At this point there are two ways to go. I hypothesize that the roots of P x are the reciprocals of the roots of Q x , in general.
If I'm not yet sure, I should try a factorable cubic or two. Now, I can try to generalize the argument above, but it's not all that straightforward; not every polynomial can be factored, and keeping track of the coefficients may not be that easy. It may be worth stopping, re-phrasing my conjecture, and trying it from scratch:. Let P x and Q x be two polynomials with "reversed" coefficients. Prove that the roots of P x and Q x are reciprocals. All right, let's take a look at what the problem asks for.
What does it mean for some number, say r , to be a root of P x? Now the conjecture says that the reciprocal of r is supposed to be a root to Q x. Let me go back to the quadratic case, and see what happens.
All right, now it's time for a postmortem. Observe that the proof, like a classical mathematical argument, is quite terse and presents the results of a thought process. But where did the inspiration for the proof come from? If you go back over the way that the argument evolved, you'll see there were two major breakthroughs.
The first had to do with understanding the problem, with getting a feel for it. The problem statement, in its full generality, offered little in the way of assistance. What we did was to examine special cases in order to look for a pattern. We had to get even more specific, as follows: Look at a series of straightforward examples that are easy to calculate, in order to see if some sort of pattern emerges.
With luck, you might be able to generalize the pattern. In this case, we were looking for roots of polynomials, so we chose easily factorable ones. Obviously, different circumstances will lead to different choices.
But that strategy allowed us to make a conjecture. The second breakthrough came after we made the conjecture. Although we had some idea of why it ought to be true, the argument looked messy, and we stopped to reconsider for a while.
What we did at that point was important, and is often overlooked: We went back to the conditions of the problem, explored them, and looked for tangible connections between them and the results we wanted.
Questions like "what does it mean for r to be a root of P x? Next, he gives the class problems to solve that lend themselves to the use of the heuristics he has introduced. During this collective problem solving, he acts as a moderator, soliciting heuristics and solution techniques from the students while modeling the various control strategies for making judgments about how best to proceed.
This division of labor has several effects. First, he turns over some of the problem-solving process to students by having them generate alternative courses of action but provides major support or scaffolding by managing the decisions about which course to pursue, when to change course, etc.
Second, significantly, he no longer models the entire expert problem-solving process but a portion of it. In this way, he shifts the focus from the application or use of specific heuristics to the application or use of control strategies in managing those heuristics. Like Scardamalia and Bereiter, Schoenfeld employs a third kind of modeling that is designed to change students' assumptions about the nature of expert problem solving. He challenges students to find difficult problems and at the beginning of each class offers to try to solve one of their problems.
Occasionally, the problems are hard enough that the students see him flounder in the face of real difficulties. During these sessions, he models for students not only the use of heuristics and control strategies but the fact that one's strategies sometimes fail. In contrast, textbook solutions and classroom demonstrations generally illustrate only the successful solution path, not the search space that contains all of the dead-end attempts.
Such solutions reveal neither the exploration in searching for a good method nor the necessary evaluation of the exploration.
Seeing how experts deal with problems that are difficult for them is critical to students' developing a belief in their own capabilities. Even experts stumble, flounder, and abandon their search for a solution until another time. Witnessing these struggles helps students realize that thrashing is neither unique to them nor a sign of incompetence. In addition to class demonstrations and collective problem solving, Schoenfeld has students participate in small-group problem-solving sessions.
During these sessions, Schoenfeld acts as a "consultant" to make sure that the groups are proceeding in a reasonable fashion. Typically he asks three questions: What are they doing, why are they doing it, and how will success in what they are doing help them find a solution to the problem?
Asking these questions serves two purposes: First, it encourages the students to reflect on their activities, thus promoting the development of general self-monitoring and diagnostic skills; second, it encourages them to articulate the reasoning behind their choices as they exercise control strategies. Gradually, the students, in anticipating his questioning, come to ask the questions of themselves, thus gaining control over reflective and metacognitive processes in their problem solving.
In these sessions, then, he is fading relative to both helping students generate heuristics and, ultimately, to exercising control over the process. In this way, they gradually gain control over the entire problem-solving process. Schoenfeld advocates small-group problem solving for several reasons. First, it gives the teacher a chance to coach students while they are engaged in semi-independent problem solving; he cannot really coach them effectively on homework problems or class problems.
Second, the necessity for group decision-making in choosing among alternative solution methods provokes articulation, through discussion and argumentation, of the issues involved in exercising control processes. Such discussion encourages the development of the metacognitive skills involved, for example, monitoring and evaluating one's progress. Third, students get little opportunity in school to engage in collaborative efforts; group problem solving gives them practice in the kind of collaboration prevalent in real-world problem solving.
Fourth, students are often insecure about their abilities, especially if they have difficulties with the problems. Seeing other students struggle alleviates some of this insecurity as students realize that difficulties in understanding are not unique to them, thus contributing to an enhancement of their beliefs about self, relative to others. We believe that there is another important reason that small-group problem solving is useful for learning: the differentiation and externalization of the roles and activities involved in solving complex problems.
Successful problem solving requires that one assume at least three different, though interrelated, roles at different points in the problem-solving process: that of moderator or executive, that of generator of alternative paths, and that of critic of alternatives.
Small-group problem solving differentiates and externalizes these roles: different people naturally take on different roles, and problem solving proceeds along these lines. And here, as in reciprocal teaching, students may play different roles, so that they gain practice in all the activities they need to internalize. There is one final aspect of Schoenfeld's method that we think is critical and that is different from the other methods we have discussed: What he calls postmortem analysis.
As with other aspects of Schoenfeld's method, students alternate with the teacher in producing postmortem analyses. First, after modeling the problem-solving process for a given problem, Schoenfeld recounts the solution method, highlighting those features of the process that can be generalized see math sidebar.
For example, he might note the heuristics that were employed, the points in the solution process where he or the class engaged in generating alternatives, the reasons for the decision to pursue one alternative before another, and so on. In short, he provides what Collins and Brown have labeled an abstracted replay, that is, a recapitulation of some process designed to focus students' attention on the critical decisions or actions.
Postmortem analysis also occurs when individual students explain the process by which they solved their homework problems.
Here students are required to generate an abstracted replay of their own problem-solving process, as the basis for a class critique of their methods.
The alternation between expert and student postmortem analyses enables the class to compare student problem-solving processes and strategies with those of the expert; such comparisons provide the basis for diagnosing student difficulties and for making incremental adjustments in student performance. Our discussion of cognitive apprenticeship raises numerous pedagogical and theoretical issues that we believe are important to the design of learning environments generally.
To facilitate consideration of these issues, we have developed a framework consisting of four dimensions that constitute any learning environment: content, method, sequence, and sociology.
Relevant to each of these dimensions is a set of characteristics that we believe should be considered in constructing or evaluating learning environments. These characteristics are summarized in the adjacent sidebar and described in detail below, with examples from reading, writing, and mathematics. Recent cognitive research has begun to differentiate the types of knowledge required for expertise. In particular, researchers have begun to distinguish among the concepts, facts, and procedures associated with expertise and various types of strategic knowledge.
We use the term strategic knowledge to refer to the usually tacit knowledge that underlies an expert's ability to make use of concepts, facts, and procedures as necessary to solve problems and accomplish tasks. This sort of expert problem-solving knowledge involves problem-solving heuristics or "rules of thumb" and the strategies that control the problem-solving process.
Another type of strategic knowledge, often overlooked, includes the learning strategies that experts use to acquire new concepts, facts, and procedures in their own or another field.
We should emphasize that much of experts' strategic knowledge depends on their knowledge of facts, concepts, and procedures. For instance, in the math example discussed earlier, Schoenfeld's students could not begin to apply the strategies he is teaching if they did not have a solid grounding in mathematical knowledge. Domain knowledge includes the concepts, facts, and procedures explicitly identified with a particular subject matter; these are generally explicated in school textbooks, class lectures, and demonstrations.
This kind of knowledge, although certainly important, provides insufficient clues for many students about how to solve problems and accomplish tasks in a domain. Moreover, when it is learned in isolation from realistic problem contexts and expert problem-solving practices, domain knowledge tends to remain inert in situations for which it is appropriate, even for successful students. And finally, although at least some concepts can be formally described, many of the crucial subtleties of their meaning are best acquired through applying them in a variety of problem situations.
Indeed, it is only through encountering them in real problem solving that most students will learn the boundary conditions and entailments of much of their domain knowledge. Examples of domain knowledge in reading are vocabulary, syntax, and phonics rules. Heuristic strategies are generally effective techniques and approaches for accomplishing tasks that might be regarded as "tricks of the trade"; they don't always work, but when they do, they are quite helpful.
Most heuristics are tacitly acquired by experts through the practice of solving problems; however, there have been noteworthy attempts to address heuristic learning explicitly Schoenfeld, For example, a standard heuristic for writing is to plan to rewrite the introduction and, therefore, to spend relatively little time crafting it in the first draft.
In mathematics, a heuristic for solving problems is to try to find a solution for simple cases and see if the solution generalizes. Control strategies , as the name suggests, control the process of carrying out a task. These are sometimes referred to as "metacognitive" strategies Palinscar and Brown, ; Schoenfeld, As students acquire more and more heuristics for solving problems, they encounter a new management or control problem: how to select among the possible problem-solving strategies, how to decide when to change strategies, and so on.
Control strategies have monitoring, diagnostic, and remedial components; decisions about how to proceed in a task generally depend on an assessment of one's current state relative to one's goals, on an analysis of current difficulties, and on the strategies available for dealing with difficulties.
For example, a comprehension-monitoring strategy might be to try to state the main point of a section one has just read; if one cannot do so, then one has not understood the text, and it might be best to reread parts of the text.
In mathematics, a simple control strategy for solving a complex problem might be to switch to a new part of a problem if one is stuck. Learning strategies are strategies for learning any of the other kinds of content described above. Knowledge about how to learn ranges from general strategies for exploring a new domain to more specific strategies for extending or reconfiguring knowledge in solving problems or carrying out complex tasks. For example, if students want to learn to solve problems better, they need to learn how to relate each step in the example problems worked in textbooks to the principles discussed in the text Chi, et al.
If students want to write better, they need to find people to read their writing who can give helpful critiques and explain the reasoning underlying the critiques most people cannot. They also need to learn to analyze other's texts for strengths and weaknesses. Teaching methods should be designed to give students the opportunity to observe, engage in, and invent or discover expert strategies in context.
Such an approach will enable students to see how these strategies combine with their factual and conceptual knowledge and how they use a variety of resources in the social and physical environment. The six teaching methods advocated here fall roughly into three groups: the first three modeling, coaching, and scaffolding are the core of cognitive apprenticeship, designed to help students acquire an integrated set of skills through processes of observation and guided practice.
The next two articulation and reflection are methods designed to help students both to focus their observations of expert problem solving and to gain conscious access to and control of their own problem-solving strategies. The final method exploration is aimed at encouraging learner autonomy, not only in carrying out expert problem-solving processes but also in defining or formulating the problems to be solved. Modeling involves an expert's performing a task so that the students can observe and build a conceptual model of the processes that are required to accomplish it.
In cognitive domains, this requires the externalization of usually internal processes and activities—specifically, the heuristics and control processes by which experts apply their basic conceptual and procedural knowledge. For example, a teacher might model the reading process by reading aloud in one voice, while verbalizing her thought processes in another voice Collins and Smith, In mathematics, as described above, Schoenfeld models the process of solving problems by having students bring difficult new problems for him to solve in class.
Coaching consists of observing students while they carry out a task and offering hints, scaffolding, feedback, modeling, reminders, and new tasks aimed at bringing their performance closer to expert performance.
Coaching may serve to direct students' attention to a previously unnoticed aspect of the task or simply to remind the student of some aspect of the task that is known but has been temporarily overlooked. The content of the coaching interaction is immediately related to specific events or problems that arise as the student attempts to accomplish the target task.
In Palincsar and Brown's reciprocal teaching of reading, the teacher coaches students while they ask questions, clarify their difficulties, generate summaries, and make predictions. Scaffolding refers to the supports the teacher provides to help the student carry out the task. These supports can take either the forms of suggestions or help, as in reciprocal teaching, or they can take the form of physical supports, as with the cue cards used by Scardamalia, Bereiter, and Steinbach to facilitate writing, or the short skis used to teach downhill skiing Burton, Brown, and Fisher, When scaffolding is provided by a teacher, it involves the teacher in executing parts of the task that the student cannot yet manage.
A requisite to such scaffolding is accurate diagnosis of the student's current skill level or difficulty and the availability of an intermediate step at the appropriate level of difficulty in carrying out the target activity. Fading involves the gradual removal of supports until students are on their own. Articulation involves any method of getting students to articulate their knowledge, reasoning, or problem-solving processes.
We have identified several different methods of articulation. First, inquiry teaching Collins and Stevens, , is a strategy of questioning students to lead them to articulate and refine their understanding of concepts and procedures in different domains.
For example, an inquiry teacher in reading might systematically question students about why one summary of the text is good but another is poor, to get the students to formulate an explicit model of a good summary. Second, teachers might encourage students to articulate their thoughts as they carry out their problem solving, as do Scardamalia, et al. Third, they might have students assume the critic or monitor role in cooperative activities, as do all three models we discussed, and thereby lead students to formulate and articulate their ideas to other students.
Reflection involves enabling students to compare their own problem-solving processes with those of an expert, another student, and ultimately, an internal cognitive model of expertise. Reflection is enhanced by the use of various techniques for reproducing or "replaying" the performances of both expert and novice for comparison.
The level of detail for a replay may vary depending on the student's stage of learning, but usually some form of "abstracted replay," in which the critical features of expert and student performance are highlighted, is desirable Collins and Brown, For reading or writing, methods to encourage reflection might consist of recording students as they think out loud and then replaying the tape for comparison with the thinking of experts and other students.
Exploration involves pushing students into a mode of problem solving on their own. Forcing them to do exploration is critical, if they are to learn how to frame questions or problems that are interesting and that they can solve. Exploration is the natural culmination of the fading of supports. It involves not only fading in problem solving but fading in problem setting as well. But students do not know a priori how to explore a domain productively. So exploration strategies need to be taught as part of learning strategies more generally.
Exploration as a method of teaching involves setting general goals for students and then encouraging them to focus on particular subgoals of interest to them, or even to revise the general goals as they come upon something more interesting to pursue.
For example, in reading, the teacher might send the students to the library to investigate theories about why the stock market crashed in In writing, students might be encouraged to write an essay defending the most outrageous thesis they can devise.
In mathematics, students might be asked to generate and test hypotheses about teenage behavior given a database on teenagers detailing their backgrounds and how they spend their time and money. Domain knowledge: subject matter specific concepts, facts, and procedures. Heuristic strategies: generally applicable techniques for accomplishing tasks. Learning strategies: knowledge about how to learn new concepts, facts, and procedures. Modeling: teacher performs a task so students can observe.
Coaching: teacher observes and facilitates while students perform a task. Scaffolding: teacher provides supports to help the student perform a task. Articulation: teacher encourages students to verbalize their knowledge and thinking. Reflection: teacher enables students to compare their performance with others. Exploration: teacher invites students to pose and solve their own problems.
Global before local skills: focus on conceptualizing the whole task before executing the parts. Increasing complexity: meaningful tasks gradually increasing in difficulty. Increasing diversity: practice in a variety of situations to emphasize broad application. Situated learning: students learn in the context of working on realistic tasks.
Community of practice: communication about different ways to accomplish meaningful tasks. Intrinsic motivation: students set personal goals to seek skills and solutions. Cooperation: students work together to accomplish their goals. In sequencing activities for students, it is important to give students tasks that structure their learning but that preserve the meaningfulness of what they are doing.
This leads us to three principles that must be balanced in sequencing activities for students. Global before local skills. In tailoring Lave, , apprentices learn to put together a garment from precut pieces before learning to cut out the pieces themselves.
The chief effect of this sequencing principle is to allow students to build a conceptual map, so to speak, before attending to the details of the terrain Norman, In general, having students build a conceptual model of the target skill or process which is also encouraged by expert modeling accomplishes two things: First, even when the learner is able to accomplish only a portion of a task, having a clear conceptual model of the overall activity helps him make sense of the portion that he is carrying out.
Second, the presence of a clear conceptual model of the target task acts as a guide for the learner's performance, thus improving his ability to monitor his own progress and to develop attendant self-correction skills. This principle requires some form of scaffolding. In algebra, for example, students may be relieved of having to carry out low-level computations in which they lack skill in order to concentrate on the higher-order reasoning and strategies required to solve an interesting problem Brown, Increasing complexity refers to the construction of a sequence of tasks such that more and more of the skills and concepts necessary for expert performance are required VanLehn and Brown, ; Burton, Brown, and Fisher, ; White, For example, in the tailoring apprenticeship described by Lave, apprentices first learn to construct drawers, which have straight lines, few pieces, and no special features, such as waistbands or pockets.
They then learn to construct blouses, which require curved lines, patch pockets, and the integration of a complex subpiece, the collar. There are two mechanisms for helping students manage increasing complexity.
The first mechanism is to sequence tasks in order to control task complexity. The second key mechanism is the use of scaffolding, which enables students to handle at the outset, with the support of the teacher or other helper, the complex set of activities needed to accomplish any interesting task.
For example, in reading, increasing task complexity might consist of progressing from relatively short texts, employing straightforward syntax and concrete description, to texts in which complex interrelated ideas and the use of abstractions make interpretation difficult. Increasing diversity refers to the construction of a sequence of tasks in which a wider and wider variety of strategies or skills are required. Although it is important to practice a new strategy or skill repeatedly in a sequence of increasingly complex tasks, as a skill becomes well learned, it becomes increasingly important that tasks requiring a diversity of skills and strategies be introduced so that the student learns to distinguish the conditions under which they do and do not apply.
Moreover, as students learn to apply skills to more diverse problems, their strategies acquire a richer net of contextual associations and thus are more readily available for use with unfamiliar or novel problems. For reading, task diversity might be attained by mixing reading for pleasure, reading for memory studying , and reading to find out some particular information in the context of some other task.
The final dimension in our framework concerns the sociology of the learning environment. For example, tailoring apprentices learn their craft not in a special, segregated learning environment but in a busy tailoring shop. They are surrounded both by masters and other apprentices, all engaged in the target skills at varying levels of expertise.
And they are expected, from the beginning, to engage in activities that contribute directly to the production of actual garments, advancing quickly toward independent, skilled production. As a result, apprentices learn skills in the context of their application to realistic problems, within a culture focused on and defined by expert practice.
Furthermore, certain aspects of the social organization of apprenticeship encourage productive beliefs about the nature of learning and of expertise that are significant to learners' motivation, confidence, and most importantly, their orientation toward problems that they encounter as they learn. From our consideration of these general issues, we have abstracted critical characteristics affecting the sociology of learning.
Situated learning. A critical element of fostering learning is to have students carry out tasks and solve problems in an environment that reflects the multiple uses to which their knowledge will be put in the future. Situated learning serves several different purposes. They drew sketches of their work, loaded photos and movie clips into the computer workstations, and began to type the text of their stories. The next eight days or so would be spent working in small groups to design and develop the multimedia program into a final product.
As the students worked, Ms. Reed would guide them toward considering certain questions, organizing their thoughts and their work, and consulting a variety of resources, including books, videos, the Internet, and, of course, other people. Clarke would check in to provide technical support. Abrams would come by several more times to provide additional information and reactions to the project as it developed.
Reed would lead the group in discussing their experiences working on the project, including what they had learned about the Great Depression and why it was important for people in the town to know about it.
When the students returned to school, Ms. Reed would ask them to record a personal reflection in their electronic journals about the entire learning experience. How would you describe Ms. Both Ms. Reed use some effective strategies for learning. Both incorporate a variety of media, including books and video, as well as a variety of activities including reading, writing, and presentation. Yet, the nature of the experience is quite different in each classroom.
In Ms. In educational terms, Ms. Her classroom is illustrative of a classic model of teaching and learning. This is supposed to be a flash animation.
Cognitive apprenticeship practices, along with anchored instruction, learning communities, and in-situ assessment, are educational approaches derived from Situated Learning Theory.
These practices strive, first and foremost, to place teaching and learning practices within a rich and varied context that is meaningful and authentic to students.
An apprenticeship is distinguished from tutoring, mentoring, coaching, and volunteerism by its focus on interaction that is a specific socially and culturally valued activity at which the adult is more skilled Tisdale Like the apprentice electrician or the interning future physician, cognitive apprenticeship seeks to engage learners in real-world scenarios in which they act and interact to achieve useful outcomes.
The workplace has a number of strengths as a learning environment: authentic, goal-oriented activities; access to guidance; everyday engagement in problem solving; and intrinsic reinforcement Kerka Although children cannot experience all aspects of the typical craft apprenticeship nor should they , they can benefit from some of its common practices, such as modeling of certain skills by more advanced individuals and coaching by mentors toward higher levels of knowledge and practice.
Cognitive apprenticeship is one example of situated learning in which learners participate in a community of practice that is developed through activity and social interaction in ways similar to that in craft apprenticeships McLellan What is the context in which Ms.
In what ways does it provide variety, depth, meaning, and authenticity for learners? Beyond striving to engage learners in activity in real-world, meaningful contexts, cognitive apprenticeship is known to embody certain characteristics known as modeling, coaching, scaffolding, reflection, articulation, and exploration. The following sections explore how each of these concepts are applied in the fourth-grade classrooms of Ms.
Modeling takes place constantly in everyday life. Learning simple tasks, such as how to wash dishes, involves more physical skills and processes than cognitive processes. A task can be imitated simply by observing another person demonstrating how to wash dishes.
Complex tasks that require complicated cognitive processes are more difficult to model because it is impossible to observe what takes place in the human mind. A cognitive modeling strategy, with teachers and competent students serving as cognitive role models, is a key characteristic of cognitive apprenticeships.
The models should put their thoughts and reasons into words while explaining and demonstrating certain actions, because students cannot otherwise monitor the thinking process Meichenbaum, ; Shunk, Modeling in cognitive apprenticeship means showing how a process unfolds and giving reasons why it happens that way Collins, There are two kinds of modeling that can be used in education:. These two kinds of modeling can be interwoven, especially when the problem includes the invisible parts of the process.
In applying these two types of modeling in educational settings, two strategies are available to teachers:. Because it involves a process that cannot be directly observed and experienced, cognitive modeling requires more sophisticated planning to apply in classrooms than does modeling of physical performance.
The modeling of cognitive processes requires the following:. I have to find the topic sentence of the paragraph. The topic sentence is what the paragraph is about. It is a good strategy to include a demonstration of performance that displays typical fears and deficiencies of learners at the outset, and gradually reveals the improvements in the modeling Shunk, What should I look for then?
Oh, this sentence seems to be connecting the idea of the previous paragraph to the idea of this paragraph. A key component of cognitive apprenticeship is that students learn the cognitive processes in realistic contexts so that they may process their thoughts accordingly in actual situations. In the teaching of reading comprehension, teachers might use an authentic newspaper and go through the process of reading and comprehending an article.
Returning to the story of the fourth grade at Cedars Elementary reveals how Ms. Reed provide or could have provided cognitive apprenticeships starting with modeling.
As mentioned earlier, Ms. Beauchamp leads the class in a very traditional way. She presents knowledge, gives instructions, and corrects students if they are wrong. Students listen to Ms. There is no continuum of activities from the teacher to the students because Mrs. Beauchamp provides no demonstration of student activities. No aspect of modeling is found in her class.
Problem-solving activities play an insignificant role in Ms. She often begins the class by reviewing and correcting the answers to the textbook questions that students have individually prepared as assignments. Thus, this approach provides no cognitive modeling for solving problems.
Unlike Ms. Reed conducts the class as a facilitator and collaborator in its activities. In her class, there is little distinction between the activities of the teacher and those of the students. The students creatively replicate the activities of the teacher and others. Coaching and scaffolding are two critical components of the cognitive apprenticeship model. These elements are addressed together because they share many characteristics. Scaffolding, while distinct from coaching, can actually be categorized as a type of coaching.
In this section we will discuss why this is the case. Although it is considered a separate component of cognitive apprenticeship, coaching has as much in common with the process of scaffolding. Both involve a teacher or a more knowledgeable other providing some type of assistance to a learner to facilitate attainment of a goal.
Coaching may be seen as a broader term than scaffolding, however. In fact, scaffolding can be considered only one form of coaching see Figure 1. At this point a closer examination of coaching is in order. The process of ensuring this goal may begin with helping learners choose their tasks admittedly, not always an option , and may end with providing feedback to learners on their completed products. In between these steps, many other coaching strategies may be employed, including providing hints and scaffolding, evaluating how learners actually go about the process of learning, diagnosing problems, offering verbal and nonverbal encouragement, structuring lessons in ways that facilitate learning, and working with learners to overcome weaknesses.
So, it can be said that coaching is the process of doing whatever it takes to assist learners in their learning, from start until finish. It is now instructive to turn to one of the components of coaching—scaffolding. Of the six characteristics of the cognitive apprenticeship model, scaffolding is perhaps the best known and most discussed in the literature. Although there are numerous definitions of this term, any one of them is likely to provide the basic idea of what scaffolding is all about.
At first glance, the more detailed first definition may not appear to have as much application to an educational environment as the more general second definition. A scaffold is a structure that supports students while they work at a level higher than their ability allows without assistance. Of course, when educational researchers, practitioners, or theorists talk or write about the process of scaffolding, each has a specific conception of what this process refers to.
Although scaffolding has some very specific components that will be discussed later, in almost all cases, it refers to any situation in which two processes occur. The first process involves providing support to the student by a more knowledgeable other MKO , whether a teacher, a better informed peer, a community member, a domain expert, a parent, or in some cases, even a computer.
The second process inherent in the scaffolding experience involves the gradual removal of the support system in a way which leaves the student able to perform unassisted the task which was previously possible only with the scaffolding.
Further, once the student, with the benefit of scaffolding, masters the task, the scaffolding can be removed. Just as a building remains erect after its scaffolding is removed, a student should be able to achieve the task again without the aid of scaffolding. Zhao and Orey identify six elements of ideal scaffolding. The first element is the sharing of a specific goal, which typically refers to achieving a task.
Sharing the goal increases intersubjectivity between the learner and the MKO and also helps decrease learner frustration because the learner knows that he is not alone in trying to achieve the task. The second element of ideal scaffolding is a whole-task approach. This simply means that the focus is on learning the task as a whole, not concentrating on individual sub-skills of the task. The third element is the immediate availability of help.
This is in alignment with the primary basis of scaffolding: help the learner when he is at a point where he needs help in order to continue the task. When learners are left for too long at a point where they cannot make progress, they may lose interest and motivation and become frustrated. The fourth element is that the scaffolding should assist the learner in his intentions. The MKO should help the learner on whatever he is currently struggling with, so as not to interrupt another train of thought.
This meshes well with the previous element of immediacy—helping the learner when he needs it, not after he moves to another task or problem. The fifth element of ideal scaffolding is providing an optimal level of help. The MKO should provide assistance that is tailored to the needs of the learner. It should be just enough to get the learner past his current difficulties. The sixth and final element of scaffolding is the conveying of an expert model.
An expert model is a model of a task that will lead the learner to accomplish the task efficiently. This model provides a framework around which learners can organize their skills.
Now that some of the background and components of coaching and scaffolding have been described, the ways in which the two teachers employed them in their classrooms may be examined. It is also productive to speculate on how they could have further helped their students to learn. She structures class events to provide multiple opportunities to learn about the New Deal and the Depression.
She asks her students to read ahead and answer textbook questions, goes over the answers in class, provides a short film for her students, conducts a review, has her students act out a play, and then assesses student learning with a test.
Can any of this be accomplished in a way that will engage her students with the material and help them gain a better understanding of the events that occurred during this period in history? To begin, it is worthwhile to examine Ms.
To increase learning beyond the simple recitation of names and dates, Ms. Beauchamp could lead the class in a discussion of why each answer is correct or incorrect, which would be an excellent use of coaching. She could also ask more open-ended questions about important points, rather than the basic questions in the textbook that can be answered with one or two words.
It also provides Ms. Beauchamp more opportunities to provide hints to students, allowing them to piece together answers from what they are reading or discussing in class. For example, students might be asked to work in small groups to create their own mini-plays. Beauchamp could then work with individual groups, providing ideas to improve their productions and correcting any mistaken ideas they have.
Also, it would give her a chance to encourage her students to use research materials and artifacts from outside the class, as well as to express their own interpretations of history in a dramatic form. In considering the notion of scaffolding in the context of the story, Ms. While Ms. Considering the inferred goals of Ms. Do students require support to remember that the Great Depression began in ? However, the appropriateness of these goals are a legitimate object of question.
How have student knowledge and understanding been affected at the completion of this unit? Is it likely that Ms. The most likely answer: probably not. If anything, they may recall that FDR wanted to provide more jobs to Americans and that the Great Depression started around In addition, Ms. Reed uses coaching and scaffolding strategies in her classroom. She chooses a variety of learning tasks from which her students may choose: reading their textbook, interacting with contemporaries of the historical era under study, synthesizing information into a multimedia presentation, watching videos, and other activities.
Not only does Ms. Reed choose these activities wisely, she implements them effectively. She sees that support is available to her students during each activity, through both human and non-human resources.
This very deliberate decision-making is an excellent way of overseeing the student learning process, and, within each activity, coaching occurs. In the scenario, Ms. For instance, while student groups are interviewing the classroom guests, Ms.
Reed challenges them to take on different roles in the interviewing process, even if the students are not completely comfortable doing this. She encourages them, and likely expresses her confidence in their abilities, while also reminding them that she is available to assist them with any questions or problems they encounter. Coaching also occurs during the development of the multimedia presentation. Reed keeps her eye on the groups and helps them organize their thoughts and work.
In addition to Ms. All in all, the students in Ms. As a result, Ms. Thus, Ms. Admittedly, this goal requires more work from her and her students. Simply stated, this goal is more difficult. However, while Ms. To promote this goal of understanding, Ms. Reed provides numerous types of scaffolding. Reed brings three visitors into her class with whom her students are encouraged to discuss the Depression, the New Deal, and various other components of their lesson unit.
Not only is this social context made available to the students, so too are various physical artifacts, such as clothing, food stamps, and scrapbooks. These items can also be considered part of the scaffolding process, as they help students understand how people in their community or state lived in the late s and early s.
Other scaffolds are present in Ms. But what about Ms. What happens after Mr. Abrams make their last visit to the classroom, and after the classroom discussion turns to the next series of historical events? It appears so. In the process, she also increases the likelihood that her students will internalize and retain much of their learning experience once they complete the unit and leave her classroom.
Which of the two teachers do you identify with and why? Scardamalia Eds. Hillsdale: Erlbaum. Brown, J. Situated cognition and the culture of learning. Educational Researcher, 18 , 32— Collins, A. Cognitive apprenticeship: teaching the craft of reading, writing, and mathematics. Technical Report No. Center for the Study of Reading. ERIC Document Hacker, D. Implementing reciprocal teaching in the classroom: Overcoming obstacles and making modifications. Journal of Educational Psychology, 94 , — New models of teacher-student interaction: A critical review.
European Journal of Psychology of Education, 11 , — Mayer, R. Thinking, problem solving, cognition. New York: Worth. Palinscar, A.
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