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6Cognitive Models for Teaching

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Learning Objectives

After studying this chapter you will be able to:

ሁ Define constructivism and explain how it relates to teaching. ሁ Identify some of the conditions that facilitate learning through discovery. ሁ Identify some of the conditions that foster reception learning. ሁ Explain the development of metacognition. ሁ Analyze various approaches to teaching students how to think.

If a little knowledge is dangerous, where is the man who has so much as to be out of danger?

—Thomas Henry Huxley, Science and Culture

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Introduction

Pretest

Determine if the following statements are true or false.

1. Current constructivist theories are similar to Dewey’s ideas about progressive education. (T/F)

2. The discovery approach to teaching involves less teacher involvement than most other approaches. (T/F)

3. Discovery learning avoids going beyond or generalizing the information being learned. (T/F)

4. Cognitive strategies to make students more effective and efficient learners can be taught. (T/F)

5. Only trained teachers may serve as experts in cognitive apprenticeships. (T/F)

Answers can be found at the end of the chapter.

Introduction Decision making, problem solving, analyzing, synthesizing, evaluating, remembering—these are all cognitive (intellectual) activities: Understanding them is the goal of cognitive theories. In this chapter we look at these activities and at what teachers can do to foster them. Also, we examine two cognitive theories: that of Jerome Bruner, which advocates discovery-oriented learning; and David Ausubel’s theory, which supports the methods of direct instruction.

On a nearly perfect day in May when I was in tenth grade, our teacher, Sister Marie-Reine, took us on a field trip.

“It’s all part of progressive education,” she explained as she outlined her plan. We’d leave right after the morning bell, everybody packing a lunch, and we’d go up into the hills behind the lake. The objective of the trip: “We’ll learn something.”

And so, when the sounds of the morning bell had scarcely died down, away we went, laughing and singing and absolutely loving progressive education, as you can imagine, twenty-some 15-year-olds larking about on a May morning instead of sitting at hard school desks like everybody else in the world.

Back and forth, darting here and there, running, jumping, teasing the girls, we scrambled down the cowpaths, knowing not to step where we shouldn’t, laughing, giggling, until—bong-a-bang!—we heard the clanging of the bell Sister Marie-Reine had had the foresight to throw into her bag. And we ran to

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Section 6.1 Progressive Education

gather before her on the edge of the slough so that we could listen to the lesson she would now tell us; such a small price to pay for a day in May almost taken from us, as so many were (and still are) but, at the last minute, given back.

Sister Marie-Reine stood on the edge of the slough, her shoes covered with mud. Streaks of perspiration smeared her cheeks but she grinned triumphantly as she stood there. “What is it? Who can tell me what it is?” she challenged as she raised a gnarled, snakelike yellowy-gold length of vegetable material above her head like some primitive conqueror. What she held was about as thick as my arm, four or five feet long, looking very much like a piece of bleached octopus tentacle.

No one had any idea what it was, even though we knew it had come out of the slough. So we guessed this and that and the other thing until the good sister said, “No, that’s enough guessing, you’re not learning anything just guessing, use your brains.” And right there on the spot she divided us into groups of four or five and gave us our assignment: Find out what this thing is, write a paper, and present it to the class in three weeks.

6.1 Progressive Education In the end, all the groups identified the piece of vegetation that Sister Marie-Reine had sucked out of the muddy slough: It was a chunk of cattail root. Louis Boutin’s group found out because his father knew what it was as soon as he saw it. Augustin Bonneau’s group found out because they put a piece of it in a little box and sent it to the university in Saskatoon, and somebody wrote back and told them what it was and told them all about it. The rest of us found out from somebody in one of the other groups because it’s hard to keep important secrets in small communities. And Martin Pelletier, once he knew it was a cattail root, looked it up in Father Paradis’ encyclopedia so that, when we made our presentations, every group said that there were at least eight species of cattails in the world and that you could eat the root and weave baskets with the plants, and on and on. We all got good marks.

I still remember a little about cattails and their roots and a little about progressive educa- tion. Progressive education was John Dewey’s term for his brand of educational reform. He advocated highly child-centered, discovery-based approaches to education much like what are now termed constructivist approaches. Like progressive education, constructivism is based on a learner- rather than a teacher-oriented view of the teaching–learning process. It emphasizes the importance of learners’ constructing their own information and knowledge.

Constructivist approaches are often contrasted with the methods of direct instruction. These methods are highly teacher-centered because they view the teacher as the primary source of information and knowledge. The attitudes and methods of direct instruction are highly com- patible with behavioristic theories of learning, as well as with the theory of David Ausubel. (Figure 6.1 compares constructivist approaches and direct instruction.)

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Section 6.1 Progressive Education

Constructivist approaches to teaching are directly grounded in beliefs and assumptions that are common to many cognitive theories of learning and development (such as those of Piaget, Vygotsky, and Bruner). We’ll take a look at these common beliefs and assumptions in the fol- lowing sections.

Current Learning Builds on Previous Learning Cognitive approaches to human behavior stress the importance of the learner’s previous knowledge and skills. Unlike behaviorism, which tends to view all learners as initially equal— equally susceptible to the effects of the consequences of behavior—cognitivism emphasizes

Figure 6.1: Direct instruction and constructivist approaches ሁ Educational reform has typically advocated changes that correspond with what is now labeled

constructivism. But the methods of direct instruction have continued to dominate in most schools.

Some descriptive terms

Metaphors of learning

Some approaches to teaching

Models of the teacher

Some associated theories

Direct instruction Constructivism

Teacher-centered Traditional

Old Didactic

Behavioristic

Learner-centered Progressive

New Reflective

Humanistic

Acquisition Participation

Lecturing, telling, showing, directing, guiding, explaining

Discovery learning, cooperative learning,

cognitive apprenticeship, learning styles, problem

solving

Teacher as executive Teacher as director

Teacher as therapist Teacher as liberator

Behavioristic theories such as Skinner’s;

cognitive theories such as Ausubel’s

Cognitive theories such as Piaget’s and Bruner’s; Dewey’s ideas; Maslow’s

theory

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Section 6.1 Progressive Education

that we often derive different meanings from experience. Learners come with different motives, background information, and characteristics (gender, ethnicity, intelligence, person- ality characteristics, and so on). As a result, as learners discover and construct meaning, they often learn different things.

Learning Involves Information Processing Cognitive theories assume that the learner is a processor and not simply a recipient of infor- mation. Accordingly, these theories attempt to analyze learning in terms of what is often labeled “cognitive structure.” At a simple level, cognitive structure is the content of the mind. It includes concepts, relationships that the learner establishes among concepts, and strate- gies used for abstracting concepts and organizing them in long-term memory. This view of the learner as an information processor emphasizes the active rather than the passive nature of learning.

Meaning Depends on Relationships Cognitive theorists maintain that knowledge does not exist in a vacuum but that it depends on relationships.

Consider the following passage:

If it were heavy, they couldn’t go very far. And another problem is that it would be very slow. And they would have to stop to eat and drink quite often. Besides, control could be a problem and you could end up where you didn’t want to go. Of course, the person could try to lead. But usually it would be very hot and how could you cool off ? Also, you couldn’t take that much so it might not be worth all the work. I think it would be much better if they tried something more modern.

If you find this passage confusing and unclear, don’t despair; so does almost everyone else. It’s a frustrating experience because the language is clear and simple, the sentences are short and straightforward, none of the concepts is very difficult—yet the whole thing makes no sense.

Look now at the photo at right.

If you reread the passage now, it makes sense. Why? Simply because the picture provides a framework of relationships for understanding it.

Teaching and Learning Should Stress Relationships and Strategies Cognitive approaches to teaching recognize the importance of relationships among items of information, and emphasize the strategies learners use to derive meaning from experience. Table 6.1 summarizes some of the implications of these approaches.

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Section 6.2 Bruner’s Theory: Discovery Learning

Two theories that reflect these educational applications are those of Jerome Bruner and David Ausubel. Although both are cognitive theories, in one important way, they are dramati- cally different from each other: Bruner advocates a constructivist approach to instruction in the form of discovery learning. In contrast, Ausubel presents a strong case for more direct instruction—for what he terms reception learning rather than discovery.

6.2 Bruner’s Theory: Discovery Learning Learning and perception, explains Bruner, are information-processing activities that reflect our need to simplify and make sense of the environment (Bruner, Goodnow, & Austin, 1956; Bruner, 1973). Essentially, we simplify and make sense of the world by forming concepts (Bruner’s term for concepts is category). We do so by abstracting common elements among events and experiences. From these abstractions, we derive implicit rules that allow us to categorize (conceptualize) the world.

Coding As we form concepts (categories), we discover and invent a wealth of relationships among them. These relationships among concepts define what Bruner calls a coding system. Coding systems are simply metaphors for what is assumed to be a hierarchical arrangement of con- cepts. Thus, our long-term memories—our relatively permanent store of knowledge, strate- gies, impressions, and so on—can be seen as a complex arrangement of categories (concepts) and coding systems.

All school subjects, as well as topics within these subjects, can also be seen as being struc- tured in terms of relationships. To truly learn a subject and be able to think about it, learners need to develop their own mental representations of the important ideas and relationships that define the subject. In other words, they need to develop their own coding systems repre- senting that subject. And according to Bruner, the best way of developing a coding system is to discover it with the guidance of the teacher rather than to have it presented in final form by the teacher (Olson, 2007). (See Figure 6.2 for a graphic illustration of a coding system.)

Table 6.1: Beliefs and assumptions of cognitive explanations of learning

Beliefs/Assumptions Explanations/Implications

Current learning builds on previous learning. Learners aren’t equal; given their different backgrounds and motivation, they often construct different meanings from identical experiences.

Learning involves information processing. Learning is an active process, highly dependent on what the learner already knows.

Meaning involves relationships. Meaning derived (constructed) from experience reflects relationships between previous and new learning.

Teaching and learning should stress relationships and strategies.

The emphasis is on meaningful rather than on rote learning; the objective is to help students learn how to learn, contrasted with simply acquiring isolated bits of information.

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Section 6.2 Bruner’s Theory: Discovery Learning

Discovery Learning in Schools Like Piaget, Bruner believes that learners construct their own notions of reality—that they discover their own meanings (Bruner, 1990). This belief is fundamental to constructivist approaches to teaching. The functions of schools, Bruner insists emphatically, should be to provide conditions that will foster the discovery of relationships. Education, he insists, is a matter of understanding and of meaning-making (Takaya, 2013).

Discovery learning can be defined as the learning that takes place when students are not pre- sented with subject matter in its final form but rather are encouraged to organize it them- selves. This requires that learners discover relationships that exist among items of informa- tion. In Bruner’s theory, discovery is the formation of categories or, more often, the formation of coding systems, which are defined in terms of relationships (similarities and differences) that exist among objects and events.

The most important and most obvious characteristic of a discovery approach to teaching is that it requires less summarizing, explaining, and direct presentation by the teacher than most other methods. However, this does not imply that the teacher ceases to give any guid- ance once the initial problem has been presented. Although learners are encouraged to learn and discover for themselves, teacher guidance during the learning process is critical if learn- ers are to complete their tasks successfully. As Olson (2007) puts it, “discovery is not merely a matter of hacking around until something interesting turns up” (p. 38). Discovery, explains Bruner (2003), comes to those who are best prepared. And, without guidance, most students are not prepared to discover very much at all.

The advantages of a discovery approach, claims Bruner, are that such learning facilitates trans- fer and retention, improves problem-solving ability, and increases motivation. This doesn’t mean that Bruner believes that learners should go around reinventing all they need to know.

Figure 6.2: Example of part of a coding system ሁ Bruner’s metaphor of the coding system assumes that our knowledge can be represented in

hierarchies of relationships.

Consumables

Collected PreparedVegetables FruitMeats

Goat Cow

Beef Turkey Carrot Turnip Milk Water Coffee

Solids Liquids

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Section 6.2 Bruner’s Theory: Discovery Learning

In Olson’s (2007) words, “Children cannot be expected to rediscover the basic principles of nature nor would we want them to. Rather the educational goal is to let them participate in the processes of the sciences and rediscover for themselves the basic ideas of the domain and the excitement that comes with understanding” (p. 39).

Very often, discovery in the classroom takes the form of systematically following logical steps that guide the search for generalizable conclusions, very much as might be done in scientific investigation. The guidance that the “teacher as learning facilitator” provides can be based on the deliberate and systematic application of these steps. Summarized briefly, these involve:

• Formulating and clarifying a question or problem • Collecting examples; making relevant observations • Arriving at hypotheses (intelligent, observation-based guesses) • Devising and conducting tests, experiments, and other observations to confirm or

refute hypotheses • Applying, extending, generalizing, “going beyond” the new information

The case entitled “Making Dew” provides one example of the application of this method of inquiry and problem solving in a discovery-oriented science unit. Keep in mind that although the most obvious illustrations are often in science, these methods can also be used in a variety of other subjects.

C A S E S F R O M T H E C L A S S R O O M : M A K I N G D E W The Place: Tremont Elementary School

The Situation: Mr. Creasy’s eighth-grade science class

The Topic: The formation of dew

Mr. Creasy: So the question is: What causes dew?

Paul: I know. It’s just rain.

Jackie: It’s not. ’Cause there’s dew when there’s no rain.

Mr. Creasy: What’s our method? How do we find out?

Chorus of answers: The scientific method.

Patiently, then, Bob Creasy leads his class through what they have previously established as the steps of the scientific method. Next, they clarify what is meant by “dew,” and stu- dents are charged with collecting relevant real-life observations and facts.

In a later class, they pool their observations and they develop intelligent guesses, or hypotheses, based on these facts (dew falls from the sky; dew comes out of the air; dew comes out of objects themselves). Creasy guides the students so that they make pertinent observations, sometimes devising experiments to do so (dew forms on comparatively cool objects; there is dew on cloudless nights; dew forms even on objects that are initially com- pletely dry).

Eventually students begin to agree on a conclusion (the cooling of moist air by a relatively cool object “squeezes” out water droplets that collect on the object’s surface). Students devise various experiments to determine whether this conclusion is always correct.

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Section 6.3 Ausubel’s Theory: Reception Learning

6.3 Ausubel’s Theory: Reception Learning Not all educators agree that discovery is the best approach. Perhaps most outspoken among those who advocate a different approach is David Ausubel (1963, 1977). Most people learn primarily through reception learning and not through discovery, claims Ausubel. That is, most of what students learn they receive in relatively final form rather than having to discover it for themselves. In the vast majority of school situations, he insists, discovery is ineffective and largely a waste of time. In this respect, the Ausubelian classroom is decidedly a classroom where direct instruction prevails. At the same time, however, much of Ausubel’s cognitive theory supports some of the basic characteristics of the constructivist classroom.

Ausubel’s cognitive theory of learning deals almost exclusively with what he calls “meaningful verbal learning.”

Meaning According to Ausubel, an object or an idea has meaning when it can be related to something the learner already knows. In other words, for a stimulus or concept to have meaning, there must be something in the learner’s cognitive structure (pre-existing ideas and knowledge) to which it can be related. For example, the word car has meaning for an individual only when it can be related to a mental representation of what cars are.

Meaningful learning, says Ausubel, requires that the learner already have learned related con- cepts. In Ausubel’s terms, the learner must already have learned concepts that can “subsume” new learning. Learning therefore involves what Ausubel labels subsumption.

In Ausubel’s model of learning, the construction of new knowledge is absolutely dependent on previous meaningful learning. In this sense, Aus- ubel’s theory is very similar to Bruner’s. Recall that in Bruner’s theory, the learner goes “beyond the information given”—that is, makes inferences and decisions—by relating new learning (new stimulus input) to previously learned concepts (which he labels categories and coding systems). Thus, both theories emphasize the importance of previous learning—in other words, of cognitive structure.

Cognitive Structure Cognitive structure consists of more or less organized and stable concepts (or ideas) in a learner’s consciousness. Much like Bruner’s, Ausubel’s metaphor for cognitive structure assumes that this organization is hierarchical, with the most inclusive concept at the apex and increasingly specific concepts toward the base. Therefore, argues Ausubel, instruction should proceed from the most general and inclusive idea toward details of specific instances. The fundamental difference between Bruner and Ausubel, with respect to their instructional theories, is that Ausubel argues that learners should be provided with organized information to which they can subsume new information. This approach, as Miller (2008) points out, is

czarny_bez/iStock/Thinkstock ሁ Cognitive theories like Ausubel’s and

Bruner’s emphasize the importance of previous learning. It is our previously acquired mental representations of automobiles that allow us to recognize that this is a car.

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Section 6.3 Ausubel’s Theory: Reception Learning

primarily deductive (from general to specific). In contrast, Bruner’s approach is more induc- tive (from specifics to the general). Bruner, as we saw, maintains that students should be presented with specifics and allowed to discover their own organization (coding systems).

Expository Teaching If reception learning accounts for most of what students learn, then expository teaching is the instructional technique of choice. Expository teaching is a technique in which the teacher, who bears the major responsibility for finding and organizing information for learners, pre- sents that information in relatively final form. Accordingly, the learner is not called upon to discover relationships but rather to learn them.

Expository teaching is, in effect, another label for direct instruction. It is the teaching method that has dominated North American classrooms for at least the last two centuries. And it is still the most common approach to instruction in today’s schools.

Ausubel’s emphasis on expository teaching and its outcome, reception learning, stems in part from the observation that most classroom learning seems to be of that type. Ausubel also believes that meaningful verbal learning occurs mainly in the course of expository teaching. He argues that this type of learning is not passive and does not stifle creativity or encourage rote learning. Indeed, meaningful verbal learning is anything but rote, says Ausubel, because it involves relating new material to existing structure. In contrast, rote learning involves ingesting isolated bits of information.

Effective teaching, says Ausubel, is greatly helped by the use of advance organizers— complex sets of ideas or concepts given to the learner before the material to be learned is presented. Organizers are meant to provide cognitive structure to which the new learning can be anchored (subsumed). They are presented before the lesson, and are often designed to bring to mind prior knowledge that is relevant to the lesson. Typically, they are highly general concepts (Ausubel & Robinson, 1969). (See, for example, the case entitled “Why Turbo-Charged WZ 222As Cost So Much.”)

Notice that Eddie Lemming’s lesson is preceded by a single, very abstract concept: the prin- ciple of supply and demand. Notice, too, that he promises to relate this concept to the ques- tion that defines the substance of today’s lesson: Why is gold so expensive? The students have been reminded of a single, abstract, highly generic, stable concept upon which to anchor their new learning.

Research examining the effectiveness of advance organizers has often used organizers much like this one, sometimes presented in the form of a written paragraph, sometimes described by the teacher, sometimes elicited from students. Typically, the subsequent performance of a group of students that is given advance organizers is compared with that of a control group that is given the lesson without advance organizers.

The results of much of this research are not entirely clear. Some researchers report signifi- cant positive effects (for example, Rezende & de Souza Barros, 2008; Safdar, Hussain, Shah, & Rifat, 2012); others conclude that advance organizers provide no measurable advantage (McEneany, 1990). Keep in mind that teaching strategies such as these do not always lead to immediately measurable effects, so this should not be taken as clear evidence that the strategies are a waste of time. Many good things that teachers do are never measured—and perhaps they should not be.

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Section 6.3 Ausubel’s Theory: Reception Learning

Discovery or Reception? It is not especially difficult to reconcile the two apparently opposing views presented by Bruner and Ausubel: They are not nearly as different as their juxtaposition here might make them seem. In fact, in many ways they simply offer different emphases. Neither theory is nec- essarily superior to the other, and the approaches each recommends need not be used to the exclusion of other approaches. Clearly, both have their uses. Even Ausubel suggests that dis- covery learning can be useful (Ausubel & Robinson, 1969): For example, it can be used with younger learners who do not yet have a large store of information to which new learning can be related. And it can also be used to test the meaningfulness of new learning.

Although Ausubel accepts the usefulness of discovery approaches in some instances, he remains a strong advocate of expository teaching. He argues that most learning is of the reception variety and that any alternative would be highly inefficient in terms of the time involved, the costs incurred, and the benefits to the learner. Relatively little school learning can be discovered by students, says Ausubel, not only because it would take too long but also because students are not always capable of discovering much that is significant.

What, then, should the teacher conclude? Should teachers use mostly discovery or mostly expository approaches? The simple answer is that the question is not as uncomplicated as it sounds, nor are the choices as clear. A good teacher will, of course, use both.

C A S E S F R O M T H E C L A S S R O O M : W H Y T U R B O - C H A R G E D W Z 2 2 2 A S C O S T S O M U C H

The Place: Carpenter Mid-Valley School

The Setting: Introduction to Mr. Eddie Lemming’s seventh-grade unit on gold and other pre- cious metals

Mr. Lemming: So can anyone tell me why turbo-charged WZ 222As are so expensive?

Bruce: Is it ‘cause they cost more to make?

Mr. Lemming: Well, no, Bruce, not really. That’d be a good reason, though, if they did cost more.

Jack: ‘Cause everybody wants one?

Sally: ‘Cause there’s not enough for everyone who wants one?

Mr. Lemming: Right. Right. You’re both right.

Jack: It’s like you said before, about workers and their pay. Too much demand . . .

Sally: And too little supply.

Mr. Lemming: Supply and demand. Keep that in mind. If nobody wants a thing, or if there’s a lot of it, it won’t cost very much. Like your textbook. Everybody wants it, so it costs an arm and a leg! Heh, heh. Supply and demand. Now, today we’re going to talk about gold! Pretty exciting stuff, gold! And pretty expensive. Is that because of supply? demand? some- thing else? Let’s see what we can find out. . . .

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Section 6.4 Metacognition

The juxtaposition of apparently opposing points of view is sometimes a useful teaching device. It highlights differences and, if Ausubel is correct, makes the points of view more memora- ble—more easily separated from each other.

But there is also a disadvantage to this approach: It exaggerates differences and masks simi- larities. It leaves the impression that the points of view are more different and the theorists more adamant in their beliefs than is actually the case.

This chapter is a case in point. Juxtaposing the theories of Bruner and Ausubel has underlined the differences between them—especially the discovery-versus-expository debate. At the same time, this approach has perhaps glossed over important points of agreement between them—especially the conviction of each that the key to successful cognitive processing is to be found in the learner’s own organization of knowledge. Both positions are, after all, unwav- eringly cognitive. Both present a view of the learner as an active, information-processing organism for whom the environment is meaningful to the extent that new material can be related to existing cognitive structure. In the final analysis, discovery and reception learning are not totally incompatible approaches to teaching and learning: Each is intended to lead to the acquisition of meaningful concepts; to maximize transfer, retention, and motivation; and to prevent school learning from becoming merely a passive exercise in rote learning.

Disturbing as this might be for those who prefer the uncomplicated comfort of a black-or- white position, it is quite often impossible to use only one instructional approach to the com- plete exclusion of others. Johnny, intensely motivated to discover the mating habits of that noble barnyard fowl, the turkey, runs to the local library and finds a learned exposition on turkeys. From this he learns a bewildering amount. Is this discovery learning? In contrast, Frank’s teacher, a devoted reception-learning convert, presents a brilliant essay on the mating habits of turkeys to his bench-bound students. During the course of this exposition, it occurs to Frank that turkeys have been unnecessarily and unjustly demeaned in recent times, as evi- denced by the popular expression, “You turkey!” In the course of Frank’s inspired musings, he discovers that turkeys might better be ranked along with eagles as birds worthy of our respect and admiration. Reception learning?

The confusion arising from these illustrations may be lessened by the realization that learn- ing is what students do and teaching is what teachers do. A teacher who emphasizes dis- covery will try to arrange the teaching–learning situation so that students are encouraged to experiment, to think, to gather information, and, most important, to arrive at their own organization of that information. Teachers who emphasize expository teaching will be more concerned with organizing information so that it is immediately meaningful for students and therefore becomes a stable part of their existing cognitive structure. In the end, however, it is the student who learns. And, in spite of a teacher’s emphases to the contrary, students may discover new information and new relationships for themselves or they may simply ingest a structured exposition ready to be learned and assimilated as is.

6.4 Metacognition Young children are less able to organize material and discover its meaning than are older children. And although they can learn to organize and look for meaning, they are less aware of the importance of doing so. One of the very important differences between young children and older learners is that the former are not yet as reflective and aware about themselves

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Section 6.4 Metacognition

as knowers. They have yet to recognize and develop all the special skills that allow adults and older children to extract infor- mation, to organize, to learn, and of course to remember: They know far less about knowing; they understand less about under- standing. Using the current jargon, they still lack many of the skills of metacognition that they will later develop.

Metacognition, as we saw in Chapter 3, is our knowledge and beliefs about knowing. The skills of metacognition allow us to mon- itor our progress when we try to under- stand and learn something. They provide us with ways of estimating the effects of our efforts, and they allow us to predict the like- lihood of being able to remember the mate- rial later. Metacognitive knowledge tells us that there are ways to organize material to make it easier to learn and remember, that some rehearsal and review strategies are more effective for one kind of material than another, and that some forms of learning require the deliberate application of specific strategies whereas others do not. Accordingly, the skills of metacognition are centrally involved in what is termed self-regulated learning—autonomous, self-directed learning where learners are responsible for setting their own learning goals and selecting and applying strategies to achieve them.

The Development of Metacognition That metacognitive skills are not as evident in very young children does not mean that they make no use of cognitive strategies; it simply means that they are not as aware of them and often do not apply them consciously. As a result they are less able to monitor, evaluate, and direct their own learning, or to reflect on its effectiveness. But, as Robson (2016) points out, there is considerable evidence that they do possess and use some basic metacognitive skills in directing and regulating their learning. And there is evidence too that, even among young children, metacognitive skills are among the best predictors of later academic achievement (Bryce, Whitebread, & Szucs, 2015).

Younger children do not always realize that there are strategies that might make it easier to learn and remember. And even when questioning reveals that they know about these strate- gies, they sometimes fail to use them. Similarly, they seldom question the sources of their information—or misinformation. Unlike us, who pride ourselves on not being naïve and gull- ible, very young children just as readily believe what another misinformed child says as some- thing a teacher might say.

Specific strategies of metacognition can be taught to young children, but children also need to be taught when to use them (Gildroy & Deshler, 2008). It’s important that teachers teach these strategies systematically to younger learners rather than expecting that they will discover them on their own. One way of doing this, as Salmon (2016) explains, is to encourage children to consider their thinking processes—to engage them in conversations that require them to reflect on the sequence of ideas that has led them to their current thinking.

Sasiistock/iStock/Thinkstock ሁ Very young children are often unaware of

cognitive strategies. They are less able to monitor, evaluate, and direct their own learning, or to reflect on its effectiveness. But sometimes they are remarkably effective at finding the right response.

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Section 6.5 Approaches to Teaching Thinking

The Strategies of Cognition Fortunately, we appear to have a natural tendency to extract generalities from experience and to learn how to learn and remember. As we learn how to learn, we begin to see ourselves as players of what Flavell (1985) calls the game of cognition, and we become aware of an increas- ing number and variety of strategies that can make us better players of this game. The object of the game of cognition is not to beat someone else. Winners of this game are those who are successful in making sense of information and who can recall and use it effectively.

Some people play the game of cognition very badly. They learn and remember with difficulty; much that they encounter is bewildering and frustrating. Others play the game extraordi- narily well; they learn rapidly and with apparent ease, and their understanding is often star- tling. One difference between those who play the game of cognition well and those who do not play it as well may involve how clearly each understands the process of learning and remem- bering. In other words, it has to do with their awareness and use of the strategies of cognition.

Among other things, the best players of the game of cognition are those who have learned the best strategies and know when to use them. Simply defined, cognitive strategies are the tools of intellectual activity, tools that allow us to learn, to solve problems, to study, and to understand. They are general, relatively abstract, “contentless” collections of tactics or proce- dures. They include the skills involved in being able to reflect and make critical judgments, to generalize, and to make abstractions.

Historically, most of the teaching (and learning) of cognitive strategies has occurred inciden- tally in the course of teaching other things. Recently, though, concerted attempts have been made to develop programs designed specifically to teach cognitive strategies.

6.5 Approaches to Teaching Thinking Cognitive approaches to education ask how children become thinkers and how we can make better, more critical, more creative, more autonomous thinkers of them. These approaches suggest a two-pronged answer to these important questions: First, learners must develop an awareness of themselves as thinkers, learners, and information processors; second, they must develop and practice the approaches and strategies involved in critical, creative, and effective thinking and problem solving. In other words, the cognitive perspective argues that learners must develop metacognitive skills as well as appropriate cognitive strategies. These are the skills involved in learning to learn.

As we noted earlier, schools have traditionally devoted the bulk of their formal efforts to teaching specific curriculum content; the learning of cognitive strategies and the develop- ment of metacognitive awareness have been largely incidental—and sometimes accidental. But the best teachers, suggests McGregor (2006), are those whose own metacognitive skills are most highly developed and are reflected in their classroom practice. And the best learn- ers are those who are most skilled in understanding the meanings of things, making infer- ences, finding relationships, and monitoring their own progress—in short, those who are most advanced in cognitive and metacognitive skills. These learners possess strategic as well as domain-specific (content) knowledge. Strategic knowledge deals with how to do things: how to solve problems, how to learn and memorize, how to understand, and, perhaps most important, how to monitor, evaluate, and direct these activities as they occur. In other words, strategic knowledge is metacognitive knowledge.

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There are various programs designed specifically to fos- ter cognitive skills in learners. Many of these programs are designed both to make students aware of the exis- tence of cognitive strategies and to teach them to monitor and evaluate their use of these strategies. Such programs advocate a variety of approaches to teaching, includ- ing group learning (for example, cooperative learning), individual instruction (for example, teachers’ questions designed to foster specific thinking skills), modeling procedures (for example, a cognitive strategy is verbal- ized as it is being executed), reflective learning (actively reflecting about the effectiveness and direction of learn- ing activities), and various programs where learners are trained to use specific strategies. The main objective that these programs share is to develop in learners metacog- nitive knowledge—knowledge that allows children to learn how to learn and that will help them become self- regulated learners.

Teaching Problem Solving When Sister Marie-Reine raised the cattail root above her head and asked “What is it?”, someone could have said “It’s a cattail root,” and there would have been no problem.

But nobody in the class knew it was a cattail root. And that, by definition, is a problem—a situation where there is a goal (find out what this is) and no clear and immediate path to the goal.

Problems and problem solving have been extensively investigated by psychologists and edu- cators. Teachers need to know about how students solve problems and how problem-solving skills can be developed and improved.

There are, of course, many different ways to solve problems. Some, like packing up a cattail root and shipping it to some vague university address, are time consuming and uncertain. Others, like asking an authority, are clever and effective. And some, like consulting an online encyclopedia or using a search engine, are not only effective, but also encourage important information-finding and problem-solving skills.

Bransford and Stein (1993) suggest a simple, five-step strategy for general problem solving, the basic elements of which can be explained and taught in schools. The strategy, memorable because of its IDEAL acronym, is defined by these five steps:

Identify problems and opportunities

Define goals and represent the problem

Explore possible strategies

Anticipate outcomes and Act

Look back and Learn

Creatas/Creatas/Thinkstock ሁ Effective learners can think

critically and solve problems. They also know how to make connections and monitor their progress. This student uses flash cards to improve her mathematical skills.

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Because teachers are encouraged to use real-world problems in mathematics and science, these problems are often very straightforward. They can also lead to practical applications and to critical and creative thinking: Find the area of a rectangle whose sides are 24 by 10; calculate what Joe’s average speed needs to be if he is to go 115 miles in exactly 10 hours.

But problems in real life are seldom written out in black and white. Many of the problems that students face are not simple, textbook- or teacher-given problems. What song to sing for the year-end concert, on which science fair project to embark, what topic to select for a his- tory essay, and on and on: These are real-life, day-to-day problems that need to be identified before they can be attacked.

Having identified the problem, the first line of attack involves defining it and finding ways to represent it. To define a problem is to specify what the final goal is. Representing a problem involves focusing on its important aspects and perhaps illustrating it graphically or in writing, or using various mathematical or scientific strategies to clarify and simplify it. For example, consider the following problem:

Suppose that one day you walk from Pascal to Shell River. You leave at 8:00 a.m., stop five times to rest, each time for 20 minutes, fish off the bridge for one hour at lunchtime, and finally arrive at Shell River at 4:00 p.m. You spend the night in Shell River and return to Pascal the next day, following exactly the same route. Again you leave at 8:00 a.m., but this time you don’t stop and you reach Pascal by noon. Is it true that at some point on your return trip you will be at a specific place at exactly the same time you were at that place the day before? (Lefrançois, 2001, p. 414)

First, focusing on the important aspects of this problem requires that you eliminate informa- tion that is extraneous and distracting. That you stopped to rest or fish, where you did so, and for how long, is information that is unnecessary to the solution. All you need to know to solve the problem is that you left both places at exactly the same time—although on different days—and that you followed exactly the same route—although in reverse.

This problem, like many others, might be represented with a diagram or chart, with a map, a visual image, or perhaps even with a formula. Another useful way of representing the prob- lem would be to change the time scale. Imagine, if you will, that both events take place on the same day. Say you leave Pascal for Shell River at 8:00 and I leave Shell River for Pascal, also at 8:00 on the same day, and we follow the same road. There is little doubt that we will meet— that is, that we will be at the same place at the same time. If you go more slowly than I do, we’ll simply meet at a different place. Thus, the answer to the original question is yes; we are simply “meeting” ourselves on different days.

Some problems can be solved from memory; for others, we know the rules and procedures that will lead to a solution. But for some, we need to explore different strategies, try different approaches.

Scientists differentiate between two classes of problem-solving strategies. On the one hand are algorithms—strategies that pretty well guarantee a correct solution. The rules that allow you to divide 20 by 5, to add 2 and 2, or to figure out how much money you’ll have left after you take your significant other to a movie are algorithms. Similarly, the rules that allow you to recognize parts of speech or to predict correctly the effects of mixing various barnyard

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chemicals and igniting them are algorithms. One of the responsibilities of schools is to teach students as many useful algorithms as possible.

Unfortunately, most of life’s problems don’t lend themselves to solution by algorithm. They are more vague, their solutions less definite. Often they require a tolerance of ambigu- ity, a sort of fuzzy logic that admits exceptions and uncertainty. These problems need to be attacked with heuristics rather than algorithms. Heuristics are approaches or guidelines that lead to a solution that is not necessarily the correct solution but that is something like a best educated guess. Common heuristics include trial and error, where different resolutions are attempted until a correct—or at least satisfactory—solution is encountered; means-end analysis, where the problem solver assesses the final goal, compares it with the present situ- ation, and determines what is required to eliminate the difference between the desired goal and the present situation; and analogic reasoning, where an attempt is made to solve the problem by means of comparison or simile. As an example, when Leonardo da Vinci was faced with the problem of developing a flying machine, he looked at the structure and movements of birds’ wings. And while this analogy presented important solutions for some of the prob- lems involved (for example, in terms of the ideal shape of flying machine wings), it presented a poorer solution for others (for example, his early belief that a flying machine would have wings that moved like a bird’s). He later realized that an analogy to a bird gliding, rather than beating its wings, was more likely to lead to a functional flying machine.

To anticipate an outcome is, in effect, to generate a hypothesis. Hypotheses are educated guesses that can be tested. And the “act” part of this step in the IDEAL approach to prob- lems is precisely what allows the problem-solver to test the usefulness of the hypothesis.

In science, the “act” part might involve gath- ering information, perhaps by conducting an experiment that allows the hypothesis to be refuted or supported. In day-to-day problem solving, anticipating might involve imagining what the consequences of one’s actions will be.

The final step in the IDEAL model under- lines the usefulness of reflecting on one’s problem-solving behavior as well as on one’s solutions. It’s important to evalu- ate the appropriateness of each and, by so doing, learn things that might be useful in the future. Looking back and learning is a fundamental part of “learning how to learn.”

Reciprocal Teaching One program designed to teach students how to think and understand, specifically with respect to what they read, is Palincsar and Brown’s (1984) reciprocal teaching. In reciprocal teaching, students are taught four cognitive strategies for increasing reading comprehension: generating questions, summarizing, attempting to clarify word meanings and confusing text, and predicting what will happen next. In the early stages, teachers use direct instruction to help students with each of these strategies by modeling and illustrating them with various examples of written text.

Monkeybusinessimages/iStock/Thinkstock ሁ Conducting an experiment is one way of

completing the “Anticipate outcomes and Act” step in the IDEAL approach.

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As students systematically practice these strategies, they assume increasing responsibility for helping each other with hints, feedback, additional modeling, and explanations—hence, the label reciprocal teaching. They are encouraged to ask questions, comment on each other’s predictions, ask for clarification, and help clear up misunderstandings. Gradually, teachers do less and less of the work as students do more. Eventually, the procedure becomes somewhat like a cooperative instructional approach as one student asks questions, a second answers, a third comments on the answer, another elaborates, and so on. There is considerable research that suggests that reciprocal teaching can be highly effective in developing cognitive strate- gies and metacognitive skills, and in fostering self-regulated learning (for example, Tarchi & Pinto, 2016; Pratt & Urbanowski, 2016). Table 6.2 provides an illustration of reciprocal teaching.

The Montessori Approach The Montessori Method is another approach based on self-directed activity and marked by hands-on learning and collaborative learning. It dates back to the early 20th century when Dr. Maria Montessori first developed the method for use with children with learning chal- lenges (Montessori, 1912). It has since proven to be highly effective and popular as a general program (Rich, 2015). And although it was first developed as a preschool and kindergarten program, it has been adapted for use in elementary and high schools.

The most distinctive feature of the Montessori approach is the use of specially developed materials and the detailed procedures for their use. Perhaps best known among these materi- als are large letters of the alphabet, covered with sandpaper. These are used to teach children reading skills. The prescribed teaching method requires not only that children look at the let- ters, but also that they trace them with their fingertips, enunciating their sounds at the same time. This is a part of the sense training that is basic to the Montessori approach.

Among the objectives of the Montessori approach is the development of independence and persistence as well as the development of individual skills and self-regulated learning (Bah- maee, Saadatmand, & Yarmohammadian, 2016). In addition, Montessori schools focus on social development as well as imaginative exploration, collaboration, and creative expression (American Montessori Society, 2016).

Cognitive Apprenticeship Another of several programs designed to teach cognitive strategies is cognitive apprentice- ship (Collins, 2006). This model views the learner as an apprentice in much the same sense as novices who are apprenticed to experts to learn new trades and skills. In the cognitive sphere, the experts are parents, siblings, other peers or adults, and, most important, teachers. Cogni- tive apprenticeship has been widely used and extensively researched both with elementary and secondary students as well as at the postsecondary level. Research suggests that it can be highly effective in motivating students as well as in developing metacognitive skills and cognitive strategies (for example, Greer, Cathcart, & Neale, 2016; Stefaniak & Tracey, 2015).

In cognitive apprenticeship, the role of the teacher is less about filling the learner’s mind with information, facts, figures, procedures, and so on than about presenting examples, inviting students to explore, and providing guidance and encouragement. This model suggests that teachers need to develop a variety of cognitive strategies so that their students are equipped to explore, organize, discover, and learn on their own.

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Table 6.2: Reciprocal teaching

Student-student–teacher-student dialogue Features of reciprocal teaching illustrated

(Students work in groups of four or five. The goal is the development of reading comprehension skills.) Teacher: Who’s our first leader today? Sam: Me. Teacher: Okay, Sam. The story we’re going to read is called George Is Okay. Do you want to make a prediction, Sam? Sam: Yeah. Hmm, George Is Okay . . . I think the story’s about an accident. Teacher: Interesting prediction. Being Okay could mean not being hurt in an accident. Jane: I predict it’s going to be about a kid, George, who people don’t like to begin with, but they do in the end. Teacher: Why do you make that prediction, Jane? Jane: Because we’ve been talking about what to do about bullying and, well, that’s what made me think, it would fit with the title. Thomas: It could mean, like maybe George is good at something, not an accident or bullying or anything but maybe good at some sport or video game or something. Allysa: Can I summarize the predictions? Okay. I . . . the predictions are that it’s gonna be about somebody—George—in an accident, or about being good at something, or about one of the anti-bullying strategies we talked about. Teacher: Okay. We have some interesting predictions. And reasonable too. Now what do we need to find out when we read the story? Sam: Who George is. We need to know who George is. And what hap- pened to him. Thomas: And we need to know why he’s okay ‘cause it could mean differ- ent things. That’s what we don’t know. Sam: I think that’s a good point. Teacher: Now, the story’s on page 28. Has everybody turned to that page? Okay, everybody read the first two paragraphs. (Students read silently.) Teacher: That was an interesting prediction, Jane. About bullying. Sam: But it might be the reverse. Right? I mean, I thought George might be the one being bullied. But he could be the guy who tries to stop the bullying. Jane: And I think he might use that mediator strategy we talked about. Sam: Should we make more predictions? Like what do you think is going to happen? What kinds of questions can we ask? Allysa: It depends on what “is okay” really means. Sam: Look at the last sentence. Allysa: Yeah. That makes sense . . . the last sentence of the paragraph is where George says they should invite the new kid to try out for the foot- ball team. So maybe the new kid will make the team. Teacher: Good hint, Sam, because the last sentence often tells you what’s coming up next. Sam: Maybe Allysa could be the next leader. Allysa: Okay. Let’s summarize what we know and make some predictions before we read some more.

Small group

Teacher begins process Student acts as leader Students make predictions

And more predictions

Clarify meanings

Summarize

Teacher acts as facilitator

Students encourage each other

Ask questions

Give each other hints, comment on predictions, clarify meanings

Take turns leading and teaching each other—hence reciprocal teaching

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Cognitive apprenticeship advocates the use of a number of specific techniques designed to clarify the role of the teacher (expert) and the learner (apprentice) (Farnham-Diggory, 1992). These include the following:

Cognitive Modeling In its simplest sense, cognitive modeling involves having teachers show learners how some intellectual activity can be accomplished. The object is not so much for learners to simply copy the expert’s performance, but rather to help learners learn how to learn. If an expert is to show a novice how to perform a cognitive task, it’s necessary for the steps and procedures involved in the task to be made explicit and evident—among other things, by describing how specific cognitive strategies, such as rehearsal or organization, are being used and by demon- strating different forms of “thinking out loud.”

Coaching Coaching involves guiding specific aspects of the student’s performance. Just as a cognitive apprenticeship approach uses modeling to demonstrate the performance of cognitive tasks, coaching, too, is aimed at guiding the learner’s cognitive behavior. Teachers might use any of a variety of techniques designed to teach thinking (to develop cognitive and metacognitive strategies).

Scaffolding Scaffolding involves providing support so that students can accomplish tasks that would oth- erwise be too difficult for them. This concept is discussed in Chapter 2 in connection with Vygotsky’s zone of proximal development. Recall that scaffolding is defined in terms of the various types of support that teachers need to provide for children if they are to learn. Scaf- folding often takes the form of directions, suggestions, and other forms of verbal assistance and is most effective when it involves tasks within the child’s zone of proximal development— that is, tasks that the child is initially incapable of performing without the support and guid- ance of others.

Wood, Bruner, and Ross (1976) describe six techniques that can be used in scaffolding. These are summarized and illustrated in Table 6.3.

Fading In a sense, fading is the complement of scaffolding. Scaffolding involves providing support and guidance so that learners can perform tasks within the zone of proximal development (by definition, tasks that require the support and assistance of others). In contrast, fading involves removing supports as the learner becomes capable of performing a given task with- out assistance—in other words, as the task moves from Vygotsky’s zone of proximal develop- ment to within the sphere of the learner’s acquired competence. Fading assures that students eventually assume responsibility for solving problems and for learning.

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Articulation Articulation involves verbalizing ideas or putting them into words. As a cognitive appren- ticeship technique, articulation encourages learners to put conclusions, descriptions, and the principles they have discovered into words. Deliberate verbalization forces students to think more clearly about their cognitive processes and is frequently an important technique in pro- grams designed to foster the development of cognitive strategies.

Reflection Closely related to articulation, reflection also requires that the learner think about and ver- balize the execution and results of cognitive tasks. But when reflecting, learners are encour- aged to think more abstractly and perhaps to compare their cognitive activity with a concep- tual model, or sometimes with an actual physical model.

Table 6.3: Some scaffolding techniques

Technique Description Example

Recruitment Gaining the child’s attention and focusing it on the requirements of the task

Okay, what we want to do is calculate the area of this right-angle triangle when we know the length of all its sides. How many square inches (cm) does it contain?

Reduction in degrees of freedom

Reducing the tasks to manage- able subtasks

Remember how to find the area of a rectangle? Can you make this triangle into a rectangle?

Direction maintenance

Keeping the learner on track and motivated

Why don’t you draw out the triangle, make it into a rectangle, and measure each of the sides? Maybe try another triangle and see if it’s the same.

Marking critical features

Drawing attention to the most relevant aspects of the task

How many identical right-angle triangles do you need to make a rectangle? Why don’t you draw a triangle on the corner of this piece of paper and cut three or four out and make squares with them? Do you always need the same number of triangles?

Frustration control Easing frustration associated with difficulties the child might experience

This is sometimes a hard problem even for eighth-graders. You’re doing really well.

Demonstration Imitating the child’s attempts, but modifying them slightly so that they are more appropriate and can then be imitated in turn by the child

Here, let me cut out two triangles exactly the same and, here, let me make a square. Now what’s the area of this square? And . . . that’s it . . . exactly half. And . . . right! That is the formula, you genius!

Source: Based on Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17, 89–100.

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Exploration Exploration is the final step in the cognitive apprenticeship instructional process—as in most instructional approaches. It involves generalizing about what has been learned or accom- plished, and it is analogous to what is called transfer or generalization.

Promoting Cognitive Skills in Your Classroom Two things seem clear at this point: First, our attempts to teach students how to think and how to learn are not always as deliberate and as focused as they might be; and second, sys- tematic programs can significantly improve learning and thinking for a variety of individuals and in many different contexts.

The foregoing should not be taken to suggest that teachers who do not use systematic pro- grams for teaching their students thinking/learning skills are failing to meet their responsi- bilities. As Billing (2007) points out, there are a wide variety of strategies and approaches that teachers can use to promote cognitive skills, even if these aren’t always entirely system- atic. These strategies include various kinds of questioning and a variety of problems, exer- cises, and examples designed to encourage learners to analyze, match, encode, and otherwise become aware of and improve their information processing. Following a detailed review of the literature on developing some of the key cognitive skills that learners need to learn and be able to transfer to different situations, Billing presents a number of principles important for teaching. These are summarized in the following list (Billing, 2007), with reference to chap- ters in this text that are especially relevant to each recommendation. The key recommenda- tions for increasing the transferability of cognitive skills include the following:

• Pay particular attention to student motivation, which is critical in determining how well students learn. (Chapter 8)

• Teach/develop specific learning/thinking strategies; that is, teach learners how to reason and how to monitor their reasoning processes. (Chapters 6, 7)

• Teach principles and concepts rather than simply facts to be memorized. (Chapter 6) • Pair abstract principles and rules with concrete examples. (Chapter 6) • Arrange for learning to occur in a social context to stimulate production of explana-

tions and abstraction of principles. (Chapters 2, 3, 8) • Provide feedback so that learners understand the applicability or inapplicabil-

ity of their generalizations as well as the appropriateness of their strategies. (Chapters 5, 10)

• Arrange for cooperative learning. (Chapter 8) • Point out similarities and differences among problems. (Chapter 6) • Provide a large variety of different, meaningful examples. (Chapter 6) • Encourage learners to learn by discovering for themselves relationships, rules, and

principles. (Chapter 6)

It would clearly be premature to suggest that teachers should now begin using this or that program for this or that purpose. But it is not at all premature to repeat the claim of many education critics that the schools have not always done much to teach thinking and learning skills. The contemporary cognitive sciences are based on the assumption that much more can be done. They have also begun to show us how.

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Key Points • Direct instruction describes teacher-centered instructional approaches such as

lecturing, explaining, and assigning. Constructivist approaches, which are more learner-centered, try to provide opportunities for learners to construct their own meaning.

• Cognitive theories stress the importance of the individual learner’s cognitive struc- ture and look at how information is processed, organized, and recalled. Cognitive theories view knowledge as consisting of vast networks of relationships in which learning is built on previous knowledge and involves information processing.

• Bruner’s cognitive theory describes learning as an information-processing activ- ity that involves the formation of concepts (categories) that result from abstract- ing commonalities among events and experiences. The theory advocates discovery learning and supports constructivist approaches to teaching. Learning through discovery requires the learner to construct information by discovering the relation- ships that exist among concepts or principles.

• Ausubel’s theory attempts to explain meaningful verbal learning in the classroom. He defines meaning as involving a relationship between new material and old mate- rial (cognitive structure). To learn is to subsume new material to existing cognitive structure.

• Ausubel’s most important instructional technique involves the use of advance orga- nizers—highly generic concepts presented before the lesson, designed to bring to mind relevant prior knowledge and intended to clarify relationships between new and old learning.

• Discovery methods and expository teaching are not mutually exclusive. Both are useful. In the end, teaching is what teachers do, and learning is what students do. Discovery teaching does not always lead to discovery learning. And expository teach- ing might well lead to discovery learning.

• As we learn about things (facts, problem-solving techniques, and so on), we also learn about learning. Knowledge about our own cognitive processes is called meta- cognition. The skills of metacognition allow us to direct, monitor, evaluate, and modify our ongoing learning and thinking. Cognitive (learning/thinking) strategies are the tools of cognitive behavior.

• Teaching problem-solving is an important part of constructivist approaches to instruction. The IDEAL problem-solving strategy is defined by five steps: identify the problem, define goals, explore strategies, anticipate outcomes and act, and look back and learn.

• Palincsar and Brown’s reciprocal teaching attempts to develop strategies to increase reading comprehension by asking students to eventually assume responsibility for helping one another. The Montessori Method encourages hands-on learning, self- directed activity, the development of independence and persistence, and the promo- tion of self-regulated learning.

• The cognitive apprenticeship model suggests a range of instructional approaches including modeling, coaching, scaffolding, fading, articulation, and reflection.

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Posttest

1. Unlike behaviorism, constructivism claims that learners a. are initially all equally susceptible to consequences. b. are basic recipients of information. c. passively learn information in a vacuum. d. derive meaning from experiences.

2. Mr. Gundersen presents problems to students and allows them to work with materi- als and resources in order to figure out the answer and find relationships within the information. His approach best fits a. reciprocal learning. b. reception learning. c. discovery learning. d. expository learning.

3. Which of the following is NOT true of expository teaching? a. Expository teaching is fairly traditional and common in North America. b. Expository teaching presents just the initial information to the learners. c. Expository teaching leads to reception learning outcomes. d. Expository teaching is another label for direct instruction.

4. In using discovery and reception learning, a. both can be used successfully depending on the learners and material. b. Ausubel argues that discovery learning is more efficient. c. Ausubel claims that most learning can occur through discovery. d. research strongly supports that discovery learning is superior.

5. Representing the problem in a chart or graph falls within which step of the IDEAL problem-solving strategy? a. Identify problems and opportunities b. Anticipate outcomes and Act c. Explore possible strategies d. Define goals and represent the problem

Answers: 1(d), 2(c), 3(b), 4(a), 5(d)

Critical Thinking Exercises • What are the differences between constructivist approaches and direct instruction?

Provide classroom examples. • How would you design a guided discovery lesson? • What would you include in a specific expository lesson making use of various kinds

of advance organizers? • Resolve a problem using the IDEAL problem-solving strategy. Did you find the strat-

egy useful? Why or why not? • What would you include in a basic program designed to teach students how to

think?

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Web Resources For a more detailed discussion of the distinctions between cognitive and behavioristic approaches to learning, visit:

http://www.simplypsychology.org/cognitive.html

For a demonstration of how reciprocal teaching can be used in the classroom, visit:

http://www.youtube.com/watch?v=rbnwBVrJVdY

For a humorous summary of the main principles of cognitive apprenticeship in the classroom, visit:

http://www.aect.org/edtech/ed1/31.pdf

Answers to Pretest

1. True. John Dewey promoted an environment that was focused on child-oriented and discovery-based learning.

2. True. The discovery learning approach allows students to take more responsibility for their learning, while teachers are available for guidance.

3. False. A step related to discovery learning involves making generalizations and encourages learners to apply information.

4. True. Metacognitive strategies can be taught to children, and it is also important to teach children when to apply these strategies.

5. False. In a cognitive apprenticeship, the apprentice is the learner, while the expert can be parents, siblings, other children, and teachers.

Answers to Posttest

1. Behaviorism typically views all learners as equals, while constructivism emphasizes that learners are different. Learners can have different motivations, take away differ- ent meanings from experiences, and learn different things.

2. Discovery learning involves teachers being more like facilitators in learning, encour- aging learners to explore and discover relationships on their own.

3. A characteristic of expository teaching is providing learners with the information rather than students discovering it.

4. Opposing teaching approaches, such as Bruner’s discovery learning and Ausubel’s reception learning, have differences, but also similarities, such as making learning more active. These similarities make them both effective approaches to teaching.

5. This step in the IDEAL problem-solving strategy involves defining goals and repre- senting the problem. A problem can be represented through an illustration, such as a chart or graph. Another way to represent a problem is to write it down.

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http://www.simplypsychology.org/cognitive.html

http://www.youtube.com/watch?v=rbnwBVrJVdY

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Key Terms advance organizer Introductory informa- tion given to learners to help them under- stand, learn, and remember new material.

algorithm A strategy or rule that leads to a correct solution for a problem.

analogic reasoning A commonly used heu- ristic (problem-solving strategy) in which problem solving is based on comparison or simile.

articulation A cognitive apprenticeship technique. Learners are encouraged to put their conclusions, descriptions, and prin- ciples into words.

category A term used by Bruner to describe a grouping of related objects or events; a rule for classifying things as equal. See also coding system.

coaching A technique sometimes used in cognitive apprenticeship approaches to instruction. The learner’s cognitive behavior is guided by an expert.

coding system Bruner’s label for a hierar- chical arrangement of related categories. See also category.

cognitive apprenticeship An instructional model wherein parents, siblings, other adults, and especially teachers serve as a combination of model, guide, tutor, men- tor, and coach to foster intellectual growth among learners.

cognitive modeling An approach in cog- nitive apprenticeship where the teacher models (explains, describes, illustrates) intellectual activities involved in learning how to learn.

cognitive strategy A strategy for learning and remembering such as might be used for identifying problems, selecting approaches to their solution, monitoring progress in solving problems, and using feedback. See also metacognition.

constructivist approaches A general label for instructional methods that are highly learner-centered and that reflect the belief that meaningful information is constructed by students rather than given to them. See also progressive education.

deductive A type of reasoning that involves making inferences from general principles.

discovery learning The acquisition of new information or knowledge largely as a result of the learner’s own efforts. See also recep- tion learning, constructivist approaches.

exploration A cognitive apprenticeship procedure that requires learners to apply or generalize what they have learned, and to investigate and test the potential applica- tions of their learning.

expository teaching A reception learning instructional technique strongly advocated by Ausubel in which the teacher bears the responsibility of organizing and presenting information in relatively final form. See also reception learning.

fading A cognitive apprenticeship tech- nique in which supports (scaffolds) are gradually withdrawn as learners progress.

heuristic A problem-solving approach that serves as a guide for solving the problem but that leads to a speculative rather than a definitely correct solution.

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inductive A type of reasoning that pro- ceeds from particular instances to a general conclusion.

means-end analysis A heuristic whereby a problem solver compares the current situ- ation with the desired goal and determines what is required to reduce the difference between the two.

metacognition Knowledge about knowing. Includes strategies that allow learners to recognize limitations and to monitor prog- ress. See also cognitive strategy.

modeling Learning through observation (imitation).

The Montessori Method A teaching method initially developed for very young children with learning challenges, but now widely used at all grade levels and with students of all abilities. It is characterized by the use of specially designed materials and methods that emphasize self-directed, col- laborative learning.

problem A situation involving a desired goal and the task of discovering how to reach that goal. A question that needs to be solved or answered.

progressive education An educational reform movement closely associated with John Dewey and identified primarily by child- rather than teacher-centered instruc- tional approaches.

reception learning A type of learning that involves direct instruction or tuition rather than the learner’s own efforts to discover and organize. See also discovery learning.

reciprocal teaching An instructional tech- nique that involves teaching four cognitive strategies for increasing reading compre- hension: generating questions, summarizing, clarifying word meanings and confusing text, and predicting what will happen next.

reflection In cognitive apprenticeship, a procedure where learners are asked to think about their cognitive activities and to compare them with those of others or with abstract models.

subsumption Ausubel’s term for the inte- gration of new material or information with existing information.

trial and error A heuristic that involves trying a number of solutions one after the other until a satisfactory solution is encountered.

ሁ The much-feared grizzly bear (Ursus horribilis) weighs about 900 pounds at maturity. Many experts consider the grizzly to be a species of the brown bear (Ursus arctos). The grizzly’s prodigal strength is attested to by one bear that moved an 850-pound trap one-quarter of a mile and then escaped (Soper, 1964).

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