time of learning a new
editor when it was not taught first. They found that students learned
subsequent text editors more rapidly and that the number of procedural
elements shared by two text editors predicted the amount of this
transfer. In fact, there was large transfer across editors that were
very different in surface structures but that had common abstract
structures. Singley and Anderson also found that similar principles
govern transfer of mathematical competence across multiple domains when
they considered transfer of declarative as well as procedural knowledge.
A study by Biederman
and Shiffrar (1987) is a striking example of the benefits of abstract
instruction. They studied a task that is typically difficult to learn
in apprentice-like roles: how to examine day-old chicks to determine
their sex. Biederman and Shiffrar found that twenty minutes of
instruction on abstract principles helped the novices improve
considerably (see also Anderson et al., 1996). Research studies
generally provide strong support for the benefits of helping students
represent their experiences at levels of abstraction that transcend the
specificity of particular contexts and examples (National Research
Council, 1994). Examples include algebra (Singley and Anderson, 1989),
computer language tasks (Klahr and Carver, 1988), motor skills (e.g.,
dart throwing, Judd, 1908), analogical reasoning (Gick and Holyoak,
1983), and visual learning (e.g., sexing chicks, Biederman and Shiffrar,
1987).
Studies show that
abstracted representations do not remain as isolated instances of events
but become components of larger, related events, schemata (Holyoak,
1984; Novick and Holyoak, 1991). Knowledge representations are built up
through many opportunities for observing similarities and differences
across diverse events. Schemata are posited as particularly important
guides to complex thinking, including analogical reasoning: "Successful
analogical transfer leads to the induction of a general schema for the
solved problems that can be applied to subsequent problems" (National
Research Council, 1994:43). Memory retrieval and transfer are promoted
by schemata because they derive from a broader scope of related
instances than single learning experiences.
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Active Versus Passive Approaches to Transfer |
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It is important to view
transfer as a dynamic process that requires learners to actively choose
and evaluate strategies, consider resources, and receive feedback. This
active view of transfer is different from more static views, which
assume that transfer is adequately reflected by learners' abilities to
solve a set of transfer problems right after they have engaged in an
initial learning task. These "one-shot" tests often seriously
underestimate the amount of transfer that students display from one
domain to another (Bransford and Schwartz, in press; Brown et al., 1983;
Bruer, 1993).
Studies of transfer
from learning one text editor to another illustrate the importance of
viewing transfer from a dynamic rather than a static perspective.
Researchers have found much greater transfer to a second text editor on
the second day of transfer than the first (Singley and Anderson,
1989): this finding suggests that transfer should be viewed as
increased speed in learning a new domain--not simply initial
performance. Similarly, one educational goal for a course in calculus
is how it facilitates learning of physics, but not necessarily its
benefit on the first day of physics class.
Ideally, an individual
spontaneously transfers appropriate knowledge without a need for
prompting. Sometimes, however, prompting is necessary. With prompting,
transfer can improve quite dramatically (e.g., Gick and Holyoak, 1980;
Perfetto et al., 1983). "The amount of transfer depends on where
attention is directed during learning or at transfer" (Anderson et al.,
1996:8).
An especially sensitive
way to assess the degree to which students' learning has prepared them
for transfer is to use methods of dynamic assessment, such as "graduated
prompting" (Campione and Brown, 1987; Newman et al., 1989). This method
can be used to assess the amount of help needed for transfer by counting
the number and types of prompts that are necessary before students are
able to transfer. Some learners can transfer after receiving a general
prompt such as "Can you think of something you did earlier that might be
relevant?" Other learners need prompts that are much more specific.
Tests of transfer that use graduated prompting provide more fine-grained
analysis of learning and its effects on transfer than simple one-shot
assessments of whether or not transfer occurs.
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Transfer and Metacognition |
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Transfer can be
improved by helping students become more aware of themselves as learners
who actively monitor their learning strategies and resources and assess
their readiness for particular tests and performances. We briefly
discussed the concept of metacognition in Chapters
1 and 3 (see Brown, 1975; Flavell, 1973).
Metacognitive approaches to instruction have been shown to increase the
degree to which students will transfer to new situations without the
need for explicit prompting. The following examples illustrate research
on teaching metacognitive skills across domains of reading, writing, and
mathematics.
Reciprocal teaching to
increase reading comprehension (Palincsar and Brown, 1984) is designed
to help students acquire specific knowledge and also to learn a set of
strategies for explicating, elaborating, and monitoring the
understanding necessary for independent learning. The three major
components of reciprocal teaching are instruction and practice with
strategies that enable students to monitor their understanding;
provision, initially by a teacher, of an expert model of metacognitive
processes; and a social setting that enables joint negotiation for
understanding. The knowledge-acquisition strategies the students learn
in working on a specific text are not acquired as abstract memorized
procedures, but as skills instrumental in achieving subject-area
knowledge and understanding. The instructional procedure is reciprocal
in the sense that a teacher and a group of students take turns in
leading the group to discuss and use strategies for comprehending and
remembering text content.
A program of procedural
facilitation for teaching written composition (Scardamalia et al., 1984)
shares many features with reciprocal teaching. The method prompts
learners to adopt the metacognitive activities embedded in sophisticated
writing strategies. The prompts help learners think about and reflect
on the activities by getting them to identify goals, generate new ideas,
improve and elaborate existing ideas, and strive for idea cohesion.
Students in the procedural facilitation program take turns presenting
their ideas to the group and detailing how they use prompts in planning
to write. The teacher also models these procedures. Thus, the program
involves modeling, scaffolding, and taking turns which are designed to
help students externalize mental events in a collaborative context.
Alan Schoenfeld (1983,
1985, 1991) teaches heuristic methods for mathematical problem
solving to college students. The methods are derived, to some extent,
from the problem-solving heuristics of Polya (1957). Schoenfeld's
program adopts methods similar to reciprocal teaching and procedural
facilitation. He teaches and demonstrates control or managerial
strategies and makes explicit such processes as generating alternative
courses of action, evaluating which course one will be able to carry out
and whether it can be managed in the time available, and assessing one's
progress. Again, elements of modeling, coaching, and scaffolding, as
well as collective problem solving and whole-class and small group
discussions, are used. Gradually, students come to ask self-regulatory
questions themselves as the teacher fades out. At the end of each of
the problem-solving sessions, students and teacher alternate in
characterizing major themes by analyzing what they did and why. The
recapitulations highlight the generalizable features of the critical
decisions and actions and focus on strategic levels rather than on the
specific solutions (see also White and Frederickson, 1998).
An emphasis on
metacognition can enhance many programs that use new technologies to
introduce students to the inquiry methods and other tools that are used
by professionals in the workplace (see Chapter
8). The important role of metacognition for learning has been
demonstrated in the context of a "thinker tools" program that lets
students run simulations of physics experiments (White and Frederickson,
1998), as well as in adding a metacognitive component to a computer
program designed to help college students learn biology (Lin and
Bielaczyc, in press). The value of using video to model important
metacognitive learning procedures has also been shown to help learners
analyze and reflect on models (Bielaczyc et al., 1995). All of these
strategies engage learners as active participants in their learning by
focusing their attention on critical elements, encouraging abstraction
of common themes or procedures (principles), and evaluating their own
progress toward understanding.
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LEARNING AS TRANSFER FROM PREVIOUS EXPERIENCES |
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When people think about
transfer, it is common to think first about learning something and then
assessing the learner's abilities to apply it to something else. But
even the initial learning phase involves transfer because it is based on
the knowledge that people bring to any learning situation; see Box 3.8. The principle that people
learn by using what they know to construct new understandings (see Chapter 1) can be paraphrased as "all learning
involves transfer from previous experiences." This principle has a
number of important implications for educational practice. First,
students may have knowledge that is relevant to a learning situation
that is not activated. By helping activate this knowledge, teachers can
build on students' strengths. Second, students may misinterpret new
information because of previous knowledge they use to construct new
understandings. Third, students may have difficulty with particular
school teaching practices that conflict with practices in their
community. This section discusses these three implications.
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Building on Existing Knowledge |
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Children's early
mathematics knowledge illustrates the benefits of helping students draw
on relevant knowledge that can serve as a source of transfer. By the
time children begin school, most have built a considerable knowledge
store relevant to arithmetic. They have experiences of adding and
subtracting numbers of items in their everyday play, although they lack
the symbolic representations of addition and subtraction that are taught
in school. If children's knowledge is tapped and built on as teachers
attempt to teach them the formal operations of addition and subtraction,
it is likely that children will acquire a more coherent and thorough
understanding of these processes than if they taught them as isolated
abstractions. Without specific guidance from teachers, students may
fail to connect everyday knowledge to subjects taught in school.
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Understanding Conceptual Change |
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Because learning
involves transfer from previous experiences, one's existing knowledge
can also make it difficult to learn new information. Sometimes new
information will seem incomprehensible to students, but this feeling of
confusion can at least let them identify the existence of a problem
(see, e.g., Bransford and Johnson, 1972; Dooling and Lachman, 1971). A
more problematic situation occurs when people construct a coherent (for
them) representation of information while deeply misunderstanding the
new information. Under these conditions, the learner doesn't realize
that he or she is failing to understand. Two examples of this
phenomenon are in Chapter 1: Fish Is Fish
(Lionni, 1970), where the fish listens to the frog's descriptions of
people and constructs its own idiosyncratic images, and attempts to help
children learn that the earth is spherical (Vosniadou and Brewer, 1989).
Children's interpretations of the new information are much different
than what adults intend.
The Fish Is Fish
scenario is relevant to many additional attempts to help students learn
new information. For example, when high school or college physics
students are asked to identify the forces being exerted on a ball that
is thrown vertically up in the air after it leaves the hand, many
mention the "force of the hand" (Clement, 1982a, b). This force is
exerted only so long as the ball is in contact with the hand, but is not
present when the ball is in flight. Students claim that this force
diminishes as the ball ascends and is used up by the time the ball
reaches the top of its trajectory. As the ball descends, these students
claim, it "acquires" increasing amounts of the gravitational force,
which results in the ball picking up speed as it falls back down. This
"motion requires a force" misconception is quite common among students
and is akin to the medieval theory of "impetus" (Hestenes et al., 1992).
These explanations fail to take account of the fact that the only
forces being exerted on the ball while it is traveling through the air
are the gravitational force caused by the earth and the drag force due
to air resistance. (For similar examples, see Mestre, 1994.)
In biology, people's
knowledge of human and animal needs for food provides an example of how
existing knowledge can make it difficult to understand new information.
A study of how plants make food was conducted with students from
elementary school through college. It probed understanding of the role
of soil and photosynthesis in plant growth and of the primary source of
food in green plants (Wandersee, 1983). Although students in the higher
grades displayed a better understanding, students from all levels
displayed several misconceptions: soil is the plants' food; plants get
their food from the roots and store it in the leaves; and chlorophyll is
the plants' blood. Many of the students in this study, especially those
in the higher grades, had already studied photosynthesis. Yet formal
instruction had done little to overcome their erroneous prior beliefs.
Clearly, presenting a sophisticated explanation in science class,
without also probing for students' preconceptions on the subject, will
leave many students with incorrect understanding (for a review of
studies, see Mestre, 1994).
For young children,
early concepts in mathematics guide students' attention and thinking
(Gelman, 1967; we discuss this more in Chapter
4). Most children bring to their school mathematics lessons the
idea that numbers are grounded in the counting principles (and related
rules of addition and subtraction). This knowledge works well during
the early years of schooling. However, once students are introduced to
rational numbers, their assumptions about mathematics can hurt their
abilities to learn.
Consider learning about
fractions. The mathematical principles underlying the numberhood of
fractions are not consistent with the principles of counting and
children's ideas that numbers are sets of things that are counted and
addition involves "putting together" two sets. One cannot count things
to generate a fraction. Formally, a fraction is defined as the division
of one cardinal number by another: this definition solves the problem
that there is a lack of closure of the integers under division. To
complicate matters, some number-counting principles do not apply to
fractions. Rational numbers do not have unique successors; there is an
infinite number of numbers between any two rational numbers. One cannot
use counting-based algorithms for sequencing fractions: for example,
1/4 is not more than 1/2. Neither the nonverbal nor the verbal counting
principle maps to a tripartite symbolic representations of
fractions--two cardinal numbers X and Y separated by a line. Related
mapping problems have been noted by others (e.g., Behr et al., 1992;
Fishbein et al., 1985; Silver et al., 1993). Overall, early knowledge
of numbers has the potential to serve as a barrier to learning about
fractions--and for many learners it does.
The fact that learners
construct new understandings based on their current knowledge highlights
some of the dangers in "teaching by telling." Lectures and other forms
of direct instruction can sometimes be very useful, but only under the
right conditions (Schwartz and Bransford, in press). Often, students
construct understandings like those noted above. To counteract these
problems, teachers must strive to make students' thinking visible and
find ways to help them reconceptualize faulty conceptions. (Strategies
for such teaching are discussed in more detail in Chapters 6 and 7.)
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Transfer and Cultural Practices |
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Prior knowledge is not
simply the individual learning that students bring to the classroom,
based on their personal and idiosyncratic experiences (e.g., some
children will know many things because they have traveled widely or
because their parents have particular kinds of jobs; some children may
have suffered a traumatic experience). Prior knowledge is also not only
a generic set of experiences attributable to developmental stages
through which learners may have passed (i.e., believing that heaven is
"up" or that milk comes from refrigerated cartons). Prior knowledge
also includes the kind of knowledge that learners acquire because of
their social roles, such as those connected with race, class, gender,
and their culture and ethnic affiliations (Brice-Heath, 1981, 1983;
Lave, 1988; Moll and Whitmore, 1993; Moll et al., 1993-1998; Rogoff,
1990, 1998; Saxe, 1990). This cultural knowledge can sometimes support
and sometimes conflict with children's learning in schools (Greenfield
and Suzuki, 1998); see Box 3.9.
School failure may be
partly explained by the mismatch between what students have learned in
their home cultures and what is required of them in school (see Allen
and Boykin, 1992; Au and Jordan, 1981; Boykin and Tom, 1985; Erickson
and Mohatt, 1982). Everyday family habits and rituals can either be
reinforced or ignored in schools, and they can produce different
responses from teachers (Heath, 1983). For example, if young learners
are never asked questions at home that seem obvious to some
families--such as "What color is the sky?" or "Where is your
nose?"--teachers who ask such questions may find students reluctant or
resistant to answer. How teachers interpret this reticence or
resistance has consequences for how intelligent or academically capable
they judge students and their instructional approaches toward them.
These differences have
their roots in early adult-infant interactions (Blake, 1994). Whereas
middle-class Anglo mothers tend to have frequent language interactions
that are focused on didactic naming and pointing with their infants
around objects ("Look at that red truck!"), African American mothers
show comparable frequency levels of language interactions with their
infants, but focused on affective dimensions of language ("Isn't that a
pretty toy? Doesn't it make you feel happy?"). The language that
children bring with them to school involves a broad set of skills rooted
in the early context of adult-child interactions. What happens when the
adults, peers, and contexts change (Suina, 1988; Suina and Smolkin,
1994)? This is an important question that relates to the transfer of
learning.
The meanings that are
attached to cultural knowledge are important in promoting transfer--that
is, in encouraging people to use what they have learned. For example,
story-telling is a language skill. Topic-associative oral styles have
been observed among African American children (Michaels, 1981a,b; 1986).
In contrast, white children use a more linear narrative style that more
closely approximates the linear expository style of writing and speaking
that schools teach (see Gee, 1989; Taylor and Lee, 1987; Cazden et al.,
1985; Lee and Slaughter-Defoe, 1995). Judgments may be made by white
and black teachers as they listen to these two language styles: white
teachers find the topic-associative stories hard to follow and are much
more likely to infer that the narrator is a low-achieving student; black
teachers are more likely to positively evaluate the topic-associative
style (Cazden, 1988:17). African American children who come to school
speaking in a topic-associative style may be seen by many teachers as
having less potential for learning. Teachers can be helped to view
different cultural backgrounds as strengths to be built on, rather than
as signs of "deficits."
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TRANSFER BETWEEN SCHOOL AND EVERYDAY LIFE |
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We began this chapter
by stressing that the ultimate goal of learning is to have access to
information for a wide set of purposes--that the learning will in some
way transfer to other circumstances. In this sense, then, the ultimate
goal of schooling is to help students transfer what they have learned in
school to everyday settings of home, community, and workplace. Since
transfer between tasks is a function of the similarity by transfer tasks
and learning experiences, an important strategy for enhancing transfer
from schools to other settings may be to better understand the nonschool
environments in which students must function. Since these environments
change rapidly, it is also important to explore ways to help students
develop the characteristics of adaptive expertise (see Chapter 1).
The question of how
people function in a number of practical settings has been examined by
many scientists, including cognitive anthropologists, sociologists, and
psychologists (e.g., Lave, 1988; Rogoff, 1990). One major contrast
between everyday settings and school environments is that the latter
place much more emphasis on individual work than most other environments
(Resnick, 1987). A study of navigation on U.S. ships found that no
individual can pilot the ship alone; people must work collaboratively
and share their expertise. More recent studies of collaboration confirm
its importance. For example, many scientific discoveries in several
genetics laboratories involve in-depth collaboration (Dunbar, 1996).
Similarly, decision making in hospital emergency rooms is distributed
among many different members of the medical team (Patel et al., 1996).
A second major contrast
between schools and everyday settings is the heavy use of tools to solve
problems in everyday settings, compared with "mental work" in school
settings (Resnick, 1987). The use of tools in practical environments
helps people work almost error free (e.g., Cohen, 1983; Schliemann and
Acioly, 1989; Simon, 1972; see also Norman, 1993). New technologies
make it possible for students in schools to use tools very much like
those used by professionals in workplaces (see Chapter 8). Proficiency with relevant tools may
provide a way to enhance transfer across domains.
A third contrast
between schools and everyday environments is that abstract reasoning is
often emphasized in school, whereas contextualized reasoning is often
used in everyday settings (Resnick, 1987). Reasoning can be improved
when abstract logical arguments are embodied in concrete contexts (see
Wason and Johnson-Laird, 1972). A well-known study of people in a
Weight Watchers program provides similar insights into everyday problem
solving (see Lave et al., 1984). One example is of a man who needed
three-fourths of two-thirds of a cup of cottage cheese to create a dish
he was cooking. He did not attempt to multiply the fractions as
students would do in a school context. Instead, he measured two-thirds
of a cup of cottage cheese, removed that amount from the measuring cup
and then patted the cheese into a round shape, divided it into quarters,
and used three of the quarters; see Box 3.10. Abstract arithmetic was never used. In
similar examples of contextualized reasoning, dairy workers use
knowledge, such as the size of milk cases, to make their computational
work more efficient (Scribner, 1984); grocery store shoppers use
nonschool mathematics under standard supermarket and simulated
conditions (Lave, 1988); see Box
3.11.
There are potential
problems with contextualized reasoning, which are similar to those
associated with overly contextualized knowledge in general. The "pat it
out" strategy used for cottage cheese works in only a narrow range of
situations; the man would have difficulty if he were trying to measure
molasses or other liquids rather than cottage cheese (Wineburg, 1989a,
b; see also Bereiter, 1997). Could he generate a new strategy for
molasses or other liquids? The answer to this question depends on the
degree to which he can relate his procedure to more general sets of
solution strategies.
Analyses of everyday
environments have potential implications for education that are
intriguing but need to be thought through and researched carefully.
There are many appealing strengths to the idea that learning should be
organized around authentic problems and projects that are frequently
encountered in nonschool settings: in John Dewey's vision, "School
should be less about preparation for life and more like life itself."
The use of problem-based learning in medical schools is an excellent
example of the benefits of looking at what people need to do once they
graduate and then crafting educational experiences that best prepare
them for these competencies (Barrows, 1985). Opportunities to engage in
problem-based learning during the first year of medical school lead to a
greater ability to diagnose and understand medical problems than do
opportunities to learn in typical lecture-based medical courses (Hmelo,
1995). Attempts to make schooling more relevant to the subsequent
workplace have also guided the use of case-based learning in business
schools, law schools, and schools that teach educational leadership
(Hallinger et al., 1993; Williams, 1992).
The transfer literature
also highlights some of the potential limitations of learning in
particular contexts. Simply learning to perform procedures, and
learning in only a single context, does not promote flexible transfer.
The transfer literature suggests that the most effective transfer may
come from a balance of specific examples and general principles, not
from either one alone.
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SUMMARY AND CONCLUSION |
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A major goal of
schooling is to prepare students for flexible adaptation to new problems
and settings. The ability of students to transfer provides an important
index of learning that can help teachers evaluate and improve their
instruction. Many approaches to instruction look equivalent when the
only measure of learning is memory for information that was specifically
presented. Instructional differences become more apparent when
evaluated from the perspective of how well the learning transfers to new
problems and settings.
Several critical
features of learning affect people's abilities to transfer what they
have learned. The amount and kind of initial learning is a key
determinant of the development of expertise and the ability to transfer
knowledge. Students are motivated to spend the time needed to learn
complex subjects and to solve problems that they find interesting.
Opportunities to use knowledge to create products and benefits for
others are particularly motivating for students.
While time on task is
necessary for learning, it is not sufficient for effective learning.
Time spent learning for understanding has different consequences for
transfer than time spent simply memorizing facts or procedures from
textbooks or lectures. In order for learners to gain insight into their
learning and their understanding, frequent feedback is critical:
students need to monitor their learning and actively evaluate their
strategies and their current levels of understanding.
The context in which
one learns is also important for promoting transfer. Knowledge that is
taught in only a single context is less likely to support flexible
transfer than knowledge that is taught in multiple contexts. With
multiple contexts, students are more likely to abstract the relevant
features of concepts and develop a more flexible representation of
knowledge. The use of well-chosen contrasting cases can help students
learn the conditions under which new knowledge is applicable. Abstract
representations of problems can also facilitate transfer. Transfer
between tasks is related to the degree to which they share common
elements, although the concept of elements must be defined cognitively.
In assessing learning, the key is increased speed of learning the
concepts underlying the new material, rather than early performance
attempts in a new subject domain.
All new learning
involves transfer. Previous knowledge can help or hinder the
understanding of new information. For example, knowledge of everyday
counting-based arithmetic can make it difficult to deal with rational
numbers; assumptions based on everyday physical experiences (e.g.,
walking upright on a seemingly flat earth) can make it difficult for
learners to understand concepts in astronomy and physics and so forth.
Teachers can help students change their original conceptions by helping
students make their thinking visible so that misconceptions can be
corrected and so that students can be encouraged to think beyond the
specific problem or to think about variations on the problem. One
aspect of previous knowledge that is extremely important for
understanding learning is cultural practices that support learners'
prior knowledge. Effective teaching supports positive transfer by
actively identifying the relevant knowledge and strengths that students
bring to a learning situation and building on them.
Transfer from school to
everyday environments is the ultimate purpose of school-based learning.
An analysis of everyday environments provides opportunities to rethink
school practices in order to bring them into alignment with the
requirements of everyday environments. But it is important to avoid
instruction that is overly dependent on context. Helping learners
choose, adapt, and invent tools for solving problems is one way to
facilitate transfer while also encouraging flexibility.
Finally, a
metacognative approach to teaching can increase transfer by helping
students learn about themselves as learners in the context of acquiring
content knowledge. One characteristic of experts is an ability to
monitor and regulate their own understanding in ways that allows them to
keep learning adaptive expertise: this is an important model for
students to emulate.
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