"How Experts Differ from Novices
-People who are experts are able to think effectively in the areas they are experts in.
- Understanding expertise is important because it provides insights into the nature of thinking
and problem solving.
-Expertise is more than general abilities like memory or intelligence. Instead, experts have acquired extensive knowledge that affects what they notice and how they organize, represent, and interpret information in their environment, in turn, affecting their abilities to remember, reason, and solve problems.
-This chapters focuses on the development of expertise considering the following principles:
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.
"Learning is a complex set of processes that may vary according to the developmental level of the learner, the nature of the task, and the context in which the learning is to occur. As already indicated, no one theory can capture all the variables involved in all learning.
Each theory, therefore, begins with an assumption or set of assumptions about the nature of learning and then proceeds to develop a set of principles consistent with the assumptions. The behavioristic perspec-
tive, for example, assumes that the environment is the primary agent responsible for learning. These theories describe the various ways that events in the environment influence behavior.
In contrast, the cognitive theories assume that the learner's mental processes are the major factor in learning. These theories therefore emphasize the ways that the learner's processing and application of information change one's thoughts and internal mental structures.
The interactionist perspective, however, assumes that behavior, mental processes, and the environment are interrelated. Thus, they describe the interactive role of these elements during learning
"Over 400 years before the birth of Christ, philosophers began their deliberations on the nature of thinking and learning. Using the only method available at the time, logical analysis, they developed explanations of the ways in which human beings acquire knowledge. However, the information developed is often limited in nature because only gen-
eral questions are asked.
The importance of experimentation in developing knowledge
about the physical sciences was demonstrated by Galileo in the 16th century. However, research on the mind was delayed for some 300 years until an acceptable rationale was developed for subjecting a gift of God to research. Both Darwin's concept of evolution and Helmholtz's discovery of many basic facts about sight and hearing set the stage for
The separation of psychology from philosophy was initiated by Wilhelm Wundt in his 1874 text on physiological psychology. His experimental laboratory, established 5 years later, drew individuals from many nations, including the United States. In less than 20 years, psychological research was firmly established in several American universities.
The chief architects of American psychology—William James, John Dewey, G. Stanley Hall, and Edward Thorndike —forged a dynamic new science responsive to issues in both human life and education. James provided the rationale for a functional psychology and gave the discipline a broad knowledge base in his two-volume text. He also translated his views into guidelines for teachers. Dewey and Hall provided leadership for school reform. Dewey saw the school as the mechanism for reforming a society that must adjust to the industrial revolution. Education should develop knowledgeable citizens, and the emphasis should be on personal experimentation, planning, and reinvention by the child.
Dewey's views became the rallying cry for educational reformers seeking to change the school. Hall, in contrast, emphasized the use of data about children in planning curriculum. His views initiated the child-study movement.
Edward Thorndike exemplified the educational scientist working to improve education. His innovative dissertation study established the first learning theory and demonstrated the feasibility of behavioral research in generating information about learning. His work initiated both the scientific movement in education and educational psychology.
"The concept of " development" is critical to understanding the changes in children's thinking, such as the development of language, causal reasoning, and rudimentary mathematical concepts. Young children are actively engaged in making sense of their worlds. In some particular domains, such as biological and physical causality, number, and language, they have strong predispositions to learn rapidly and readily.
These predispositions support and may even make possible early learning and pave the way for competence in early schooling. Yet even in these domains, children still have a great deal of learning to do. Children's early understanding of the perceptual and physical world may jump-start the learning process, even making learning possible, but one should look with caution for ways in which early knowledge may impede later learning. For example, children who treat rational numbers as they had treated whole numbers will experience trouble ahead. Awareness of these roadblocks to learning could help teachers anticipate the difficulty. Although children learn readily in some domains, they can learn practically anything by sheer will and effort. When required to learn about nonprivileged domains they need to develop strategies of intentional learning.
In order to develop strategic competence in learning, children need to understand what it means to learn, who they are as learners, and how to go about planning, monitoring, revising, and reflecting upon their learning and
that of others. Children lack knowledge and experience but not reasoning ability. Although young children are inexperienced, they reason facilely with the knowledge they have. Children are both problem solvers and problem generators: children attempt to solve problems presented to them, and they also seek novel
challenges. They refine and improve their problem-solving strategies not only in the face of failure, but also by building on prior success. They persist because success and understanding are motivating in their own right.
Adults help make connections between new situations and familiar ones for children. Children' s curiosity and persistence are supported by adults who direct their attention, structure their experiences, support their learning attempts, and regulate the complexity and difficulty levels of information for
Children, thus, exhibit capacities that are shaped by environmental experiences and the individuals who care for them. Caregivers provide supports, such as directing children's attention to critical aspects of events, commenting on features that should be noticed, and in many other ways providing structure to the information. Structure is critical for learning and for moving toward understanding information. Development and learning are not two parallel processes. Early biological underpinnings enable certain types of interactions, and through various environmental supports from caregivers and other cultural and social supports, a child's experiences for learning are expanded. Learning is promoted and regulated both by children' s biology
and ecology, and learning produces development.
"It is often popularly argued that advances in the understanding of brain development and mechanisms of learning have substantial implications for education and the learning sciences. In addition, certain brain scientists have offered advice, often with a tenuous scientific basis, that has been incorporated into publications designed for educators (see, e.g., Sylwester, 1995:Ch. 7). Neuroscience has advanced to the point where it is time to think critically about the form in which research information is made available to educators so that it is interpreted appropriately for practice— identifying which research findings are ready for implementation and which are not.
This chapter reviews the evidence for the effects of experience on brain development, the adaptability of the brain for alternative pathways to learning, and the impact of experience on memory. Several findings about the brain and the mind are clear and lead to the next research topics:
1. The functional organization of the brain and the mind depends on and benefits positively from experience.
2. Development is not merely a biologically driven unfolding process,
but also an active process that derives essential information from experience.
3. Research has shown that some experiences have the most powerful effects during specific sensitive periods, while others can affect the brain over a much longer time span.
4. An important issue that needs to be determined in relation to education is which things are tied to critical periods (e.g., some aspects of phonemic perception and language learning) and for which things is the time of
exposure less critical. From these findings, it is clear that there are qualitative differences among kinds of learning opportunities. In addition, the brain " creates" informational experiences through mental activities such as inferencing, category formation, and so forth. These are types of learning opportunities that can be facilitated. By contrast, it is a bridge too far, to paraphrase John Bruer (1997), to suggest that specific activities lead to neural branching (Cardellichio and Field, 1997), as some interpreters of neuroscience have implied.
"A two-store (dual) memory model has been widely applied. Information enters through the sensory registers. Although there is a register for each sense, most research has been conducted on the visual and auditory registers. At any one time, only a limited amount of information can be attended to. Attention may act as a filter or a general limitation on capacity of the human system. Inputs attended to are perceived by being com-
pared with information in LTM. Information enters STM (WM), where it is retained through rehearsal and linked with related information in LTM. Information may be encoded for storage in LTM. Encoding is facilitated through organization, elaboration, meaningfulness, and links with schemas. LTM is organized by content, and information is cross-referenced with related content. Control processes monitor and direct the flow of information through the system. Alternative views of memory conceive of it in terms of levels of processing, activation level, connectionism, and parallel distributed processing. Each of these views has advantages and disadvantages, and some integration of views may best characterize memory.
"The word attention is heard often in educational settings. Teachers and parents complain that students do not pay attention to instructions or directions. (This does not seem to be the problem in the opening scenario; rather, the issue involves meaningfulness of processing.) Even high-achieving students do not always attend to instructionally relevant events. Sights, sounds, smells, tastes, and sensations bombard us; we cannot and should not attend to them all. Our attentional capabilities are limited; we can attend to a few things at once. Thus, attention can be construed as the process of selecting some of many potential inputs.
Alternatively, attention can refer to a limited human resource expended to accomplish one's goals and to mobilize and maintain cognitive processes (Grabe, 1986).
Attention is not a bottleneck in the information processing system through which only so much information can pass. Rather, it describes a general limitation on the entire human information processing system.
Attention is a necessary prerequisite of learning. In learning to distinguish letters, a child learns the distinctive features: To distinguish b from d, students must attend to the position of the vertical line on the left or right side of the circle, not to the mere presence of a circle attached to a vertical line. To learn from the teacher, students must attend to the teacher's voice and ignore other sounds. To develop reading comprehension skills, students must attend to the printed words and ignore such irrelevancies as page size and color.
Attention is a limited resource; learners do not have unlimited amounts of it. Learners allocate attention to activities as a function of motivation and self-regulation (Kanfer & Ackerman, 1989, Kanfer & Kanfer, 1991). As skills become routine, information processing requires less conscious attention. In learning to work multiplication problems, students must attend to each step in the process and check their computations. Once students learn multiplication tables and the algorithm, working problems becomes automatic and is triggered by the input. Research shows that much cognitive skill processing becomes automatic (Phye, 1989).
"STM is a working memory (WM) and corresponds roughly to awareness, or what one is conscious of at a given moment. WM is limited in capacity. Miller (1956) proposed that it holds seven plus or minus two units of information. A unit is a meaningful item: a letter, word, number, or common expression (e.g., ""bread and butter""). WM also is limited in duration, for units to be retained in WM they must be rehearsed (repeated). Without rehearsal, information is lost after a few seconds.
While information is in WM, related knowledge in long-term memory (LTM), or permanent memory, is activated and placed in WM to be integrated with the new information. To name all the state capitals beginning with the letter A, students recall the names of states—perhaps by region of the country—and scan the names of their capital cities. When students who do not know the capital of Maryland learn ""Annapolis,"" they can store it with ""Maryland"" in LTM.
"Ways in which a person, environment, behavior interact to produce a given result.
Social cognitive theory favors a conception of interaction based on triadic reciprocality (Bandura, 1977a, 1978a). In this
model of reciprocal determinism, behavior, cognitive and other personal factors, and environmental influences all operate interactively as determinants of each other.
In this triadic reciprocal determinism, the term reciprocal refers to the mutual action between causal factors. The term determinism is used here to signify the production of effects by certain factors, rather than in the doctrinal sense of actions being completely determined by a prior sequence of causes operating independently of the individual. Many factors are often needed to create a given effect. Because of the multi-
plicity of interacting influences, the same factor can be a part of different blends of conditions that have different effects. Particular factors are, therefore, associated with effects probabilistically rather than inevitably.
"People learn through observing others' behavior, attitudes, and outcomes of those behaviors. "Most human behavior is learned observationally through modeling: from observing others, one forms an idea of how new behaviors are performed, and on later occasions this coded information serves as a guide for action." (Bandura). Social learning theory explains human behavior in terms of continuous reciprocal interaction between cognitive, behavioral, and environmental influences.
Necessary conditions for effective modeling:
Attention — various factors increase or decrease the amount of attention paid. Includes distinctiveness, affective valence, prevalence, complexity, functional value. One's characteristics (e.g. sensory capacities, arousal level, perceptual set, past reinforcement) affect attention. Retention — remembering what you paid attention to. Includes symbolic coding, mental images, cognitive organization, symbolic rehearsal, motor rehearsal Reproduction — reproducing the image. Including physical capabilities, and self-observation of reproduction. Motivation — having a good reason to imitate. Includes motives such as past (i.e. traditional behaviorism), promised (imagined incentives) and vicarious (seeing and recalling the reinforced model)
"Without going into the details of the radical change of epistemological perspective inherent in the move to constructivism, I want to suggest that there are certain circumscribed areas in which a constructivist orientation can modify a teacher's attitude. It could, for instance, bring home the realization that students perceive their environment in ways that may be very different from those intended by the educators. And this environment includes curricula, textbooks, didactic props including computer programs and micro worlds, tasks they are given, and, of course, the teachers. This emphasizes the teacher's need to construct a hypothetical model of the particular conceptual worlds of the students they are facing. One can hope to induce changes in their ways of thinking only if one has some inkling as to the
domains of experience, the concepts, and the conceptual relations the students possess at the moment (cf. von Glasersfeld & Steffe, 1991). Similarly, the consideration of how meanings are constituted, and how, consequently, linguistic communication works, would dismantle the still widespread notion that conceptual knowledge can be transferred from teacher to student by the means of words. This is not to say that language is not important. In fact, it is the most powerful tool available to the teacher, but it does not transport meanings or concepts. Language enables the teacher to orient the student's conceptual construction by precluding certain pathways and making others more likely.
These are only two facets of the constructivist model, but they go a long way toward establishing the fundamental principle that learning is a constructive activity that the students themselves have to carry out. From this point of view, then, the task of the educator is not to dispense knowl-
edge but to provide students with opportunities and incentives to build it up.
"The concept of adaptation stems from biology, and it indicates a particular relationship between living organisms or species and their environment.
To say that they are adapted means no less but also no more than that they have been able to survive given the conditions and the constraints of the world in which they happen to be living. In other words, they have managed to evolve a fit or, as I prefer to say, their physical characteristics and their ways of behaving have so far proven viable in their environment.
Piaget took the notion of adaptation out of the biological context and turned it into the cornerstone of his genetic epistemology. He had realized early on that whatever knowledge was, it was not a copy of reality. The relationship of viable biological organisms to their environment provided a means to reformulate the relationship between the cognitive subject's conceptual structures and that subject's experiential world. Knowledge, then, could be treated not as a more or less accurate representation of external things, situations, and events, but rather as a mapping of actions and conceptual operations that had proven viable in the knowing subject's experience.
The use Piaget makes of the notion of adaptation is therefore not the same as that suggested by the contemporary school of thought that goes by the name of evolutionary epistemology. Unlike this school, which formed around the work of Konrad Lorenz, in Piaget's constructivist theory one cannot draw conclusions about the character of the real world from an organism's adaptedness or the viability of schemes of action. In his view, what we see, hear, and feel—that is, our sensory world—is the result of our own perceptual activities and therefore specific to our ways of perceiving and conceiving. Knowledge, for him, arises from actions and the agent's reflection on them. The actions take place in an environment and are grounded in and directed at objects that constitute the organism's experiential world, not things in themselves that have an independent existence. Hence, when Piaget speaks of interaction, this does not imply an organism that interacts with objects as they really are, but rather a cognitive subject that is dealing with previously constructed perceptual and conceptual structures.
"Experimental investigation of the egocentric speech of children engaged in various activities such as that illustrated by Levina produced the second fact of great importance demonstrated by our experiments: the relative amount of egocentric speech, as measured by Piaget's methods, increases in relation to the difficulty of the child's task.14 On the basis of these experiments my collaborators and I developed the hypothesis that children's egocentric speech should be regarded as the transitional form between external and internal speech. Functionally, egocentric speech is the basis for inner speech, while in its external form it is embedded in communicative speech.
One way to increase the production of egocentric speech is to
complicate a task in such a way that the child cannot make direct use of tools for its solution. When faced with such a challenge, the children's emotional use of language increases as well as their efforts to achieve a less automatic, more intelligent solution. They search verbally for a new plan, and their utterances reveal the close connection between ego-
centric and socialized speech. This is best seen when the experimenter leaves the room or fails to answer the children's appeals for help. Upon being deprived of the opportunity to engage in social speech, children immediately switch over to egocentric speech.
While the interrelationship of these two functions of language is apparent in this setting, it is important to remember that egocentric speech is linked to children's social speech by many transitional forms.
The first significant illustration of the link between these two language functions occurs when children find that they are unable to solve a problem by themselves. They then turn to an adult, and verbally describe the method that they cannot carry out by themselves. The greatest change in children's capacity to use language as a problem-solving tool takes place somewhat later in their development, when socialized speech (which has previously been used to address an adult) is turned inward.
Instead of appealing to the adult, children appeal to themselves; language thus takes on an intrapersonal function in addition to its interpersonal use. When children develop a method of behavior for guiding themselves that had previously been used in relation to another person, when they organize their own activities according to a social form of behavior, they succeed in applying a social attitude to them-
selves. The history of the process of the internalization of social speech is also the history of the socialization of children's practical intellect.
To summarize what has been said thus far in this section: The specifically human capacity for language enables children to provide for auxiliary tools in the solution of difficult tasks, to overcome impulsive action, to plan a solution to a problem prior to its execution, and to master their own behavior. Signs and words serve children first and foremost as a means of social contact with other people. The cognitive and communicative functions of language then become the basis of a new and superior form of activity in children, distinguishing them from animals.
"Four philosophies of learning are contrasted, namely 'simple' constructivism, radical constructivism, enactivism and social constructivism. Their underlying explanatory metaphors and some of their strengths and weaknesses are contrasted, as well as their implications for teaching and research. However, it is made clear that none of these 'implications' is incompatible with any of the learning philosophies, even if they sit more comfortably with one of them.
Ultimately, the import of a learning theory concerns its implications for practice, both pedagogically, in the teaching (and learning) of mathematics, and in the practice of conducting educational research. However, in my view, there is little in any pedagogy that is either wholly necessitated or wholly ruled out by the other elements of a learning theory. Similarly, learning theories do not imply particular research approaches. Nevertheless, certain emphases are foregrounded by different learning theories, even if they are not logical consequences of them.
However, each one of these eight focuses in the teaching and learning of mathematics could legitimately be attended to by teachers drawing on any of the learning theories for their pedagogy, or by researchers employing one of the learning theories as their underlying structuring framework.
"We have used the distinction that DeCorte et al. (1996) draw
between the first and second waves of the cognitive revolu-
tion to organize our discussion of the cognitive and situated
perspectives. Our purpose in doing so was to clarify differ-
ences in the use of key terms by relating them to differences
in the underlying metaphors of the two theoretical perspectives. In the course of the discussion, we also developed our own position and differentiated it from some of the claims made in the name of situated learning theory. For example, we concurred with Anderson et al.'s (1996) argument that many of the instructional recommendations made in the name of situated learning theory are unsubstantiated. However, we questioned Anderson et al.'s assumption that these erroneous recommendations can be traced back to basic theoretical commitments. We instead suggested that the practice of translating basic theoretical tenets directly into instructional prescriptions involves a category error. The deeper issue is the relationship between theory and practice, and here we also critiqued the positivist stance taken by Anderson et al. (1997). Regarding the alternative view we developed, we would acknowledge that the reflexive relation between theory and practice implicit in our classroom-based research activity is itself situated. In this regard, we agree with Nuthall's (1996) contention that
differences between theories of classroom learning ... re-
flect differences in the paradigm that researchers have in
mind as they think about how their research relates to
classroom practice and theory. The evolution of research
and theory is itself a sociocultural activity shaped by the
working relationships that researchers establish with
those whose lives and experiences they study and whose
lives and experiences they hope to influence. (p. 6)
A second point on which we differ with some of the more uncompromising versions of situated learning theory follows from our discussion of units of analysis. We described the theoretical approach that has emerged in the course of
our work in which we view students' reasoning as nec-
essarily situated while simultaneously attending to qual-
itative differences in the ways that they participate in
communal practices. We therefore have difficulty with epistemological behaviorist positions that identify meaning exclusively with use and limit their focus to observed social
activity. By the same token, however, we questioned the
treatment of meaning in Anderson et al.'s (1996) cognitive
perspective. For our purposes, it is essential to go beyond
cognitive behavior by analyzing the quality of students' inferred, socially situated mathematical experience. As we
noted, the distinction between these two perspectives'
treatments of mathematical meaning corresponds to that
which MacKay (1969) makes between the observer's and
the actor's viewpoints. Our strong preference for the actor's
Viewpoint is rooted in our activity as researchers who co-participate in the learning-teaching process with teachers and their students. As Rommetveit (1992) and Schutz (1962) both emphasize, to co-participate is to engage in communicative interactions that involve a reciprocity of perspectives characteristic of the actor's viewpoint.position does not demonstrate that it is wrong in the sense that it somehow fails to capture the essence of individual and collective human activity. Instead, our central claim has been that the characterizations of meaning and learning that this perspective offers do not address our concerns as classroom-based researchers and instructional designers.
We readily acknowledge that this theoretical orientation
might well be appropriate for other purposes such as de-
signing expert systems or supporting the development of
competent performance on a clearly delineated range of
tasks. Further, in light of the numerous references that Anderson et al. (1996) make to empirical findings, we accept
that the cognitive perspective might be judged to be pro-
A second point on which we differ with some of the more
In closing, we stress that our critique of Anderson et al.'s
gressive when assessed in terms of its own internal criteria.
We do, however, question whether it has made significant
progress in recent years on issues that are relevant to those
of us who conduct classroom-based research and instruc-
tional design. In general, the conclusions we have reached
are less generous than those of Greeno (1997), who speaks
of exchanges between cognitive and situated learning the-
orists spurring the development of more comprehensive
theories of learning. The contrast in Greeno's and our views
on the potential contributions of the cognitive perspective
appears to reflect our concerns as members of different re-
"Learning science is interdisciplinary in nature. It is holistic and eclectic. It draws from a myriad of fields like education, instructional design, computer design, constructivism, and cognitive science. These fields combine in a way that allow for a multifaceted approach to comprehensively explain how people learn in both formal and informal settings and the cognitive and social processes that best support effective learning.
Since the beginning of the modern institution of schools, there has been debate about whether education is a science or an art. The language of science makes some educators nervous. Everyone can remember the artistry of a great teacher - a teacher who somehow against all odds got every student to perform better than they thought they could. Teachers themselves know how complex their job is - every minute of every hour, a thousand different things are going on, and it can seem so unlikely that the cutting-and-slicing reductionist approach of science could ever help us understand what's happening. The history of scientific approaches to education is not promising; in the past, scientists studied learning in a university laboratory and then delivered pronouncements from the Ivory Tower that teachers were expected to adopt unquestioningly (Cremin, 1961).
Unlike these previous generations of educational research, learning scientists spend a lot of time in schools - many of us were full-time teachers before we became researchers. And learning scientists are committed to improving classroom teaching and learning - many are in schools every week, working directly with teachers and districts. Some even take time off from university duties and return to the classroom, teaching alongside teachers and learning how to make theories work in the real world. This is a new kind of science, with the goal of providing a sound scientific foundation for educational innovations including
-How does learning happen? The transition from novice to expert
-How does learning happen? Using prior knowledge
-Promoting Better Learning: Scaffolding
-Promoting Better learning: Externalization and Articulation
-Promoting better learning: Reflection
-Promoting better learning: Building from concrete to abstract knowledge