The revolution in the study of the mind that has occurred in the last three or four decades has important implications for education. As we illustrate, a new theory of learning is coming into focus that leads to very different approaches to the design of curriculum, teaching, and assessment than those often found in schools today. Equally important, the growth of interdisciplinary inquiries and new kinds of scientific collaborations have begun to make the path from basic research to educational practice somewhat more visible, if not yet easy to travel. (loc: 98-102)

Research from cognitive psychology has increased understanding of the nature of competent performance and the principles of knowledge organization that underlie people’s abilities to solve problems in a wide variety of areas, including mathematics, science, literature, social studies, and history. ˇ Developmental researchers have shown that young children understand a great deal about basic principles of biology and physical causality, about number, narrative, and personal intent, and that these capabilities make it possible to create innovative curricula that introduce important concepts for advanced reasoning at early ages. ˇ Research on learning and transfer has uncovered important principles for structuring learning experiences that enable people to use what they have learned in new settings. ˇ Work in social psychology, cognitive psychology, and anthropology is making clear that all learning takes place in settings that have particular sets of cultural and social norms and expectations and that these settings influence learning and transfer in powerful ways. ˇ Neuroscience is beginning to provide evidence for many principles of learning that have emerged from laboratory research, and it is showing how learning changes the physical structure of the brain and, with it, the functional organization of the brain. ˇ Collaborative studies of the design and evaluation of learning environments, among cognitive and developmental psychologists and educators, are yielding new knowledge about the nature of learning and teaching as it takes place in a variety of settings. In addition, researchers are discovering ways to learn from the “wisdom of practice” that comes from successful teachers who can share their expertise. ˇ Emerging technologies are leading to the development of many new opportunities to guide and enhance learning that were unimagined even a few years ago. (loc: 108-21)

At different points in history, scholars have worried that formal educational environments have been better at selecting talent than developing it (see, e.g., Bloom, 1964). Many people who had difficulty in school might have prospered if the new ideas about effective instructional practices had been available. (loc: 144-46)

This report builds on research that began in the latter part of the nineteenth century—the time in history at which systematic attempts were made to study the human mind through scientific methods. Before then, such study was the province of philosophy and theology. Some of the most influential early work was done in Leipzig in the laboratory of Wilhelm Wundt, who with his colleagues tried to subject human consciousness to precise analysis—mainly by asking subjects to reflect on their thought processes through introspection. By the turn of the century, a new school of behaviorism was emerging. In reaction to the subjectivity inherent in introspection, behaviorists held that the scientific study of psychology must restrict itself to the study of observable behaviors and the stimulus conditions that control them. An extremely influential article, published by John B. Watson in 1913, provides a glimpse of the behaviorist credo: … all schools of psychology except that of behaviorism claim that “consciousness” is the subject-matter of psychology. Behaviorism, on the contrary, holds that the subject matter of human psychology is the behavior or activities of the human being. Behaviorism claims that “consciousness” is neither a definable nor a useable concept; that it is merely another word for the “soul” of more ancient times. The old psychology is thus dominated by a kind of subtle religious philosophy (p. 1). Drawing on the empiricist tradition, behaviorists conceptualized learning as a process of forming connections between stimuli and responses. Motivation to learn was assumed to be driven primarily by drives, such as hunger, and the availability of external forces, such as rewards and punishments (e.g., Thorndike, 1913; Skinner, 1950). In a classic behaviorist study by Edward L. Thorndike (1913), hungry cats had to learn to pull a string hanging in a “puzzle box” in order for a of Sciences. All rights reserved. LEARNING: FROM SPECULATION TO SCIENCE 7 door to open that let them escape and get food. What was involved in learning to escape in this manner? Thorndike concluded that the cats did not think about how to escape and then do it; instead, they engaged in trialand-error behavior; see Box 1.1. Sometimes a cat in the puzzle box accidentally pulled the strings while playing and the door opened, allowing the cat to escape. But this event did not appear to produce an insight on the part of BOX 1.1 A Cat’s Learning “When put into the box, the cat would show evident signs of discomfort and impulse to escape from confinement. It tries to squeeze through any opening; it claws and bites at the wire; it thrusts its paws out through any opening and claws at everything it reaches… . It does not pay very much attention to the food outside but seems simply to strive instinctively to escape from confinement… . The cat that is clawing all over the box in her impulsive struggle will probably claw the string or loop or button so as to open the door. And gradually all the other unsuccessful impulses will be stamped out and the particular impulse leading to the successful act will be stamped in by the resulting pleasure, until, after many trials, the cat will, when put in the box, immediately claw the button or loop in a definite way” (Thorndike, 1913:13). (loc: 154-78)

A limitation of early behaviorism stemmed from its focus on observable stimulus conditions and the behaviors associated with those conditions. This orientation made it difficult to study such phenomena as understanding, reasoning, and thinking—phenomena that are of paramount importance for education. Over time, radical behaviorism (often called “Behaviorism with a Capital B”) gave way to a more moderate form of behaviorism (“behaviorism with a small b”) that preserved the scientific rigor of using behavior as data, but also allowed hypotheses about internal “mental” states when these became necessary to explain various phenomena (e.g., Hull, 1943; Spence, 1942). In the late 1950s, the complexity of understanding humans and their environments became increasingly apparent, and a new field emerged— cognitive science. From its inception, cognitive science approached learning from a multidisciplinary perspective that included anthropology, linguistics, philosophy, developmental psychology, computer science, neuroscience, and several branches of psychology (Norman, 1980,1993; Newell and Simon, 1972). New experimental tools, methodologies, and ways of postulating theories made it possible for scientists to begin serious study of mental functioning: to test their theories rather than simply speculate about thinking and learning (see, e.g., Anderson, 1982, 1987; deGroot, 1965,1969; Newell and Simon, 1972; Ericsson and Charness, 1994), and, in recent years, to develop insights into the importance of the social and cultural contexts of learning (e.g., Cole, 1996; Lave, 1988; Lave and Wenger, 1991; Rogoff, 1990; Rogoff et al., 1993). The introduction of rigorous qualitative research methodologies have provided perspectives on learning that complement and enrich the experimental research traditions (Erickson, 1986; Hammersly and Atkinson, 1983; Heath, 1982; Lincoln and Guba, 1985; Marshall and Rossman, 1955; Miles and Huberman, 1984; Spradley, 1979). (loc: 183-96)

The new science of learning does not deny that facts are important for thinking and problem solving. Research on expertise in areas such as chess, history, science, and mathematics demonstrate that experts’ abilities to think and solve problems depend strongly on a rich body of knowledge about subject matter (e.g., Chase and Simon, 1973; Chi et al., 1981; deGroot, 1965). However, the research also shows clearly that “usable knowledge” is not the same as a mere list of disconnected facts. Experts’ knowledge is connected and organized around important concepts (e.g., Newton’s second law of motion); it is “conditionalized” to specify the contexts in which it is applicable; it supports understanding and transfer (to other contexts) rather than only the ability to remember. For example, people who are knowledgeable about veins and arteries know more than the facts noted above: they also understand why veins and arteries have particular properties. They know that blood pumped from the heart exits in spurts and that the elasticity of the arteries helps accommodate pressure changes. (loc: 204-11)

Because they understand relationships between the structure and function of veins and arteries, knowledgeable individuals are more likely to be able to use what they have learned to solve novel problems—to show evidence of transfer. For example, imagine being asked to design an artificial artery—would it have to be elastic? Why or why not? An understanding of reasons for the properties of arteries suggests that elasticity may not be necessary—perhaps the problem can be solved by creating a conduit that is strong enough to handle the pressure of spurts from the heart and also function as a one-way (loc: 213-17)

An emphasis on understanding leads to one of the primary characteristics of the new science of learning: its focus on the processes of knowing (e.g., Piaget, 1978; Vygotsky, 1978). Humans are viewed as goal-directed agents who actively seek information. They come to formal education with a range of prior knowledge, skills, beliefs, and concepts that significantly influence what they notice about the environment and how they organize and interpret it. This, in turn, affects their abilities to remember, reason, solve problems, and acquire new knowledge. Even young infants are active learners who bring a point of view to the learning setting. The world they enter is not a “booming, buzzing confusion” (James, 1890), where every stimulus is equally salient. Instead, an infant’s brain gives precedence to certain kinds of information: language, basic concepts of number, physical properties, and the movement of animate and inanimate objects. In the most general sense, the contemporary view of learning is that people construct new knowledge and understandings based on what they already know and believe (e.g., Cobb, 1994; Piaget, 1952, 1973a,b, 1977, 1978; Vygotsky, 1962, 1978). (loc: 220-28)

A logical extension of the view that new knowledge must be constructed from existing knowledge is that teachers need to pay attention to the incomplete understandings, the false beliefs, and the naive renditions of concepts that learners bring with them to a given subject. Teachers then need to build on these ideas in ways that help each student achieve a more mature understanding. If students’ initial ideas and beliefs are ignored, the understandings that they develop can be very different from what the teacher intends. (loc: 229-32)

A common misconception regarding “constructivist” theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1994)—even listening to a lecture involves active attempts to construct new knowledge. Fish Is Fish (Lionni, 1970) and attempts to teach children that the earth is round (Vosniadou and Brewer, 1989) show why simply providing lectures frequently does not work. Nevertheless, there are times, usually after people have first grappled with issues on their own, that “teaching by telling” can work extremely well (e.g., Schwartz and Bransford, 1998). However, teachers still need to pay attention to students’ interpretations and provide guidance when necessary. (loc: 249-56)

relevant to dicussion w cheryl (loc: 256)

Active Learning New developments in the science of learning also emphasize the importance of helping people take control of their own learning. Since understanding is viewed as important, people must learn to recognize when they understand and when they need more information. What strategies might they use to assess whether they understand someone else’s meaning? What kinds of evidence do they need in order to believe particular claims? How can they build their own theories of phenomena and test them effectively? Many important activities that support active learning have been studied under the heading of “metacognition,” a topic discussed in more detail in Chapters 2 and 3. Metacognition refers to people’s abilities to predict their performances on various tasks (e.g., how well they will be able to remember various stimuli) and to monitor their current levels of mastery and understanding (e.g., Brown, 1975; Flavell, 1973). Teaching practices congruent with a metacognitive approach to learning include those that focus on sensemaking, selfassessment, and reflection on what worked and what needs improving. These practices have been shown to increase the degree to which students transfer their learning to new settings and events (e.g., Palincsar and Brown, 1984; Scardamalia et al., 1984; Schoenfeld, 1983, 1985, 1991). Imagine three teachers whose practices affect whether students learn to take control of their own learning (Scardamalia and Bereiter, 1991). (loc: 267-77)

This volume synthesizes the scientific basis of learning. The scientific achievements include a fuller understanding of: (1) memory and the structure of knowledge; (2) problem solving and reasoning; (3) the early foundations of learning; (4) regulatory processes that govern learning, including metacognition; and (5) how symbolic thinking emerges from the culture and community of the learner. (loc: 305-7)

A critical feature of effective teaching is that it elicits from students their preexisting understanding of the subject matter to be taught and provides opportunities to build on—or challenge—the initial understanding. James Minstrell, a high school physics teacher, describes the process as follows (Minstrell, 1989: 130-131): Students’ initial ideas about mechanics are like strands of yarn, some unconnected, some loosely interwoven. The act of instruction can be viewed as helping the students unravel individual strands of belief, label them, and then weave them into a fabric of more complete understanding. Rather than denying the relevancy of a belief, teachers might do better by helping students differentiate their present ideas from and integrate them into conceptual beliefs more like those of scientists. (loc: 330-36)

2. To develop competence in an area of inquiry, students must: (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and © organize knowledge in ways that facilitate retrieval and application. This principle emerges from research that compares the performance of experts and novices and from research on learning and transfer. Experts, regardless of the field, always draw on a richly structured information base; they are not just “good thinkers” or “smart people.” The ability to plan a task, to notice patterns, to generate reasonable arguments and explanations, and to draw analogies to other problems are all more closely intertwined with factual knowledge than was once believed. But knowledge of a large set of disconnected facts is not sufficient. To develop competence in an area of inquiry, students must have opportunities to learn with understanding. Deep understanding of subject matter transforms factual information into usable knowledge. A pronounced difference between experts and novices is that experts’ command of concepts shapes (loc: 356-63)

their understanding of new information: it allows them to see patterns, relationships, or discrepancies that are not apparent to novices. They do not necessarily have better overall memories than other people. But their conceptual understanding allows them to extract a level of meaning from information that is not apparent to novices, and this helps them select and remember relevant information. Experts are also able to fluently access relevant knowledge because their understanding of subject matter allows them to quickly identify what is relevant. Hence, their attention is not overtaxed by complex events. In most areas of study in K-12 education, students will begin as novices; they will have informal ideas about the subject of study, and will vary in the amount of information they have acquired. The enterprise of education can be viewed as moving students in the direction of more formal understanding (or greater expertise). This will require both a deepening of the information base and the development of a conceptual framework for that subject matter. Geography can be used to illustrate the manner in which expertise is organized around principles that support understanding. A student can learn to fill in a map by memorizing states, cities, countries, etc., and can complete the task with a high level of accuracy. But if the boundaries are removed, the problem becomes much more difficult. There are no concepts supporting the student’s information. An expert who understands that borders often developed because natural phenomena (like mountains or water bodies) separated people, and that large cities often arose in locations that allowed for trade (along rivers, large lakes, and at coastal ports) will easily outperform the novice. The more developed the conceptual understanding of the needs of cities and the resource base that drew people to them, the more meaningful the map becomes. Students can become more expert if the geographical information they are taught is placed in the appropriate conceptual framework. A key finding in the learning and transfer literature is that organizing information into a conceptual framework allows for greater “transfer”; that is, it allows the student to apply what was learned in new situations and to learn related information more quickly (see Box 1.3). The student who has learned geographical information for the Americas in a conceptual framework approaches the task of learning the geography of another part of the globe with questions, ideas, and expectations that help guide acquisition of the new information. Understanding the geographical importance of the Mississippi River sets the stage for the student’s understanding of the geographical importance of the Nile. And as concepts are reinforced, the student will transfer learning beyond the classroom, observing and inquiring, for example, about the geographic features of a visited city that help explain its location and size (Holyoak, 1984; (loc: 365-85)

3. A “metacognitive” approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them. In research with experts who were asked to verbalize their thinking as they worked, it was revealed that they monitored their own understanding carefully, making note of when additional information was required for understanding, whether new information was consistent with what they already knew, and what analogies could be drawn that would advance their understanding. These metacognitive monitoring activities are an important component of what is called adaptive expertise (Hatano and Inagaki, 1986). Because metacognition often takes the form of an internal conversation, it can easily be assumed that individuals will develop the internal dialogue on their own. Yet many of the strategies we use for thinking reflect cultural norms and methods of inquiry (Hutchins, 1995; BriceHeath, 1981, 1983; Suina and Smolkin, 1994). Research has demonstrated that children can be taught these strategies, including the ability to predict outcomes, explain to oneself in order to improve understanding, note failures to comprehend, activate background knowledge, plan ahead, and apportion time and memory. Reciprocal teaching, for example, is a technique designed to improve students’ reading comprehension by helping them explicate, elaborate, and monitor their understanding as they read (Palincsar and Brown, 1984). The model for using the metacognitive strategies is provided initially by the (loc: 386-97)

Throwing Darts Under Water In one of the most famous early studies comparing the effects of learning a procedure with learning with understanding, two groups of children practiced throwing darts at a target under water (described in Judd, 1908; see a conceptual replication by Hendrickson and Schroeder, 1941). One group received an explanation of the refraction of light, which causes the apparent location of the target to be deceptive. The other group only practiced dart throwing, without the explanation. Both groups did equally well on the practice task, which involved a target 12 inches under water. But the group that had been instructed about the abstract principle did much better when they had to transfer to a situation in which the target was under only 4 inches of water. Because they understood what they were doing, the group that had received instruction about the refraction of light could adjust their behavior to the new task. (loc: 397-404)

teacher, and students practice and discuss the strategies as they learn to use them. Ultimately, students are able to prompt themselves and monitor their own comprehension without teacher support. The teaching of metacognitive activities must be incorporated into the subject matter that students are learning (White and Frederickson, 1998). These strategies are not generic across subjects, and attempts to teach them as generic can lead to failure to transfer. Teaching metacognitive strategies in context has been shown to improve understanding in physics (White and Frederickson, 1998), written composition (Scardamalia et al., 1984), and heuristic methods for mathematical problem solving (Schoenfeld, 1983, 1984, 1991). And metacognitive practices have been shown to increase the degree to which students transfer to new settings and events (Lin and Lehman, in press; Palincsar and Brown, 1984; Scardamalia et al., 1984; Schoenfeld, 1983, 1984, 1991). Each of these techniques shares a strategy of teaching and modeling the process of generating alternative approaches (to developing an idea in writing or a strategy for problem solving in mathematics), evaluating their merits in helping to attain a goal, and monitoring progress toward that goal. Class discussions are used to support skill development, with a goal of independence and self-regulation. (loc: 405-14)

ˇ Schools of education must provide beginning teachers with opportunities to learn: (a) to recognize predictable preconceptions of students that make the mastery of particular subject matter challenging, (b) to draw out preconceptions that are not predictable, and © to work with preconceptions so that children build on them, challenge them and, when appropriate, replace them. 2. Teachers must teach some subject matter in depth, providing many examples in which the same concept is at work and providing a firm foundation of factual knowledge. This requires that: ˇ Superficial coverage of all topics in a subject area must be replaced with indepth coverage of fewer topics that allows key concepts in that discipline to be understood. The goal of coverage need not be abandoned entirely, of course. But there must be a sufficient number of cases of indepth study to allow students to grasp the defining concepts in specific domains within a discipline. Moreover, indepth study in a domain often requires that ideas be carried beyond a single school year before students can make the transition from informal to formal ideas. This will require active coordination of the curriculum across school years. ˇ Teachers must come to teaching with the experience of indepth study of the subject area themselves. Before a teacher can develop powerful pedagogical tools, he or she must be familiar with the progress of inquiry and the terms of discourse in the discipline, as well as understand the relationship between information and the concepts that help organize that information in the discipline. But equally important, the teacher must have a grasp of the growth and development of students’ thinking about these concepts. The latter will be essential to developing teaching expertise, but not expertise in the discipline. It may therefore require courses, or course supplements, that are designed specifically for teachers. ˇ Assessment for purposes of accountability (e.g., statewide assessments) must test deep understanding rather than surface knowledge. Assessment tools are often the standard by which teachers are held accountable. A teacher is put in a bind if she or he is asked to teach for deep conceptual understanding, but in doing so produces students who perform more poorly on standardized tests. Unless new assessment tools are aligned with new approaches to teaching, the latter are unlikely to muster support among the schools and their constituent parents. This goal is as important as it is difficult to achieve. The format of standardized tests can encourage measurement of factual knowledge rather than conceptual understanding, but it also facilitates objective scoring. Measuring depth of understanding can pose challenges for objectivity. Much work needs to be done to minimize the tradeoff between assessing depth and assessing objectively. of Sciences. All rights reserved. LEARNING: FROM SPECULATION TO SCIENCE 21 3. The teaching of metacognitive skills should be integrated into the curriculum in a variety of subject areas. Because metacognition often takes the form of an internal dialogue, many students may be unaware of its importance unless the processes are explicitly emphasized by teachers. An emphasis on metacognition needs to accompany instruction in each of the disciplines, because the type of monitoring required will vary. In history, for example, the student might be asking himself, “who wrote this document, and how does that affect the interpretation of events,” whereas in physics the student might be monitoring her understanding of the underlying physical principle at work. ˇ Integration of metacognitive instruction with discipline-based learning can enhance student achievement and develop in students the ability to learn independently. It should be consciously incorporated into curricula across disciplines and age levels. ˇ Developing strong metacognitive strategies and learning to teach those strategies in a classroom environment should be standard features of the curriculum in schools of education. Evidence from research indicates that when these three principles are incorporated into teaching, student achievement improves. (loc: 424-52)

Thinker Tools Curriculum for teaching physics in an interactive computer environment focuses on fundamental physical concepts and properties, allowing students to test their preconceptions in model building and experimentation activities. The program includes an “inquiry cycle” that helps students monitor where they are in the inquiry process. The program asks for students’ reflective assessments and allows them to review the assessments of their fellow students. In one study, sixth graders in a suburban school who were taught physics using Thinker Tools performed better at solving conceptual physics problems than did eleventh and twelfth grade physics students in the same school system taught by conventional methods. A second study comparing urban students in grades 7 to 9 with suburban students in grades 11 and 12 again showed that the younger students taught by the inquiry-based approach had a superior grasp of the fundamental principles of physics (White and Frederickson, 1997, 1998). (loc: 453-59)

If, instead, the point of departure is a core set of learning principles, then the selection of teaching strategies (mediated, of course, by subject matter, grade level, and desired outcome) can be purposeful. The many possibilities then become a rich set of opportunities from which a teacher constructs an instructional program rather than a chaos of competing alternatives. Focusing on how people learn also will help teachers move beyond either-or dichotomies that have plagued the field of education. One such issue is whether schools should emphasize “the basics” or teach thinking and problemsolving skills. This volume shows that both are necessary. Students’ abilities to acquire organized sets of facts and skills are actually enhanced when they are connected to meaningful problemsolving activities, and when students are helped to understand why, when, and how those facts and skills are relevant. And attempts to teach thinking skills without a strong base of factual knowledge do not promote problemsolving ability or support transfer to new situations. (loc: 480-87)

four interrelated attributes of learning environments that need cultivation. 1. Schools and classrooms must be learner centered. Teachers must pay close attention to the knowledge, skills, and attitudes that learners bring into the classroom. This incorporates the preconceptions regarding subject matter already discussed, but it also includes a broader understanding of the learner. For example: ˇ Cultural differences can affect students’ comfort level in working collaboratively versus individually, and they are reflected in the background knowledge students bring to a new learning situation (Moll et al., 1993). ˇ Students’ theories of what it means to be intelligent can affect their performance. Research shows that students who think that intelligence is a fixed entity are more likely to be performance oriented than learning oriented—they want to look good rather than risk making mistakes while learning. These students are especially likely to bail out when tasks become difficult. In contrast, students who think that intelligence is malleable are more willing to struggle with challenging tasks; they are more comfortable with risk (Dweck, 1989; Dweck and Legget, 1988). Teachers in learnercentered classrooms also pay close attention to the individual progress of each student and devise tasks that are appropriate. of Sciences. All rights reserved. 24 HOW PEOPLE LEARN, EXPANDED EDITION Learnercentered teachers present students with “just manageable difficulties”—that is, challenging enough to maintain engagement, but not so difficult as to lead to discouragement. They must therefore have an understanding of their students’ knowledge, skill levels, and interests (Duckworth, 1987). 2. To provide a knowledge-centered classroom environment, attention must be given to what is taught (information, subject matter), why it is taught (understanding), and what competence or mastery looks like. As mentioned above, research discussed in the following chapters shows clearly that expertise involves well-organized knowledge that supports understanding, and that learning with understanding is important for the development of expertise because it makes new learning easier (i.e., supports transfer). Learning with understanding is often harder to accomplish than simply memorizing, and it takes more time. Many curricula fail to support learning with understanding because they present too many disconnected facts in too short a time—the “mile wide, inch deep” problem. Tests often reinforce memorizing rather than understanding. The knowledge-centered environment provides the necessary depth of study, assessing student understanding rather than factual memory. It incorporates the teaching of metacognitive strategies that further facilitate future learning. Knowledge-centered environments also look beyond engagement as the primary index of successful teaching (Prawaf et al., 1992). Students’ interest or engagement in a task is clearly important. Nevertheless, it does not guarantee that students will acquire the kinds of knowledge that will support new learning. There are important differences between tasks and projects that encourage handson doing and those that encourage doing with understanding; the knowledge-centered environment emphasizes the latter (Greeno, 1991). 3. Formative assessments—ongoing assessments designed to make students’ thinking visible to both teachers and students—are essential. They permit the teacher to grasp the students’ preconceptions, understand where the students are in the “developmental corridor” from informal to formal thinking, and design instruction accordingly. In the assessment-centered classroom environment, formative assessments help both teachers and students monitor progress. An important feature of assessments in these classrooms is that they be learner-friendly: they are not the Friday quiz for which information is memorized the night before, and for which the student is given a grade that ranks him or her with respect to classmates. Rather, these assessments should of Sciences. All rights reserved. LEARNING: FROM SPECULATION TO SCIENCE 25 provide students with opportunities to revise and improve their thinking (Vye et al., 1998b), help students see their own progress over the course of weeks or months, and help teachers identify problems that need to be remedied (problems that may not be visible without the assessments). For example, a high school class studying the principles of democracy might be given a scenario in which a colony of people have just settled on the moon and must establish a government. Proposals from students of the defining features of such a government, as well as discussion of the problems they foresee in its establishment, can reveal to both teachers and students areas in which student thinking is more and less advanced. The exercise is less a test than an indicator of where inquiry and instruction should focus. 4. Learning is influenced in fundamental ways by the context in which it takes place. A community-centered approach requires the development of norms for the classroom and school, as well as connections to the outside world, that support core learning values. The norms established in the classroom have strong effects on students’ achievement. In some schools, the norms could be expressed as “don’t get caught not knowing something.” Others encourage academic risk-taking and opportunities to make mistakes, obtain feedback, and revise. Clearly, if students are to reveal their preconceptions about a subject matter, their questions, and their progress toward understanding, the norms of the school must support their doing so. Teachers must attend to designing classroom activities and helping students organize their work in ways that promote the kind of intellectual camaraderie and the attitudes toward learning that build a sense of community. In such a community, students might help one another solve problems by building on each other’s knowledge, asking questions to clarify explanations, and suggesting avenues that would move the group toward its goal (Brown and Campione, 1994). Both cooperation in problem solving (Evans, 1989; Newstead and Evans, 1995) and argumentation (Goldman, 1994; Habermas, 1990; Kuhn, 1991; Moshman, 1995a, 1995b; Salmon and Zeitz, 1995; Youniss and Damon, 1992) among students in such an intellectual community enhance cognitive development. Teachers must be enabled and encouraged to establish a community of learners among themselves (Lave and Wegner, 1991). These communities can build a sense of comfort with questioning rather than knowing the answer and can develop a model of creating new ideas that build on the contributions of individual members. They can engender a sense of the excitement of learning that is then transferred to the classroom, conferring a sense of ownership of new ideas as they apply to theory and practice. of Sciences. All rights reserved. 26 HOW PEOPLE LEARN, EXPANDED EDITION FIGURE 1.2 Students spend only 14 percent of their time in school. Not least, schools need to develop ways to link classroom learning to other aspects of students’ lives. Engendering parent support for the core learning principles and parent involvement in the learning process is of utmost importance (Moll, 1990; 1986a, 1986b). (loc: 489-541)

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. (loc: 573-78)

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 outthink 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. (loc: 580-600)

there are limits on the amount of information that people can hold in shortterm memory, shortterm memory is enhanced when people are able to chunk information into familiar patterns (Miller, 1956). (loc: 601-3)

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, (loc: 611-22)

the expert teachers had very different understandings of the events they were watching than did the novice teachers; (loc: 639)

like language learning. learning chinese (loc: 639)

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). (loc: 642-44)

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. (loc: 667-70)

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 problemsolving contexts (Chi et al., 1981). (loc: 680-83)

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). (loc: 728-33)

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 = MC 2, or E = MC 3. 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. (loc: 744-61)

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). (loc: 770-80)

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. (loc: 781-82)

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. (loc: 783-96)

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. (loc: 797-98)

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). (loc: 799-802)

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. (loc: 839-45)

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 Inagaki, 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.” (loc: 847-59)

Learning and Transfer (loc: 911)

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). (loc: 915-17)

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 (loc: 917-27)

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). (loc: 939-47)

In the discussion below we explore key characteristics of learning and transfer that have important implications for education: ˇ Initial learning is necessary for transfer, and a considerable amount is known about the kinds of learning experiences that support transfer. ˇ Knowledge that is overly contextualized can reduce transfer; abstract representations of knowledge can help promote transfer. ˇ Transfer is best viewed as an active, dynamic process rather than a passive end-product of a particular set of learning experiences. ˇ All new learning involves transfer based on previous learning, and this fact has important implications for the design of instruction that helps students learn. (loc: 947-52)

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 shortterm memory limitations. The implication is that learning cannot be rushed; the complex cognitive activity of information integration requires time. (loc: 1021-27)

Beyond “Time on Task” 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 (loc: 1027-29)

Students in Group 1 read and summarized a text on the topic of schema theory and then listened to a lecture designed to help them organize their knowledge and learn with understanding. Group 2 did not read the text but, instead, actively compared simplified data sets from schema experiments on memory and then heard the same lecture as Group 1. Group 3 spent twice as much time as Group 2 working with the data sets but did not receive the organizing lecture. On the transfer test, students in Group 2 performed much better than those in Groups 1 and 3. Their work with the data sets set the stage for them to learn from the lecture. The lecture was necessary, as indicated by the poor performance of Group 3. (loc: 1033-37)

“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 of Sciences. All rights reserved. 60 HOW PEOPLE LEARN, EXPANDED EDITION 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., 1999). (loc: 1039-51)

Motivation to Learn 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. (loc: 1062-65)

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., 1999). For example, young learners are highly motivated to write stories and draw pictures that they can share with others. First graders in an innercity 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 innercity 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.) (loc: 1066-85)

The problem of overly contextualized knowledge has been studied in instructional programs that use case-based and problembased 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 sixthgrade 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 of Sciences. All rights reserved. LEARNING AND TRANSFER 63 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). (loc: 1097-1112)

similar to massive input language learning (loc: 1112)

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. (loc: 1123-25)

“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. (loc: 1164-66)

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, 1999; 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 finegrained analysis of learning and its effects on transfer than simple one-shot assessments of whether or not transfer occurs. (loc: 1167-83)

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. (loc: 1186-87)

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 knowledgeacquisition 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 problemsolving 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. (loc: 1188-1204)

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. (loc: 1217-23)

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. (loc: 1248-52)

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 (BriceHeath, 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). (loc: 1292-98)

How Children Learn (loc: 1413)

A major move away from the tabula rasa view of the infant mind was taken by the Swiss psychologist Jean Piaget. Beginning in the 1920s, Piaget argued that the young human mind can best be described in terms of complex cognitive structures. From close observations of infants and careful questioning of children, he concluded that cognitive development proceeds through certain stages, each involving radically different cognitive schemes. While Piaget observed that infants actually seek environmental stimulation that promotes their intellectual development, he thought that their initial representations of objects, space, time, causality, and self are constructed only gradually during the first 2 years. He concluded that the world of young infants is an egocentric fusion of the internal and external worlds and that the development of an accurate representation of physical reality depends on the gradual coordination of schemes of looking, listening, and touching. After Piaget, others studied how newborns begin to integrate sight and sound and explore their perceptual worlds. For perceptual learning theorists, learning was considered to proceed rapidly due to the initial availability of exploration patterns that infants use to obtain information about the objects and events of their perceptual worlds (Gibson, 1969). As information processing theories began to emerge, the metaphor of mind as computer, information processor, and problem solver came into wide usage (Newell et al., 1958) and was quickly applied to the study of cognitive development. Although these theories differed in important ways, they shared an emphasis on considering children as active learners who are able to set goals, plan, and revise. Children are seen as learners who assemble and organize material. As such, cognitive development involves the acquisition of organized knowledge structures including, for example, biological concepts, early number sense, and early understanding of basic physics. In addition, cognitive development involves the gradual acquisition of strategies for remembering, understanding, and solving problems. The active role of learners was also emphasized by Vygotsky (1978), who pointed to other supports for learning. Vygotsky was deeply interested in the role of the social environment, included tools and cultural objects, as well as people, as agents in developing thinking. Perhaps the most powerful idea from Vygotsky to influence developmental psychology was that of a zone of proximal development (Vygotsky, 1978), described in Box 4.1. It refers to a bandwidth of competence (Brown and Reeve, 1987) that learners can navigate with aid from a supportive context, including the assistance of others. (For modern treatments of this concept, see Newman et al., 1989; (loc: 1429-48)

The zone of proximal development is the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance, or in collaboration with more capable peers (Vygotsky, 1978:86). What children can do with the assistance of others is even more indicative of their mental development than what they can do alone (Vygotsky, 1978:85). The zone of proximal development embodies a concept of readiness to learn that emphasizes upper levels of competence. These upper boundaries are not immutable, however, but constantly changing with the learner’s increasing independent competence. What a child can perform today with assistance she will be able to perform tomorrow independently, thus preparing her for entry into a new and more demanding collaboration. These functions could be called the “buds,” rather than the fruits of development. The actual developmental level characterizes mental development retrospectively, while the zone of proximal development characterizes mental development prospectively (Vygotsky, 1978:8687). (loc: 1450-57)

Moll and Whitmore, 1993; Rogoff and Wertsch, 1984; from a different theoretical perspective, see Bidell and Fischer, 1997.) This line of work has drawn attention to the roles of more capable peers, parents, and other partners in challenging and extending children’s efforts to understand. It has also contributed to an understanding of the relationship between formal and informal teaching and learning situations (Lave and Wenger, 1991) and cognition distributed across people and tools (Salomon, 1993). (loc: 1458-61)

research in another major area began to show how learners process information, remember, and solve problems in nonprivileged domains. Known as information processing (Simon, 1972; Newell and Simon, 1972), this branch of psychology was quickly adopted to explain developments in children’s learning. All human learners have limitations to their of Sciences. All rights reserved. 96 HOW PEOPLE LEARN, EXPANDED EDITION shortterm memory for remembering and for solving problems. Simon (1972) and others (e.g., Chi, 1978; Siegler, 1978; Klahr and Wallace, 1973) argued that development means overcoming information-processing constraints, such as limited shortterm memory capacity. The crucial argument for developmental psychologists is whether young learners are particularly hampered by memory limitations and whether, compared with adults, they are less able to overcome general limitations through the clever use of strategies or by lack of relevant knowledge factors. One view of learning in children is that they have a less memory capacity than adults. While there is no doubt that, in general, children’s learning and memory abilities increase with age, controversy surrounds the mechanisms that affect these changes. One view is that children’s shortterm memory capacity, or the amount of mental space they have (M-space), increases as children mature (Pascual-Leone, 1988). With more mental space, they can retain more information and perform more complex mental operations. A complementary view is that the mental operations of older children are more rapid, enabling them to make use of their limited capacity more effectively (Case, 1992). If one holds either of these positions, one would expect relatively uniform improvement in performance across domains of learning (Case, 1992; Piaget, 1970). A second view is that children and adults have roughly the same mental capacity, but that with development children acquire knowledge and develop effective activities to use their minds well. Such activities are often called strategies. There are a variety of well-known strategies that increase remembering, such as rehearsal (repeating items over and over), which tends to improve rote recall (Belmont and Butterfield, 1971); elaboration (Reder and Anderson, 1980), which improves retention of more meaningful units such as sentences; and summarization (Brown and Day, 1984), which increases retention and comprehension. These are just three of many strategies. Perhaps the most pervasive strategy used to improve memory performance is clustering: organizing disparate pieces of information into meaningful units. Clustering is a strategy that depends on organizing knowledge. In a classic paper, Miller (1956) described the persistence of a phenomenon he called the “magical number 7 ą 2” in human mental processing. Given a list of numbers to remember, sounds (phonemes) to distinguish from one another, or a set of unrelated facts to recall, there is a critical change in performance at around seven items. Up to seven items (between five and nine, actually, hence Miller’s title), people can readily handle a variety of tasks; with more than seven, they simply cannot process them handily. People have developed ways around this memory constraint by organizing information, such as grouping together or “chunking” disparate elements into sets of letters, numbers, or pictures that make sense to them. Known as the chunking effect, this memory strategy improves the per-of Sciences. All rights reserved. HOW CHILDREN LEARN 97 formance of children, as well as adults. A prototype experiment would involve, for example, presenting 4-to 10-year-olds with long lists of pictures to remember, far more than they could if they simply tried to remember them individually. Such a list might consist of pictures of a cat, rose, train, hat, airplane, horse, tulip, boat, coat, etc. Given a 20-item list, older children remember more than younger children, but the factor responsible for better recall is not age per se, but whether the child notices that the list consists of four categories (animals, plants, means of transportation, and articles of clothing). If the categories are noticed, young children often recall the entire list. In the absence of category recognition, performance is poorer and shows the age effect. Younger children employ categorization strategies less often than older ones. However, the skill is knowledge related, not age related; the more complex the categories, the older the child is before noticing the structure. One has to know a structure before one can use it. These varying views of children’s learning have different implications for what one expects from children. If one believes that learning differences are determined by gradual increases in capacity or speed of processing, one would expect relatively uniform increases in learning across most domains. But if one believes that strategies and knowledge are important, one would expect different levels of learning, depending on the children’s conceptual knowledge and their control over strategies that organize that knowledge for learning. (loc: 1693-1729)

The evidence suggests that, like other forms of learning, metacognition develops gradually and is as dependent on knowledge as experience. It is difficult to engage in self-regulation and reflection in areas that one does not understand. However, on topics that children know, primitive forms of self-regulation and reflection appear early (Brown and DeLoache, 1978). (loc: 1742-44)

This question is answered through studies in which individual children who do not yet know a strategy are given prolonged experiences (weeks or months) in the subject matter; in this way, researchers can study how children devise their various strategies (Kuhn, 1995; Siegler and Crowley, 1991; see also DeLoache et al., 1985a). These are referred to as “microgenetic” studies, meaning smallscale studies of the development of a concept. In this approach, one can identify when a new strategy is first used, which in turn allows examination of what the experience of discovery was like, what led to the discovery, and how the discovery was generalized beyond its initial use. Three key findings have emerged from these studies: (1) discoveries are often made not in response to impasses or failures but rather in the context of successful performance; (2) short-lived transition strategies often precede more enduring approaches; and (3) generalization of new approaches often occurs very slowly, even when children can provide compelling rationales for their usefulness (Karmiloff-Smith, 1992; Kuhn, 1995; Siegler and Crowley, 1991). (loc: 1790-97)

In his theory of multiple intelligences, Gardner (1983, 1991) proposed the existence of seven relatively autonomous intelligences: linguistic, logical, musical, spatial, bodily kinesthetic, interpersonal, and intrapersonal. Recently, Gardner (1997) proposed an eighth intelligence, “naturalistic.” The first two intelligences are those typically tapped on tests and most valued in schools. The theory of multiple intelligences was developed as a psychological theory, but it sparked a great deal of interest among educators, in this country and abroad, in its implications for teaching and learning. The experimental educational programs based on the theory have focused generally in two ways. Some educators believe that all children should have each intelligence nurtured; on this basis, they have devised curricula that address each intelligence directly. Others educators have focused on the development of specific intelligences, like the personal ones, because they believe these intelligences receive short shrift in American education. There are strengths and weaknesses to each approach. The application of multiple intelligences to education is a grass roots movement among teachers that is only just beginning. An interesting development is the attempt to modify traditional curricula: whether one is teaching history, science, or the arts, the theory of multiple intelligences offers a teacher a number of different approaches to the topic, several modes of representing key concepts, and a variety of ways in which students can demonstrate their understandings (Gardner, 1997). (loc: 1810-21)

Children, like their elders, have their own conceptions about their minds and those of others and how humans learn and are “intelligent” (see Wellman, 1990; Wellman and Hickey, 1994; Gelman, 1988; Gopnik, 1990). Children of Sciences. All rights reserved. 102 HOW PEOPLE LEARN, EXPANDED EDITION are said to have one of two main classes of beliefs: entity theories and incremental theories (Dweck, 1989; Dweck and Elliot, 1983; Dweck and Leggett, 1988). Children with entity theories believe that intelligence is a fixed property of individuals; children with incremental theories believe that intelligence is malleable (see also Resnick and Nelson-LeGall, 1998). (loc: 1822-27)

Self-Directed and Other-Directed Learning Just as children are often self-directed learners in privileged domains, such as those of language and physical causality, young children exhibit a strong desire to apply themselves in intentional learning situations. They also learn in situations where there is no external pressure to improve and no feedback or reward other than pure satisfaction—sometimes called achievement or competence motivation (White, 1959; Yarrow and Messer, 1983; Dichter-Blancher et al., 1997). Children are both problem solvers and problem generators; they not only attempt to solve problems presented to them, but they also seek and create novel challenges. An adult struggling to solve a crossword puzzle has much in common with a young child trying to assemble a jigsaw puzzle. Why do they bother? It seems that humans have a need to solve problems; see Box 4.4. One of the challenges of schools is to build on children’s motivation to explore, succeed, understand (Piaget, 1978) and harness it in the service of learning. (loc: 1835-42)

Effective teachers help people of all ages make connections among different aspects of their knowledge. Caregivers attempt to build on what children know and extend their competencies by providing supporting structures or scaffolds for the child’s performance (Wood et al., 1976). Scaffolding involves several activities and tasks, such as: ˇ interesting the child in the task; ˇ reducing the number of steps required to solve a problem by simplifying the task, so that a child can manage components of the process and recognize when a fit with task requirements is achieved; ˇ maintaining the pursuit of the goal, through motivation of the child and direction of the activity; ˇ marking critical features of discrepancies between what a child has produced and the ideal solution; ˇ controlling frustration and risk in problem solving; and ˇ demonstrating an idealized version of the act to be performed. Scaffolding can be characterized as acting on a motto of “Where before there was a spectator, let there now be a participant” (Bruner, 1983:60). (loc: 1877-84)

1. Learning changes the physical structure of the brain. 2. These structural changes alter the functional organization of the brain; in other words, learning organizes and reorganizes the brain. 3. Different parts of the brain may be ready to learn at different times. (loc: 2076-78)

Clearly, the brain can store information, but what kinds of information? The neuroscientist does not address these questions. Answering them is the job of cognitive scientists, education researchers, and others who study the effects of experiences on human behavior and human potential. (loc: 2202-4)

Memory is neither a single entity nor a phenomenon that occurs in a single area of the brain. There are two basic memory processes: declarative memory, or memory for facts and events which occurs primarily in brain systems involving the hippocampus; and procedural or nondeclarative memory, which is memory for skills and other cognitive operations, or memory that cannot be represented in declarative sentences, which occurs principally in the brain systems involving the neostriatum (Squire, 1997). Different features of learning contribute to the durability or fragility of memory. For example, comparisons of people’s memories for words with their memories for pictures of the same objects show a superiority effect for pictures. The superiority effect of pictures is also true if words and pictures are combined during learning (Roediger, 1997). Obviously, this finding has direct relevance for improving the long-term learning of certain kinds of information. Research has also indicated that the mind is not just a passive recorder of events, rather, it is actively at work both in storing and in recalling information. There is research demonstrating that when a series of events are presented in a random sequence, people reorder them into sequences that make sense when they try to recall them (Lichtenstein and Brewer, 1980). The phenomenon of the active brain is dramatically illustrated further by the fact that the mind can “remember” things that actually did not happen. In one example (Roediger, 1997), people are first given lists of words: sourcandy-sugar-bitter-good-taste-tooth-knife-honey-photo-chocolate-heart-caketart-pie. During the later recognition phase, subjects are asked to respond “yes” or “no” to questions of whether a particular word was on the list. With high frequency and high reliability, subjects report that the word “sweet” was on the list. That is, they “remember” something that is not correct. The finding illustrates the active mind at work using inferencing processes to relate events. People “remember” words that are implied but not stated with the same probability as learned words. In an act of efficiency and “cognitive economy” (Gibson, 1969), the mind creates categories for processing information. Thus, it is a feature of learning that memory processes make relational links to other information. In view of the fact that experience alters brain structures and that spe-of Sciences. All rights reserved. MIND AND BRAIN 125 cific experiences have specific effects on the brain, the nature of “experience” becomes an interesting question in relation to memory processes. For example, when children are asked if a false event has ever occurred (as verified by their parents), they will correctly say that it never happened to them (Ceci, 1997). However, after repeated discussions around the same false events spread over time, the children begin to identify these false events as true occurrences. After about 12 weeks of such discussions, children give fully elaborated accounts of these fictitious events, involving parents, siblings, and a whole host of supporting “evidence.” Repeating lists of words with adults similarly reveals that recalling non-experienced events activates the same regions of the brain as events or words that were directly experienced (Schacter, 1997). Magnetic resonance imaging also shows that the same brain areas are activated during questions and answers about both true and false events. This may explain why false memories can seem so compelling to the individual reporting the events. In sum, classes of words, pictures, and other categories of information that involve complex cognitive processing on a repeated basis activate the brain. Activation sets into motion the events that are encoded as part of long-term memory. Memory processes treat both true and false memory events similarly and, as shown by imaging technologies, activate the same brain regions, regardless of the validity of what is being remembered. Experience is important for the development of brain structures, and what is registered in the brain as memories of experiences can include one’s own mental activities. These points about memory are important for understanding learning and can explain a good deal about why experiences are remembered well or poorly. Particularly important is the finding that the mind imposes structure on the information available from experience. This parallels descriptions of the organization of information in skilled performance discussed in Chapter 3: one of the primary differences between the novice and the expert is the manner in which information is organized and utilized. From the perspective of teaching, it again suggests the importance of an appropriate overall framework within which learning occurs most efficiently and effectively (see evidence discussed in Chapters 3 and 4). Overall, neuroscience research confirms the important role that experience plays in building the structure of the mind by modifying the structures of the brain: development is not solely the unfolding of preprogrammed patterns. Moreover, there is a convergence of many kinds of research on some of the rules that govern learning. One of the simplest rules is that practice increases learning; in the brain, there is a similar relationship between the amount of experience in a complex environment and the amount of structural change. (loc: 2259-96)

There is growing evidence that both the developing and the mature brain are structurally altered when learning occurs. Thus, these structural changes are believed to encode the learning in the brain. Studies have found alterations in the weight and thickness of the cerebral cortex of rats that had direct contact with a stimulating physical environment and an interactive social group. Subsequent work has revealed underlying changes in the structure of nerve cells and of the tissues that support their function. The nerve cells have a greater number of the synapses through which they communicate with each other. The structure of the nerve cells themselves is correspondingly altered. Under at least some conditions, both astrocytes that provide support to the neurons and the capillaries that supply blood may also be altered. The learning of specific tasks appears to alter the specific regions of the brain involved in the task. These findings suggest that the brain is a dynamic organ, shaped to a great extent by experience—by what a living being does, and has done. (loc: 2298-2306)

In addition, the brain “creates” informational experiences through mental activities such as inferencing, category formation, and so forth. (loc: 2319-20)

Today, students need to understand the current state of their knowledge and to build on it, improve it, and make decisions in the face of uncertainty (Talbert and McLaughlin, 1993). These two notions of knowledge were identified by John Dewey (1916) as “records” of previous cultural accomplishments and engagement in active processes as represented by the phrase “to do.” For example, doing mathematics involves solving problems, abstracting, inventing, proving (see, e.g., Romberg, 1983). Doing history involves the construction and evaluation of historical documents (see, e.g., Wineberg, 1996). Doing science includes such activities as testing theories (loc: 2357-61)

We use the term “learner centered” to refer to environments that pay careful attention to the knowledge, skills, attitudes, and beliefs that learners bring to the educational setting. (loc: 2380-81)

have been called “culturally responsive,” “culturally appropriate,” “culturally compatible,” and “culturally relevant” (Ladson-Billings, 1995). The term also fits the concept of “diagnostic teaching” (Bell et al., 1980): attempting to discover what students think in relation to the problems on hand, discussing their misconceptions sensitively, and giving them situations to go on thinking about which will enable them to readjust their ideas (Bell, 1982a:7). (loc: 2384-88)

Diagnostic teaching provides an example of starting from the structure of a child’s knowledge. The information on which to base a diagnosis may be acquired through observation, questioning and conversation, and reflection on the products of student activity. A key strategy is to prompt children to explain and develop their knowledge structures by asking them to make predictions about various situations and explain the reasons for their predictions. By selecting critical tasks that embody known misconceptions, teachers can help students test their thinking and see how and why various ideas might need to change (Bell, 1982a, b, 1985; Bell et al., 1986; Bell and Purdy, 1985). The model is one of engaging students in cognitive conflict and then having discussions about conflicting viewpoints (see Piaget, 1973; Festinger, 1957). “To promote learning, it is important to focus on controlled changes of Sciences. All rights reserved. THE DESIGN OF LEARNING ENVIRONMENTS 135 of structure in a fixed context … or on deliberate transfer of a structure from one context to another” (Bell, 1985:72; see Chapter 7). (loc: 2389-97)

Learnercentered teachers also respect the language practices of their students because they provide a basis for further learning. (loc: 2402-3)

the ability of experts to think and solve problems is not simply due to a generic set of “thinking skills” or strategies but, instead, requires well-organized bodies of knowledge that support planning and strategic thinking. Knowledge-centered environments take seriously the need to help students become knowledgeable (Bruner, 1981) by learning in ways that lead to understanding and subsequent transfer. Current knowledge on learning and transfer (Chapter 3) and development (Chapter 4) provide important guidelines for achieving these goals. Standards in areas such as mathematics and science help define the knowledge and competencies that students need to acquire (e.g., American Association for the Advancement of Science, 1989; National Council of Teachers of Mathematics, 1989; National Research Council, 1996). Knowledge-centered environments intersect with learnercentered environments when instruction begins with a concern for students’ initial preconceptions about the subject matter. (loc: 2426-32)

There are interesting new approaches to the development of curricula that support learning with understanding and encourage sense making. One is “progressive formalization,” which begins with the informal ideas that students bring to school and gradually helps them see how these ideas can be transformed and formalized. Instructional units encourage students to build on their informal ideas in a gradual but structured manner so that they acquire the concepts and procedures of a discipline. The idea of progressive formalization is exemplified by the algebra strand for middle school students using Mathematics in Context (National Center for Research in Mathematical Sciences Education and Freudenthal Institute, 1997). It begins by having students use their own words, pictures, or diagrams to describe mathematical situations to organize their own knowledge and work and to explain their strategies. In later units, students gradually begin to use symbols to describe situations, organize their mathematical work, or express their strategies. At this level, students devise their own symbols or learn some nonconventional notation. Their representations of problem situations and explanations of their work are a mixture of words and symbols. Later, students learn and use standard conventional algebraic notation for writing expressions and equations, for manipulating algebraic expressions and solving equations, and for graphing equations. Movement along this continuum is not necessarily smooth, nor all in one direction. (loc: 2449-59)

Central to curriculum frameworks such as “progressive formalization” are questions about what is developmentally appropriate to teach at various ages. Such questions represent another example of overlap between learnercentered and knowledge-centered perspectives. Older views that young children are incapable of complex reasoning have been replaced by evidence that children are capable of sophisticated levels of thinking and reasoning when they have the knowledge necessary to support these activities (see Chapter 4). An impressive body of research shows the potential benefit of early access by students to important conceptual ideas. In classrooms using a form of “cognitively guided” instruction in geometry, second-grade children’s skills for representing and visualizing three-dimensional forms exceeded those of comparison groups of undergraduate students at a leading university (Lehrer and Chazan, 1998). (loc: 2463-70)

An alternative to a “rutted path” curriculum is one of “learning the landscape” (Greeno, 1991). In this metaphor, learning is analogous to learning of Sciences. All rights reserved. THE DESIGN OF LEARNING ENVIRONMENTS 139 to live in an environment: learning your way around, learning what resources are available, and learning how to use those resources in conducting your activities productively and enjoyably (Greeno, 1991:175). (loc: 2480-84)

A challenge for the design of knowledge-centered environments is to strike the appropriate balance between activities designed to promote understanding and those designed to promote the automaticity of skills necessary to function effectively without being overwhelmed by attentional requirements. Students for whom it is effortful to read, write, and calculate can encounter serious difficulties learning. The importance of automaticity has been demonstrated in a number of areas (e.g., Beck et al., 1989, 1991; Hasselbring et al., 1987; LaBerge and Samuels, 1974; see Chapter 2). (loc: 2496-2500)

Effective teachers also help students build skills of selfassessment. Students learn to assess their own work, as well as the work of their peers, in order to help everyone learn more effectively (see, e.g., Vye et al., 1998a, b). (loc: 2519-21)

Feedback is most valuable when students have the opportunity to use it to revise their thinking as they are working on a unit or project. The addition of opportunities for formative assessment increases students’ learning and transfer, and they learn to value opportunities to revise (Barron et al., 1998; Black and William, 1998; Vye et al., 1998b). Opportunities to work collaboratively in groups can also increase the quality of the feedback available to students (Barron, 1991; Bereiter and Scardamalia, 1989; Fuchs et al., 1992; Johnson and Johnson, 1975; Slavin, 1987; Vye et al., 1998a), although many students must be helped to learn how to work collaboratively. New (loc: 2526-30)

Even without technology, however, advances have been made in devising simple assessments that measure understanding rather than memorization. In the area of physics, assessments like those used in Chapter 2 to compare experts and novices have been revised for use in classrooms. One task presents students with two problems and asks them to state whether both would be solved using a similar approach and state the reason for the decision: 1. A 2.5-kilogram ball with a radius of 4 centimeters is traveling at 7 meters/second on a rough horizontal surface, but not spinning. At some later time, the ball is rolling without slipping 5 meters/second. How much work was done by friction? 2. A 0.5-kilogram ball with a radius of 15 centimeters is initially sliding at 10 meters/second without spinning. The ball travels on a horizontal surface and eventually rolls without slipping. Find the ball’s final velocity. Novices typically state that these two problems are solved similarly because they match on surface features—both involve a ball sliding and rolling on a horizontal surface. Students who are learning with understanding state that the problems are solved differently: the first can be solved by applying the work-energy theorem; the second can be solved by applying conservation of angular momentum (Hardiman et al., 1989); see Box 6.2. These kinds of assessment items can be used during the course of instruction to monitor the depth of conceptual understanding. Portfolio assessments are another method of formative assessment. They provide a format for keeping records of students’ work as they progress throughout the year and, most importantly, for allowing students to discuss their achievements and difficulties with their teachers, parents, and fellow students (e.g., Wiske, 1997; Wolf, 1988). They take time to implement and they are often implemented poorly—portfolios often become simply another place to store student work but no discussion of the work takes place— but used properly, they provide students and others with valuable information about their learning progress over time. (loc: 2545-59)

A challenge for the learning sciences is to provide a theoretical framework that links assessment practices to learning theory. An important step in this direction is represented by the work of Baxter and Glaser (1997), who (loc: 2560-61)

provide a framework for integrating cognition and context in assessing achievement in science. In their report, performance is described in terms of the content and process task demands of the subject matter and the nature and extent of cognitive activity likely to be observed in a particular assessment situation. The framework provides a basis for examining how developers’ intentions are realized in performance assessments that purport to measure reasoning, understanding, and complex problem solving. Characterizing assessments in terms of components of competence and the content-process demands of the subject matter brings specificity to generic assessment objectives such as “higher level thinking and deep understanding.” Characterizing student performance in terms of cognitive activities focuses attention on the differences in competence and subject-matter achievement that can be observed in learning and assessment situations. The kind and quality of cognitive activities in an assessment is a function of the content and process demands of the task involved. (loc: 2571-79)

knowledge are conceptualized on a continuum from rich to lean (y axis). At one extreme are knowledge-rich tasks, tasks that require indepth understanding of subject matter for their completion. At the other extreme are tasks that are not dependent on prior knowledge or related experiences; rather, performance is primarily dependent on the information given in the assessment situation. The task demands for process skills are conceptualized as a continuum from constrained to open (x axis). In open situations, explicit directions are minimized; students are expected to generate and carry out appropriate process skills for problem solution. In process-constrained situations, directions can be of two types: step-by-step, subjectspecific procedures given as part of the task, or directions to explain the process skills that are necessary for task completion. In this situation, students are asked to generate explanations, an activity that does not require using the process skills. Assessment tasks can involve many possible combinations of content knowledge and process skills; Table 6.1 illustrates the relationship between the structure of knowledge and the organized cognitive activities. (loc: 2583-91)

Talking in Class A speech-language pathologist working in an Inuit school (in northern Canada) asked a principal—who was not an Inuit—to compile a list of children who had speech and language problems in the school. The list contained a third of the students in the school, and next to several names the principal wrote, “Does not talk in class.” The speech-language pathologist consulted a local Inuit teacher for help determining how each child functioned in his or her native language. She looked at the names and said, “Well-raised Inuit children should not talk in class. They should be learning by looking and listening.” When the speech-language pathologist asked that teacher about one toddler she was studying who was very talkative and seemed to the non-Inuit researcher to be very bright, the teacher said: “Do you think he might have a learning problem? Some of these children who don’t have such high intelligence have trouble stopping themselves. They don’t know when to stop talking” (Crago, 1988:219). (loc: 2613-20)

Discussion in Chapter 2 also differentiated between expertise in a discipline and the ability to help others learn about that discipline. To use Shulman’s (1987) language, effective teachers need pedagogical content knowledge (knowledge about how to teach in particular disciplines) rather than only knowledge of a particular subject matter. Pedagogical content knowledge is different from knowledge of general teaching methods. Expert teachers know the structure of their disciplines, and this knowledge provides them with cognitive roadmaps that guide the assignments they give students, the assessments they use to gauge students’ progress, and the questions they ask in the give and take of classroom life. In short, their knowledge of the discipline and their knowledge of pedagogy interact. But knowledge of the discipline structure does not in itself guide the teacher. For example, expert teachers are sensitive to those aspects of the discipline that are especially hard or easy for new students to master. (loc: 2788-95)

Consider the case of Barb Johnson, who has been a sixthgrade teacher for 12 years at Monroe Middle School. By conventional standards Monroe is a good school. Standardized test scores are about average, class size is small, the building facilities are well maintained, the administrator is a strong instructional leader, and there is little faculty and staff turnover. However, every year parents sending their fifth-grade students from the local elementary schools to Monroe jockey to get their children assigned to Barb Johnson’s classes. What happens in her classroom that gives it the reputation of being the best of the best? During the first week of school Barb Johnson asks her sixth graders two questions: “What questions do you have about yourself?” and “What questions do you have about the world?” The students begin enumerating their questions, “Can they be about silly, little things?” asks one student. “If they’re your questions that you really want answered, they’re neither silly nor little,” replies the teacher. After the students list their individual questions, Barb organizes the students into small groups where they share lists and search for questions they have in common. After much discussion each group comes up with a priority list of questions, rank-ordering the questions about themselves and those about the world. Back together in a whole group session, Barb Johnson solicits the groups’ priorities and works toward consensus for the class’s combined lists of questions. These questions become the basis for guiding the curriculum in Barb’s class. One question, “Will I live to be 100 years old?” spawned educational investigations into genetics, family and oral history, actuarial science, statistics and probability, heart disease, cancer, and hypertension. The students had the opportunity to seek out information from family members, friends, experts in various fields, on-line computer services, and books, as well as from the teacher. She describes what they had to do as becoming part of a “learning community.” According to Barb Johnson, “We decide what are the most compelling intellectual issues, devise ways to investigate those issues of Sciences. All rights reserved. EFFECTIVE TEACHING: EXAMPLES IN HISTORY, MATHEMATICS, AND SCIENCE 157 and start off on a learning journey. Sometimes we fall short of our goal. Sometimes we reach our goal, but most times we exceed these goals—we learn more than we initially expected” (personal communication). At the end of an investigation, Barb Johnson works with the students to help them see how their investigations relate to conventional subject-matter areas. They create a chart on which they tally experiences in language and literacy, mathematics, science, social studies and history, music, and art. Students often are surprised at how much and how varied their learning is. Says one student, “I just thought we were having fun. I didn’t realize we were learning, too!” Barb Johnson’s teaching is extraordinary. It requires a wide range of disciplinary knowledge because she begins with students’ questions rather than with a fixed curriculum. Because of her extensive knowledge, she can map students’ questions onto important principles of relevant disciplines. It would not work to simply arm new teachers with general strategies that mirror how she teaches and encourage them to use this approach in their classrooms. Unless they have the relevant disciplinary knowledge, the teachers and the classes would quickly become lost. At the same time, disciplinary knowledge without knowledge about how students learn (i.e., principles consistent with developmental and learning psychology) and how to lead the processes of learning (i.e., pedagogical knowledge) would not yield the kind of learning seen in Barb Johnson’s classes (Anderson and Smith, 1987). (loc: 2802-29)

For expert history teachers, their knowledge of the discipline and beliefs about its structure interact with their teaching strategies. Rather than simply introduce students to sets of facts to be learned, these teachers help people to understand the problematic nature of historical interpretation and analysis and to appreciate the relevance of history for their everyday lives. One example of outstanding history teaching comes form the classroom of Bob Bain, a public school teacher in Beechwood, Ohio. Historians, he notes, are cursed with an abundance of data—the traces of the past threaten to overwhelm them unless they find some way of separating what is important from what is peripheral. The assumptions that historians hold about significance shape how they write their histories, the data they select, and the narrative they compose, as well as the larger schemes they bring to organize and periodize the past. Often these assumptions about historical significance remain unarticulated in the classroom. This contributes to students’ beliefs that their textbooks are the history rather than a history. Bob Bain begins his ninth-grade high school class by having all the students create a time capsule of what they think are the most important artifacts from the past. The students’ task, then, is to put down on paper why they chose the items they did. In this way, the students explicitly articulate their underlying assumptions of what constitutes historical significance. Students’ responses are pooled, and he writes them on a large poster that he hangs on the classroom wall. This poster, which Bob Bain calls “Rules for Determining Historical Significance,” becomes a lightening rod for class discussions throughout the year, undergoing revisions and elaborations as students become better able to articulate their ideas. At first, students apply the rules rigidly and algorithmically, with little understanding that just as they made the rules, they can also change them. But as students become more practiced in plying their judgments of significance, they come to see the rules as tools for assaying the arguments of different historians, which allows them to begin to understand why historians disagree. In this instance, the students’ growing ability to understand the interpretative nature of history is aided by their teacher’s deep understanding of a fundamental principle of the discipline. Leinhardt and Greeno (1991, 1994) spent 2 years studying a highly accomplished teacher of advanced placement history in an urban high school in Pittsburgh. The teacher, Ms. Sterling, a veteran of over 20 years, began her school year by having her students ponder the meaning of the statement, “Every true history is contemporary history.” In the first week of the semester, Sterling thrust her students into the kinds of epistemological issues that one might find in a graduate seminar: “What is history?” “How do we know the past?” “What is the difference between someone who sits down (loc: 2857-77)

`write history’ and the artifacts that are produced as part of ordinary experience?” The goal of this extended exercise is to help students understand history as an evidentiary form of knowledge, not as clusters of fixed names and dates. One might wonder about the advisability of spending 5 days “defining history” in a curriculum with so much to cover. But it is precisely Sterling’s framework of subject-matter knowledge—her overarching understanding of the discipline as a whole—that permits students entry into the advanced world of historical sensemaking. By the end of the course, students moved from being passive spectators of the past to enfranchised agents who could participate in the forms of thinking, reasoning, and engagement that are the hallmark of skilled historical cognition. For example, early in the school year, Ms. Sterling asked her students a question about the Constitutional Convention and “what were men able to do.” Paul took the question literally: “Uh, I think one of the biggest things that they did, that we talked about yesterday, was the establishment of the first settlements in the Northwest (loc: 2889-97)

area states.” But after 2 months of educating students into a way of thinking about history, Paul began to catch on. By January his responses to questions about the fall of the cotton-based economy in the South were linked to British trade policy and colonial ventures in Asia, as well as to the failure of Southern leaders to read public opinion accurately in Great Britain. Ms. Sterling’s own understanding of history allowed her to create a classroom in which students not only mastered concepts and facts, but also used them in authentic ways to craft historical explanations. Debating the Evidence Elizabeth Jensen prepares her group of eleventh graders to debate the following resolution: Resolved: The British government possesses the legitimate authority to tax the American colonies. (loc: 2906-12)

As her students enter the classroom they arrange their desks into three groups—on the left of the room a group of “rebels,” on the right, a group of “loyalists,” and in the front, a group of “judges.” Off to the side with a spiral notebook on her lap sits Jensen, a short woman in her late 30s with a booming voice. But today that voice is silent as her students take up the question of the legitimacy of British taxation in the American colonies. The rebels’ first speaker, a 16-year-old girl with a Grateful Dead T-shirt and one dangling earring, takes a paper from her notebook and begins: England says she keeps troops here for our own protection. On face value, this seems reasonable enough, but there is really no substance to their claims. First of all, who do they think they are protecting us from? The French? Quoting from our friend Mr. Bailey on page 54, `By the settlement in Paris in 1763, French power was thrown completely off the continent of North America.’ Clearly not the French then. Maybe they need to protect us from the Spanish? Yet the same war also subdued the Spanish, so they are no real worry either. In fact, the only threat to our order is the Indians … but … we have a decent militia of our own… . So why are they putting troops here? The only possible reason is to keep us in line. With more and more troops coming over, soon every freedom we hold dear will be stripped away. The great irony is that Britain expects us to pay for these vicious troops, these British squelchers of colonial justice. A loyalist responds: We moved here, we are paying less taxes than we did for two generations in England, and you complain? Let’s look at why we are being taxed— the main reason is probably because England has a debt of Ł140,000,000… . This sounds a little greedy, I mean what right do they have to take our money simply because they have the power over us. But did you know that over one-half of their war debt was caused by defending us in the French and Indian War… . Taxation without representation isn’t fair. Indeed, it’s tyranny. Yet virtual representation makes this whining of yours an untruth. Every British citizen, whether he had a right to vote or not, is represented in Parliament. Why does this representation not extend to America? A rebel questions the loyalist about this: Rebel: What benefits do we get out of paying taxes to the crown? Loyalist: We benefit from the protection. Rebel: (cutting in) Is that the only benefit you claim, protection? Loyalist: Yes—and all the rights of an Englishman. Rebel: Okay, then what about the Intolerable Acts … denying us rights of British subjects. What about the rights we are denied? Loyalist: The Sons of Liberty tarred and feather people, pillaged homes— they were definitely deserving of some sort of punishment. Rebel: So should all the colonies be punished for the acts of a few colonies? (loc: 2913-34)

For a moment, the room is a cacophony of charges and countercharges. “It’s the same as in Birmingham,” shouts a loyalist. A rebel snorts disparagingly, “Virtual representation is bull.” Thirty-two students seem to be talking at once, while the presiding judge, a wiry student with horn-rimmed glasses, bangs his gavel to no avail. The teacher, still in the corner, still with spiral notebook in lap, issues her only command of the day. “Hold still!” she thunders. Order is restored and the loyalists continue their opening argument (from Wineburg and Wilson, 1991). Another example of Elizabeth Jensen’s teaching involves her efforts to help her high school students understand the debates between Federalists and anti-Federalists. She knows that her 15-and 16-year-olds cannot begin to grasp the complexities of the debates without first understanding that these disagreements were rooted in fundamentally different conceptions of human nature—a point glossed over in two paragraphs in her history textbook. Rather than beginning the year with a unit on European discovery and exploration, as her text dictates, she begins with a conference on the nature of man. Students in her eleventh-grade history class read excerpts from the writings of philosophers (Hume, Locke, Plato, and Aristotle), leaders of state and revolutionaries (Jefferson, Lenin, Gandhi), and tyrants (Hitler, Mussolini), presenting and advocating these views before their classmates. Six weeks later, when it is time to study the ratification of the Constitution, these now-familiar figures—Plato, Aristotle, and others—are reconvened to be courted by impassioned groups of Federalists and anti-Federalists. It is Elizabeth Jensen’s understanding of what she wants to teach and what adolescents already know that allows her to craft an activity that helps students get a feel for the domain that awaits them: decisions about rebellion, the Constitution, federalism, slavery, and the nature of a government. Conclusion These examples provide glimpses of outstanding teaching in the discipline of history. The examples do not come from “gifted teachers” who know how to teach anything: they demonstrate, instead, that expert teachers have a deep understanding of the structure and epistemologies of their disciplines, combined with knowledge of the kinds of teaching activities that will help students come to understand the discipline for themselves. As we previously noted, this point sharply contradicts one of the popular—and dangerous—myths about teaching: teaching is a generic skill and a good teacher can teach any subject. Numerous studies demonstrate that any curriculum—including a textbook—is mediated by a teacher’s understanding of the subject domain (for history, see Wineburg and Wilson, 1988; for math, see Ball, 1993; for English, see Grossman et al., 1989). (loc: 2935-55)

Teachers, it is claimed, will use their knowledge to make appropriate instructional decisions to assist students to construct their mathematical knowledge. In this approach, the idea of domains of knowledge for teaching (Shulman, 1986) is extended to include teachers’ knowledge of individual learners in their classrooms. Cognitively guided instruction is used by Annie Keith, who teaches a combination first-and second-grade class in an elementary school in Madison Wisconsin (Hiebert et al., 1997). Her instructional practices are an example of what is possible when a teacher understands children’s thinking and uses that understanding to guide her teaching. A portrait of Ms. Keith’s classroom reveals also how her knowledge of mathematics and pedagogy influence her instructional decisions. Word problems form the basis for almost all instruction in Annie Keith’s classroom. Students spend a great deal of time discussing alternative strategies with each other, in groups, and as a whole class. The teacher often participates in these discussions but almost never demonstrates the solution to problems. Important ideas in mathematics are developed as students explore solutions to problems, rather than being a focus of instruction per se. For example, place-value concepts are developed as students use base10 materials, such as base-10 blocks and counting frames, to solve word problems involving multidigit numbers. Mathematics instruction in Annie Keith’s class takes place in a number of different settings. Everyday first-grade and second-grade activities, such as sharing snacks, lunch count, and attendance, regularly serve as contexts for problemsolving tasks. Mathematics lessons frequently make use of math centers in which the students do a variety of activities. On any given day, children at one center may solve word problems presented by the teacher while at another center children write word problems to present to the class later or play a math game. She continually challenges her students to think and to try to make sense of what they are doing in math. She uses the activities as opportunities for her to learn what individual students know and understand about mathematics. As students work in groups to solve problems, she observes the various solutions and mentally makes notes about which students should present their work: she wants a variety of solutions presented so that students will have an opportunity to learn from each other. Her knowledge of the important ideas in mathematics serves as one framework for the selection process, but her understanding of how children think about the mathematical ideas they are using also affects her decisions about who should present. She might select a solution that is actually incorrect to be presented so that she can initiate a discussion of a common misconception. Or she of Sciences. All rights reserved. 170 HOW PEOPLE LEARN, EXPANDED EDITION may select a solution that is more sophisticated than most students have used in order to provide an opportunity for students to see the benefits of such a strategy. Both the presentations of solutions and the class discussions that follow provide her with information about what her students know and what problems she should use with them next. Annie Keith’s strong belief that children need to construct their understanding of mathematical ideas by building on what they already know guides her instructional decisions. She forms hypotheses about what her students understand and selects instructional activities based on these hypotheses. She modifies her instruction as she gathers additional information about her students and compares it with the mathematics she wants them to learn. Her instructional decisions give her clear diagnoses of individual students’ current state of understanding. Her approach is not a free-for-all without teacher guidance: rather, it is instruction that builds on students’ understandings and is carefully orchestrated by the teacher, who is aware of what is mathematically important and also what is important to the learner’s progress. (loc: 3057-85)

students to organize their knowledge is as important as the knowledge itself, since knowledge organization is likely to affect students’ intellectual performance. These examples demonstrate the importance of deliberate practice and of having a “coach” who provides feedback for ways of optimizing performance (see Chapter 3). If students had simply been given problems to solve on their own (an instructional practice used in all the sciences), it is highly unlikely that they would have spent time efficiently. Students might get stuck for minutes, or even hours, in attempting a solution to a problem and either give up or waste lots of time. In Chapter 3, we discussed ways in which learners profit from errors and that making mistakes is not always time wasted. However, it is not efficient if a student spends most of the problemsolving time rehearsing procedures that are not optimal for promoting skilled performance, such as finding and manipulating equations to solve the problem, rather than identifying the underlying principle and procedures that apply to the problem and then constructing the specific equa-of (loc: 3208-16)

In deliberate practice, a student works under a tutor (human or computer based) to rehearse appropriate practices that enhance performance. Through deliberate practice, computer-based tutoring environments have been designed that reduce the time it takes individuals to reach realworld performance criteria from 4 years to 25 hours (see Chapter 9)! (loc: 3224-26)

Another effective strategy for helping students overcome persistent erroneous beliefs are interactive lecture demonstrations (Sokoloff and Thornton, 1997; Thornton and Sokoloff, 1997). This strategy, which has been used very effectively in large introductory college physics classes, begins with an introduction to a demonstration that the instructor is about to perform, such as a collision between two air carts on an air track, one a stationary light cart, the other a heavy cart moving toward the stationary cart. Each cart has an electronic “force probe” connected to it which displays on a large screen and in real-time the force acting on it during the collision. The teacher first asks the students to discuss the situation with their neighbors and then record a prediction as to whether one of the carts would exert a bigger force on the other during impact or whether the carts would exert equal forces. The vast majority of students incorrectly predict that the heavier, moving cart exerts a larger force on the lighter, stationary cart. Again, this prediction seems quite reasonable based on experience—students know that a moving of Sciences. All rights reserved. 180 HOW PEOPLE LEARN, EXPANDED EDITION Mack truck colliding with a stationary Volkswagen beetle will result in much more damage done to the Volkswagen, and this is interpreted to mean that the Mack truck must have exerted a larger force on the Volkswagen. Yet, notwithstanding the major damage to the Volkswagen, Newton’s Third Law states that two interacting bodies exert equal and opposite forces on each other. After the students make and record their predictions, the instructor performs the demonstration, and the students see on the screen that the force probes record forces of equal magnitude but oppositely directed during the collision. Several other situations are discussed in the same way: What if the two carts had been moving toward each other at the same speed? What if the situation is reversed so that the heavy cart is stationary and the light cart is moving toward it? Students make predictions and then see the actual forces between the carts displayed as they collide. In all cases, students see that the carts exert equal and opposite forces on each other, and with the help of a discussion moderated by the instructor, the students begin to build a consistent view of Newton’s Third Law that incorporates their observations and experiences. Consistent with the research on providing feedback (see Chapter 3), there is other research that suggests that students’ witnessing the force displayed in real-time as the two carts collide helps them overcome their misconceptions; delays of as little as 20-30 minutes in displaying graphic data of an event occurring in real-time significantly inhibits the learning of the underlying concept (Brasell, 1987). Both bridging and the interactive demonstration strategies have been shown to be effective at helping students permanently overcome misconceptions. This finding is a major breakthrough in teaching science, since so much research indicates that students often can parrot back correct answers on a test that might be erroneously interpreted as displaying the eradication of a misconception, but the same misconception often resurfaces when students are probed weeks or months later (see Mestre, 1994, for a review). (loc: 3241-64)

Teaching as Coaching One of the best examples of translating research into practice is Minstrell’s (1982, 1989, 1992) work with high school physics students. Minstrell uses many researchbased instructional techniques (e.g., bridging, making students’ thinking visible, facilitating students’ ability to restructure their own knowledge) to teach physics for understanding. He does this through classroom discussions in which students construct understanding by making sense of physics concepts, with Minstrell playing a coaching role. The following quote exemplifies his innovative and effective instructional strategies (Minstrell, 1989:130-131): of Sciences. All rights reserved. EFFECTIVE TEACHING: EXAMPLES IN HISTORY, MATHEMATICS, AND SCIENCE 181 Students’ initial ideas about mechanics are like strands of yarn, some unconnected, some loosely interwoven. The act of instruction can be viewed as helping the students unravel individual strands of belief, label them, and then weave them into a fabric of more complete understanding. An important point is that later understanding can be constructed, to a considerable extent, from earlier beliefs. Sometimes new strands of belief are introduced, but rarely is an earlier belief pulled out and replaced. Rather than denying the relevancy of a belief, teachers might do better by helping students differentiate their present ideas from and integrate them into conceptual beliefs more like those of scientists. Describing a lesson on force, Minstrell (1989:130-131) begins by introducing the topic in general terms: Today we are going to try to explain some rather ordinary events that you might see any day. You will find that you already have many good ideas that will help explain those events. We will find that some of our ideas are similar to those of the scientist, but in other cases our ideas might be different. When we are finished with this unit, I expect that we will have a much clearer idea of how scientists explain those events, and I know that you will feel more comfortable about your explanations … A key idea we are going to use is the idea of force. What does the idea of force mean to you? Many views emerge from the ensuing classroom discussion, from the typical “push or pull” to descriptions that include sophisticated terms, such as energy and momentum. At some point Minstrell guides the discussion to a specific example: he drops a rock and asks students how the event can be explained using their ideas about force. He asks students to individually formulate their ideas and to draw a diagram showing the major forces on the rock as arrows, with labels to denote the cause of each force. A lengthy discussion follows in which students present their views, views that contain many irrelevant (e.g., nuclear forces) or fictitious forces (e.g., the spin of the earth, air). In his coaching, Minstrell asks students to justify their choices by asking questions, such as “How do you know?” “How did you decide?” “Why do you believe that?” With this approach, Minstrell has been able to identify many erroneous beliefs of students that stand in the way of conceptual understanding. One example is the belief that only active agents (e.g., people) can exert forces, that passive agents (e.g., a table) cannot. Minstrell (1992) has developed a framework that helps both to make sense of students’ reasoning and to design instructional strategies. (For a related theoretical framework for classifying and explaining student reasoning, see the discussion of “phenomenological primitives” in DiSessa, 1988, 1993.) Minstrell describes identifiable pieces of students’ knowledge as “facets,” a facet being a convenient unit of thought, a piece of knowledge, or a strategy seemingly used by the student in addressing a particular situation. Facets may relate to conceptual of Sciences. All rights reserved. 182 HOW PEOPLE LEARN, EXPANDED EDITION knowledge (e.g., passive objects do not exert force), to strategic knowledge (e.g., average velocity can be determined by adding the initial and final velocities and dividing by two), or generic reasoning (e.g., the more the X, the more the Y). Identifying students’ facets, what cues them in different contexts, and how students use them in reasoning are all helpful in devising instructional strategies. (loc: 3264-96)

One of the obstacles to instructional innovation in large introductory science courses at the college level is the sheer number of students who are taught at one time. How does an instructor provide an active learning experience, provide feedback, accommodate different learning styles, make students’ thinking visible, and provide scaffolding and tailored instruction to meet specific student needs when facing more than 100 students at a time? Classroom communication systems can help the instructor of a large class accomplish these objectives. One such system, called Classtalk, consists of both hardware and software that allows up to four students to share an input device (e.g., a fairly inexpensive graphing calculator) to “sign on” to a classroom communication network that permits the instructor to send questions for students to work on and permits students to enter answers through their input device. Answers can then be displayed anonymously in histogram form to the class, and a permanent record of each student’s response is recorded to help evaluate progress as well as the effectiveness of instruction. This technology has been used successfully at the University of Massachusetts-Amherst to teach physics to a range of students, from non-science majors to engineering and science majors (Dufresne et al., 1996; Wenk et al., 1997; Mestre et al., 1997). The technology creates an interactive learning environment in the lectures: students work collaboratively on conceptual questions, and the histogram of students’ answers is used as a visual springboard for classwide discussions when students defend the reasoning they used to arrive at their answers. This technology makes students’ thinking visible and promotes critical listening, evaluation, and argumentation in the class. The teacher is a coach, providing scaffolding where needed, tailoring “mini-lectures” to clear up points of confusion, or, if things are going well, simply moderating the discussion and allowing students to figure out things and reach consensus on their own. The technology is also a natural mechanism to support formative assessment during instruction, providing both the teacher and students with feedback on how well the class is grasping the concepts under study. The approach accommodates a wider variety of learning styles than is possible by lectures and helps to foster a community of learners focused on common objectives and goals. (loc: 3297-3313)

One fact is clear, however: there are relatively few opportunities available if measured in financial terms. Overall, there is minimal public investment in formal opportunities for professional development for practicing teachers. Most school districts spend only between 1 and 3 percent of their operating budgets for professional development, even with salaries factored in. This lack of investment in personnel is unheard of either in leading corporations or in schools in other countries (Kearns, 1988). (loc: 3488-92)

Four philosophical traditions of practice have dominated teacher education in the twentieth century (Zeichner and Liston, 1990:4): 1. an academic tradition that emphasizes teachers’ knowledge of subject matter and their ability to transform that subject matter to promote student understanding; 2. a social efficiency tradition that emphasizes teachers’ abilities to apply thoughtfully a “knowledge base” about teaching that has been generated through research on teaching; 3. a developmentalist tradition that stresses teachers’ abilities to base their instruction on their direct knowledge of their students—their mental readiness for particular activities; and 4. a social reconstructionist tradition that emphasizes teachers’ abilities to analyze social contexts in terms of their contribution to greater equality, justice, and elevation of the human condition in schooling and society. (loc: 3667-73)

Attempts to use computer technologies to enhance learning began with the efforts of pioneers such as Atkinson and Suppes (e.g., Atkinson, 1968; Suppes and Morningstar, 1968). (loc: 3751-53)

In this chapter we explore how new technologies can be used in five ways: ˇ bringing exciting curricula based on realworld problems into the classroom; ˇ providing scaffolds and tools to enhance learning; ˇ giving students and teachers more opportunities for feedback, reflection, and revision; ˇ building local and global communities that include teachers, administrators, students, parents, practicing scientists, and other interested people; and ˇ expanding opportunities for teacher learning. (loc: 3773-76)

Scaffolded experiences can be structured in different ways. Some research educators advocate an apprenticeship model, whereby an expert practitioner first models the activity while the learner observes, then scaffolds the learner (with advice and examples), then guides the learner in practice, and gradually tapers off support and guidance until the apprentice can do it alone (Collins et al., 1989). Others argue that the goal of enabling a solo approach is unrealistic and overrestrictive since adults often need to use tools or other people to accomplish their work (Pea, 1993b; Resnick, 1987). Some even contend that well-designed technological tools that support complex activities create a truly human-machine symbiosis and may reorganize components of human activity into different structures than they had in pretechnological designs (Pea, 1985). Although there are varying views on of Sciences. All rights reserved. TECHNOLOGY TO SUPPORT LEARNING 215 the exact goals and on how to assess the benefits of scaffolding technologies, there is agreement that the new tools make it possible for people to perform and learn in far more complex ways than ever before. In many fields, experts are using new technologies to represent data in new ways—for example, as three-dimensional virtual models of the surface of Venus or of a molecular structure, either of which can be electronically created and viewed from any angle. Geographical information systems, to take another example, use color scales to visually represent such variables as temperature or rainfall on a map. With these tools, scientists can discern patterns more quickly and detect relationships not previously noticed (e.g., Brodie et al., 1992; Kaufmann and Smarr, 1993). Some scholars assert that simulations and computer-based models are the most powerful resources for the advancement and application of mathematics and science since the origins of mathematical modeling during the Renaissance (Glass and Mackey, 1988; Haken, 1981). The move from a static model in an inert medium, like a drawing, to dynamic models in interactive media that provide visualization and analytic tools is profoundly changing the nature of inquiry in mathematics and science. Students (loc: 3906-22)

Sophisticated tutoring environments that pose problems are also now available and give students feedback on the basis of how experts reason and organize their knowledge in physics, chemistry, algebra, computer programming, history, and economics (see Chapter 2). With this increased understanding has come an interest in: testing theories of expert reasoning by translating them into computer programs, and using computer-based expert systems as part of a larger program to teach novices. Combining an expert model with a student model—the system’s representation of the student’s level of knowledge—and a pedagogical model that drives the system has produced intelligent tutoring systems, which seek to combine the advantages of customized one-on-one tutoring with insights from cognitive research about expert performance, learning processes, and naive reasoning (Lesgold et al., 1990; Merrill et al., 1992). A variety of computer-based cognitive tutors have been developed for algebra, geometry, and LISP programming (Anderson et al., 1995). These cognitive tutors have resulted in a complex profile of achievement gains for the students, depending on the nature of the tutor and the way it is inte-of (loc: 4038-46)

Another example of the tutoring approach is the Sherlock Project, a computer-based environment for teaching electronics troubleshooting to Air Force technicians who work on a complex system involving thousands of parts (e.g., Derry and Lesgold, 1997; Gabrys et al., 1993). A simulation of this complex system was combined with an expert system or coach that offered advice when learners reached impasses in their troubleshooting attempts; and with reflection tools that allowed users to replay their performance and try out possible improvements. In several field tests of techni— (loc: 4062-65)

cians as they performed the hardest realworld troubleshooting tasks, 20 to 25 hours of Sherlock training was the equivalent of about 4 years of on-thejob experience. Not surprisingly, Sherlock has been deployed at several U.S. Air Force bases. Two of the crucial properties of Sherlock are modeled on successful informal learning: learners successfully complete every problem they start, with the amount of coaching decreasing as their skill increases; and learners replay and reflect on their performance, highlighting areas where they could improve, much as a football player might review a game film. (loc: 4078-82)

Intelligent Tutoring in High School Algebra A largescale experiment evaluated the benefits of introducing an intelligent algebra tutoring system into an urban high school setting (Koedinger et al., 1997). An important feature of the project was a collaborative, client-centered design that coordinated the tutoring system with the teachers’ goals and expertise. The collaboration produced the PUMP (Pittsburgh urban mathematics program) curriculum, which focuses on mathematical analyses of realworld situations, the use of computational tools, and on making algebra accessible to all students. An intelligent tutor, PAT (for PUMP Algebra Tutor) supported this curriculum. Researchers compared achievement levels of ninth-grade students in the tutored classrooms (experimental group) with achievement in more traditional algebra classrooms. The results demonstrated strong benefits from the use of PUMP and PAT, which is currently used in 70 schools nationwide.. (loc: 4103-10)

WEBCSILE, an Internet version of the CSILE program described above, is being used to help create teacher communities. (loc: 4151-52)