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Philosophical perspectives on constructivist views oflearningRichard S. Prawat & Robert E. FlodenPublished online: 08 Jun 2010.

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EDUCATIONAL PSYCHOLOGY, 1994,29(1), 37-48 Copyright O 1994, Lawrence Erlbaum Associates, Inc.

Philosophical Perspectives on Constructivist Views of Learning

Richard S. Prawat and Robert E. Floden bfichigan State University

At present, soda1 constructivists agree on little more than the important assumption that knowledge is a social product. Beyond this, there is little agreement about proems. Different viewpoints about what it means to negotiate meaning and what the object of that negotiation ought to be (i.e., strategieslskills versus big ideas) reflect different assumptions about learning and the nature of truth. We examine these assumptions by contrasting three underlying world views: mechanistic-information processing, organismic-radical constructivism, and Deweyan contextualism or transactional realism. This third world view, we argue, is most consistent with idea-based social constructivism.

Constructivist learning theory is based on the now com- monplace idea that knowledge: is actively constructed by the learner. This notion has led to calls for a dramatic shift in classroom focus away from the traditional transmission model of teaching toward one that is much more complex and interactive. In response to these calls, various "con- structivism~" have emerged in the last decade, each with its own views about how best to facilitate the knowledge construction process. Although information processing and radical constructivist versions of the constructivist approach are the most popular alternatives, social con- structivist theory appears to be gaining ground. Social constructivists are distinctive in their insistence that knowledge creation is a shared rather than an individual experience; they maintain that, to quote Goodman (1986), knowledge is developed "by the dialectical interplay of many minds, not just one mind" (y. 87).

Interest in social constructivism is fueled, in part, by the growing realization that both information processing and radical constructivism~ have weaknesses inherited from similar approaches developed 30 years ago during the last great educational refonm effort in this country. At that time, one group of reformers took its cue from the academic disciplines and another opted for a "learner centered" approach that emphasized more general inquiry and prob- lem-solving skills (Prawat, 1992). As we argue in this article, social constructivism, with strong links to Deweyan philosophy, provides the best oplportunity to redefine the terms of the longstanding truth (subject matter

Requests for reprints should be sent to Richard S. Pmwat, College of Education, Michigan State University, &st Lansing, MI 413824.

centered) versus competencies (student skill centered) de- bate.

At present, the only common link connecting all avowed social constructivists is the premise that knowl- edge is a social product. From this, of course, other import- ant assumptions follow, including the notion that knowledge evolves through a process of negotiation within discourse communities and that the products of this activ- ity-like those of any other human activity-are influ- enced by cultural and hisforical factors. Still, this set of core assumptions is too small to allow social constructiv- ists to reach agreement on a growing set of pragmatic issues.

In the case of social-constructivist theory, there is general agreement about outcome (i.e., socially pro- duced knowledge), but there is little agreement about basic process: what aspects of knowledge best lend themselves to negotiation, and what it means to negoti- ate this knowledge. The purpose of this article is to examine the "whatw-and "how" of negotiation from a philosophical perspective, It is our hope that this effort will provide much needed theoretical grounding for so- cial constructivism, the newest kid on the block. In our philosophical analysis, we draw heavily on Pepper's (1942) World Hypotheses,, a metaphysical treatise that has been rediscovered recently by developmental psy- chologists (e.g., Overton, 1984, 199 1; Reese, 1991).

The fociis in this article is on contextualism, one of three world views discussed by Pepper. We believe that contextualism provides the most promising theoretical rationale for social constructivism. Because this view is best understood contrastively, however, we discuss the two most popular alternative views presented by Pepper:

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mechanism and organicism. Information-processing theory and radical constructivism, we argue, are best understood as offshoots of these two world views.' Ex- amples of how each of the three different world views (mechanism, organicism, and contextualism) influence cur- rent classroom research are presented, with mathematics teaching and learning as the focus.

We begin by briefly examining the larger question of why educational researchers should trouble themselves with Pepper's (1942) world views. Rather than strive for theoreti- cal purity, it may make more sense to reach across theoretical boundaries, selecting those aspects of each world view that seem most appropriate for the task at hand. One prominent developmental psychologist, Willis Overton, suggested that researchers in his field do just that. Overton's (1984) advo- cacy of "hybrid" theories is based on the belief that one of the three theories- contextualism-is too imprecise to serve as the "hard core" of a rigorous research program. Instead, he suggested that mainstream theorists in developmental psy- chology, those who embrace mechanistic or organismic world views, make selective use of contextualism. By adopt- ing a hybrid mechanistic-contextual perspective, mechanistic theorists can be sensitized to the important role of antecedent events as an influence on behavior. In a similar vein, a dose of contextualism heightens the organicists' tendency to focus on the organism as a whole and thus reinforces a key aspect of their thinking.

Overton's (1984) pejorative view of contextualismis based on two widely shared assumptions about contextualism that have limited its use to this point: First, and most seriously, it is ill suited to the scientific goal af control and prediction because of its "dispersive" nature. This questionable quality reflects the fact that contextualists, unlike their mechanist or organicist counterparts, assign a prominent role to change and novelty.' According to contextualists, the meaning of an act may undergo change as it unfolds in a shifting environment, and new acts can spring up willy-nilly. "Anything can hap- pen," Reese (1991) explains, 'This particular act (in the root metaphor) may or may not end, and may or may not be followed by another act, which we may or may not expect" (p. 198).

Integrative theories, such as mechanism and organicism,

'1t may seem strange to argue that information processing theory repre- sents, simultaneously, a mechanistic and a constructivist view of learning. In this article, we argue that information processors proposed are scientific realists-which is to say, they rely on formal as opposed to contingent explanations of learning (Overton, 1991). The mediating processes proposed as part of a formal explanation of learning form the basis for any construc- tivist claims information processors may wish to make. However, because the output of these processes reflects environmental structure, we argue that the theory is, at root, mechanistic.

'1n mechanistic and organismic theory, chance or unpredictability is an admission of ignorance. As Pepper (1942) pointed out, if it cannot be explained away, it is "corralled out in certain restricted areas of the world where the unpredictable is declared predicted, possibly in accordance with a law of probability" (p. 143).

may be better bets in a theoretical sense than a dispersive theory, such as contextualism.

We argue, however, that indeterminacy is hardly grounds for rejecting a world view from a postmodernist perspective. Postmodernists share the contextualist assumption that, in science, there can be no final or complete analysis of anything (Rosenau, 1992)-no "top" or "bottom" to the world, to use Pepper's terminology.

The second pejorative assumption about contextualism is harder to characterize. Pepper himself worried about the contextualist's ability to stay the course, speculating that those who embrace the theory suffer from an "identity crisis" that leads them to question the feasibility of sticking to a middle-ground position (i.e., one that is centered around neither subject nor learner). Contextualists, he speculated, are "constantly on the verge of falling back upon underlying mechanistic structures, or of resolving into the overarching implicit integrations of organicism" (p. 235). What might be described as a "slippage" problem was the bane of Dewey's existence. Dewey, whom Pepper regards as one of the most prominent contextualists, expressed constant concern about his followers' tendency to slip off into either an outside-in, "subject-centered" version of his educational philosophy or, more likely, a "naive" learner-centered version that empha- sizes the enjoyment value of an experience rather than its educational value.

Slippage may be less of problem today than it was 50 years ago because contextualist theory no longer stands alone, as it were. The most controversial aspects of this world view, in its current instantiation as social constructivism, find support in current learning theory and in a host of related views: posmodornism, open-systems theories in science, and recent views in evolutianary theory.

THE PROBLEM WITH A HYBRID APPROACH: DIFFERENT THEORIES OF

TRUTH

Despite concerns about the theoretical feasibility of con- textualism, there is ample reason to reject the hybrid ap- proach. Pepper's treatment of the three world views made it evident why contextualist adjustments to mechanistic or or- ganismic world views do not, to use his phrase, "work hap- pily" (p. 147). "The damage they do to each other's interpretations," Pepper asserts, "does not seem to me in any way to compensate for an added richness" (p. 147). This is because, at root, each world view takes a different stance on the nature of truth. More needs to be said on this point.

As Pepper argued, the mechanistic or information-process- ing world view embraces a correspondence theory of truth. According to this view, a belief is truthful to the extent that it accurately represents what is outside the mind; mental structures must correlate with or correspond to those struc- tures afforded by the environment. The organismic approach, taken by radical constructivists, subscribes to a coherence

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PERSIPECTIVES ON LEARNING 39

theory of truth. As Putnam (1981) explained, '"Truth,' in an internist view, is some sort of (idealized) rational acceptabil- ity-som~ sort of ideal coherence of our beliefs with each other" @. 49).

In the contextualist world view, which we believe underlies social constructivist views of learning, a third, transactional approach to truth is advanced: Pepper terms this approach the "qualitative confirmation" test of truth. It relies on verifica- tion linked to actions and events. He stated that, "The refer- ential structure of a true hypothesis therefore does carry through a set of operations and enter into the structure of the event referred to by the hypothesis as its successful verifica- tion. (1942, p. 276)

As we argue in this article, the approach to truth embodied in contextualist theory is at variance with our current views about learning. Information processing and radical construc- tivism make a similar, important assumption about the locus of mental activity: It occurs deep within the human mind. Both of these views favor what might be described as a "head-fitting" model of learning. In information-pr~ocessing theory, mental activity flown from the periphery to the core. During this process, irrelevant or incidental aspects of stim- ulus input are extracte~d and discarded, leaving an abstract representation of the most important structure provided by the environment. To be judged valid, this representation must bear some direct relationship to important information con- tained in the original input (Neisser, 1976).

Radical constructivists, in contrast, focus their attention on subjective experience, viewing coherence as the most reliable test of truth. "Rightness," to quote the most prominent pro- ponent of this view, "must be seen as the fit with an order one has established oneself' (Glasersfeld, 1987, p. 329). As with information-processing theory, cognitive regulation is thought to occur far from the boundary betweem the individ- ual and the environment. This reinforces the dualistic notion that mind and material world are separate and distinct realms.

The test of truth favored by contextualists suggests a different model--one tlhat locates the process more on the periphery between the organism and the envirorment, As the notion of qualitative confirmation suggests, contextualists believe that our intellectual relationship with the vvorld is fluid and permeable. Dewey, one of the early proponents of contextualist thinking, captured the nature of this relation- ship well: "Both idea anti 'facts' are flexible," he wrote, "and verification is the process of rnutttal adjusmzcnr, or organic interaction [italics added]" (189C~11969y p. 87). As we argue in this article, the model of learning that best fits the con- textualist view of truth is one that, relies on perceptioh.

Perception, defined interactively, rather than as the pas- sive registration of stimuli, is clearly transactional in nature. Historically, perception was thought to be closely connected to th~tlght.~ In recent tirmes, as Gibson (1979) explained, psychologists have drawn a sharp distinction between see ing, "having temporary sensations one after another," and knowing, "having permanent concepts stored i~n memory" (p. 258). Neisser (1976) argued that the adoption of a com-

puter metaphor by information processors had a good deal to do with this. Piagetians, o n the other side of the objectiv- istfsubjectivist divide, must share part of the blame; Piaget, after all, insisted that the "figurative" or perceptual aspects of thought were at the beck and call of the operational.

Neisser (1976) developed an argument for a view similar to the one espoused in this article---namely, that perception plays a central role in cognition. Ideas and mental imqes derived from perceptual schemata represent the anticipatory phase of the perceptual process. Ideas "educate attention," allowing us to access aspects of our enviromnent that otherwise would be ignored or overlooked (Praw'at, 1991,1993). In constructing an idea, individuals, in concert with others, prepare a kind of plan for picking up information that might be provided by the envi- ronment. This view fits well with that of Dewey, who also considered knowledge an "'anticipation'': 'To understand," wrote Dewey, "is to anticipate together" (192511981, p. 141).

Tlhe contextualist approach to truth, then., pints the way toward a particular model of leaning--one that highlights the role of perception in cognition. This is important because a perceptual model of learning is far from neutral as regards the practical issues that currently divide social cons~mctivists (i.e., present-day contextualists). 'The: argument, which is central to this paper, goes something like this: The approach to truth developed by contextualism (i.e., qualitative confirnation) is biased towards a perceptual moldel of learning; this model of learning, in turn, fits better with a certain kind of intellectual outcome-ideas-than it doles with the currently more popu- lar alttwative-cognitive skillls and strategies. The social construction of ideas, in turn, fits better with a disciplinary- oriented view of classroom discourse than it does with the most prominent current dternative-cooperative learning. These notions are expanded in the next section.

DIFFERING VllEWS ABOUT THE NATURE OF INTELLECTUAL

PRODUCTS AlND CLASSROOM DISCOURSE

As indicated previously, social constructivists currently disagree about two aspects of the theory that have practical (and theoretical) significance: What kind of intellectual

- -

3 ~ h e word theory derives from the Greek "theamai," or "I behold," suggesting that the ancients saw a elations ship between the visual and the ideational (Coles, 1989). Wamock (1976) traces the development of this notion in several prominent philosophers, including Kant, who wrote, "What is first given to us is appearance. When combined with consciousness it is called perception" (in Wamock, 1976, p. 28). More recently, therelationship between perception and cognition is highlighted in Miller's (1987) fascinat- ing account of scientific discovery in physics. Creativity in science, Miller documents, is closely linked to imagination and perception. Bloor (1991) made a similar point in mathematics, attributing such achievements as Archimedes's geometric proofs to thought experiments that were perceptu- ally based. Proofs come at the end ofthis process and thus misrepresent the nature of thought that gave rise to the discovery. "Even in mathematics, that most cerebral of all subjects," Bloor misted, "it is people who govern ideas and not ideas which control people" ((1991, p. 155).

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product ought to be assigned highest priority-strategies or ideas-and what it means to construct knowledge through negotiation. The stances social constructivists take on these two issues are not unrelated. Those who come down on the side of cooperatively negotiated strategy instruction opt for a tamer, gentler version of social constructivism. This group, which tends to favor a hands-on, project-based approach, is clearly in the majority. The scenario associated with idea- based social constructivism is less familiar. The image this approach evokes is more akin to the give-and-take of aca- demic disciplinary communities. Ideas are instantiated or made concrete through various underlying representations; the teacher's task is that of initiating youngsters into particu- lar interpretive stances vis- a-vis these representations (Cobb, 1989; Prawat, 1993).

Strategies Versus Ideas

Those who regard cognitive skills and strategies (e.g., prob- lem-solving heuristics in mathematics) as the most important products take their inspiration from recent studies of out-of- school learning. They argue that students should learn how to use disciplinary-based cognitive tools in the same way that apprentice craftsmen learn to use the tools of their trade. Absent this sort of authentic cultural support, students will continue to acquire very limited, school-based versions of these powerful intellectual skills and strategies (Brown, Col- lins, & Duguid, 1989).

A smaller group of theorists argues that big ideas are the most important products produced by disciplinary communities (Prawat, 1993). The problem with a focus on cognitive skills and strategies, according to this perspective, is that it shifts the focus away from a transformative approach to education toward one that is informative in a narrowly practical sense. Big ideas (e.g., the way numbers can be taken apart and put together in mathe matics or photosynthesis in science) can enlarge a child's field of vision, and thus have the potential to transform thinking in a way that is sadly missing in most of what passes for contempo- rary education (Prawat, 1993). Idea-based social constructivism, however, may require a radically different view of learning.

As indicated previously, an idea-based approach fits best with a perceptual model of learning. This model of learning, in turn, is more compatible than others with the contextualist theory of truth. The fust issue that divides social constructivists, then, is not a trivial one. The way in which it gets resolved is important both practically and theoretically. It also bears on the second issue discussed further in this article, which relates to the nature of the negotiation process in the classroom.

Negotiation

As has been pointed out elsewhere (Prawat, 1989), there are two distinctly different meanings associated with the term negotiation. The first emphasizes the importance of compro- mise and consensus building; the goal, according to this view,

is to get people to agree to something. As Mellin-Olsen (1993) pointed out, consensus-building requires a certain amount of give and take on the part of participants: "In order to receive something both parts have to give away something" (p. 4). Advocates of cooperative learning have adopted this perspective. If handled skillfully, participants are expected to "own" the results of the bargaining process.

The second meaning associated with the term negotiation defines the process differently: In this sense, to negotiate means to "skillfully overcome obstacles," as in "negotiating a winding road." In the classroom context, obstacles to un- derstanding may include such variables as common misun- derstandings or preconceptions that interfere with one's ability to grasp new material. Negotiation is thus viewed as an opportunity to surface and clarify points of agreement and disagreement. Compromise rarely leads to insight; in fact, it can be argued, when reaching agreement is the overriding goal, important differences are often papered over or ignored. Disagreements provide impetus for research in the disciplines and can provide motivation for learning in the classroom.

The problem with the second approach to negotiation is that it rarely occurs outside the academy. The key for teachers who want to structure discourse in this way is to convince students that they can defend a view or opinion without feeling they have to defend fhemselves. In this approach, "oppasing views become alternatives to be explored rather than competitors to be eliminated" (Roby, 1988, p, 173). Because of the difficulties involved in orchestrating this sort of discourse, it is typically carried out in a wholeclass con- text. The teacher's role in this regard, according to Lampert (1990), is not unlike that of a dance instructor. Like that form of instruction, it requires "some telling, some showb, and some doing it with them along with regulw rehe~sals" @. 58).

As the Lampert quote demonstrates, when the negotiation process is defined as one of overcoming obstacles, teachers are actively involved throughaut. Their role has been likened to that of a cross-country guide who is helping a goup traverse new cognitive territory (Prawat, 1989). An important aspect of the guidds role is to point out the cliff6 apd thick- ets-those aspects of the terrain that are most likely to impede the group's progress. In the classroom, this would involve probing the limits of students' understanding with difficult cases or "entrapments" (i.e., questions that are designad to lure students into agreeing yith certain enoncoys ideas). Teachers are apt to feel camfvmble in this role only if they view uncertainty and conflict as natural and potentially growth producing far rnaabers af tlw leiarxrimg community.

Teachers play a diEerant;role in coppexative IeMng-that of orchestrator and managm. Teachers es&hli$h the ground rules for grorrp work, drafine the task, h e l ~ smcttlre smdent- to-student interaction, aften by assigning ~pecifiq ralgs to group members, and provide incentives far rgbdents to work together. Once the system is establisheg, it i~ $upplrbsed to be self-systaining, free& aacherg to &cula?e md mciirit~r each group's progress and provide advice or as&istanoe as needed.

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PERSPECTIVES ON LEARNING 41

It is our contention that the social construction of ideas is best advanced when teachers abandon the orchestrator role and join the fray, becoming active participants as they attempt to guide the group toward the disciplinary high ground. The important point to keep in mind is that teachers' views about negotiating meaning in the classrolom are likely to1 vary de- pending on what kind of disciplinary product they choose to emphasize.

The focus shifts now to an examination of the basic tenets of each of the world views discussed by Pepper (1942).

THE MECHANISTIC WORLD VIEW AND INFORMATION-PROCESSING APPROACHES TO LEARNING

Not surprisingly, in view of its name, the mechanistic world view is based on a machine m~etaphor. The e:nvhnment is regarded as the key determinant of behavior. The human "cognizer" is thought to play a relatively subordinate role vis-6-vis the environment. Thelemer's task, a~ccording to the mechanistic view, is to develop greater responsivity to what- ever important structure the environment affords.

Discrete Versus Consolidated Mlechanisms

Pepper's distinction between discrete and consolidated mech- anisms foreshadowed the distinction in psychology between stimulus-response learning and the mediated 1e;lming favored by information-processing psychologists. In a discrete mech- anism, such as the lever, there is a one-to-one relationship between cause and effect, event and experience. Discrete mechanisms, to use House's (199 1) language, are well suited to a "flat ontology," which assumes that one's view of reality emerges directly from sensory data, without the need for any intervening cognitive mechanism.

Those who favor a more complex approach share the mechanist assumption that the environment is the only im- portant source of knowledge about reality. Their view of reality, however, is more complex. Because reality is strati- fied, or multilayered, our knowledge of it cannot be derived directly from sensory input. Physiological data, although more or less in tune with the environment, do not constitute knowledge. Knowledge, rather, h the end product of a series of intervening processes. Advocates of consolidated mecha- nisms thus reject the idea that there is a direct relationship between knowledge and experience. Their way of character- izing the process foreshadows the approach favored by con- structivist information processors, They bel'ieve, Pepper (1942) wrote, that we learn

... about the structure of the great machine by a sort of detective work. We note changes among our private second- ary qualities (i.e., symbolic ways of knowing), infer their correlations with the physiological configurations which are

in our organism, and thence infer the structural characters of the: surrounding field from, its effects upon the configuration of our organism. (p. 229)

The modified version of correspondence theory described above bears more than a passing resemblance to a perspective developed by philosophers of science known as scientific realism (Bhaskar, 1978). This view assumes that all events- inside or outside the human mind-are best explained with reference to underlying entities or structures. House's (1991) example is useful: Although the naive realist assumes that a lemon really is yellow, the rscirmtific realist looks beneath the surface, seeking an explanation based on the: way light waves are refracted off the surface of the lemon and how our vision system processes this information.

The example of classroom research that follows is consis- tent with Pepper's notion of consolidation. Despite the fact that it relies on mediated as opposed to direct learning, it reflects a mechanistic world view. According to this perspec- tive, learning is a process of acquiring accurate understand- ings of fixed entities and re1,ationships that are thought to exist independently of human activity (Cobb, Yackel, & Wood, 1992). Given the environmentally driven nature of this orien- tation, it is not surprising that researchers who embrace it focus on getting the instructiolnal materials right. In mathe- matics, in particular, it is assumed that concnete representa- tions serve as a bridge betwwn truths present it1 the real world and the subsequent instantiation of those truthis in the form of disciplinary knowledge.

Before presenting our example, a few words need to be said about our use of studies on mathematics to illustrate the impact of world views on classroom practice. lTis may strike some ,as odd, given the generally abstract nature of this type of disciplinary knowledge. As Resnick (1988) pointed out, however, even though ma~theimatical statements deal with such abstract entities as numbers, lines, and points, they can still be mapped onto vario~ls real-world situations. Indeed, some mathematicians assign the highest priority to this map- ping function in defining the discipline. Hoffman (1989), a professor of mathematics ;at IbZIT, argues that the aim of mathematics is "to classify, explain, and understand patterns in all their manifestations-whether patterns have to do with quantity, shape, arrangement, or form" @. 18). Becausemath- ematics involves knowledge about abstract systems as well as practical applications, it may provide the sbrpest contrasts between different views of learning and knowledge, particu- larly at the elementary school 11evel.

A Research Example

Nesher's (1989) approach involves cognitive modeling, or the presentation of carefully crafted external representations that exemplify important math~ematical ideas. According to Nesher and others (cf. Cobb, Yackel, & Wood, 1992) who subscribe to an internalization view of knowledge, it is im-

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portant to get these representations right. Representations used for instruction must strike a difficult balance between being comprehensible in their own right and providing a structure or framework for the more abstract mathematics yet to come. On the surface, Nesher wrote, these demands may appear contradictory; the success of the approach, however, rests on their satisfaction. What is called for, Nesher believes, is a system based on what she calls pedagogical realism. Pedagogical realism addresses (a) the need for students to construct knowledge thraugh direct interaction with the en- vironment and (b) the need to arrive at mathematical truth.

The exemplifications designed by Nesher are consistent with pedagogical realism, she believes, because they allow the child to test the truth value of mathematical sentences (e.g., 3 + 2 = 5) through the use of a "dummy reference," which stands in for themoreabstract real-worldinstantiations of those sentences. "The exemplification component," Nesher wrote, "is only a pedagogical device that serves as a 'dummy reference' on which to build a sense that is analogous to the mathematical sensey' (1989, p. 202).

The representation Nesber used to exemplify an additive relationship among three numbers (e.g., 3 + 2 = 5) consists of three rods that fit together to form a triplet. The two top rods represent the numbers on the left side of the equation, and the bottom rod represents the number on the bottom. If the number sentence is correct, the top two rods, when laid end to end, should form a perfect triplet. These exemplifications are transparent enough so as to require little additional nego- tiation; once internalized, they form the semantic basis for mathematical understanding.

According to Nesher, children learn by internalizing the structures they encounter in the curriculum. She assumes that good materials unambiguously represent the structure that the curriculum designer wished students to learn. Differences between what students have learned and the desired structures represent errors, which may be eliminated through im- provements in the design of materials. The criterion for success in student learning is correspondence between the structure represented in the classroom environment and the structure in the student's mind.

THE ORGANISMIC WORLD VIEW AND RADICAL CONSTRUCTIVISM

Organicists attribute whatever order or structure exists in the human mind to an act of individual creation rather than discovery. As Piaget (1974) put it, human intelligence is the expression of a "general tendency toward endogenous recon- struction (by new variations and 'intraselection') of unstable, exogenous acquisitions" @. 75). It is not surprising, then, that organicists look inward for the ultimate test of truth. Learners know instinctively when they have hit on a feasible way of dealing with important aspects of experience. The radical constructivist point of view says:

. . . it makes no sense to assume that any powerful cognitive satisfaction springs from being told that one has done some- thing right, as long as "rightness"is assessed by someone else. To become a source of real satisfaction, rightness must be seen as the fit with an order one has established oneself. (Glasersfeld, 1987, p. 329)

For the organicist, the test of truth involves more than consistency. Truth is also dependent on the inclusiveness of the system of beliefs. In a Hegelian manner, systems of belief tend naturally to become more encompassing and integrative, leading towards an absolute, complete understanding. The process of integration, according to Pepper, is self-initiating. It is thought to work this way: In our initial encounters with a domain, we experience primarily fragmentary bits and pieces of data. Truth is only partial, a situation that is inher- ently unstable. Fortunately, fragments have "nexuses"; as part of the dialectical process, these nexuses reach out "like tentacles" to fragments that are the exact opposite. This produces conflict, which eventually is resolved through the process of integration. The resulting synthesis, however, soon runs afoul of other, equally rich fragments, thus creating a renewed need for integration, 'With each level," Pepper (1942) assures us, "the fragment is richer and more nearly complete, and the progress prefigures the goal where all fragments are united and harmonized'' (p. 293).

Radical constructivists, who study mathematics learning, seldom take a position of extreme idealism. For them, envi- ronment still plays a role, albeit a negative one. Individuals propose theories, which remain feasible as long as they es- cape coming in conflict with the environment. Nonetheless, the fact that a theory survives tells us very little about the nature of the world. As Glasersfeld put it:

While we can know when a theory knocks against the con- straints of our experiential world, the fact that it does not knock against them but "gets by" and is still viable, does in no way justify the belief that the theory or model therefore depicts a "real" world. (1987, p. 140)

To determine whethex the theory is justified, one must turn to internal criteria, such as explanatory breadth, simplicity, and the like.

A Research Example

Steffe's work (1988, 1992) is an example of the organismic or radical constructivist approach to mathematics teaching and learning. Like Piaget, Steffe developed a model of the various stages youngsters go through in constructing a num- ber sequence. These stages are characterized by a decreasing dependence on concrete props in the counting act: At the first, perceptual stage of counting, children develop an awareness of plurality (but not numerosity) that is tied to a particular experiential situation. Through a kind of "procedural accom- modation," the child arrives at a composite count of objects

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PE,RSPE(JIIVES ON LEARNING 43

by connecting the specified collection with the last number word.

At the second, figurative stage, children still needl concrete support for counting but can now generate this support on their own, in the absence of the items to becounted. Typically, children at this stage first rely on finger patterns to create the figurative collection of items to be counted (Steffe, 1992). This represents a halfway point at this stage, however: "For a counting scheme to be truly figurative, both the activity of the scheme and the items that are to be counted must be internalized" (1992, p. 89).

As a transition to the next stage, children begin to lift the sequence out of its concrete embeddedness: "Where there were once sensory items, there are now only empty containers or 'slots' that contain records of the sensory items" (Steffe, 1988, p. 125). At the initial number sequence stage, children have fully internalized the number-word sequence. This al- lows them to coordinate the number sequence-counting on, for example, or counting back. It also allovvs children to self-consciously monitor the process: 'When counting, the child is aware of the counting acts between the beginning and end of counting7'(Steffe, 1992, p. 94). Whal children still don't understand very well at this stage is the ''nested'' nature of the number sequence-the sense in which one is included in two, two in three, and so on. This develops as part of the fourth stage of the counting scheme. What is lacking in the child's understanding at this stage is an appreciation of the fact that an embedded number also exists apart h m the embedding (e.g., that seven is nested in nine but also is separate from nine). It is not until the fifth andl final stage in the development of the number sequence that the child devel- ops a full awareness ofpart-vvhole numerical relations. At this stage, according to Steffe (1992), the number sequence is "explicitly nested."

The key to teaching, from a radical constructivist perspec- tive, according to Arcavi and Schoienfeld (1992) is to care- fully attend to what students have to say:

It is not enough to detect sources of students' difficulties and then to look for predesigned ways to get it o~ut of them. Listening calls for detecting the germs of genuine knowledge in what students say and thinkirlg about ifhow those ideas can be exploited, even when the paths they imply diverge from the "traditional" avenues to a nlew topic. (p. 333)

One way to exploit student knowledge in mathematics is to get them to use it in challenging problem situations. Teachers can use their awareness of student knowledge to devise these situations to create just the right level of challenge or impasse. When children encounter impasse or perturbation in the course of goal-directed mathematical activity, it forces them to reflect on their own constructs. This individual reflection, in turn, leads to a reorganization of knowledge or undcrstand- ing. "In trying to solve practical problems," Eleanor Duckworth wrote, "children spend time reorganiihg their 1e:vel of under- standing" (1987, p. 49). Steffe (1990) expressed it this way:

Essentially, mathematical leaning involves accommodation of current mathematical concepts to neutralize perturbations that can arise in one of several ,ways. As such, it includes what Pollya (1962) meant when he stated that to have a problem means "to search consciously for some action appropriate to attain a clearly conceived, but not immediately attainable aim." (p. 393)

Th~ls, radical constructivists believe that students learn through a uniform sequence of internal reorganizations, each more encompassing and integrative than its predecessor. To promote learning, the teach~er or cumculum designer tries to accelerate the pace of reorganization by helping students examine the coherence sf their current ways of thinking. Getting stuck at some stage, at which the individual is unable to see how he or she might reach a more integrative synthesis, represents a weakness in the environment for cognitive growth; this might be addressed by offering the child more opportunities to explore holw .well the various pieces of un- derstanding fit together or cohere. The success of schooling is indicated by students who make rapid progress towards the most encompassing, integrative understandings in the field.

THE CONTEXTLIALIST WORLD VIEW AND SOCIAL CONSTRUCTIVISM

The root metaphor for contextualism is that of the act or event unfolding in context. This metaphor connotes an open-ended- ness, in marked contrast to the deterministic orientation em- braced by mechanistic and organismic theorists. The c~nte~tualist emphasis on change or novelty is one of its most distinctive features. Anything can happen (Rieese, 1991). The term used by pragmatists to describe this phenomenon is that of emergence. According to Mead (1934), emergence de- scribes a unique kind of relationship between environment and organism, one in which new "characters" or features can arise by virtue of this interaction.

Emergence, as a key aspect of learning, has not been handled well by information-processing or radical construc- tivist theories. In fact, it represents the most vexing problem for researchers in these two camps, largely because they both represent assimilatory as c~pposed to accomanodatory a p proaches to learning. An assimilatory approach is one that emphasizes the relationship between prior knowledge and subsequent knowledge. Thk creates a paradoxCL'having to attribute to the learner prior knowledge that is at least as complex as the new learning to be explained" (Bereiter, 1985, p. 201). Inf~rmation-processing theory, given its affinity for the computer, has special diflliculty dealing with this paradox. Frame-based systems, of necessity, emphasize the role that preknowledge (i.e., the system's collection ad frames) plays in interpreting new situatioins {(Winograd & Flores, 1986). Piagetian radical constructivism fares little better in this regard. The &embracing equilibrium toward which all minds tend is hard to explain without recourse to an entirely

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44 PRAWAT AND FXODEN

internal, maturationist explanation (Chomsky, cited in Phil- lips, 1982).

Contextualism, thanks to the influence of such pragmatists as Pierce and James, turns the issue of stability versus change on its head: The problem for these philosophers is not in accounting for novelty; rather, it is the converse: How is it, in a world marked by constant flux, that we achieve some sense of structure or order? This way of stating the problem reflects the pragmatist agenda, which is to question the certainties associated with rationalist and realist views. Pragmatism's nonfoundationalist, nonpositivist agenda strikes some ma- lysts as negative in nature (cf. House, 1992). According to the pragmatists, the state of indeterminacy associated with reality cannot be alleviated once and for all. It can only be interrupted temporarily as individuals carve out islands of meaning in their daily existence.

To deal with the indeterminacy problem, later pragmatists, such as Mead and Dewey, assigned more importance to the social dimensions of human existence. As Shalin (1986) explained,

Without society, pragmatists realized, there would be no rational human beings, no world of meaning and structure, and the primordial chaos would never be tamed. Precisely because the world out there is not fully determinate, because it can be carved out in so many ways, there is a need for an organizing principle, a reference frame that can guide the efforts of disparate individuals engaged in the process of determination. The individual learns to do the "carving" against the background of meaningful objects shared with others. (p. 12)

Dewey was keenly aware of the difficulties involved in trying to reconcile the sense of change or flux with that of order and regularity in the world. He argued that our intellect is preoccupied with the attempt to resolve this impasse: "The striving to make stability of meaning prevail over the insta- bility of events is the main task of intelligent human effort," Dewey wrote (192511981, p. 49). As indicated, Dewey be- lieved that this task could not be carried out by individuals acting alone. Society, through its use of language and other artifacts, shapes the individual's view of reality. Through language, members of a discourse community learn to "carve out" the world in similar ways; they develop similar "antici- pations" about external reality.

Sounding a theme that figures prominently in Pepper's (1942) perceptual approach to contextualism, Dewey empha- sized the extent to which any attempt to test the validity of these anticipations had to be viewed in strictly interactive terms. Knowledge, for Dewey, was not a mental state; rather, as he expresses it, "It is an experienced relation of things, and it has no meaning outside of such relations'' (191011981, p. 185). As this quote suggests, Dewey believed strongly in the situated nature of knowledge: "The object of a knowledge is always strictly correlative to that particular thing which means it" (p. 185). This is not to say that Dewey believed that one's understanding of an object did not become deeper over

time. He did, however, view this process through a similar interactive lens. "As the meaning gets more complex, fuller, more finely discriminated," he wrote, "the object which real- izes or fulfils the meaning grows similarly in quality" (Dewey, 191011981, p. 191). Dewey's use of the language "realizes or fulfils" in this last quotation is not accidental. There is a strong perceptual component in Dewey's interac- tional view of knowledge, a component Pepper (1942) capi- talized on in his own treatment of contextualism.

According to Dewey (1910/198 I), sy stematic (i.e., scien- tific) inquiry allows a discourse community to test its antici- pations. This requires collective reflection after the fact or during the course of the "fulfilling experience":

To think of prior schemes, symbols, meanings, as fulfilled in a subsequent experience, is reflectively to present in their relations to one another both the meanings and the experi- ences in which they are, as a matter of fact, embodied. This reflective attitude cannot be identical with the fulfillment experience itself; it occurs only in retrospect when the worth of the meanings, or cognitive ideas, is critically inspected in light of their fulfillment; or it occurs as an interruption of the fulfilling experience. (lglO/ 1981, p. 18 1)

Dewey argued that there is nothing eternal about the truths that emerge as a result of this process. In fact, the criteria used to evaluate knowledge claims are them- selves social products, accepted for the time being by members of the discourse community but subject to revi- sion or change. For this reason, even the most reliable of knowledge claims-so-called "scientific lawsw-must be viewed as functional and transitory, merely serving "to structure our experience here and now" (Garrison, in press).

Based on a reexamination of Dewey's views, Sleeper (1986) argued that interpreters have overemphasized the role that instrumentalism played in Dewey's thinking. Sleeper pointed out that action, for Dewey, was not some- thing valued for its own sake, but only as a means to ontological change. Garrison (in press), building on this argument, believed that Dewey is best thought of as a transactional realist. According to Garrison, this label does a better job of fixing Dewey's middle-ground position between transcendent realism-the notion that there is an enduring structure to the world apart waiting to be discov- ered-and pure subjectivism;

Inquirers, their language, tools and values, are real and have real causal consequences, but they do not entirely determine the consequences of inquiry in a given context. TO think they do is subjectivist. Neither, however, does the context, apart from the inquirers' participation, entirely determine the con- sequences of inquiry. To think it does is to be an objectivist. The reality, including the functional structure of a given context, is in the transactions among all those events that participate in the context including the participation of the inquirer. (Garrison, in press)

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PERSPECTIVES ON LENRNING 45

Pepper (1942) pulled these various threads together in his description of the contextualist world view. He began by contrasting the vertical cosmology underlying the mechanis- tic and organismic world views with the horizmtal cosmol- ogy of contextualism: "There is no top or lbottom to the contextualistic world,'" he wrote. "There is no cosmological mode of analysis that guarantees the whole truth or d m arrival at the ultimate nature of things'yp. 25 1). Thus, although an ongoing act is almost always conceptualized as a structured whole, it can be broken down into separate elements for analytic purposes-each of which then becomes an act in its own right. As Reese (199 1) explained:

Real wholes exist in contextualism but the whole does not exist-no delimited all-inclusive whole exists. Reality is a continuous flux of acts ongoing in an endless range of con- texts. The whole, for anyone's purposes, is that part of the flux that he or she wants to describe. (p. 196)

This does not mean that individuals are free to construe events in any way they 'wish. Variables that influence: how we experience an event, 1ik.e the sense of pastness or forwardness (i.e., spread), or our awareness of how well things hang together as the event unfolds (i.e., jbsion), are not imported from the outside. They emerge through our involvement in the event. As Pepper explained, "One of the strong arguing points for contextualism is that dl of its categories (i.e., change, novelty, qualily, and texture) are derived from the immediacy of the given present event" (p. 265). This process of negotiation occurs even in the case of direct perception.

Pepper (1942) employed a fabric: metaphor to emphasize the extent to which perceiver and perceived exert a mutual influence on one another: 'When I perceive a table," he wrote, "there is, according to the contexttrxalist, an interlocking of two or more continuous textures" (1942, p. 266). In addition to the texture we associate with the table, there is our own textural continuity as m org;mislm.

Previous to the interlocking of the strands of the continuous textures of table and organism there were no . . . colors or shapes in existence (at least, not there in the texture d the perception). These are emergent qualitative and integrative novelties arising from a texhwe of strands partly derived from the so-called physical table and partly from the so-called physical body of me. . . . The important point to note is that the qualities arise in the integration of the texture and belong neither to me alone nor to the table alone, but to the common texture. (p. 266)

Social influence is an integral part of the here md now experience described previously. Individuals may choose to downplay the importance of social factors in analyzing a particular event, Pepper argued, but it is nevertheless part of the fabric or texture of the event: "The contextualist insists that a study of any private event carries of itself into a public world. The context of a private texture is already some other texture, and the two textures are thus mutually conjoined and

interpenetrating" (Pepper, 194.2, p. 265). According to Pep- per, the role played by social factors is most readily apparent in our use of schemes (e<g., symbol syst~ems, maps, and diagrams). These function outside of perception, and repre- sent both "a summary of past social experience and a guide to future experience" (p. 267). Pepper left the issue of how, exactly, schemes or ideas are created in a social context to other theorists. As "instruments of prediction," schemes cre- ate mlicipations about the texture of an object or its relational structure. As an example, Pepper used the diagram of a gasoline engine. No one arssumes that the structure of an engine is literally one and the same with the structure of its diagram. "The diagram doels contain a system of references," however, "which when fa1low1:d enter without blocking into the texture of the engine-tlhat is, the diagram is verified and found true" @. 268). As we argue, the process through which an individual or group's anticipations are ve~fied is at the core of the contextualist theory of truth. Befgre elaborating on this point, however, we discuss parallels between Pepper's work ,and the more recent 'work of Varela, Thompson, and Roscb (1991).

Struclural Coupling in Ev~olutionary Theonj

Contextualkt theory represents a more complex world view precisely because it recognizes the need to shift back and forth between environmental and organismic reference points, assign- ing top priority to neither. The most recent view of evolution- whichutilizes the concept of structural coupling-resembles the process that Pepper believed underlies the contextualist theory oftruth. Structural coupling, as described by Vmla, Thompson, and Rosch (1991), is a kind of fortuitous coming together of structures emergent in the orgiani~m and in the environment. This contrasts with the Darwinian view favored by radical construc- tivists. In this more traditional view, organismic structure is thou&t to be independent of' environment. The organism pro- poses md the environment disposes. This independence is rejected in current evolutionary the

ory. As Varela, Thompson, and Rosch put it, "'The world is not a landing pad into which organisms parachute" (1991, p. 199). Instead, living things and their environments are in- volved in a complex reciprocal relationship., ane that is co- implicative. As with the contextualist world view, chance or indeterminacy is assumed tot pliay a key role in the process of structural coupling. Varela, Thompson, and Rosch use the term bricolage to describe the process that gives rise to structural couplings; this is the coming together of elements to fom complex patterns 'bot because they fi~lfrill some ideal design but simply because they are possible" @. 196).

The "head-fitting" approach favored by information pro- cessors and radical constructivists does not mesh well with the ideas advanced by Vaela, Thompson, alnd Rosch. The perceplnal &el of cognition that underlies Pepper's ap- proach to truth does, however, fit with these views. Like Dewey, Pepper argued that individuals, through a process of

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social construction, develop hypotheses (i.e., ideas and theo- ries) that create expectations about the texture and quality of the events to which they refer. The subsequent realization- or lack thereof-of these expectations determines the truth value of the hypotheses. "A true hypothesis," Pepper (1942) wrote, "does in its texture and quality give some insight into the texture and quality of the event it refers to for verification" @. 277). Pepper added,

Thus, in a certain sense, a true hypothesis corresponds with the event that verifies it, for the references carry through continuously into the verifying event. In a certain sense a true hypothesis coheres with the event that verifies it, for its references are not blocked, but are integrated there [italics added]. (p. 277)

Thus, one's anticipations about what will be found in the environment bear fruit-they carry through into the verifying event, opening up possibilities that hitherto went unnoticed. This is the correspondence aspect of the cognitive-perceptual process. The object of perception is not a passive "landing pad," however; in the absence of blockage, it talks back, forcing the individual to rethink the initial expectation. When this feedback is incorporated, the original hypothesis (or idea) becomes more "coherentn-more "densely textured" to quote Brown, Collins, and Duguid (1989). In this sense, the truth of a hypothesis is determined through a process that resembles that of structural coupling in evolutionary theory.

A Research Example

Ball (1993) described her attempts to teach second graders a mathematics topic that goes beyond the standard curricu- lum-negative numbers. In her approach to instruction, stu- dents formulate, challenge, and defend conjectures, starting from questions she poses about familiar situations. In this specific example, she began the discussion of negative num- bers by asking students to imagine a building with 12 floors above ground and 12 below, and further imagining people who ride an elevator. Ball appreciated the strengths and weaknesses associated with the building representation of negative numbers. Although it highlights one aspect of the concept-the location of negative numbers relative to zero- it handles the second aspect-magnitude or absolute value- much less well. The building representation would therefore help students understand how -5 is further away from 0 than -1 is. Ball speculated that it would not be as helpful in developing an appreciation of the complexity of magnitude as it relates to negative numbers. This is problematic because, as Ball points out, "Simultaneously understanding that -5 is, in one sense, more than -1 and, in another sense, less than -1 is at the heart of understanding negative numbers" @. 379). Still, given her students' tendency to regard all negative numbers as equivalent to zero, the building model seemed a good place to begin.

Ball had students use mathematical symbols to represent

various actions with the elevator: -2 + 5 = 3, for example, to represent a person getting on the elevator two floors below ground and moving up five floors. As students mastered this convention, Ball introduced more and more complicated problems. In one, she asked students to figure out how many ways there are to get to the second floor. This immediately provoked what Ball describes as an "intense discussion," with one group of students assuming that the problem called for "one-stop" solutions, another "many-stop" trips.

'This argument," Ball continued, "afforded us the oppor- tunity to talk about the role of assumptions in framing and solving problems" (p. 380). The one-stop group itself was divided, with one child proposing that there were exactly 24 solutions (the building had 12 floors above ground and 12 below), while another argued for 25 on the grounds that the "zero floor" should be included in the total. Those who assumed that the problem could be solved in amany-stop way held out for an infinite number of solutions. According to Ball, other interesting conjectures were offered as students worked with negative numbers. One child, for example, ven- tured the guess that "any number below zero plus that same number above zero equds zero" @. 381); the class examined this possibility with various numbers.

Ball aswmes that students learn by working with one another to canstnfct ideal; that they can apply to the challenges she poses. They build agreement about the meanings af key tenns (e.g., many-stop trips, neg~tive numbers) by refining their rule for usage to accommodalte difficulties that arise as they confrant new situations. The classroom lessons go well if they ancourage students to learn patterns that incorporate standards of justification as well as the focal mathematical ideas. The instruction is succmisful to the extent that students, as a group, are able to put togathor ideas that lead to further fruitful discussions.

DILEMMAS OF TEACHING FROM A SOCIAL CONSTRUCTIVIST

PERSPECTIVE

As this summary suggests, discourse-oriented teaching pres- ents its own unique challenges and dilemmas. "Representing content, respecting students, creating and using cornrnu- nity-these are not aims simply resolved," Ball concluded (1993, p. 395). Issues that seem particularly salient in this regard relate to the difficulties of choosing representations that do justice to the content and to the students-that is, representations that can illuminate important ideas in a way that students find meaningful. Further complicating the pic- ture is the fact that choosing good representations is only half the battle; the constructivist teacher must figure out how to "work" these representations as well. This involves knowing how to phrase things so as to highlight certain aspects of the representation while simultaneously downplaying those that might mislead or misinform.

Another important issue surfacing in Ball's teaching has

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PElRSPlECTlVES ON LEARNING 47

been discussed by others who use a social-constructivist, discourse-oriented approach: How does the teacher manage the negotiation process so that both the individual student and the discipline receive their just due? Striking the right bal- ance between honoring the individual student's own effort after meaning while steering the group toward some "intel- lectually honest" (i.e., disciplinarily correct) c~onstn~ction of meaning has been described as the 'konstructivist dilemma." It is one of the most vexing issues faced by social-eonstruc- tivist teachers.

There are a host of other issues associated with idea-based social constructivism. Because this approach is more intellec- tually demanding, teachers need increased time to engage in reflective thought with1 colleagues and outside consultants. Given the way we now organize the workplace:, there is little opportunity for teachers to work cellaboratively on curricu- lum development. This is in marked contrast to what one observes in other countries, most notably ~ a p a n . ~ We need to examine alternative structures at the school level to see which, if any, support teachers in their efforts to explore the matrix of ideas associated with specific subject matter do- mains.

Another issue that needs to be examined concerns the use of technology to advance student understanding of "big ideas" in various domains. Jeremy Roschelle's (1993) work provides a glimpse of the exciting possibilities in this regard; he and his colleagues have developed computer simulations that advance student understanding of difficult concepts in physics (e.g., acceleration, velocity). Another thorny issue, somewhat distinct from the one raised earlier, has surfaced recently. Hatano and Inagaki (1991:) presented data showing that vocal students learn more from group discussion than those who remain silent. This study has iinportant im- plications for teachers committed to the social construction of knowledge in the classroom. It may be that, through the use of student journals, we can increase the level of partici- pation in the ongoing conversation to near 100%.

Assessment of student understanding is another important issue. Those who rely on written work to evaluate student understanding are faced with a diffficult problem: How to structure products so that they provide insight into student thinking. A recent study by Scardamalia and Bereiter (1992) shows how difficult this can be. The questions students were directed to ask before investigating specific topics were of lower quality than those generated in an informal, 'wonder- ment" context. This phenomenon, if replicated, creates a dilemma for the teacher who wishes to use classroom-based written products to assess student learning: The pra~cedures used to structure written responses-procedures that students

4~ccording to Stevenson and Stigler (1990), Japanese! teachers at the elementary level devote a good art of the school week to curricular issues. - *

Regular meetings, held during school hours, are organizedl specifically for this purpose: "A whole meeting,"they explain, "might be de3voted to themost effective ways to phrase questions about a topic or the most absorbing ways of capturing children's interes$ in a lesson" (p. 160).

themselves have become accustomed to-may, in fact, hinder high-qualily writing.

There are other matters (sf equal import that demand our attention. Greater clarity about what is being proposed under the rubric of social constructivism should contribute to our ability to address practical issues of the sort discussed pre- viously. It is hoped that our article contributes to this clarity.

ACKNOWLEDGMENTS

The authors would like to thank Ralph R~tnarn and King Beach for their insightful comments on an earlier draft of this article.

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