(PDF) Configuring Learning Theory to Support Teaching

Kirshner, D. (2016). Configuring learning theory to support teaching. In L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd Ed) (pp. 98-149). New York: Taylor & Francis. Chapter 4: Configuring Learning Theory to Support Teaching1 David Kirshner, Louisiana State University Paradigms, wholly new ways of going about things, come along not by the century, but by the decade; sometimes, it almost seems, by the month. It takes either a preternaturally focused, dogmatical individual, who can shut out any ideas but his or her own, or a mercurial, hopelessly inquisitive one, who can keep dozens of them in play at once, to remain upright amidst this tumble of programs, promises, and proclamations. (Geertz, 2000, p. 188) INTRODUCTION This chapter addresses the multiparadigmatic character of social sciences that Geertz (2000) laments, particularly the presence of multiple, independently conceived notions of learning that educators somehow must negotiate to establish a sound and coherent basis in psychology for theorization of teaching. For education, learning constitutes the essential goal of professional practice. Thus, its diverse theorization in distinct branches of psychology poses a considerable challenge not faced by paradigmatic professions like medicine and engineering, those informed by what Kuhn (1970) called paradigmatic sciences (e.g., physics, chemistry, biology, genetics, anatomy, etc.) that have achieved a consensus about theory and method. As Kennedy (1999) observed, “The relationship between teaching and learning is the most central issue in teaching, and it is also the most perplexing and least understood” (p. 528). For the most part, educators’ strategy for dealing with psychology’s multiple paradigms has consisted simply in identifying with one or another extant branch in an effort to derive guidance for educational practice. Through the past century educators, variously, have found inspiration in behavioral psychology, Gestalt psychology, Dewey’s functional psychology, Piagetian developmental psychology, Vygotskian sociocultural theory, ecological psychology, information processing psychology (Gardner, 1987), conceptual change theory, situated cognition theory, and various constructivist and constructionist theories (Spivey, 1997), among others. The central consequence for education of selecting a single branch from among psychology’s offerings might be labeled the Babel Effect. Given a diverse menu of psychological approaches, educators in a given era vary in their choice of preferred paradigm. As a consequence, theorists are speaking many different languages as they attempt to articulate foundations for pedagogy, and they are robbed of the opportunity to build a professional discourse of teaching together. The Babel Effect manifests itself within our pedagogical discourse primarily as complementary tendencies toward conflict and confusion. Conflict arises when educators guided by alternative visions of learning formulate models of teaching practice that are seen as antithetical to one another. Historically, the key example is the conflict between Progressive Educators rallying under the banner of John Dewey’s functional psychology and Traditionalists -98- guided by the more reductive sense of stimulus-response learning advanced by Edward Thorndike and his colleagues (Lagemann, 1989). Contemporary conflicts include the “Reading Wars” and the “Math Wars” (Loveless, 2001; these conflicts are analyzed later in the chapter). Less salient for our community, but more debilitating in its consequence, is the sense of confusion and eventually dissipation that ensues from multiple sources for pedagogical precepts. Within each pedagogical enclave things may not seem terribly amiss. Whether we are behaviorists or constructivists or situativists or critical theorists (to name a few prominent schools) we have coherent and convergent conversations about learning and teaching, and perhaps a sense that we are making progress. But in aggregate, this Balkanization of educational thought is dysfunctional. Unless teachers locate themselves squarely within a single tradition of pedagogical theory—and most don’t—they are faced with a discordant array of pedagogical advice: Learning requires continual practice. Repetitive practice is the antithesis of learning. Learning is facilitated by group work. Individualized study allows each student to progress optimally and at their own rate. Lecture is the most efficient method to transfer Knowledge doesn’t transfer but has to be constructed knowledge to students. by each individual student. From this chaotic assembly, only the most general and platitudinous of invocations—“Care about the children. Prepare well for class. Be ‘with-it.’” (Pressman, 2007)—escape censure and emerge as uncontested advice for teachers. Our general pedagogical discourse is a poor and pale reflection of the intense intellection within the various enclaves of theory. To be clear, what is at stake here is not just the rhetoric of pedagogy, but the very character and quality of pedagogical thought and practice. Consider the chain of reasoning underlying development of a chemotherapeutic treatment for cancer. To begin, cell biologists provide insight into cell pathology relevant to this ailment. Then a strategy, say, for interfering with cancer cell reproduction is theorized, and experiments are initiated with lab animals to determine if the strategy has merit. Finally, clinical trials are established to verify efficacy with humans, and to empirically address matters such as dosage levels that theory is insufficiently refined to determine (Arthur & Hancock, 2007). At the foundation of this collective enterprise is broad agreement across the medical field as to the underlying mechanisms of disease and health. It is this consensus that ensures practitioners are educated in the relevant theories and prepared to expertly perform their assigned role in the treatment process. Surely inductive generalization—noting unexpected successes—and even blind luck have a role to play, but “medicine is a rational enterprise built on a scientific tradition that operates with logical arguments, the laws of causality and the epistemic strategies of observation and experimentation” (Kottow, 1992, p. 19). In the case of education, the entire infrastructure for rational organization of practice is undermined by the presence of unreconciled theorizations of learning, as emblematized by the typical educational psychology textbook in which the diverse offerings of learning theorists are presented as separate chapters together with recommendations for practice (e.g., Eggen & Kauchak, 2013; Ormrod, 2009). Such an approach abdicates collective responsibility for rationally organized educational practice, leaving individual teachers to find their own way through the thicket of diverse and competing claims (Wojcikiewicz & Wenzel, 2012). Nothing drives home the ineffectiveness of the current utilization of psychology more strongly than the fact that researchers looking into practices of good teaching ignore learning theory. For instance, in an OECD-funded multinational project in the early 1990s, teachers noted for their excellence were carefully studied to determine effective teaching practices. -99- A synthesis of findings from each country carried out by Hopkins and Stern (1996) identified the six most important characteristics of excellent teachers, as summarized in Nuthall (2004): 1. a passionate commitment to doing the very best for their students 2. a love of children enacted in warm, caring relationships 3. pedagogical content knowledge, e.g., knowing how to identify, present, and explain key concepts 4. use of a variety of models of teaching and learning 5. a collaborative working style with other teachers to plan, observe, and discuss each other’s work 6. a constant questioning of, reflecting on, and modifying of their own practice. (p. 282) Such an approach to identifying effective teaching practices is the educational equivalent of seeking a cure for cancer by observing the practices of successful physicians. What it yields, as we see, is little more than a catalog of education’s bedside manner. With the exception of educational practices nurtured under the auspices of teams of theorists (e.g., as in design research; see Design-Based Research Collaborative, 2003), to be discussed later, this kind of focus on the surface structure of educational practice is endemic to educational practice: For the most part, “teachers are not explicitly concerned with student learning as they manage student participation in classroom activities . . . [based on the belief that] ‘student interest and involvement constitutes both a necessary and sufficient condition for worthwhile learning’ (Prawat, 1992, p. 389)” (Nuthall, 2004, p. 276). As Windschitl (2002) noted in an incisive review, even reform pedagogy designed to perturb conventional ideas about teaching and learning is enacted as a kind of mimicry of prescribed methods: “activities, as opposed to ideas, are the starting points and basic units of planning” (p. 138). Except in rare cases, the rich insights into learning that psychologists have generated within psychology’s many branches simply are being lost to the profession of teaching. These travails of educational practice stemming from the multiplicity of learning theories are broadly misunderstood, both by educators and by policy makers. For policy makers (and others in the academy) teaching and the scholarship of teaching is “low-status work” (Lagemann, 2000, p. xii); educators are simply too dull witted (or else too ideologically driven) to figure out what seems a relatively straightforward matter of determining and implementing effective practices. The current policy solution in the U.S. context directs research dollars to the final empirical phase of scientific research—fine-tuning and validating of proposed practices—completely ignoring the need for sound theoretical foundations (Schoenfeld, 2007). Educationists, on the other hand, chalk up the challenges of educational theorizing to the “irreducible complexity” of our domain, seeing theoretical heterogeneity as an index of this complexity, rather than as a fundamental problem in its own right: “What we know about teaching is always contingent on a vast array of intervening variables that mediate between a teacher’s action and a student’s response” (Labaree, 2000, p. 231; see also Otterness, 2009; Regehr, 2010).2 The purpose of this chapter is to articulate a new strategy for exploiting the rich insights into learning that psychology, in its diverse paradigms, has uncovered, without generating the competing prescriptions that divide and weaken the educational enterprise. Given the long-standing and intractable problematic of education’s uptake of learning theory, the strategy proposed here is surprisingly straightforward: accept, rather than resist, the multiparadigmatic character of learning theory. When we educators adopt a single theorization of learning as a basis for pedagogical practice, we are failing to acknowledge that psychology itself has not resolved the multiplicity of learning theory. We are pinning our educational fortunes on the learning theory we hope and believe eventually will prevail, ignoring that psychology, in its multiple paradigms, has produced several distinct theorizations of learning that motivate us as a community. -100- The alternative proposed here is to work across education to identify the distinct notions of learning that motivate educational practice. Honoring each of these as legitimate, the strategy is to articulate pedagogical practice in genres, each addressing a single notion of learning, and each informed by a theorization specific to that particular notion of learning. This simple move of aligning learning goal –> learning theory –> pedagogical genre puts educational practice on the same footing as paradigmatic professions like medicine and engineering, in which a single theoretical framework informs prescribed professional practices. The professional educator, therefore, can be schooled in the relevant theorizations for each separate genre and can practice teaching based on a rational plan that explicates how recommended practices are intended to lead to the desired learning outcome. The genres approach yields diversity, but without conflict or confusion endemic to our current discourse. Before proceeding, it is best to anticipate an objection that may be forming for some readers: how can we take seriously a proposal to construct learning as separate, independent processes in the face of its well-established standing as a complex whole (Regehr, 2010)—multifaceted, to be sure, but composed of mutually interdependent elements (Bransford, Stevens, Schwartz, et al., 2006; Greeno, 2011). Yet the history of psychology does not bear out the current wisdom of learning as a complex whole. Behavioral psychology did not establish itself as a complement to mentalistic approaches, but as an alternative (Watson, 1913). Likewise sociocultural psychology, cognitive psychology, developmental psychology, and other foundational theories have worked mightily to establish independent claims to account for learning/development. In the current era of dialectical, integrative, and holistic theorizing learning tends to come to us as a complex whole; in a previous era, learning more often came to us as a unitary mechanism (rooted in conditioning, or in developmental schemas, or in serial information processing). My point here is not to settle the matter in advance, but to forestall a priori judgment. A case for the utility of independent theorizations of learning is demonstrated in the current chapter, and it can be assessed directly, on its merits. The foregoing provides a general rationale for the genres approach, but two clarifications are needed to see the contours of the proposed strategy: the first addresses the role of values decisions in a discursive space that legitimizes separate interpretations of learning; and the second addresses the special character of multiparadigmatic science and its implications for uptake of psychology’s learning theories. Values Decisions To be sure, the one-to-one alignment of goals to theories to practices advocated does not suddenly transform psychology into a paradigmatic science, nor education into a paradigmatic profession. Indeed, organizing pedagogical practice into independent genres crystallizes a new problematic for education not paralleled within the paradigmatic professions: the need for values decisions pertaining to selection of the teaching genre(s) appropriate for a given student, classroom, subject area, school, or educational jurisdiction. Values issues concerning learning goals already are implicated in our current educational discourse, as evidenced by conflicts like the Reading Wars and Math Wars (Loveless, 2001). However, in our current discourse in which each sect of theorists recognizes only one’s own paradigm as legitimate, one’s opponents are cast not only as wrong-headed in their choice of learning goals, but also as misguided in their teaching methods (e.g., Draper, 2002; Klein, 2005). Reifying several distinct theorizations of learning as legitimate, and establishing recognized standards for pedagogical practice associated with each, means that differences about goals no longer bleed over into criticisms of the competence and efficacy of professionals making different values decisions. Teaching assumes a more professional demeanor. Legitimating various notions of learning and associated genres of teaching also should have the effect of removing the theorist from the fray of values decisions. The learning theorist -101- provides technical knowledge relevant to the shaping of pedagogical practices. However, the genres of teaching are not alternative paths to the same end—this is not about different learning styles (North, 2015; Pashler, McDaniel, Rohrer, & Bjork, 2009)—they lead to different ends, and it is properly the province of the world of practice to make the decisions as to what form(s) of learning are to be valued in a given circumstance. This devolution of values decisions to the world of practice creates a new political dimension of educational policy that may have far-reaching consequence for the organization of schooling: Do teachers decide within their own classrooms? Are these school- or district-level decisions? Do we develop a decentralized model of schooling to allow for more parent choice? Such questions are beyond the scope of the current chapter, but it is worth keeping this consequence of the genres approach in mind. Theorization in Multiparadigmatic Science The final issue to be addressed in this introduction concerns the nature of theory development in multiparadigmatic sciences like psychology. Our assumption as educators has been that theorizing in psychology follows the same basic strictures and adheres to the same basic standards as theorizing in any other science. In the next section, I subject this assumption to critical scrutiny from a sociology of science perspective, finding instead that learning theorists are prone to overextension and exaggeration of results, and to systematically minimizing and eliding differences between theoretical approaches. The consequence for the genres strategy is that after identifying the notions of learning motivating educational practice we cannot simply adopt a ready-made learning theory for each from which to derive guidance for pedagogical practice. Rather, we must compose these theorizations of learning ourselves, drawing selectively from the corpus of results psychologists have obtained relevant to that notion of learning. This usurpation of psychology’s traditional role as interpreter of learning theory for educators is bound to create tension between the two fields. However, as we shall see in the sociology of science section, our practice over the past century of selecting one learning paradigm to inform pedagogy, rather than coordinating several paradigms, always has been in the service of psychology’s interest in achieving a unified paradigm. Adopting the genres approach in the interests of regularizing our own discourse requires that we step out from behind the shadow of that great science. Outline of this chapter: Following this introduction, “A Sociological Glimpse at Theorization of Learning” approaches the nature of theory construction in psychology from a sociology of science perspective based on Kuhn’s (1970, 2000) analysis of the competitive process through which multiparadigmatic sciences achieve the initial consensus that marks the transition to the status of a mature science. The next section, “Education’s Uptake of Learning Theory,” reviews the history of education’s uptake of learning theory, noting a succession of four phases of thinking about this problem. The following section, “The Genres Approach,” identifies the valued notions of learning that motivate educational practice and lays out the constraints on utilizing psychological theory. The next section, “The Crossdisciplinary Framework” (the heart of the chapter), articulates the theorizations of learning and associated genres of teaching. The penultimate section, “Crossdisciplinary Analysis of Pedagogical Practice,” applies this coordinated framework of theories and pedagogies to analyzing—and providing new insights into—a wide variety of issues and problems of educational practice. This is intended to make plausible the claim that the genres approach, rather than elaborating a new regime of thought for educational practice, serves to untangle the strands of ideation knotted together within our current integrative discourse about learning and teaching. A concluding section, “Problems and Prospects,” reviews the intentions of the chapter and argues for taking the considerable risks associated with this genres approach. -102- A SOCIOLOGICAL GLIMPSE AT THEORIZATION OF LEARNING The overall theme of this chapter is that psychology has amassed brilliant and powerful insights into learning that are being underutilized as resources for educational practice owing to the multiparadigmatic character of that science. This is not a problem we can solve by looking to the paradigmatic professions or to the paradigmatic sciences for guidance. We need to carefully and independently analyze the processes of knowledge creation in multiparadigmatic psychology as a first step to outlining a strategy for utilization of its knowledge products. In this section, I take a Sociology of Scientific Knowledge (SSK) perspective to understand the sociological constraints that guide the development of learning theories (Barnes, 1985; Collins & Pinch, 1993). Sociology of science, and SSK in particular, seeks to identify not only how institutions of science are shaped within the broader cultures in which they are embedded, but how the very knowledge products of those sciences bear the marks of the societal context (Shapin, 1995). The idea that sociological factors constrain scientific theorizing is not one that scientists generally welcome. As Danziger (1990) remarked, psychologists often are uncomfortable with the suggestion that “personal, cultural, and historical factors play important roles in the elaboration and acceptance of psychological theory, . . . this state of affairs is hardly compatible with the claims by the discipline for the objectivity of its insights into human behavior” (p. 5). Indeed, sociology of science perspectives can be “profoundly destabilizing” for scientists whose field of study comes in for critique (Pinch, 2007, p. 266). This is sensitive terrain we traverse. My analysis of the development of psychological theory is rooted in Thomas Kuhn’s (1962/1970, 2000) well-known theory of scientific paradigms. Taking issue with the long-standing image of scientific progress as an ongoing accumulation of knowledge and technique, Kuhn (1970) distinguished between two kinds of scientific progress. During periods of normal science, there is broad agreement among scientists as to the nature of their subject matter and appropriate methods for advancing the science. Indeed, during these periods of paradigmatic consensus progress is cumulative—a kind of extended puzzle-solving activity (p. 35). However, as Kuhn (1970) pointed out, normal science is powerful precisely because it is very focused and limited in its scope. As a consequence, it has no way to assimilate “new and unsuspected phenomena [that] are . . . repeatedly uncovered by scientific research” (p. 52). Eventually, someone may take up one or more of these anomalies as sites of investigation outside of the strictures of the existing paradigm. In some cases, these investigations lead to a new theoretical and methodological frame for the science, setting the ground for a period of paradigm conflict and possible scientific revolution, after which a new period of normal science ensues (Kuhn, 1970). In addition to detailing how mature sciences cycle through periods of normal science and revolution, Kuhn (1970) described the process whereby proto-sciences—what he called preparadigm (p. 17) sciences—mature into paradigmatic sciences. Preparadigmatic sciences are characterized by a multiplicity of scientific schools, each with its own perspective on the new science. The transition from preparadigmatic to paradigmatic coincides with achievement of the science’s initial paradigmatic consensus, and hence the first period of normal science. The process is very similar to scientific revolution, except instead of two conflicting paradigms—the established one and the challenger—there are several contenders, all challengers, none already established. It is this process of paradigm competition that will concern us in this section. There has been considerable discussion as to whether social sciences in general, and psychology in particular, fit Kuhn’s definition of preparadigmatic. Driver-Linn (2003) notes that “Kuhn used psychology as an example of a pre-paradigmatic science (to be compared with paradigmatic sciences such as physics)” (p. 272; see Rosenberg, 2005, p. 272, and Staats, 1981, for concurring viewpoints).3 Nevertheless, opinions have varied. -103- One point of view that seems to me to be popular with psychologists was voiced by Weimer and Pallermo (1973), who observed that psychology achieved an initial consensus around behaviorism and has since had a revolution (cognitive psychology) so it therefore must be paradigmatic. To update the record, we can note that cognitive psychology itself has subsequently clashed with newer upstarts like situated cognition theory (Anderson, Reder, & Simon, 1996, 1997; Greeno, 1997). The contrary point of view is that whereas behaviorism has fallen from dominance in psychology, it still continues as an active paradigm as evidenced by the continuing presence of journals, conferences, and organizations of its advocates(see Leahey, 1992). Certainly, from our point of view as educators, we experience psychology as preparadigmatic, in that contemporary efforts to inform pedagogical practice reference theories of learning in many different branches of psychology (e.g., Eggen & Kauchak, 2013). I proceed with this sociological analysis of learning theory, mindful that psychologists may object to the very idea that psychology is preparadigmatic. Ironically, as we shall see, the act of construing one’s field as paradigmatic may itself be a strategy of preparadigmatic competition! Incommensurability What is most striking about Kuhn’s (1970) theory is his portrayal of the conflicting paradigms as “incommensurable” (p. 4): theorists engaged in different paradigms “see different things, and they see them in different relations to one another” (p. 150). Because the very problems that scientists choose to address are tied to their paradigmatic perspectives, differences of viewpoint can never be resolved through rational debate or adjudicated through empirical evidence. The scientific revolution succeeds if and when the new school is able to offer a sufficiently compelling account of the subject matter to attract established researchers from other schools—and especially new researchers just entering the field—to the new paradigmatic perspective. For the defeated paradigms, “their disappearance is caused by their members’ conversion to the new paradigm. But there are always some men who cling to one or another of the older views, and they are simply read out of the profession”(Kuhn, 1970, pp. 18–19). Paradigm shift is ultimately a sociological event as the prior viewpoint is abandoned, not overturned. Kuhn’s notion of incommensurability has been subject to intense critique. Davidson’s (1974) much-cited essay argued that the idea of incommensurable theories is incoherent, thereby raising fundamental challenges to Kuhn’s thesis. Davidson (1974) objected to Kuhn’s (1962) statements that suggested incommensurability implies incomprehensibility across paradigm lines, for example, Kuhn’s suggestion that “after discovering oxygen Lavoisier worked in a different world” (1962, p. 118). However, as Oberheim and Hoyningen-Huene (2013) noted, “Kuhn developed and refined his initial idea over the following decades, repeatedly emphasizing that incommensurability [does not] impl[y] incomparability” (p. 3). My own interpretation is informed by the perceptual dynamics revealed through bi-stable ambiguous figures like the famous vase-faces graphic developed by Danish psychologist Edgar Rubin, see Figure 4.1; one can experience it as a vase or as faces, but not simultaneously. By analogy, the fact that incommensurable theories cannot be brought into the same intellectual frame does not imply an inability for scientists oriented by different paradigms to understand one another, but it does imply that the differences in point of view cannot be resolved within a shared scientific perspective. Thus the process of resolution inevitably has to play out in a Figure 4.1 Bi-stable ambiguous figure, vase-faces graphic. -104- broader sociological arena (Kuhn, 1970). This viewpoint is consistent with Kuhn's belief that “revolutionary change in science requires a gestalt switch” (Driver-Linn, 2003, p. 272).4 Paradigm Competition A preparadigmatic science advances to paradigmatic status if and only if one of its paradigms is able to establish itself so completely as to lead to the demise of its competitors. Thus the competition among paradigms is existential, and winning out (or at least fending off attackers) forms the central imperative of each paradigmatic school.5 As we shall see, this competition among incommensurable paradigms sets up dynamics with respect to both the presentation of psychological theory and the trajectory of such theories that define the very character of preparadigmatic science. What incommensurability does is create separate intra- and inter-paradigm dynamics of scientific research. Within the paradigm, one is working with colleagues who share one’s paradigmatic perspectives to advance knowledge in the field. This work adopts conservative standards of incremental progress and methodological rigor that are hallmarks of normal science and a principal source of its credibility and success (Kuhn, 1970, Chapter 8). But externally, as noted earlier, the battle for supremacy plays out in the sociological realm and depends primarily on one’s ability to attract new researchers just entering the field to one’s own paradigm. Because the superiority of one position over another cannot be established through rational argument (a consequence of incommensurability), the tendency for theorists is to exaggerate the accomplishments of their school and minimize the uncertainties. This exuberant and optimistic posture marks preparadigmatic science as a distinct kind of scientific enterprise.6 We see this discursive dynamic mostly easily in the case of the dominant paradigm in a given era, the one best positioned to establish hegemony over the field. As illustrated with behaviorism and cognitive science, the trajectory for these paradigms moves from initiation to (conservative) extension to (incautious) projection: Paradigm Initiation: To begin, a paradigm is established around a powerful and distinctive accomplishment that illuminates some aspect of psychological functioning. For behaviorism it was Pavlov’s (1897/1910, 1927) discovery of the “conditional reflex” (Murray, 1988) and Thorndike’s (1898) discovery of the Law of Effect that formed the eventual basis for classical and operant conditioning, respectively (Hunt, 1993). Based on their studies of animal behavior, these authors established the comparative psychology principle of parsimony first introduced by Morgan (1894/1903) that higher mental processes should not be invoked if the behavior can be explained by lower mental processes. This established a strong break with the mentalism then prevailing in psychological research (Benjamin, 2007, p. 137). For cognitive science, developments in a variety of fields (neuroscience, logic, anthropology, psycholinguistics, and computer science) coalesced into a new interdisciplinary field challenging the antimentalism enshrined in behavioral psychology (Hunt, 1993). Particularly, the serial digital computer provided an inspectable model of how symbolic elements could be encoded and manipulated computationally to simulate human problem solving (Newell & Simon, 1972). The Information Processing (IP) model became the "guiding metaphor" for cognitive psychology (Hunt, 1993, p. 516). Paradigm Extension: Next ensues a period of conservative and careful research and theory construction in which the initial insight is extended over the domain of phenomena to which it most directly and obviously applies. For behaviorism, we have refinement and elaboration of classical and operant conditioning extended through experimental research into an antimentalist psychology of human behavior (Murray, 1988). For cognitive science, IP simulation was successfully applied to various domains of logical problem solving and decision making, as well as to subcognitive processes like visual processing (e.g., Marr, 1982), even as cognitive psychologists developed and fine-tuned the basic cognitive structures underlying a wide range of functions: pattern recognition, attention, categorization, and semantic and procedural memory (Gardner, 1987; Smith, 2001). -105- Paradigm Projection: Eventually, however, to establish hegemony, the paradigm must project itself to phenomena of interest in the broader field remote from its initial sphere of insight. This effort at a big leap in theory distinguishes preparadigmatic science from the incremental progress of normal science, wherein the scientist “concentrate[s] his attention upon problems that he has good reason to believe he will be able to solve” (Kuhn, 1970, p. 164). At this point, preparadigmatic theory tends to move from relative clarity toward opacity, and claims for the accomplishments of the paradigm are most likely to be exaggerated, with hoped-for advances touted as faits accomplis. Reliably, this hegemonic effort is met with push-back from other paradigms, and/or establishment of new paradigms that hope to address these phenomena more successfully. For behaviorism, this played out in Skinner’s (1958a) attempt to extend operant theory from unmediated response conditioning to verbal behavior. This effort was rewarded with a withering critique in which Chomsky (1959) identified such severe weaknesses in Skinner’s theory construction as to constitute “play-acting at science” (p. 559). Indeed, this episode is cited as ushering in the ascendancy of cognitivism over behaviorism (Gardner, 1987). For cognitive psychology, the attempt to project the successes of decontextualized puzzle solving to contextual reasoning critiqued by Lave (1988) generated defections from traditional cognitive science to situated cognition theory (e.g., Brown, Collins, & Duguid, 1989; Greeno, 1993; Hirst & Manier, 1995), a conflict in points of view that remains unresolved (Anderson, Reder, & Simon, 1996, 1997; Anderson, Greeno, Reder, & Simon, 2000; Greeno 1997). As noted earlier, this pattern of attempting big leaps in theory is uncharacteristic of normal science but is consistent with the sociological process of preparadigmatic competition (Kuhn, 1970). What we can draw from this analysis is that educators should be critical and discerning consumers of psychology’s knowledge products: not all claims by psychologists are equally well grounded or credible. But, as we shall see, education has its own history with respect to psychology which conditions obedience and subservience, rather than critical scrutiny. Psychology and Education Historically, since the founding of scientific psychology in the late 1800s, Education and Psychology have been closely intertwined. One of the first preoccupations of the new science was to investigate the educational belief in “transfer of training” (e.g., Thorndike & Woodworth, 1901). Prior to that time, educators had relied on Aristotle’s doctrine of Faculty Psychology (reworked over the millennia) as guidance for pedagogy. According to this belief system, the mind could be thought of as consisting of relatively independent “mental faculties” each of which could be strengthened, like a muscle, through exercise. Crucially, “a mind so sharpened and so stored with knowledge was believed ready for any calling; indeed, it was considered ‘trained’ and equipped for life. Thus . . . transfer of training resulted from sharpening the ‘faculties’ or powers of the mind, instead of from the specific benefits derived from a particular subject or method of study” (Rippa, 1971, p. 208). What Thorndike and his colleagues established is that educators had greatly overestimated transfer of training effects (Hall, 2003). These findings discredited education’s claims to prepare students for daily life, in the process effectively stripping education of its intellectual authority. Over a short span of years educational psychology emerged as a “guiding science of the school” (Cubberly, 1920, p. 206). Nor was this interest without practical benefit to psychology: “The promise of providing useful answers to practical educational questions may have been the impetus for the establishment of psychology departments in colleges and universities around the turn of the [20th] century”(White, 1991, quoted in Beatty, 1996, p. 102). It is in this historical context that we need to understand the role that education plays in the psychologists’ life-world. Rather than a disinterested senior partner, psychology has maintained a keen interest in how education incorporates psychological theory. As Thorndike (1910) put it, “school-room life itself is a vast laboratory in which are made thousands of experiments -106- of the utmost interest to ‘pure’ psychology” (p. 12), and many psychologists have actively participated in applying their theories to education. But it is a mistake for us to interpret the psychologists’ contributions to education outside of the general sociological imperatives of their field. Asserting influence over education is an important advertisement of the fitness of one’s paradigm. If fear of push-back from other paradigms may serve to moderate rhetorical embellishment of one’s scientific accomplishments, no such restraint is evident in pronouncements regarding educational applications. For instance in their landmark Academy of Sciences publication, Bransford, Brown, and Cocking (2000) declare foundations for educational practice that rest on “a new theory of learning [that] is coming into focus” (p. 3). Clearly no responsible paradigmatic science formulates applications to another field based on emergent theorizing. Such pronouncements can only be sensibly interpreted in the context of preparadigmatic competition in which “capturing” education serves to enhance the cachet and credibility of one’s paradigm (Beatty, 1996). I need to stress that what I’m suggesting here is not the outlines of a conscious strategy of subterfuge or exaggeration on the part of psychologists but rather the dynamics of how preparadigmatic competition shapes the discursive practice of psychological theorizing. Psychologists, confronted with intra- and inter-paradigmatic imperatives of their science, simply have accommodated their world view to enable these two imperatives to be met, the tensions between them being borne internally as part of the cultural practice of preparadigmatic science. As a departure from the conservative norms of paradigmatic science, psychologists make bold—even reckless—claims for their paradigm because in their practice of science they have come to sit on the proverbial “edge of their seats” respecting the emergent potential and promise of their paradigm: “Researchers become emotionally involved in their paradigm; it becomes part of their lives” (Hergenhahn, 2009, p. 11). Psychologists’ pronouncements reflect the truth they experience. EDUCATION’S UPTAKE OF LEARNING THEORY Having presented a picture of how psychology functions as a preparadigmatic science, and of how education is positioned with respect to psychology, I conclude this sociological overview with an analysis of four strategies educators have used to deal with the multiple theorizations of learning that psychology has offered. These strategies are sequential, in the sense that they have been introduced at distinct historical moments in response to problems encountered with previous strategies; however, none has replaced its predecessors and all continue to be utilized today. Foundational Theory: The initial strategy is to accept guidance for educational practice from advocates of what might be called foundational paradigms spawned by major branches of psychology—for example, behavioral, functional (Dewey), Gestalt, developmental, cognitive, sociocultural. Foundational paradigms articulate a focused and coherent, but specialized, vision of the learning process. As Alexander (2007) noted, adherents of such theories tend to deny the legitimacy of other theories and other visions as they stake a claim for the sufficiency of their paradigm. As noted earlier, the principal challenge of such theories is one of scope, as theorists seek to convince the field that their seemingly limited paradigmatic perspective actually encompasses remote concerns of the field addressed in other paradigms. Integrative Theory: Partly as a response to the inability of any foundational paradigm to prevail against its competitors, psychologists have developed what might be termed integrative theories like social constructivism and situated cognition that attempt to weave together perspectives from the foundational theories (Alexander, 2007, makes essentially the same distinction between foundational and integrative theories, though using a different terminology). Such theories offer education relief from the exclusionary politics of the foundational theories, laying the groundwork for a richer and more encompassing vision of learning, and hence of teaching. That new theories can be created from the combination of existing theories was -107- noted by Kuhn (1970) in his discussion of the preparadigm period before the science of optics coalesced around Newton’s Opticks. At that time there were “a number of competing schools and sub-schools, most of them espousing one variant or another of Epicurean, Aristotelian, or Platonic theory . . . and other combinations and modifications besides” (p. 12, emphasis added). However, the challenges of theorizing linkages across paradigms are not to be underestimated. As Lave (1988) noted, for a true synthesis “units of analysis, though traditionally elaborated separately, must be defined together and consistently” (p. 146). Holistic Theory: Alternative to the notable efforts of integrative theorists to create a true synthesis, there is a tendency in the literature to provide pedagogical frameworks encompassing a multiplicity of learning paradigms, without resolving their contradictory aspects and implications. This holistic tendency is most notably evident in canonical texts of the learning sciences community, How People Learn (Bransford, Brown, & Cocking, 2000), and How Students Learn (Donovan & Bransford, 2005), wherein the authors embrace behaviorism, cognitive psychology, cultural psychology, developmental psychology, Gestalt psychology, information processing theory, neuropsychology, situated cognition, and sociocultural psychology. As noted earlier, all of these are coalescing into “a new theory of learning [that] is coming into focus” (Bransford, Brown, & Cocking, 2000, p. 3), a state of affairs that apparently obviates the need to resolve theoretical divergences. Dialectical Relations and Postpositive Fragmentation: As noted earlier, bona fide integrative theorizing across paradigmatic divides is a challenging undertaking. However, in many current cases, the theories to be integrated are not only understood as incommensurable with one another, but also as dialectically related. For instance, a central assumption of situated cognition theory is that “practice is constituted in a dialectical relation between persons acting and the settings of their activity” (Lave, 1988, p. 145). Likewise, Ernest (1998) finds that “at the center of social constructivism lies an elaborated theory of both individual or subjective knowledge and social or objective knowledge—equally weighted. . .and the dialectical relation between them” (p. 241). Dialectic relations imply “reflexivity” as described by Cobb (2007): “This is an extremely strong relationship that does not merely mean that the two perspectives are interdependent. Instead, it implies that neither exists without the other in that each perspective constitutes the background against which mathematical activity is interpreted from the other perspective” (p. 29). What dialectical relations do is lock the theories together into a fixed mutual interdependence, but without ever resolving the discrepant viewpoints. This, I would argue, makes a true integrative theory impossible. For example, as Kuhn (1970) noted with respect to the wave/particle dialectic of light, “the period during which light was ‘sometimes a wave and sometimes a particle’ was a period of crisis—a period when something was wrong—and it ended only with the development of wave mechanics and the realization that light was a self-consistent entity different from both waves and particles” (p. 114). Similarly, a true synthesis of social and cognitive notions of learning must get beyond their dialectical opposition to one another. Mindful of the severe challenges of integration across paradigms, some of our most sophisticated theorists are coming to question whether establishing epistemic foundations for learning and teaching is even possible. As Sfard (1998) lamented in her essay on incommensurable learning metaphors, we’d best “give up the hope that the little patches of coherence will eventually combine into a consistent global theory. It seems that the sooner we accept the thought that our work is bound to produce a patchwork of metaphors rather than a unified, homogeneous theory of learning, the better for us and for those whose lives are likely to be affected by our work” (p. 12). Similarly, in framing mathematics education as a design science, Cobb (2007) explicitly rejects the possibility of epistemic knowledge as the product of theory/research. For Cobb (2007), the theorist is recast as “bricoleur . . . a handy man who invents pragmatic solutions in practical situations. . . . Similarly, I suggest that rather than adhering to one particular theoretical perspective, we act as bricoleurs by adapting ideas from a range of theoretical sources” (p. 29). Indeed, Cobb (2007) “question[s] the assumption that theory consists of decontextualized -108- propositions, statements, or assertions that are elevated above and stand apart from the activities of practitioners” (p. 5), and consequently, he “sh[ies] away from the approach of first surveying currently fashionable philosophical [and psychological] positions and then deriving implications for mathematics education research and practice from them” (pp. 6–7).7 In my view, abandoning the pretension that psychological theory has provided epistemic foundations for educational practice is an intellectually responsible answer to our inability to coherently marshal the divergent epistemic knowledge of learning that psychology has generated in its varied paradigms. Still, the postpositive turn away from epistemic knowledge is a drastic step.8 For in reifying knowledge of learning and teaching as ineluctably local we abandon the possibility that the knowledge base for teaching ever can be systematized, that teacher expertise can be scaled-up beyond the local regime of theory within which it is nurtured, and consequently that teaching ever can attain to the stature and authority of professions whose knowledge base is informed by epistemic science. This is a verdict we shall try to avoid. THE GENRES APPROACH The foregoing review of education’s uptake of psychological theory highlighted four strategies: • Foundational theory: adopt a single foundational paradigm that provides a clear, but limited, vision of learning. • Integrative theory: adopt an integrative theory struggling to bridge across inconsistent units of analysis. • Holistic approach: ignoring incommensurability, in eclectic fashion, create pedagogical ensembles that draw from a broad range of learning theories. • Postpositive approach: abandoning the possibility of epistemic theorization of learning, reconstitute theory as local to the particular situational interests in a given educational setting. The genres approach constitutes a new strategy designed to better exploit the significant insights into learning forged within the foundational paradigms. The strategy involves identifying the distinct notions of learning that inspire educational practice, determining the psychological theorization that best explicates each of these, and then using the theorizations to inform the articulation of genres of teaching—distinct pedagogical methods, each specific to one of the identified notions of learning. Of course, a theory of learning does not determine a teaching method, any more than a theory of cell pathology determines a cure for cancer. Nevertheless, in both cases having a clear understanding of underlying mechanisms is a major asset in formulating sound professional methods. The strategy of aligning learning goals with learning theories with pedagogical practices is intended as an alternative to the current strategies that have led to conflict, confusion, banality, and abandonment, respectively. Culturally Shared Metaphors for Learning The first challenge of the genres approach is to identify the notions of learning explored by psychologists that capture our fundamental interests as educators. My personal exploration of the learning theory landscape has evolved over the past 18 years, finally settling into three metaphors for learning: Learning as habituation, informed primarily by behavioral psychology; learning as construction, informed by developmental psychology (Piaget); and learning as enculturation, informed by sociocultural psychology. Remarkably, essentially these same metaphors have been identified by other researchers (Bredo, 1994; Case, 1992; Greeno, Collins, & Resnick, 1996; Richey, Klein, & Tracey, 2011; Shulman, 1987, p. 7; Wojcikiewicz, 2010). Furthermore, these metaphors for learning dovetail with the canonical goals of learning—skills, -109- knowledge (concepts), and dispositions (cultural practices), respectively—that have been identified by the U.S. National Council for Accreditation of Teacher Education (NCATE, 2002; see also AERA, 2005). Rather than write off this happy convergence to coincidence, I am mindful of the observation of many commentators that psychology often draws from our culture’s basic metaphors for its foundational images and intuitions (Fletcher, 1995; Leary, 1994; Olson & Bruner, 1996; Sternberg, 1997). As Fletcher (1995) put it, our culture’s “folk psychology is built into scientific psychological theories in a more thoroughgoing fashion than is commonly realized” (p. 97). Following these observations, the genres approach takes as its working premise that the learning goals motivating educational practice reflect notions of learning that psychologists also have pursued. Thus my intention in articulating genres of teaching is not so much to provide new foundations for pedagogical practice as to disentangle the existing intuitions about teaching and learning knotted together within an integrative theories discourse (Kirshner, 2002). If fully successful, the system of genres that I outline presents a refined and organized version of the varied streams of ideation that already constitute pedagogical thought and practice across the broad spectrum of education. Utilizing Learning Theory The second challenge of the genres approach is to identify and utilize the learning theories that best illuminate the metaphors for learning that motivate educators. Given the shared wellspring of metaphors for learning that nourish both education and psychology (Fletcher, 1995; Leary, 1994; Olson & Bruner, 1996; Sternberg, 1997), the obvious strategy would be to adopt extant theories of learning from the menu of available paradigms. There are two problems with that approach: (A) Although psychology’s major learning paradigms do seem to be driven by the metaphors for learning adopted for the genres approach, the match-up is not quite neat. Sometimes more than one branch of psychology is informed by a given metaphor, in which case our theorization of learning may draw from more than one paradigm. Other times, a theory of learning, though inspired primarily by the learning metaphor at hand, adopts a more complex unit of analysis. Such cases may necessitate forays beyond psychology into neighboring disciplines. (B) As discussed earlier under “Paradigm Projection” (p. 106), the trajectory of learning theory projects beyond the natural, intuitive paradigmatic boundaries in an attempt to encompass notions of learning pursued in other paradigms. Such projection is a necessary part of the competitive process whereby psychology may hope one day to become paradigmatic, but it runs counter to our interest in articulating coherent and distinct theorizations of learning. These concerns are not just hypothetical; they directly impact the theorizations of all three learning metaphors addressed in the genres approach: • Habituation: (A) The habituation metaphor for learning of skills is informed not only by behaviorism, but also by implicit learning theory of cognitive psychology. (B) Furthermore, despite the nonmentalist rhetoric of behaviorism, applications to education have implicated the learning of “facts” (Skinner, 1958b), which constitutes encroachment of behaviorism onto the terrain of concept learning. • Construction: (B) For the construction metaphor for learning of concepts, both Piaget’s developmental psychology (Piaget, 1965/1995) and its interpretation in radical constructivism (von Glasersfeld, 1995) resist the natural solipsistic limitations of the theorizations as they seek to embrace some sense of intersubjectivity. • Enculturation: (A) Despite the clear sociogenetic orientation of sociocultural theory as a basis for theorizing learning of cultural practices, Vygotsky’s (1978) vision ultimately is dialectical, thereby necessitating a reliance on sociological theory to explicate the enculturation metaphor. -110- All of these issues are explored, in depth, in the next section. Their relevance here is to explain the necessity of moving beyond the simple and straightforward strategy of adopting an intact theory of learning from psychology for each of the three learning metaphors. Instead, the genres strategy is to identify the learning theories relevant to each metaphor and, drawing selectively from their results, to assemble a theorization of learning particular to the learning metaphor at hand. A priority in this constructive process is to establish clear boundaries between the learning metaphors. In our current discourse, we typically talk of “understanding the skill,” “inculcating thinking skills,” and “practicing the concept,” each of which intermixes the learning metaphors. A system of genres works only if the learning goals for the genres are distinct from one another, and the selective activity of assembling theorizations works toward that goal. The result of this selective process, presented in the next section, is a set of theoretical framings of learning that are assembled from psychological theory, but do not directly match the authorized versions of extant theories. Their purpose is to present for educators as clear and focused an analysis as possible of each learning metaphor, as informed by psychological theory. Yet, these sketches of learning are not comfortably part of educational psychology, which as a bona fide branch of psychology “is much determined by the larger field of psychology” (Pressley & Roehrig, 2003, p. 340), and seeks first and foremost to promote the authorized knowledge products of that science. Rather, these sketches of learning come from the education side of the relationship with psychology, a new assertion of autonomy for educators to interpret learning for our own purposes. Of course this interpretive effort could benefit from positive participation of psychologists, but given the tribal character of science (McRae, 2011) this is improbable. Rather, psychologists are likely to view these unauthorized framings of learning as “weak” psychological theorizing, or perhaps, more generously, simply as “wrong” psychological theorizing. Educational theorists, too, are likely to be hesitant in embracing the genres approach. As noted earlier, education, has hitherto gained much of its intellectual authority through co-participation with psychology in pursuit of its goals (Lagemann, 2000). As well, as we have evolved into the current era of integrative and dialectical theorizing, philosophical and theoretical breadth and depth have become our markers of academic fitness (see Lester, 2010, p. 82, for a long list of theories invoked by mathematics educators). The reduction of theory to a small set of psychological approaches proposed here goes against this grain. Of course, it is precisely this reduction and organization of theory that enables educational research to attain to what Nuthall (2004) called “pragmatic validity . . . research that actually answers the question of how teaching is related to learning in a way that is comprehensible and practically useful for teachers” (p. 273). Still, this new approach disrupts our hierarchies of status and accomplishment. In the next section I present the framework of learning theorizations and associated pedagogical methods. I then use the framework as a refractive lens to analyze the learning theory foundations of a wide range of educational practices and problems—from Skinner’s programmed instruction to the Reading Wars and the Math Wars to critical pedagogies to metacognitive interests to identity development to ethical issues—in each case bringing a sense of clarity to what otherwise are experienced as deeply complex and sharply contested problematics. In this way, I press the case that the genres approach, though disruptive to our internal and external relations, captures a level of simplicity from which our work as educators can progress. THE CROSSDISCIPLINARY FRAMEWORK As noted earlier, the genres approach seeks to assemble theorizations of learning as habituation, construction, and enculturation, each clearly demarcated from the others. In this respect, the three theorizations can be said to constitute a framework of learning theories relevant to -111- Table 4.1 Crossdisciplinary framework. Learning Metaphor Habituation Construction Enculturation What is Acquired Skills Concepts Dispositions Theoretical Resources Behaviorism; Implicit Developmental Sociocultural Theory; Learning Theory Psychology; Radical Sociological Theory Constructivism Key Theorists Thorndike; Skinner; Reber Piaget; von Glasersfeld Vygotsky; Parsons Learning Process Subcognitive connections Discrepant experience –> Osmosis and/or emulation among input/output elements conceptual restructuring of forms of engagement Pedagogical Objective Proficiency With Routine More Viable Concept Culturally Normative Exercises Participation Student-centered Pedagogy Extrinsically Motivated Hypothetical Learning Nurture Classroom Repetitive Practice Trajectory Microculture Teacher-centered Pedagogy Repetitive Practice Lecture Modeling/Coaching (Acculturation) Necessary Student Independently Motivated Metacognitively Culturally Identified Characteristic Learners Sophisticated Learners Learners the practices of teaching. I use the modifier crossdisciplinary (as opposed to interdisciplinary) to emphasize that the branches of psychology (behavioral, developmental, sociocultural) are being coordinated (as opposed to integrated) together, at the same time highlighting their independence from one another as separate sub-disciplines of psychology. Table 4.1 provides an overview of the crossdisciplinary framework, which includes three metaphors for learning, associated theoretical resources and theorists, learning goals and processes, and teaching genres. Student-Centered and Teacher-Centered Pedagogies As can be seen in Table 4.1, each learning metaphor yields two teaching approaches, depending on whether or not the students possess a key characteristic that facilitates achievement of the given learning goal. The idea is that a student endowed with this characteristic is positioned to utilize instructional resources independently. In this case, a teacher-centered pedagogy is appropriate in which the teacher need only focus on providing the learning resources. However, if students lack the key characteristic, a student-centered pedagogy expands the teacher role to include facilitating student uptake of instructional resources. The relevant student characteristic is indexed to the specific learning metaphor; there is a separate teacher-centered and student-centered pedagogy for each metaphor. This usage differs from standard usage in which student centered (or learner centered) and teacher centered are code for reform- oriented instruction and traditional instruction within a polarized discursive frame (McCombs, 2003). LEARNING AS HABITUATION In keeping with Thorndike’s connectionism, habituated learning is understood as the association between sense impressions constituting a stimulus and impulses to action constituting a response. Associations are strengthened with use (Law of Exercise), particularly when the behavioral response is closely followed by a satisfying result (Law of Effect, Thorndike, 1911a). With repetition, responses to stimuli can become established patterns. This creates the possibility of shaping behavior through administration of rewards and punishments, a matter extensively and productively researched in behavioral psychology (e.g., Ormrod, 2000). -112- Having first been discovered and studied in the context of (non-human) animal research, a critical aspect of learning from a behaviorist perspective is its operation below the level of conscious thought or intention. As Watson (1913) laid it out in his inaugural vision for the new approach, “I believe we can write a psychology, define it as [the science of behavior], and never go back upon our definition: never use the term consciousness, mental states, mind, content, introspectively verifiable, imagery, and the like” (p. 166). As the dominant paradigm of psychology through much of the early/middle part of the 20th century, behaviorism exerted a strong influence over education, its antimentalist premise conflicting with educational traditions rooted in notions of mind and consciousness that trace back to Plato (Egan, 1997); indeed, many commentators have lamented the effect that behaviorism had in reducing curriculum to mindless behavior (e.g., von Glasersfeld, 1987; Schoenfeld, 1992). In fact, however, behaviorists rarely have been rigorous in their antimentalist educational projects, most often seeking to attribute acquisition of (low level) information to behavioral learning: “Research that has studied teaching and learning in didactic environments has confirmed the assumptions of behaviorist theory regarding conditions that favor learning of components of information and routine skills” (Greeno, Collins, & Resnick, 1996, p. 28, italics added). Indeed, even Skinner (1958b, p. 974) promoted learning of “facts.” Certainly, rote memorization of a string of words (e.g., a telephone number) can be learned as a behavior, and sometimes educators insist on verbatim memorization of say, definitions, in science. “Facts,” in this sense, are behaviors. But even in the heyday of behaviorism, behaviorist educators rarely intended or enforced verbatim memorization. For example, in their textbook on behavioral objectives, Sund and Picard (1972) offered as an exemplar: “The child is able to identify the stages of mitosis and to describe in his own words the changes which occur in the cell at each stage” (p. 2). As Chomsky (1959) argued, behaviorists’ tolerance for stimuli and responses that are not objectively defined simply imports conceptual content through the back door. Implicit Learning Theory: For purposes of the crossdisciplinary framework, we need to adhere rigorously to learning of skills as a subcognitive accomplishment. To gain a better sense of habituated learning at the subcognitive level we supplement behavioral theory with the implicit learning domain of cognitive psychology. This area of research demonstrates the scope and power of the cognitive processor to establish complex correlations among stimuli and responses through repetitive engagement in a task domain (Reber, 1967; Kirsner, Speelman, Maybery, et al., 2013). As Reber (1993) noted: There are remarkably close ties between the typical experiment on implicit learning and the standard study of conditioning. The commonality lies in the detection of covariation between events, which, I will argue, is the deep principle in processes as seemingly disparate as classical conditioning and implicit learning. Moreover, this conceptual parallel can be shown to hold, even though on the surface the implicit learning experiment appears to be one of abstract induction and the conditioning experiment one of simple association. (p. 7) In this tradition of research, complex correlations among stimuli and responses are established through repetitive exposure. In a typical study, subjects are provided some pretext for attending to a stimulus set, without reference to underlying structures that are the actual learning target. For instance, subjects may be directed to memorize a list of letter strings without being told the strings have been generated by a finite state grammar according to fixed rules Reber (1967). With sufficient exposure, subjects show evidence of having acquired competencies related to the grammar, for instance, they can identify grammatical strings they’ve not encountered more frequently than nongrammatical strings consisting of the same letters. Interestingly, subjects in such studies typically have no conscious awareness that they have -113- learned a pattern, or even that there is a pattern to be learned—at least, when conscious knowledge is ascertained through self-reports (Fu, Fu, & Dienes, 2008, p. 186).9 Skills Versus Concepts This idea that habituated learning plays out unconsciously, as patterns of co-occurrence and covariation become operationally linked in the cognitive system, is emphasized in Reber (1993): When a cognitive scientist constructs a stimulus environment, he or she may do so on the basis of some set of principles that have the effect of creating an environment that reflects particular patterns of co-occurrence and covariation among its elements. But [for subjects] there are no rules here, just patterns of co-occurrence and covariation. The cognitive scientist may think that there are rules that characterize these covariations, and in fact, she or he is certainly entertaining a particular clutch of these—namely, the ones begun with. (p. 116) Complicating the distinction between skills and concepts is the fact that conscious processes and explicit instruction can play a facilitative role in habituated learning. What explicit instruction about underlying relations does is to focus the perceptual apparatus on relevant aspects of the stimulus display thereby facilitating the implicit process of feature correlation, and consequently increasing the rate of learning. Yet this facilitative effect is independent of actually understanding the underlying relations: The most plausible interpretation [of our study] here, and the one that has interesting applications for theories of instruction, is that the function of providing explicit instructions at the outset is to direct and focus the subjects’ attention. It alerts them to the kinds of structural relations that characterize the stimuli that follow and permits appropriate coding schemes to be implemented. Yet, these instructions do not teach the grammar in any full or explicit fashion; instead they oriented the subjects toward the relevant invariances in the display that followed. (Reber, 1993, p. 51) The fact that instructors may use a set of rules to generate a stimulus set, for example a set of math problems, and that students benefit from explicit presentation of those rules, has led to considerable confusion about the nature of the learning that ensues from repetitive practice. Educators often conclude that students demonstrating intended skills have understood the rules conceptually, and that this understanding is the basis for successful performance (see Kirshner & Awtry, 2004, for an extended discussion). Neither of these conclusions is warranted given the interpretation of habituated learning presented here. Habituated learning is necessarily and exclusively a subcognitive process. Skills Versus Dispositions To demarcate skills from dispositions, we return to the issue of objectivity that Chomsky (1959) raised respecting Skinner's (1958a) efforts to extend the analysis of behavior to include verbal behavior. The issue is primarily methodological. Experimentally, or instructionally, one can set out to shape behavior instrumentally only to the extent one can objectively characterize stimulus and response events for organizing regimes of practice and feedback (Ormrod, 2000). For instance, one can shape the habituated response of raising one’s hand in class and being recognized by the teacher before speaking because the discrete elements that comprise this event can be objectively characterized. Similarly, one can interpret, say, solving of mixture problems or factoring of polynomials as skills in that each involves discernible, codified problem types and routine solution steps. -114- However, such methods break down when stimuli and/or responses cannot be objectively demarcated. For instance, nonroutine mathematics problems resist rigid codification, in that expertise in solving requires flexible use of heuristics (Polya, 1957). Use of such rules-of-thumb is best conceived of as a cultural disposition rather than a skill, and effective instruction needs be framed in terms of cultural participation rather than repetitive practice. As Stanic and Kilpatrick (1988) noted, 1980s curricula that “reduc[ed] the rule-of-thumb heuristics to procedural skills” (p. 17) failed to nurture in students the art of problem solving. Similarly, one can teach individual behaviors of classroom participation as habituated learning, but classroom citizenship conceived beyond discrete rules of behavior requires an enculturational frame (Millei, Griffiths, & Parkes, 2010). Habituationist Pedagogies Teacher Centered: Because habituation learning is based on gradual establishment of feature correlation over repetitive exposure to a stimulus set, the basic requirement of habituationist instruction is to organize systematic repetitive practice across the range of stimulus conditions. Additionally, as noted earlier, demonstration of procedures can serve to activate certain features of the stimulus set that are thereby increasing the rate of habituated learning. Finally, corrective feedback can be crucial for learning, assuring that correct performances are being practiced and learned (Thorndike & Gates, 1929). Student Centered: The student's motivation to persist with repetitive practice is a crucial determinant of instructional method. If the student is independently motivated, the teacher-centered instructor's work is simply to provide appropriately structured opportunities to practice. If not, the student-centered habituationist instructor uses a variety of devices to extrinsically motivate students. Behavioral psychology provides significant guidance for provision of rewards and perhaps punishments to sustain engagement, including judicious use of praise and encouragement, game formats and competition, benefits and payment, and the like (Ormrod, 2000). LEARNING AS CONSTRUCTION The metaphor of learning as construction is elaborated through Piaget’s theorization of conceptual development. Piaget is best known for his macrogenetic studies of how individuals pass through stages of intellectual development. However, it is his microgenetic studies of development in particular conceptual domains (e.g., space, time, number, etc.) that became drivers of pedagogy and research for mathematics and science educators.10 What we pick up on in Piaget’s system of ideas is his basic approach to genetic epistemology, his viewpoint on the genesis and evolution of our ability to gain knowledge of the world through experience. Rather than an empiricist view in which the structure of the world is directly perceived, Piaget understands knowledge as constructed through our actions on the world: In order to know objects, the subject must act upon them, and therefore transform them: he must displace, connect, combine, take apart, and reassemble them. From the most elementary sensorimotor actions (such as pulling and pushing) to the most sophisticated intellectual operations, which are interiorized actions, carried out mentally (e.g., joining together, putting in order, putting into one-to-one correspondence), knowledge is constantly linked with actions or operations. (Piaget, 1970/1983, p. 104, quoted in Paz & Leron, 2009, p. 20) For Piaget, conceptual structures have their basis in the experienced regularities of our actions as they form “action schemas, . . . whatever there is in common between various -115- repetitions or superpositions of the same action” (Piaget, 1971, p. 7). Such schemas form the base of hierarchically organized structures that enable knowledge construction up and down the abstraction ladder: If logic and mathematics are so-called “abstract” sciences, the psychologist must ask, Abstracted from what? . . . The origin of these logicomathematical structures should be sought in the activities of the subject, that is, in the most general forms of coordination of his actions, and, finally, in his organic structures themselves [basic infant action reflexes like sucking and grasping]. (Piaget, 1970/1983, p. 106) From his initial training as a zoologist, Piaget approached conceptual development as adaptation, which he understood as complementary processes of assimilating elements of the environment to our existing conceptual structures, and accommodating our cognitive structures to better fit with elements of the environment (Piaget, 1977a). The process is dynamically driven by disequilibrium with the environment, which Piaget theorized in terms of cognitive conflicts, contradictions, or discrepancies within cognitive structures, or between expectations and actual events (Sigel, 1979). It is the attempt to achieve a higher equilibrium, or equilibration, that produces learning: “what Piaget calls ‘equilibration’ is a form of learning . . . that is motivated by conflict and reinforced by conflict reduction” (Berlyne, 1970, p. 968, quoted in Cantor, 1983, p. 44). Crucially, conflicts must be experienced (in some sense, at some level) in order for them to become productive of conceptual restructuring (Inhelder, Sinclair, & Bovet, 1974). Piaget developed a highly refined set of constructs to understand how experience is recorded in conscious and nonconscious ways within the cognitive system (von Glasersfeld, 1991). Non-conscious empirical abstraction involves the isolating of one’s experience of sensory properties of an object or situation that can be used to recognize it at a later time. However, for learning to happen—for schemas to be coordinated together into higher level constructs—one needs to reproduce the experience independently of its physical instantiation. This reflective abstraction involves a “limited form of awareness” (von Glasersfeld, 1991). This is still different from reflected abstraction, a “process of retroactive thematization” (Piaget, 1977b, quoted in von Glasersfeld, 1991) that we normally associate with conscious reflection. From this we glean that cognitive conflict, as intended by Piaget, is not necessarily what we associate with conscious struggle with an idea or conundrum. Radical Constructivism: As noted earlier, Piaget’s motivating interest was in elaborating the macrogenesis of stages of intellectual development, and his microgenetic studies of conceptual development in particular domains subserved that objective. In this respect, the redirecting of Piaget’s genetic epistemology toward microgenesis dramatically extended the scope of the framework from just the core structures of development to include conceptual development in any and all domains (Steffe & Kieren, 1994). Radical constructivism is the epistemological position (or postepistemological position, Noddings, 1990) that takes that broadened mandate of genetic epistemology to heart. That all concept development is rooted in structures derived from our actions upon the world implies the impossibility of any direct knowledge of the world. For intelligence that serves the organism’s adaptation to the world, the question is never “Do my constructed understandings match what is really out there?” but rather, “Do they fit the world in such a way as to enhance my viability?” Constructions that produce dissonance with the world cause perturbations to the cognitive system that may lead to conceptual restructuring and more viable knowledge structures (von Glasersfeld, 1987, 1995). The idea that all knowledge, including knowledge of other people, is constructed by the individual has led to vociferous criticism of radical constructivism as solipsistic, and consequently as unable to account for intersubjective knowledge (e.g., Gergen, 2002; Howe & Berv, -116- 2000; Lewin, 1995; McCarty & Schwandt, 2000; Phillips, 1995). Piaget, too, faced criticisms that his theory failed to account for the social aspects of human knowledge (e.g., Vygotsky, 1934/1986, pp. 154–155). Perhaps it was in anticipation of and/or response to such criticisms that both Piaget and von Glasersfeld argued that their theories do account for intersubjective knowledge: “Piaget placed great emphasis on the idea of decentering, or attempting to adopt a viewpoint that differs from your own. He used the term intersubjective operations to describe thoughts that are directed at another” (Thompson, 2013, pp. 62–63). Likewise, von Glasersfeld (1995), in fending off charges of solipsism, talked of an “intersubjective level” that “reaches beyond the field of our individual experience into that of others” (p. 120). The complication of one’s basic ontology, in an effort to account for intersubjective knowledge, may be necessary for psychological or philosophical theories framed in competitive relation with other theories. However, in this crossdisciplinary project, which seeks after local coherence, the solipsistic limitation of radical constructivism is a crucial asset in framing a constructivist pedagogy that highlights the teacher’s isolation from the student—the tentative, conjectural nature of her or his model of students’ conceptual structures, and the impossibility of transferring one’s own ideas to them. Student-Centered Constructivist Pedagogy11 Once we learn to think within the severe epistemological and theoretical constraints imposed by Piagetian psychology and radical constructivism, the basic approach of student-centered constructivist pedagogy is fairly straightforward to understand (even if dauntingly difficult to enact). Shorn of intersubjective possibility, the student is seen to learn only from goal-directed encounters with the world, particularly those encounters in which they come to experience dissonances within their conceptual structures. Such a vision of learning would seem to leave little, if any, role for a teacher. Indeed, “for Piaget, the key ingredient of construction episodes was the active self-discovery of discrepancies between current concepts and actual outcomes. He argued that this is absolutely essential for children to stumble across such discrepancies on their own if cognitive development is to occur” (Brainerd, 2003, p. 271). Nevertheless, constructivist researchers, working within his basic framework, have adapted Piaget's clinical interview methods to occasion transitions in children’s conceptual structures (i.e., learning) (Cobb & Steffe, 1983; Steffe & Thompson, 2000). This constructivist teaching experiment methodology provides grounding for student-centered constructivist methods in this crossdisciplinary framework. The key point is that the teacher-researcher acts only indirectly to produce learning by shaping a task environment in which the student encounters experiences that may be productive of conceptual restructuring. Learning ensues from the student’s actions and reflective dynamics within the task environment: “Learning is not spontaneous in the sense that the provocations that occasion it might be intentional on the part of the teacher-researcher. In the child’s frame of reference, though, the processes involved in learning are essentially outside of his or her awareness” (Steffe & Thompson, 2000, p. 290). This is the solipsistic principle in action. As accounted by Steffe and Thompson (2000), the first requirement for shaping such a task environment is for the teacher to come to have a model of the student’s current conceptual structures, including the limitations of those structures relative to a mature understanding of the content to be taught (as construed by the teacher). Whereas this model has on occasion been formulated using Piaget’s own theoretical constructs (e.g., Steffe, 1994; Thompson, 1994), much of the detail of Piaget’s theory has proven “too vague to provide satisfying explanations” (diSessa, 2006, p. 535; see also Goodson-Espy, 1998). Historically, a variety of framings have served as guides for this modeling including cognitive science (e.g., Sloboda & Rogers, 1987); “conceptual metaphor” (Lakoff & Núñez, 2000); “embodied objects” -117- (Gray & Tall, 2001); and in science education, fixed misconceptions (based on Kuhn), and malleable preconceptions (diSessa, 2006). Even though Piaget’s theoretical apparatus is rarely used, his basic framework of ideas has been deeply informative as to (A) the nature of a useful model, (B) the characteristics of effective task environments, and (C) the teacher’s supporting role in the constructive process. (A) In concert with Piaget’s emphasis on the subject’s actions as the foundation of conceptual schemas, to the extent possible a model should trace the student’s intuitions and preconceptions to physical and perceptual operations. As Lakoff and Núñez (2000) put it, “for the most part, human beings conceptualize abstract concepts in concrete terms, using ideas and modes of reasoning grounded in the sensory-motor system” (p. 5). Probative models of students’ understanding should trace back to these perceptual and sensory-motor underpinnings. (B) In concordance with this first principle, task environments designed to produce conceptual learning should establish activity systems that evoke this perceptual and sensory-motor level of grounding. For, as noted earlier, it is such activity systems that can lead to “reflective abstraction” through which schemas are realigned. This rules out “‘conflict’ models of instruction” (diSessa, 2006) that merely provide empirical evidence to contradict the student’s explanations or predictions (Confrey, 1990; Simon & Tzur, 2004). Such empirical approaches rely instead on conscious “reflected abstraction,” which for Piaget is derivative (von Glasersfeld, 1995). Rather, what is needed are full-blooded activity systems that penetrate to the perceptual and sensory-motor level of conceptual structure, as it is this engagement that provides the positive resources the student draws upon in the reconstructive process. Empirical contradiction is not sufficient. (C) Finally, for a teacher to effectively support the constructive process she/he must be equipped with more than a model of the initial state of the student’s understanding, the end goal of a mature understanding, and perhaps intermediate states the student should pass through en route. The teacher also should be able to anticipate how the student’s understanding will be transformed by the tasks that are developed to help move the student forward. This total package sometimes is referred to as a Hypothetical Learning Trajectory that “consists of the goal for the students’ learning, the mathematical task that will be used to promote student learning, and hypotheses about the processes of student learning" (Simon & Tzur, 2004, p. 91). This interest in the process of conceptual change is motivating revision in the conception of the constructivist teaching experiment: In some teaching experiments (e.g., Steffe, 2003), the aim of the retrospective analysis is the characterization of the understandings of the student at different points in the learning process. . . . In our adaptation of the teaching experiment . . . the aim of our analyses is to characterize the flow of the students’ (changing) thinking, as opposed to only characterizing the resulting understandings. (Simon, Saldanha, McClintock, et al., 2010, pp. 91–92) Pulling all of this together, the teacher/researcher in a constructivist teaching experiment needs a significant knowledge base to develop a working model of the student’s conception of the content domain, devise a task environment for the student to restructure that understanding, and perceive, through the student’s eyes, how the task domain might facilitate conceptual development. As well, there are interactive competencies that need to play out as the teacher/researcher facilitates student engagement with the task: first, monitoring uptake of the task, making minor adjustments and redirection to try to ensure the student encounters the task as intended; second, assessing whether engagement with the task is progressing along the lines envisioned (one always needs to be ready to rethink and revise both the model of the student’s understanding, and the efficacy of the task environment); third (but very tentatively, without disrupting engagement), helping to juxtapose discrepant elements in the student’s workspace so as to -118- enhance the transformative potential of the task; and fourth, encouraging the student through the frustrations that arise when conceptual obstacles are encountered(Steffe, 1991). Finally, excluded from this list is the requirement that the teacher provide a neat and tidy summation of the completed activity. In many cases, the experience should be left raw, so that it can continue to work its magic on the restructuring of schemas. “Retroactive thematization” (Piaget et al., 1977, Vol. 1, p. 6) should be allowed to happen spontaneously, or prompted only after a delay; premature closure can curtail the mulling-over process that extends reflective abstraction. Classroom Implementation The pedagogical model just described is rooted in a clinical research methodology in which a teacher-researcher attends minutely to the conceptual structures of one or two students engaging with tasks devised specifically for them (Steffe & Thompson, 2000). Given an ontology that understands each person's conceptual structures as the unique product of his/her individual experience, how could this pedagogy possibly have application in a classroom context? The solution to the conundrum is that although constructivism theorizes learning as rooted in individual construction, there turns out to often be great commonality in adaptive structures across individuals; Piaget attributed this to constraints on construction imposed by biological and physical reality (Brainerd, 2003; Glick, 1983).12 In practice, though, the classroom is a complicated place to attend to student conceptual construction. Having students work on tasks at their own desks may enable individual students to engage with the task, but it limits the possibilities for verbal expression and teacher mediation. Small-group formats provide opportunity for students to express their understandings, but the group’s response to a student’s ideas generally will not be tailored toward productive reflection by that student. Whole- class instruction enables a teacher to mediate the conversation, but limits the degree of student expression. To further complicate matters, the conceptual landscape is comprised not of discrete conceptual structures, but of vertically and horizontally interconnected structures (Hiebert & Carpenter, 1992), including vertical linkages created through reification of processes at one level into conceptual objects at another level (Goodson-Espy, 1998; Sfard & Linchevski, 1994). Thus, in addition to designing lessons that target specific concepts, the student-centered constructivist teacher is constantly alert to opportunities that arise in teaching to support emergence of understanding through connections across contents; one’s conceptual agenda often is established interactively. The teacher competencies outlined with respect to the constructivist teaching experiment are crucial; however, their deployment often is highly adaptive to the circumstances at hand. Despite these limitations and complexities, it seems that student-centered constructivist classroom teaching is fairly robust. Given the wide variety of possible implementation modes, many researchers interested in classroom applications of a psychological constructivist ontology have avoided specifying pedagogical methods at all. For example, in their work with teachers, Cognitively Guided Instruction (CGI) researchers simply educated teachers with respect to children’s mathematical constructions and then observed the effects on pedagogy, documenting impressive learning gains for these teachers’ students (Carpenter, Fennema, Peterson, & Carey, 1988; Moscardini, 2014). Similarly, in science education, “the very general constructivist heuristic of paying attention to naïve ideas seems powerful. . . . Interventions that merely teach teachers about naïve ideas have been surprisingly successful” (diSessa, 2006, p. 276). Teacher-Centered Constructivist Pedagogy The pedagogy of student-centered construction just described is highly demanding, requiring intensive problem solving, a significant knowledge base, and real-time responsiveness on the part of the teacher to orchestrate cognitive dissonances and help make them salient for -119- the learner. This high-intensity effort is needed because of the chancy character of conceptual construction: Although the effectiveness of cognitive conflict in leading to subjects’ conceptual change is corroborated both in the literature on science education and reading education . . . its effect is not automatic. The effectiveness of cognitive conflict depends on the way comprehension is monitored. It depends, first, on the individual noticing the inconsistency and, second, on the way it is resolved. (Otero, 1998, p. 149) Otero's (1998) observation points to the facilitative effect that metacognitive sophistication can bestow upon the learner, as being sensitive to subtle incongruities is the key to stimulating the process of reflective abstraction that can lead to conceptual learning (Simon, Tzur, Heinz, & Kinzel, 2004). In this case, a much simpler teacher-centered constructivist pedagogy can be employed, utilizing the most obvious technique for teaching concepts: lecture, in the form of direct explanation of the mature form of a concept. (Note, this is a very particular version of lecture. Lecture also can include interactive elements, can be delivered with sensitivity to students’ likely preconceptions, and can provide other supports for student understanding that push much more toward student-centered constructivist instruction, Brown, Manogue, & Sadownik, 2001.) For the metacognitively sophisticated student, lecture can succeed because the student, sensitive to tensions between elements of the teacher’s explanation and their own intuitions, orchestrates their own cognitive conflicts by generating hypothetical situations that create dissonances with their current conceptual structures. In this case, the teacher’s role is limited to organizing and delivering the mature form of the concept. She/he need not have a model of the student’s understanding, nor design and mediate tasks relative to that model. Indeed, the teacher need not even adopt a constructivist perspective on learning and teaching, but may happily believe him or herself to be transmitting their understanding directly to the student. It should be noted that the level of metacognitive capability needed is indexed to the conceptual complexity of the content being taught. Lecture is fully appropriate as a pedagogical method whenever the student’s metacognitive sophistication is sufficient to accommodate the gap between current and mature forms of the concept. Students who are relatively sophisticated metacognitively may be unable to productively integrate lecture material concerning very difficult concepts. And even students who are relatively unsophisticated metacognitively can benefit from lecture for simple conceptual content. LEARNING AS ENCULTURATION I take enculturation to be the process of acquiring dispositions through enmeshment in a cultural community. I interpret dispositions broadly as culturally particular ways of engaging with people, problems, artifacts, or oneself. Alternatively, one might say that enculturation is the acquisition of cultural practices, except that as analytic objects, practices are located in the culture, and distributed across actors (Hutchins, 1995; Nardi, 1996), whereas dispositions are properties of an individual. For the purposes of crossdisciplinary theorizing, it seems advantageous to identify learning as attained at the level of the individual (even if the process of learning is social). The likelihood of acquiring a disposition may be influenced by genetic predispositions. For instance, one might say of someone they have a predisposition toward logical thinking, or they’re naturally inclined to be shy. However, predispositions to engage only find expression as dispositions within a cultural context. This interpretation is consistent with the personality theory of German psychologist William Stern, who believed that “all characteristics of personality are properly regarded not as fixed determinants, whether partial or complete, of behavior or states of psychological being . . . but rather as potentialities. . . . It is only through extended -120- interaction with the world that the range of such potentialities can gradually become constricted, so that what is initially but a mild tendency in one direction allowing for many other possibilities can become a relative inclination”(Lamiell, 2013, pp. 108–109). This sense of disposition differs from the more typical cognitive science rendering in which cognitive practices (e.g., critical thinking, metacognition, general problem solving strategies) are naturalized as capabilities of the cognitive apparatus, rather than understood as manifestations of culture at the level of the individual (Scribner & Cole, 1977). Dispositions, thus, are reduced to inclinations or tendencies to employ those capabilities. For instance, Perkins and Ritchhart (2004) present a framework for good thinking based on “viewing dispositions as initiators and motivators of abilities rather than [thinking] abilities themselves” (p. 179). Internalization of culture is vigorously theorized in the work of Soviet-era psychologist Lev Vygotsky, his many students and collaborators, and in the sociocultural and activity theory schools that ensued. The sociogenetic orientation of Vygotsky’s work is clearly expressed in his Genetic Law: “Any function in the child’s cultural development appears on stage twice, on two planes. First it appears on the social plane, then on the psychological, first among people as an interpsychical category and then within the child as an intrapsychical category” (Vygotsky, 1978, p. 57). However, the sociogenetic orientation of Vygotsky’s work is complicated by his desire to provide a comprehensive theory of human development and learning that accounts for both shaping and being shaped by culture. Thus he rejected “a static notion of social determination” (Penuel & Wertsch, 1995, p. 84). As Cole (1996) put it, for Vygotsky, The dual process of shaping and being shaped through culture implies that humans inhabit “intentional” (constituted) worlds within which the traditional dichotomies of subject and object, person and environment, and so on cannot be analytically separated and temporally ordered into independent and dependent variables. (p. 103) What is more, Vygotsky (1978) understood development (i.e., internalization of higher mental cultural practices) and learning (skills and concepts) as mutually interdependent: “Our hypothesis establishes the unity but not the identity of learning processes and internal developmental processes. It presupposes that the one is converted into the other” (pp. 90–91). Sociological Theory Although Vygotsky comes closest in psychology to a pure sociogenetic position, his dialectical stance and the integrative complexity of his theories limit the utility of this body of theory as a framework for the enculturation metaphor for learning (though I do draw on specific aspects of sociocultural psychology, and also find great resonance with Vygotsky’s own pedagogical insights). Indeed, Western social science has such a strong individualist slant that even in sociology, “most sociologists, both individualists and collectivists, . . . [accept the] position . . . known as ontological individualism: the ontological position that only individuals exist” (Sawyer, 2002a, p. 555). Still, within sociology, ideas of irreducible emergence stemming from the work of Emile Durkheim are consistent with a social causation position I take to be the essence of the enculturation metaphor: “Durkheim’s ([1895] 1964) emergentist account of the autonomy of sociology was foundationally based on emergent (or ‘sui generis’) social properties having causal force on the individual” (Sawyer, 2002a, p. 558; see Sawyer, 2002b, for a fuller discussion of Durkheim’s legacy). The social psychology of personal space, or proxemics (Hall, 1966; Li, 2001), provides a paradigm example of social causation. Proxemics is the tendency for members of a national culture to draw specific perimeters around their physical bodies for various social purposes. For example, natives of France tend to prefer closer physical proximity for conversation than do Americans (Remland, Jones, & Brinkman, 1991). Clearly, proxemic dispositions are acquired -121- by natives of a culture without volition or conscious awareness, through enmeshment in the cultural milieu. Indeed, according to sociologist Talcott Parsons (1951), for social norms to be “normative” they have to be outside the realm of conscious reflection, or they become merely additional instrumental resources for action: There is a range of possible modes of orientation in the motivational sense to a value standard. Perhaps the most important distinction is between that attitude of expediency at one pole, where conformity or non-conformity is a function of the instrumental interests of the actor, and at the other pole the ‘introjection’ or internalization of the standard so that to act in conformity with it becomes a need disposition in the actor’s own personality structure, relatively independently of any instrumentally significant consequences of conformity. The latter is to be regarded as the basic type of integration of motivation with a normative pattern-structure of values. (p. 37) I take unconscious introjection in Parson’s sense as the essential mechanism of enculturation. However, this pure form of enculturation is possible only in a unitary culture in which a single dispositional variation is salient for the subject. One also can come to be enculturated into a subculture with practices that are distinctive among a range of alternative subcultures (e.g., being a jock, being a scientist, being a gang member). In such instances, inductees may actively acculturate themselves to a subculture by emulating its distinctive cultural practices. Although acculturation is the more salient process, and historically was identified much earlier (Powell, 1883), it needs to be understood as supplementary to the basic unconscious processes of enculturation going on around it all the time. A culture is comprised of innumerable cultural practices, of which only a limited number can be addressed through conscious strategies of emulation (Kirshner & Meng, 2011). Student-centered Enculturation Pedagogy The enculturation/acculturation distinction defines the two pedagogical genres associated with the enculturation metaphor, a student-centered enculturation pedagogy appropriate for all students, and a teacher-centered acculturation pedagogy appropriate for students who are identified with the reference culture and seek to become part of it. In the enculturation pedagogy, the teacher begins by identifying a reference culture and target disposition(s) within that culture. The instructional focus is on the classroom microculture, which the enculturationist teacher works to shape so that it comes to more closely resemble the reference culture with respect to the target dispositions. Students, thus, come to acquire approximations of the target dispositions through their enmeshment in the surrogate culture of the classroom through the same unconscious processes by which proxemic dispositions are acquired in a national culture. Vygotsky (1926/1997) clearly articulated the foundations of enculturation pedagogy: From the psychological point of view, the teacher is the director of the social environment in the classroom, the governor and guide of the interaction between the educational process and the student. . . . Though the teacher is powerless to produce immediate effects in the student, he is all-powerful when it comes to producing direct effects in him through the social environment. The social environment is the true lever of the educational process, and the teacher’s overall role reduces to adjusting this lever. . . . Thus, it is that the teacher educates the student by varying the environment. (p. 49) Yackel and Cobb (1996) provide valuable perspectives on how such a pedagogy is structured. In their discussion of sociomathematical norms as targeted dispositions of mathematical culture (e.g., the appreciation of mathematically elegant solutions) that come to be “interactively constituted by each classroom community” (p. 475), they note what amounts to a “chicken and egg” problem: students can acquire the target dispositions only to the extent -122- these practices already are constituted within the classroom microculture. Yackel and Cobb (1996) borrow the construct of “reflexivity” from ethnomethodology (Leiter, 1980; Mehan & Wood, 1975) to elucidate the problem: With regard to sociomathematical norms, what becomes mathematically normative in a classroom is constrained by the current goals, beliefs, suppositions, and assumptions of the classroom participants. At the same time these goals and largely implicit understandings are themselves influenced by what is legitimized as acceptable mathematical activity. It is in this sense that we say sociomathematical norms and goals and beliefs about mathematical activity and learning are reflexively related. (p. 460) The solution to this problem constitutes the critical expertise of the enculturationist teacher. As Yackel and Cobb (1996) illustrate, through subtleties of attention and encouragement the teacher, over time, exerts considerable influence on the modes of engagement manifest within the classroom microculture (Vygotsky, 1926/1997). For significant enculturational goals, this must be a progressive agenda in which modes of engagement initially encouraged by the teacher reach a level of general currency in the classroom microculture, eventually to be replaced by yet more sophisticated forms of engagement. Supposing, for instance, one wishes to teach the characteristic mode of argumentation known as mathematical proof (Pedamonte, 2007; Stylianides & Stylianides, 2009) to young students who typically support their arguments with reference to the authority of textbook and teacher—Harel and Sowder (2007) refer to these as “external conviction proof schemes” (p. 809). By betraying signs of interest whenever internal conviction arguments are offered (regardless how unsophisticated), the teacher may gradually shift the norms of classroom argumentation toward “empirical proof schemes,” even though what ultimately is sought are “deductive proof schemes” (p. 809). As in this case, learning of significant cultural practices may require a coordinated effort over months and years. In keeping with the characterization of enculturation, the critical characteristic of enculturation pedagogy is that the teacher’s agenda for participation remain implicit. This does not mean the enculturationist teacher is limited to the (relatively passive) tools of encouragement. As a member of the classroom community, the teacher can introduce modes of engagement through her or his own participation. However, in either case the teacher’s agenda for participation must remain implicit (Parsons, 1951). As soon as it becomes explicit, we enter into a politics of cultural identity that demarcates a shift to acculturation pedagogy. Teacher-Centered Enculturation Pedagogy (Acculturation Pedagogy) In keeping with the characterization of acculturation, the critical student characteristic that authorizes acculturation pedagogy is self-identification with the reference culture. In this case, the teacher’s primary pedagogical role is to model the characteristic practices of the culture. This instructional process provides students who are identified with the reference culture and seek to become part of it an opportunity to appropriate these cultural resources and incorporate them into their evolving repertoire of participatory practices. The instructional process can be informally structured interactively as cultural participation of the teacher with the student (for example, when a mathematician leading investigations with a math club exhibits modes of thinking, values, and problem solving practices that are particular to mathematics culture). In this case, the agenda for appropriation of cultural practices can remain tacit. Alternatively, the teacher can coach the inductee with respect to performance of target cultural practices, in which case the curriculum of cultural practices becomes explicit. The prerequisite for the acculturationist teacher is that she or he be sufficiently well embedded within the reference culture to model cultural practices effectively—in Ma’s (1999) words, “only teachers who are acculturated to mathematics can foster their students’ ability to conduct -123- mathematical inquiry” (p. 106). Beyond that, she or he must signify for the student as a bona fide member of the reference culture, so that cultural practices modeled by the teacher are experienced as worthy of emulation. Note, this is a different requirement than that specified for the enculturationist teacher whose knowledge of the characteristic practices of the culture must be explicit, and must also include developmental perspectives on those practices. In school settings, acculturationist pedagogy has obvious application to after-school clubs or to magnet programs into which students have self-selected based on their identity aspirations; however, it may be of limited utility in general K-12 education—and even in much undergraduate level university education! A few years ago, I had the opportunity to coteach a senior-level undergraduate mathematics course with two mathematics colleagues. The purpose of the course was to help students understand, appreciate, and participate more fully in mathematical culture. My colleagues, both senior members of a highly ranked mathematics department, had considerable experience in successfully mentoring doctoral students. The approach they took in our course involved assigning the students problems, discussing the problems with them, and in the process modeling their own unprescripted solution approaches, following fascinating tangents arising from the original problem, communicating their broad perspectives on mathematics, and sharing their excitement and passion for the field. I presume these are methods they would typically employ, with good effect, with doctoral students—students already self-identified as mathematicians. However, the senior undergraduate mathematics majors in the course—many in a teacher education program—generally were not self-identified as mathematicians, and hence were unable to appreciate or make use of the rich cultural resources that these instructors offered. Identity Politics As discussed earlier, acculturation pedagogy can be practiced through an informal relationship of students with a teacher- as-cultural-representative, or it can be a formal mentorship in which the curriculum of cultural practices to be mastered is explicit. In the latter case, it is possible to configure instruction so that adoption of cultural practices is mandatory. In the case of an explicit and mandatory acculturationist curriculum, there is a risk if one applies the pedagogy to students who are not self-identified with the reference culture that the cultural demands of the instruction may produce “intrapersonal conflict” for the student (Brown, 2004, p. 810; see also, Bishop, 2012; Clark, Badertscher, & Napp, 2013; Gutiérrez, 2002; Kincheloe & Steinberg, 2007; Nasir & Saxe, 2003; Rubin, 2007; Vågan, 2011). As Aikenhead and Jegede (1999) noted with respect to science education, When the culture of science is generally at odds with a student’s life-world, science instruction will tend to disrupt the student’s worldview by trying to force that student to abandon or marginalize his or her life-world concepts and reconstruct in their place new (scientific) ways of conceptualizing. This process is assimilation. Assimilation can alienate students from their indigenous life-world culture, thereby causing various social disruptions (Baker & Taylor, 1995; Maddock, 1981); or alternatively, attempts at assimilation can alienate students from science. (p. 274) Ethical Principle: I don’t want to minimize the complexity of ethical questions that flow from the use of acculturationist pedagogy with students who are not already identified with the reference culture—for example, to suggest science should not be a universally required school subject. These questions have a long and important history (Apple & Au, 2014) that is beyond the scope of this chapter. However, the enculturation/acculturation distinction is newly introduced in the crossdisciplinary framework (Kirshner, 2004; Kirshner & Meng, 2011), giving us an opportunity to propose an important principle related to the two enculturation pedagogies: Ethical concerns regarding intrapersonal cultural conflict that may arise for acculturationist pedagogy do not arise for enculturationist pedagogy. -124- The crux of my argument is that in a pluralistic society, cultures are always in transition under the influence of contact with other cultures. Society is teeming with cultural influences that individuals are exposed to in the course of normal social intercourse. In the process, identity structures develop and morph. Yet, as Kim (1988) noted, there are inbuilt “stress-adaptation-growth dynamics of cross-cultural experiences, which bring about cultural strangers’ gradual transformation toward increased functional fitness in the host milieu” (p. 200), dynamics that are adaptive to new cultural influences, yet also responsive to the subject’s experienced need for cultural continuity. Thus students involved in enculturation pedagogy in which the curriculum of target dispositions is tacit, adapt to the evolving culture of the classroom—or not!—at their own pace, and in their own way. CROSSDISCIPLINARY ANALYSIS OF PEDAGOGICAL PRACTICE The Method of Crossdisciplinary Analysis The metaphors for learning as theorized in the preceding section are taken to reflect our culture’s basic understandings of learning (Fletcher, 1995), and thus to drive our varied pedagogical enterprises across the broad spectrum of education. In this respect, the crossdisciplinary framework is intended not so much to provide a new constellation of pedagogical practices, as to organize and refine the varied streams of ideation that currently are tangled together within our integrative discourse (Kirshner, 2002). To support this claim, I introduce a method of crossdisciplinary analysis of pedagogy. This method involves examining the details of implementation to assess whether skills are promoted, whether concepts are promoted, and whether dispositions are promoted. If it seems the answer to any of these is yes, it is incumbent upon the analyst to identify the particular skills, concepts, or dispositions being addressed, to examine the pedagogy to determine whether a student- centered or teacher-centered approach is being used, and to evaluate the efficacy of the pedagogy according to the pedagogical principles laid out in the preceding section. In case multiple pedagogical methods are invoked in the instructional approach, the analyst determines which learning goal predominates and evaluates whether the coordination of pedagogical methods is organized in a coherent and consistent fashion. In this section, I apply this method to a broad array of key pedagogical practices with the goal of demonstrating that crossdisciplinarity spans the familiar terrain of pedagogical interests—many of which are framed through the integrative and holistic perspectives on learning that currently dominate educational thought. The method of crossdisciplinary analysis serves as a refractive lens, pulling apart the component strands of ideation, often revealing weaknesses and inconsistencies that have been obscured in the prior viewpoint. As well, our current integrative frameworks lead to a kind of homogeneity of thought. The spectrum of reform pedagogies, for instance, involve a balance in which “knowledge is personally constructed and socially mediated” (Windschitl, 2002, p. 137), the variation residing in the degree of emphasis given to each. The crossdisciplinary approach has a different ethos in which, yes, diverse agendas for learning can be coordinated together—but there is no holistic or dialectical imperative to do so. Thus the palette of pedagogical possibility can include wild singletons oriented by a single learning metaphor that we’ve not previously been able to recognize or appreciate; the final subsection of this section, analyzes one such pedagogical method. Caveat emptor: Although the individual analyses presented here may be compelling for readers, the broader intention for this section is to support the proposal that a small set of theoretical tools spans (and expands) the totality of our pedagogical interests in promoting student learning. Initially, the analyses presented here may be experienced as independent critiques of educational practices. But over time, and with the experience of performing one’s own analyses (these examples are merely illustrative) the critiques coalesce as part of a coherent educational -125- viewpoint. The refractive lens of crossdisciplinarity establishes itself, reflexively, as one’s only window to the problems and possibilities of pedagogy. B. F. Skinner’s Programmed Instruction To illustrate the method of crossdisciplinary analysis, I begin with an instructional method of historical importance. Skinner (1958b) introduced individually paced programmed instruction as an application of behavioral principles, one that he regarded as central to his legacy to education (Morris, 2003). In this instructional format, students are presented with a succession of text fragments (one or two sentences) each with a blank in place of a key word. The students’ role is to read the text and supply the missing datum. The frames are sequenced in such a way as to promote incremental progress from simple initial prompts to complex terminal performance. In this way it is anticipated students easily can maintain the 95% success criterion for progress to the next programmed lesson. Feedback is immediate and ongoing so as to reinforce participation (Morris, 2003). Table 4.2 Part of a programmed instruction unit used by Skinner (1958b) to illustrate teaching machines. Sentence to be Completed Word to be Supplied 1. The important parts of a flashlight are the battery and the bulb. When we “turn on” a flashlight, we bulb close a switch which connects . . . the battery with the ______________. 2. When we turn on a flashlight, an electric current flows through the fine wire in the bulb ______________ and causes it to grow hot. 3. When the hot wire glows brightly, we say . . . it gives off or sends out heat and ______________. light 4. The fine wire in the bulb is called a filament. The bulb “lights up” when the filament is heated by electric the passage of a(n) ______________ current. 5. When a weak battery produces little current, the fine wire, or ___________, does not get very hot. filament 6. A filament which is less hot sends out or gives off ______________ light. less 7. “Emit” means “send out.” The amount of light sent out, or “emitted”, by a filament depends on hot how ______________ the filament is. To illustrate programmed instruction, Skinner (1958b, p. 973) presented a science lesson dealing with electric currents and flashlight circuitry (see also Morris, 2003, pp. 242–243). The first few statements from the sequence of 35 statements are given in Table 4.2. We examine this instruction through the three lenses of the crossdisciplinary framework to determine the nature and quality of the learning opportunities provided to students. Habituation: Given the authorship of these programmed instruction materials, we might expect to find that verbal response skills with respect to science vocabulary are promoted in this curriculum in keeping with the “traditional . . . belief that learning physics means memorizing facts, definitions, and formulas” (White, 1993, p. 5). Indeed, Skinner’s (1958b) description of his strategy does touch on repetition of terms: Technical terms are introduced slowly. For example, the familiar term “fine wire” in frame 2 is followed by a definition of the technical term “filament” in frame 4; “filament” is then asked for in the presence of the non-scientific synonym in frame 5 and without the synonym in frame 9. (p. 974) However, whereas word familiarity may be developed through this lesson, and perhaps some weak association to proximal terms, there is no rehearsal required or memorization being -126- tested (in contrast to other examples given in Skinner, 1958b, such as word spellings, p. 972). Indeed, the learning outcomes Skinner (1958b) touts relate to goals of understanding more so than response conditioning: The net effect of such material is more than the acquisition of facts and terms. Beginning with a largely unverbalized acquaintance with flashlights, candles, and so on, the student is induced to talk about familiar events, together with a few new facts, with a fairly technical vocabulary. . . . The emission of light from an incandescent source takes shape as a topic or field of inquiry. An understanding of the subject emerges which is often quite surprising in view of the fragmentation required in item building. (p. 974) Construction: Examining the pedagogical method with respect to the construction metaphor, we observe that the programmed text forms a kind of lecture on electric current that the student is expected to read and understand, the participatory activity of supplying the missing word serving to ensure the student is attending to and processing each sentence. The primary pedagogical method, therefore, is teacher-centered construction aimed at gaining an understanding of the physics of the light production in a flashlight. We might ask if a teacher-centered approach is appropriate given the conceptual complexity of electrical current flow. Indeed, Wandersee, Mintzes, and Novak (1994) noted that current flow is regularly misunderstood by students who construct a variety of incorrect conceptual models that science education needs to address: Five distinct models of a simple circuit were employed by these students. The “single-wire” notion suggests that current leaves the battery and travels through one wire to a bulb, which serves as a kind of electricity “sink.” In the “clashing currents” model, electricity leaves the battery from both terminals and travels toward the bulb, where it is “used up.” In addition to these ideas, three kinds of “unidirectional models” were identified. . . . “Unidirectional with conservation” . . . is the scientifically acceptable view. (p. 182) Thus Skinner’s (1958b) science lesson aims toward a rather cursory understanding of electrical circuits. In this respect, his instructional method, teacher-centered construction, is well matched to the content. For, as noted earlier, lecturing on complex conceptual content would be successful only for students who are metacognitively sophisticated; otherwise, student-centered construction methods would be required. Enculturation: In addition to teaching the conceptual content, programmed instruction was believed to “teach students to study, for instance, to attend selectively to texts and to reject irrelevant material” (Morris, 2003, p. 244). In the crossdisciplinary framing, these learning goals would count as dispositions—culturally specific forms of engagement. A full crossdisciplinary analysis would involve identifying the reference culture (perhaps academic culture) in which the intended dispositions are normative, and examining the culture of participation of students in working through this instruction. Students in my graduate course on theories of learning, going through the full sequence of 35 text fragments, report a tendency to word hunt to fill in the blanks, with minimal linguistic and semantic processing. So it is not obvious the extent to which enculturational goals intended by the curriculum are met. Skinner (1958b) intended his exposition on teaching machines as an illustration of the application of behavioral principles. This is consistent with his effort to interpret language production in behaviorist terms (Skinner, 1958a), which Chomsky (1959) argued did not properly meet behaviorism’s own criteria for objective analysis. From our current vantage point, and with the assistance of crossdisciplinary analysis, it seems obvious that the programmed materials presented an explanation of the physics of electrical flow in a flashlight that students -127- were expected to understand. There is no apparent habituated learning agenda being enacted. Thus, to a considerable extent, Skinner was creating conceptually oriented instructional materials without clear principles of learning to guide his efforts. In the case of these programmed materials, we were lucky: his instructional materials did provide a coherent approach for students to learn concepts, albeit at a rather unambitious level. However, flying without adequate maps is a risky business. As we point the lens of crossdisciplinarity at contemporary education we often find normative curricular methods to be deeply incoherent in their agendas for learning. The “Reading Wars” We turn to the Reading Wars, which serves also as an introduction to the next section on the Math Wars. In our current discourse these two controversies are regarded as siblings, rehearsing basic disputes about learning and teaching that trace back over a century of conflict: “The ‘education sects’ that Dewey described so long ago still exist [today]—in reading, in the proponents of ‘whole language’ and in ‘phonics,’ and in math, in the advocates and opponents of ‘NCTM math reform’” (Loveless, 2001, p. 2). Through crossdisciplinary lenses, we come to see stark differences in the structure of learning intentions underlying these controversies, and in the quality of the pedagogical practices that ensue. The Reading Wars pit advocates of “phonics” (Burns, Griffin, & Snow, 1999; Fox, 2000; Stanovich, 1986) against “whole-language” advocates (e.g., Dechant, 1993; Goodman, 1986; Serpell, 2001). The phonics method provides repetitive practice in a systematic and sequential fashion starting with basic linguistic elements (graphemes, phonemes), building up to words, sentences, and more extended texts that incorporate the constituent elements already practiced: Phonics advocates see reading primarily as a challenging cognitive, psycholinguistic accomplishment—knowing letters and sounds and being able to perform in a certain way when asked to map one onto the other. (Snow, 2001, p. 232) Whole-language methods focus on dispositions of literate society, including inclination to read and strategies of effective reading. Whole-language advocates insist that students’ involvement with text always be meaningful in the twin senses that texts are comprehensible13 and that activities of reading are motivated by personal interest and involvement. The pedagogical method is to create a social community in which children engage with reading and writing in pursuit of their interests and communicative needs: Whole-language advocates see reading as a social, cultural activity—participating in communities of practice within which reading and writing are normal activities and thus are acquired as needed by all members. (Snow, 2001, p. 232) From a crossdisciplinary reading, both of these pedagogical methods are soundly constituted. Phonics approaches the skills of reading in a systematic and effective fashion through sequenced repetitive practice. Whole language provides a coherent blending of acculturationist support for students’ evolving self-identity as readers with the enculturationist strategy of providing a social microculture within which practices of literacy are normative. Indeed, it is telling that antagonists in the Reading Wars rarely criticize their opponents with respect to the learning outcomes actually supported by instruction. Rather phonics advocates worry that whole language leaves students without needed skills (e.g., Dahl, Scharer, Lawson, & Grogan, 1999), while whole language advocates find that phonics methods neglect valued dispositions (e.g., Krashen, 2003). -128- At a pragmatic level, this might suggest the reasonableness of coordinating these two pedagogies, a suggestion sometimes labeled “a balanced approach” (Honig, 1996). However, our educational discourse, which countenances only one “true” account of learning (and hence of good teaching), makes pragmatic accommodations difficult to realize. The incendiary bitterness of the Reading Wars is well known, having spilled over from the academy into the legislative arena (Boyd & Mitchell, 2001; Goodman, 1998), thereby materially constraining the autonomy of educators to exercise professional judgment. The “Math Wars” The Math Wars pits traditionalists combining demonstration/lecture and worksheet drills against reformers who prefer inquiry teaching approaches (Draper, 2002; Klein, 2007; Schoen, Fey, Hirsch, & Coxford, 1999; Wilson, 2003). Traditional textbooks organize mathematics instruction topically, with explanation of the current topic being followed by homogeneously grouped problems related to the content. In this way, concepts and skills are intended to reinforce one another. Reformers generally provide collaborative work on open-ended tasks designed to foster valued mathematical dispositions such as autonomy, creativity, and problem-solving heuristics. As well, the tasks are centered around critical conceptual content, affording development of deep understanding of the content. Thus, in contrast with the Reading Wars, the Math Wars features competing blended pedagogies—skills and concepts versus concepts and dispositions. Traditional Instruction Characterizing the instructional position of the traditionalists in the Math Wars is hampered by the fact that “the term ‘traditional’ was never clearly defined in the debates”(Klein, 2007). Indeed, the Math Wars arose as a reaction to the NCTM's (1989) Standards, so much of the traditionalist cause has simply been to retain the traditional methods of U.S. mathematics instruction, which have been characterized as follows: “Teachers present definitions of terms and demonstrate procedures for solving specific problems. Students are then asked to memorize the definitions and practice the procedures” (Stigler & Hiebert, 1999, p. 27). What is not clear is the extent to which demonstration (Clark, Nguyen, & Sweller, 2006) and memorization are intended by traditionalists to be supplemented by explanation of underlying principles (lecture). However, since the ranks of the traditionalists included many prominent university mathematicians (Klein, Askey, Milgram, Wu, et al., 1999), perhaps explanation and demonstration are intended to go hand-in-hand. Construction: As explained earlier, from a crossdisciplinary view demonstration of procedures serves habituationist, rather than conceptual goals. Demonstration focuses the perceptual apparatus on relevant aspects of the stimulus display, thereby facilitating subcognitive correlations that are the basis of skilled performance (Reber, 1993). Thus the conceptual agenda is supported only insofar as the instructor interweaves conceptual explanation of why the procedure works along with demonstration of how it works. In cases in which explanation of principles supplements demonstration of procedures, the instructional method is teacher-centered conceptual pedagogy, effective only for those students who are sufficiently sophisticated, metacognitively, to notice incongruities between their own understanding and the explanations offered by the teacher (Otero, 1998). Thus the conceptual intentions of traditional instruction are inconsistently supported, and even then only for a small minority of students. Habituation: The habituationist agenda also is compromised in this pedagogical approach. In order to focus on conceptual content, textbooks are organized topically, with homogeneously grouped problem sets meant to reinforce concepts presented in the current chapter. The homogenous grouping of exercises means that, with the exception of review practice tests, there is no opportunity for students to learn to discriminate problem types. Students learn how -129- to apply routine solution methods, but not when to apply them, making robust skill mastery problematic (Greeno, 1978; VanderStoep & Seifert, 1993). To understand this limitation of traditional mathematics textbooks it is instructive to consider the method of “gentle repetition” developed in the early 1980s by John Saxon. Saxon’s textbooks dispense with the trappings of conceptual explanation, providing only a brief introduction of new content, moving quickly to engaging students in heterogeneous problem sets. In this way, brags Saxon, “as the problems become familiar students can look at a new problem and recognize it by type. This recognition evokes conditioned responses that lead to solutions” (Saxon Publishers, 1992, inside front cover). From a crossdisciplinary perspective, the Saxon approach is effectively structured for habituation learning, and its superiority to traditional approaches to skill development has been empirically documented (e.g., Resendez & Azin, 2007). (As an interesting historical footnote, so distraught was the mathematics education establishment at Saxon’s dropping of the trappings of a conceptual agenda that it was a request for advice concerning Saxon texts that prompted the NCTM’s initial steps toward its 1989 standards, McLeod, Stake, Schappelle, & Mellissinos, 1995.) To summarize, traditionalists in the Math Wars support an instructional format that simply juxtaposes problem sets (toward skill development) and lecture (toward concept development), based on the pervasive belief that “conceptual understanding . . . and operational procedures . . . are mutually reinforcing” (NMAP, 2008, p. xix). As discussed earlier, this is an illusory belief encouraged by the facilitative effect that explicit presentation of rules plays in the rate of skill acquisition (Kirshner & Awtry, 2004; Reber, 1993). It has kept us from seeing how deficient is the support of both skill development and concept attainment, and, indeed, how these elements of traditional instruction subvert one another. Reform Instruction Mathematics education reform participates in a broader pedagogical reform movement generally oriented by the learning metaphors of construction and enculturation as framed in a spectrum of constructivist, social constructivist, situated cognition, and sociocultural theorizations (Donovan & Bransford, 2005). Infrequently, a purely (psychological) constructivist agenda is advanced (Simon, Saldanha, McClintock, et al., 2010; Thompson, 2013), or else one finds goals and methods that are entirely enculturational (Mark, Cuoco, Goldenberg, & Sword, 2010). But these distinctions are not easily marked owing to our current integrative discourse that regards learning as a complex, multifaceted whole, with reform pedagogy “a useful synthesis . . . [wherein] knowledge is personally constructed and socially mediated” (Windschitl, 2002, p. 137). Typically the reform classroom is structured around inquiry groups, communities of learners, knowledge-building communities or other such collaborative fora intended to promote deep understanding of mathematical content in tandem with valued cultural practices, including mathematics-specific practices like mathematical argumentation (proof), problem solving heuristics, and aesthetic values, as well as more general practices of intellectual autonomy, critical thinking, and creativity (e.g., Brown & Campione, 1994; Hutchison, 2012; Mark, Cuoco, Goldenberg, & Sword, 2010; NRC, 2000, 2005; Scardamalia & Bereiter, 2003). Instruction typically involves open-ended questions, nonroutine problems, or projects that students work on and discuss. The tasks are chosen for their rich conceptual affordances, so that collaborative discussion and exploration can lead to in-depth understanding of concepts as well as evolution of valued dispositions (Brooks & Brooks, 1999). From a crossdisciplinary perspective coordination of teaching genres is viable as an instructional strategy, so long as the teacher understands that the constituent teaching approaches are inherently inconsistent with one another and hence inevitably lead to choice points in which one agenda advances only at the expense of the other. As discussed earlier, student-centered construction is very much a teacher-modulated pedagogy. The teacher creates a task environment -130- for the student based on a Hypothetical Learning Trajectory along which student engagement is anticipated to progress. To support the unfolding of this trajectory, the teacher may need to mediate students’ initial uptake of tasks and otherwise intensify students’ engagement with the task. In contrast, enculturational goals of student autonomy and creativity require the teacher to foster a classroom culture in which students are empowered to pursue evolving interests as they arise in the course of problem solving. Thus the effective reform teacher is in a state of consternation, supporting the cultural dynamics of group interaction while constantly monitoring the conversations, worrying that discussions may not be productive conceptually, and making judicious moment-by-moment decisions about whether (and how) to intervene as a mediator of conceptual construction while doing minimal damage to the agenda of student autonomy and exploration. As Lampert (1985) put it, “the juxtaposition of responsibilities that make up the teacher’s job leads to conceptual paradoxes” for which there is no single right choice. The teacher “brings many contradictory aims to each instance of her work, and the resolution of their dissonance cannot be neat or simple” (Lampert, 1985, p. 181, quoted in Ball, 1993, p. 377). Metacognition To understand how seriously this hybrid agenda of balancing and juggling is compromised within a rhetoric of reform teaching rooted in integrative or holistic visions of learning/teaching, it is instructive to examine the central and crucial role that metacognition has come to play in contemporary pedagogical theorizing. Indeed, in Bransford, Brown, and Cocking’s (2000) canonical text, How People Learn, metacognition is emphasized as one of three fundamental aspect of instruction: Integration of metacognitive instruction with discipline-based learning can enhance student achievement and develop in students the ability to learn independently. It should be consciously incorporated into curricula across disciplines and age levels. (p. 21) Current theoretical interests in metacognition trace back to foundational work of both Vygotsky and Piaget (Fox & Riconscente, 2008). As we have discussed, for Vygotsky, metacognitive capabilities (and other higher mental functions) arise from internalization of social/cultural practices. Olson (2003) applies this perspective to explain how metacognitive capabilities can develop in collaborative groups in that justification of one’s ideas to others comes to be internalized as a kind of self-scrutiny: “The normative practice of reason giving and metacognition run together. Explanation, the giving of explicit or public reasons, is . . . the route to metacognition, that is, cognition about cognition” (p. 241). For Piaget (1975), metacognition figured centrally in his genetic epistemology, deeply implicated in the notion of reflective abstraction, the primary mechanism for conceptual restructuring: Reflective abstraction always involves two inseparable features: a “reflechissement” in the sense of the projection of something borrowed from a preceding level onto a higher one, and a “reflexion” in the sense of a (more or less conscious) cognitive reconstruction or reorganization of what has been transferred. (p.41, quoted in von Glasersfeld, 1991) Pulling these two strands together, we can begin to see the contradictory implications of Bransford, Brown, and Cocking’s (2000) utilization of metacognition in their framing of pedagogical practice, as quoted above. On the one hand, “develop[ing] in students the ability to learn independently” (p. 21) is an enculturationist goal of instruction that involves developing students’ metacognitive capabilities. As we have discussed, such enculturational agendas unfold -131- over months and years. On the other hand, the idea that “metacognitive instruction with discipline-based learning can enhance student achievement” (p. 21) points to the facilitative role that metacognition plays in concept development. Thus metacognition is revealed as the soft underbelly of reform pedagogy. Like a cat trying to catch its tail, always just out of reach, metacognition is both a goal of instruction and a requirement for its effective realization. Pointing out the contradictory invocation of metacognition in reform pedagogy is not meant to discredit the agenda of teaching concepts and dispositions in tandem with one another, but rather to highlight the problematic character of such instruction, and the concomitant necessity that teachers be primed to recognize the contradictory imperatives of these teaching genres. But, this need to juggle, to retreat and advance simultaneously, is precisely what is elided in a discourse grounded in holistic thinking based on assumed “synergies”(Bransford, Stevens, Schwartz, et al., 2006), or on integrative sociocultural and situated cognition theorizations in which “the learning of a subject’s cognitive content is considered a process embedded within the more comprehensive process of enculturation” (Perrenet & Taconis, 2009, p. 182). There will always be some individual teachers like Lampert and Ball who come to sense and engage with the problematic of multiple learning agendas (see Green, 2014, for an analysis of their influence). But for most teachers, reform is simply enactment of a format of classroom activity, the hope of educational value sustained by “an inordinate amount of faith in the ability of students to structure their own learning” (Windschitl, 2002, p. 138). In summary, the Math Wars pits traditionalists valuing skills and concepts against reformers intent on fostering concepts and dispositions. In both cases, the good intentions of educators are stymied at the point of intersection of these learning agendas for the simple reason that the assumed concordance of skills and concepts or of concepts and dispositions has not been subjected to critical theoretical scrutiny. In the case of the Reading Wars our students have been lucky; the unnecessary antagonisms are between independently coherent pedagogical visions. In the case of mathematics, in the United States a student’s chances of receiving coherently conceived instruction—traditional or reform—are vanishingly small. Pedagogies of Societal Transformation This subsection and the next are devoted to the enculturation metaphor as theorized in terms of the enculturation/acculturation distinction. This distinction, separating out unconscious adaptation from conscious emulation, is newly introduced in the crossdisciplinary framework (Kirshner, 2004; Kirshner & Meng, 2011). For instance, Yackel and Cobb (1996) presented a clear theorization of enculturation pedagogy in which the teacher’s selective receptivity to student responses fosters the diffusion of desired cultural practices. But they also underscore “the critical and central role of the teacher as a representative of the mathematical community” (p. 475), a hallmark of acculturationist pedagogy, in which the teacher as cultural representative models desired practices for students to emulate. As discussed earlier under “Identity Politics,” this distinction is an important one for educators to focus on, as acculturationist instruction can result in “intrapersonal conflict” (Brown, 2004, p. 810). In the current subsection, the enculturation/acculturation distinction is applied to pedagogies oriented toward improvement of the moral and ethical fabric of the broader society. Collectively, I refer to these as pedagogies of societal transformation, including democratic education, liberatory pedagogy, values education, critical literacy, progressive education, character education, and multicultural pedagogy, among others. In our current educational discourse, these pedagogies tend to be marginalized as peripheral to the true academic mission. For instance, in her introduction to a paper on such pedagogies, Cochrane-Smith (2004) “takes up the issue of the ‘outcomes question’ . . . arguing the case for a strong focus on social justice as the necessary complement to an ongoing concern with academic excellence and rigor” (p. 193). In explaining the marginalization of equity discourses, “Secada [1995] noted that mathematics education has traditionally appropriated theoretical constructs from psychology. His -132- basic claim was that research that is not cast in what he termed the ‘dominant psychological discourse’ is viewed as marginal to the concerns of the field” (Nasir & Cobb, 2002, p. 94). But surely no pedagogical method can aspire to improve the world directly; each must depend on students learning (in some sense). Thus pedagogies of societal transformation ought to be accounted for within the same learning framework as any other pedagogies that promote student learning. Peering through crossdisciplinary lenses, two basic strategies are evident across the broad range of societal transformation pedagogies: utopian pedagogies and critical pedagogies. Utopian pedagogies (my term)—including democratic education, progressive education, some versions of multicultural pedagogy, and perhaps values education—adopt enculturation teaching methods, creating within the classroom microculture a microcosm of a more ideal society. Students enculturated into the norms of this classroom society then carry their dispositions outward to political and social engagement in the broader society. John Dewey’s educational vision included such a utopian strategy: When the school introduces and trains each child of society into membership with such a little community, saturating him with the spirit of service, and providing him with the instruments of effective self-direction, we shall have the deepest and best guarantee of a larger society which is worthy, lovely, and harmonious. (Dewey, 1900, p. 44, quoted in Hall, 2003, p. 16) In contrast to utopian pedagogies that seek to transform society from within, critical pedagogies such as liberatory pedagogy and critical literacy seek to disrupt societal arrangements by having students come to “formulate and agree upon a common understanding about ‘structures of oppression’ and ‘relations of domination’” (Burbules & Berk, 1999, p. 53). The pedagogical method here is acculturationist, the goal being to enlist students as “‘transformative intellectuals’ (Giroux, 1988), ‘cultural workers’ (Freire, 1998) capable of identifying and redressing the injustices, inequalities, and myths of an often oppressive world” (Gruenewald, 2003, p. 4). Thus students are being guided toward an identity structure as social change agents, with the teacher serving as an authentic representative of a culture of resistance. From a crossdisciplinary perspective, the marginalization of equity concerns needs to be understood as part of a broader diminution of the enculturation metaphor within traditional psychological frameworks. We already have noted the absence of any psychological paradigm focused squarely on this metaphor, necessitating a turn to sociological theory as grounding for enculturational learning. Similarly, one finds enculturational interests diminished in integrative pedagogical framings in which enculturational goals always are couple with other learning goals. For instance, Greeno, Collins, and Resnick’s (1996) situative view is an umbrella for “understand[ing] school learning environments in two ways: their effects on the subject matter knowledge and ability that students acquire, and their effects on the kinds of learners that students become” (p. 31). The crossdisciplinary approach redresses this neglect by ensuring that each learning metaphor informs a dedicated genre of teaching independent of other genres and other theorizations. The effect of this crossdisciplinary approach is to draw pedagogies of societal transformation into the same pool as other pedagogies that seek to foster students’ dispositions. This includes high-status cognitive dispositions like critical thinking, metacognitive sophistication, and logical reasoning that often have been naturalized as part of the cognitive architecture (Perkins & Ritchhart, 2004) rather than recognized as products of cultural enmeshment (Burbules & Berk, 1999; Scribner & Cole, 1977). Furthermore, the method of crossdisciplinary analysis insists that the reference culture for targeted dispositions be identified. Thus, critical pedagogues have an opportunity to point out that even such seemingly innocuous goals as critical thinking reflect class, gender, and race-based priorities (Burbules & Berk, 1999). Of course, the obligation to be explicit about cultural interests applies equally to critical and utopian -133- pedagogies, which may draw unwelcome scrutiny; but overall, the eliding of cultural interests is widely recognized to have contributed to establishing and maintaining societal positions of dominance (Delpit, 2006; Giroux, 1997; Gutstein, 2006; Lerman, 2009; Ostrove & Cole, 2003). Thus, making cultural agendas explicit in the crossdisciplinary approach tends to level the playing field for pedagogies of societal transformation, which hitherto have been more exposed as targets of cultural critique (e.g., see Wasley, 2006, for a discussion of NCATE’s dropping of its social justice requirements). The Remarkable Pedagogy of Christopher Healy I conclude this section with a crossdisciplinary analysis of Christopher Healy’s “Build-A-Book Geometry” course, an unusual offering in which students wrote the textbook collectively, deciding democratically what topics would count as geometric content, and what results are soundly reasoned. Healy began the first of several iterations of his year-long course in 1987 at the working-class California high school where he taught. His instructional format had students working together in small groups to produce ideas related to geometry. Each night, he pored over the reports that the groups produced, selecting some student contributions to be taken up by the class the next day. This did give him some influence on the content addressed by students, but in the periodic meetings in which group members presented ideas to the whole class, he ceded any direct role in adjudicating conclusions reached or the reasoning processes employed: After each presentation . . . there is a vote on whether the material presented is true and worthy of entry into the book. This process produces some of the most difficult moments for me, because students have presented and voted down things that I feel are significant parts of geometry. Still, I believe it imperative that I not interfere. (Healy, 1993a, p. 87) Healy (1993a, 1993b) used a unique method of constructed journal entries to report on the effects of his course. As intuited by Healy, these journal entries express the thoughts and feelings of his students as they engaged in the course and reflected on various aspects of their lives outside of school. Although individual elements of these constructed journal entries might be questioned on methodological grounds, his overall characterization of the course experience is consistent with actual student statements, as contained in an appendix. Whatever the methodological faults and virtues, these constructed journal entries provide us with a very clear window into what Healy attended to and valued in his interaction with his students—just what we need to perform a crossdisciplinary analysis. Healy’s (1993a, 1993b) reports focus on how his students grappled with the broad autonomy offered to the class, and also how they dealt with personal relations and life plans outside of school. For many students, the course was personally transformative, as illustrated with Chris. As we meet Chris, she is a dependent personality, in need of outside approval through her relationship with her boyfriend, David, and lacking confidence in her mathematical ability: “I do better when I have someone who will tutor me. . . . someone who knows the right answer” (Healy, 1993b, p. 10); and with no plans for further education: “I’ve got this counselor who thinks I’m going to college (the poor guy just doesn’t understand). I don’t want to disappoint him, but two more years of this education stuff and I’m done forever” (p. 10). As Healy commented, “At first in my No Book geometry class Chris was a noninvolved student. She just sat there and looked like she was going to let this experience pass her by—until she finally felt strongly enough about something that she got involved” (p. 85). The key episode for Chris occurred when she became inspired by the proposal that distance need not be defined relative to two points; it could be defined relative to two or more points. She was ready to argue for this, and went up to the board to illustrate her ideas, convincing -134- the class that they needed to reconsider this issue. As Healy noted, “It was not a big deal to the class, but to Chris it was a turning point that affected the way she approached the entire experience. It gave her involvement, confidence, a positive interaction, and a feeling of belonging” (p. 85). As the course progresses, we see evidence that Chris is reflecting on contrasts between relations of authority in class and at home: “There’s no rules in the class, no right or wrong, no ultimates. . . . It’s kind of the opposite of my house. In class what we say is important and we talk everything over before we decide on anything. I think people should talk things over—one person shouldn’t be dictator” (Healy, 1993b, p. 47). Later, schooling takes a higher priority for her: “It’s funny, for some reason going to school and graduating are so important to me now” (Healy, 1993b, p. 80), and eventually: “I’m going to college” (Healy, 1993a, p. 100). As she reflects later, her changes stem from a sense of her own agency and revaluation of her station in life: “The real miracle for me this year was learning that the positive response that really counts doesn’t come from outside, it comes from within, If I’m ever going to be someone (and I am), it won’t be to please anyone else. I’ll do it for me” (Healy, 1993b, p. 163). Analysis This pedagogy presents a considerable challenge for crossdisciplinary analysis (and the intrepid reader can pause to self-test their understanding of the framework, by anticipating the crossdisciplinary analysis that follows). Although students in the Build-A-Book course tended to do as well on achievement tests as their peers, clearly the pedagogy itself offered no direct support for skills or for student construction of particular conceptual content. (At best, these might be considered what I call advertent learning outcomes that the teacher hopes and expects will occur, but does not directly support.) What is more, the typically emphasized mathematical practices—logical argumentation, problem solving heuristics, aesthetic sensibilities—also are not supported; Healy does not mediate the intellectual environment by expressing interest in or approval of particular mathematical practices. Rather, it seems that something is going on in his classes relative to students’ identities. But what is it, and how does Healy’s pedagogy produce it? Having examined what Healy is not doing, it’s time to turn to what he is doing: constituting his classroom as a mathematical community. In this community, students are provided the opportunity to experience themselves as authors of mathematical knowledge and collectively as the adjudicators of mathematical truth. Somehow, from this invitation, personal identities and life aspirations are transformed. In the crossdisciplinary framework, student self-identification with the reference culture is the prerequisite for an acculturationist pedagogy in which the teacher, as a representative of the culture, models cultural practices. Clearly this is not the pedagogy being enacted in Healy’s classroom. First, the students entering the class are not self-identified as mathematicians. Second, Healy does not present himself as a mathematician—he’s just perceived as a goofy teacher—nor does he model mathematical dispositions. Rather, we have to look toward enculturational teaching methods, in which dispositions are grown within the context of the classroom microculture. In this case, the disposition being actively supported in the classroom is mathematical self-identity itself. Indeed, self-identification as a mathematician is a consistent disposition of mathematicians (Burton, 2004), and therefore can, itself, be a goal of enculturation pedagogy. But now we are faced with a further conundrum: According to Healy’s (1993b) account, there was only one student in his years of teaching Build-A-Book Geometry who came to perceive himself as a mathematician and to consider a career in that field. Are we, then, to consider Healy’s pedagogy as a failure? Recall that the enculturationist teacher must be equipped not only with an understanding of the target disposition, but also of the intermediate practices students may have to traverse en route to achieving that target. For the working-class students that comprised Healy’s classes, these steps would pertain to social class. Mathematicians are part of a high-status professional -135- class. They do not punch time clocks, but work on problems of their own choosing over extended time scales. Collectively, they provide the analytical relations that form the language of science. In these respects, the identity of the mathematician is remote from lower-class expectations of a work life spent in the service of plans, schemes, and enterprises of others (Kenny & Bledsoe, 2005; Burton, 2004). From this perspective, we can interpret the transitions in self-image and ambition of students like Chris as indicative of a changing sense of class identity. The disposition that Healy cultivated in his students was self-belief in their intellectual efficacy; his methodology, the intense and consistent respect for the ideas they produced as he pored over their work products each evening, until that spirit of importance invaded every nook and cranny of his classroom. As a result, students began to experience themselves not as mathematicians, per se, but as efficacious thinkers and responsible members of a knowledge community, aspects of self-identity that typically demarcate professional-class social identities (Costello, 2005). That’s why Healy did not intervene when students got the geometry wrong—not because he didn’t care, but because his teaching agenda placed students’ own role as adjudicators of mathematical truth ahead of his desire for their understanding of specific content. His pedagogy did not get students all the way to mathematical self-identification, but influencing students’ class identity is in itself a major accomplishment.14 To appreciate the magnitude of Healy’s accomplishment, it is useful to compare his methods and results with standard efforts to socialize students to more productive identities as scholars, for instance, by having teachers “serve as models and motivators for students . . . employ[ing] the use of [the teacher’s] personal story and history in an effort to provide their students with windows into their experience as mathematics learners” (Clark, Badertscher, & Napp, 2013, pp. 1, 26). As noted earlier, such acculturationist methods have the potential for creating intrapersonal conflict when used with students who are not yet identified with the reference culture. Indeed, educators who employ “upward mobility discourses construct classist hierarchies in schools and classroom practice . . . [that] may unwittingly alienate the very students they hope to inspire” (Jones & Vagle, 2013, p. 129). Healy’s Build-A-Book pedagogy is remarkable for its unique enculturationist pedagogy to foster social-class identity, and for the profound effects he achieved with his students. In sharing Healy’s (1993a) account of his pedagogy with graduate students in my Education and Cognition course, the students (most of them experienced teachers) tend to be uncomfortable with Healy’s total neglect of skills and concepts in his Build-A-Book geometry course. In the modern history of education, educators sometimes have been guided by behaviorist learning theory (focused on habituationist learning) or by psychological constructivist theory (focused on concept development); as noted in the previous subsection, enculturation learning goals always have been considered auxiliary to the academic mission of schooling. In the crossdisciplinary approach, each of the three learning metaphors is independently theorized, and each forms the basis for dedicated genres of teaching. This enables us to broaden the palette of pedagogical possibility and to appreciate the remarkable accomplishments of teachers like Healy, who step out of the well-worn ruts of received pedagogical wisdom. PROBLEMS AND PROSPECTS The past two decades have witnessed a remarkable rise of the concept of “learning” with a subsequent decline of the concept of “education.” . . . Despite the omnipresence of the concept of learning in current educational discourse, it is important to see that the new language of learning is not the outcome of one particular process or the expression of a single underlying agenda. It rather is the result of a combination of different, partly even contradictory trends and developments. (Biesta, 2009, pp. 37, 38) -136- That the intensification of interest in learning over the past 20 years has not lead to significant improvement in the lives of students and teachers—perhaps even a decline—is troubling. As Biesta’s statement suggests, and I have argued, the cause of this malaise owes to a mismatch between psychology’s multiple theorizations of learning and education’s assumption that good teaching must be characterized as some mutually coherent set of practices. We may disagree about the contents of this set; we may despair at the complexity of ever being able to adequately characterize it; but never once, in a hundred years, has it crossed our minds that multiple, independent theories of learning demand multiple, independent theorizations of teaching. Why this blind spot? I have argued that we have not chosen to see learning as separate, independently coherent processes, because psychology has not wanted us to. Psychology’s historical imperative is to become united around one paradigm, for only thus does an adolescent science reach full paradigmatic maturity (Kuhn, 1970). Education is useful to that quest only insofar as we join the partisan battle by siding with one or another of the protagonists. Reify learning in its separate paradigms, and we subvert the pretensions of sufficiency that paradigms must project out to win converts across paradigmatic boundaries. At what cost, this acquiescence to psychology’s grand design? Instead of letting learning theory, in its diverse paradigms, light the way to our varied aspirations, clinging to the hope or the illusion of unity has brought conflict, confusion, and banality to education. Our now ascendant design science mode of pedagogical research (Cobb, 2007; Lesh & Sriraman, 2005; Wittmann, 1995) mires us in theoretical particularism, it being sufficiently challenging just to assemble the theoretical tools to help guide one classroom or one lesson idea. As English (2008) noted, citing Niss (2004), “researchers are not addressing issues that focus on shaping practice, rather their issues focus on practice as an object of research” (p. 10). The prospect of any systematic prescriptive possibility for theory is fading. Nor does the world of practice look upon the science of learning as a privileged resource for teaching as educators seek foundations for pedagogy oriented by philosophical premises, or political analyses, or neurophysiological data, or moral ideals, or spiritual aspiration, or psychoanalytic method—so that eventually, the marketplace of educational ideas comes more to resemble a bazaar than the organized knowledge base of an established profession.15 Lending to the carnival atmosphere, astute educational entrepreneurs borrow the patina of scientific respectability—teach the brain!—to bolster the litany of standard-issue pedagogical truisms they are dispensing, reminiscent of the snake-oil salesmen of yore, before medical practice had fully established its scientific basis (see Kirshner, 2012, for a list of websites). Nor are policy makers—in the United States at least—turning to us for guidance as professional judgment about teaching is replaced by value-added outcome measures of student learning, reduced to a single number, as the determinant of whether a teacher has met her or his professional obligations (Briggs & Domingue, 2011; Scherer, 2011). (This is a narrative we could counter, if only we would organize around the diversity of learning, rather than skirmish among ourselves about its unity.) So irrelevant has our expertise become that the U.S. federal No Child Left Behind Act of 2001 redefined “Highly Qualified Teacher” for middle or secondary grades, removing any reference to pedagogical expertise or training: “the teacher holds at least a bachelor’s degree and has demonstrated a high level of competency in each of the academic subjects in which the teacher teaches” (NICHCY,2009). In proposing a genres approach, I have argued that multiple theorizations of learning should replace the vain hope that a single theorization can prevail as a source of guidance for pedagogy. In support of that proposal, I have identified diverse metaphors for learning that motivate both psychology and education, formulated theorizations for each, and demonstrated the clarity—across a broad span of educational issues—that can come from looking at educational practice through these multiple lenses, rather than trying to force a unified viewpoint. Yet, what likely will prove most challenging for educational theorists about the genres proposal is not its multiple instantiations of learning, but its insular character. We are braced by the open-ended nature of our discourse, which invites the challenges and the rewards of theoretical -137- erudition. As partners in psychology’s quest for the definitive learning theory, we are engaging with the enduring problems of science. 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NOTES (Note: Endnotes 1 - 7 occur on page 138 and Endnotes 8 - 15 occur on page 139 in published document, preceding References) 1 I am grateful to Steve Wojcikiewicz, whose collaboration in framing the arguments of this chapter has been indispensable. 2 This sense of the complexity of the educational project actually is inherited from psychology itself, where the difficulties in achieving a unified science are attributed to an unruly subject matter: “It is the dilemma of psychology to deal as a natural science with an object that creates history” (Boesch, 1971, p. 9); “Psychology wants to be a natural science about non-natural phenomena” (Vygotsky, 1927, p. 190)–thanks to Mike Cole for these sources. 3 Indeed, Kuhn (1962) acknowledged that “spending the year in a community composed predominantly of social scientists confronted me with unanticipated problems about the differences between such communities and those of the natural scientists among whom I had been trained. . . . Attempting to discover the source of that difference led me to recognize the role in scientific research of what I have since called ‘paradigms’” (pp. ix-x, note a). -146- 4 Kuhn (1970) also referenced bi-stable ambiguous figures, but instead focused on a sense of dissolution of the images that can ensue from efforts to switch perspectives: “Aware that nothing in his environment has changed, he directs his attention increasingly not to the figure . . . but to the lines on the paper he is looking at” (p. 114). In this way, Kuhn used the idea of ambiguous figures to reach the conclusion of mutual incomprehensibility across paradigms. 5 Although the competitive function is central to preparadigmatic science, it is rarely an active concern of most psychologists. That’s because paradigmatic change, as a sociological process, is enacted over relatively long time periods, and because the competitive ethos conflicts with the norms of paradigmatic science wherein scientists are engaged in a shared quest for truth (excepting local competition over claims to discovery) (Merton, 1942; Sarkar, 2007). Although preparadigmatic science is underpinned by competitive goals, it shares in the espoused ideals of cooperation, a factor that may mitigate against psychologists recognizing the competitive imperative that animates their science. In what follows, I present compelling evidence of preparadigmatic competition, but mindful that many psychological theorists do not perceive their science in this light. 6 I have not found this analysis of distinct intra- and inter-paradigm dynamics of research in the sociology of psychology literature; however, the historical evidence of exaggerated, even reckless, claims reviewed in this chapter seems difficult to explain otherwise. 7 Cobb (2007) bases his objection to the idea of generalized psychological principles in part on his reading of Kuhn’s (1962) “analysis of both the processes by which scientists develop theory within an established research tradition and those by which they choose between competing research traditions” (p. 5). For intra-paradigm reasoning, Cobb (2007) takes note of Kuhn’s observation that “development and use of theory necessarily involves tacit suppositions and assumptions that scientists learn in the course of their induction into their chosen specialties” (p. 5). He then goes on to inter-paradigm reasoning with the observation that “Kuhn (1962) extended this argument about the tacit aspects of scientific reasoning when he considered how scientists choose between competing research traditions by arguing that ‘there is no neutral algorithm of theory-choice, no systematic decision procedure which, properly applied, must lead each individual in the group to the same decision’ (p. 200)” (p. 6). Pulling these together, he concludes, quoting Bernstein (1983, p. 47), that scientific reasoning really “is closer to those features of rationality that have been characteristic of the tradition of practical philosophy than to many modern images of what is supposed to be the character of genuine episteme” (Cobb, 2007, p. 6). In my view, this is a misreading of Kuhn's position. That intra-paradigm scientific reasoning is a cultural practice guided by partly implicit norms does not make it equivalent to the value-laden, socially mediated practices of selecting between competing paradigms. Indeed, Kuhn’s (1970) whole point was not to “extend” from normal science to revolution, but rather to distinguish between the practices of logic-based puzzle solving that are characteristic of normal science and “the competition between paradigms [which] is not the sort of battle that can be settled by proofs” (p. 148). Kuhn's (1962/1970) re-characterization of epistemic knowledge as bounded by the paradigmatic world view within which it is created (rather than as objectively true) is not intended to erase the distinction between episteme and techne, nor to diminish the structuring function epistemic knowledge offers for fields of application. -147- 8 Indeed, Sfard's, 2008, commognitive framework offering a synthesis of communication and cognition signals her return to epistemic theoretical aspirations. 9 Various objective criteria also have been proposed that yield mixed results; or sometimes one’s ability to consciously control deployment of one’s knowledge is taken to indicate conscious knowledge(Fu, Fu, & Dienes, 2008). 10 Piaget’s microgenetic studies generally served to elaborate and strengthen his macrogenetic theories. However, stage theory encountered problems of décalage or unevenness of expression that challenged the essential idea of stages (Bruner, 1983; Fischer, 1980). This opened up a space for researchers to refocus developmental theory on school contents: “That we finally came to understand that we needed to make our own models to serve our educational purposes rather than to use Piaget’s seemed to be a major breakthrough, and it was quite liberating. In fact, the long-lasting effects of this observation can be seen in contemporary constructivist research in which the researchers seek to observe and describe mechanisms that . . . build up mathematical knowledge in a particular learning space” (Steffe & Kieren, 1994, p. 716). 11 The landscape of constructivist learning perspectives is thick and rich (Spivey, 1997). Many have spawned associated constructivist pedagogies, none of which is identical with the version offered here. 12 This has been a point of criticism of the Piagetian approach: “By and large, American educational psychologists were not satisfied by this qualification, the reason being that the limitations that are imposed by physical laws and biological structure are vague and general” (Brainerd, 2003, p. 273). Nevertheless, 30 years of teaching experiments reveal that “theoretical constructs that account for the learning of the participating students . . . prove useful when accounting for the learning of other students” (Cobb, Jackson, & Dunlap, p. 483, this volume). 13 To help clarify the distinction between the enculturation and construction metaphors, it is worth inserting that the goal in reading instruction of having students draw meaning from texts (in general) is an enculturation goal; a culturally specific form of engagement with texts is sought. This is different than the conceptual construction goal of having students understand a particular text in a particular way, for example the relation of madness and femininity in Lady Macbeth’s character (Thomas, 2004), which would require a different pedagogy. 14 That identity could be treated as a disposition, and addressed through the same pedagogical methods as any other disposition, was a breakthrough in this analysis and a confirmation of the robust capability of the crossdisciplinary framework. I am grateful to my former graduate student Marie Lord for the extensive discussions coproducing this insight into Healy’s pedagogy. 15 Of course, these are valid and valuable sources for pedagogical inspiration, but that inspiration should be mediated by learning theory, insofar as the pedagogical goal is student learning. -148-