Essay Review Human Development 446 DOI: 10.1159/000XXXXXX
Learning as the Evolution of Discourse: Accounting for Cultural, Group and Individual Development Essay Review of Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing by A. Sfard1
Paul Cobb Vanderbilt University, Nashville, Tenn., USA
Anna Sfard’s [2008] book Thinking as Communicating is broad in scope and has far-reaching implications for sociology, anthropology and education as well as for psychology. Her book is ambitious and aims to place investigations of human thinking and learning on a fully operationalized foundation while simultaneously doing justice to their richness and complexity. She develops the rationale for this project by introducing 5 quandaries that, she contends, continue to plague research on cognition. One of the quandaries or controversies that Sfard identifies centers on the range of disparate proposals that have been made to account for the well-documented dependence of human actions on aspects of the situations of action. A second controversy concerns the failure to reach consensus on the meaning of the term understanding despite the numerous attempts to pin it down. Sfard argues that the long list of unanswered questions spawned by the 5 controversies indicates that research on thinking has a long way to go. Her fundamental claim is that little progress will be made in addressing the 5 controversies unless we reconceptualize what we mean when we speak of thinking. In the first half of the book, Sfard delineates the key tenets of the reconceptualization that she proposes. In the second half of the book, she focuses specifically on mathematical activity and learning, and frames this as a context in which to introduce analytical constructs and to address methodological issues. Sfard [2008] argues that psychological constructs should satisfy 3 criteria, specified by Hubert Blumer, if they are to be considered adequate: (1) Point clearly to individual instances of the class of objects to which they refer. (2) Distinguish clearly 1
New York: Cambridge University Press, 2008.
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Paul Cobb Vanderbilt University, Peabody College Box 330 Nashville, TN 37203 (USA) Tel. +1 615 343 492, Fax +1 615 322 899 E-Mail
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this class of objects from other related classes of objects. (3) Enable the development of cumulative knowledge of the class of objects to which they refer. Sfard then clarifies that terms such as abstraction and understanding on which the 5 controversies center fail to meet all 3 criteria. She interprets this as a strong indicator that the controversies are grounded in linguistic ambiguities whereby core terms of psychological research are used in a range of different, imprecise and often conflicting ways. Sfard’s [2008] proposal for overcoming this shortcoming and thus for resolving the controversies is to view thinking as a process of communicating with one’s self and learning as a process of individualizing particular genres of interpersonal communication. She coins the term commognition to emphasize that communication and cognition are, in her view, different aspects of a single phenomenon. The potential value of this approach to researchers in the human sciences rests in part on her claim that there are no phenomena that we consider cases of thinking that cannot be regarded as instances of self-communicating. One of Sfard’s primary goals in taking this approach is to develop a perspective on human activity and learning that does not make reference to intangible mental entities. In focusing empirical analysis of thinking and learning on communication processes that are open to direct observation, she aims to develop constructs that satisfy Blumer’s 3 criteria for adequate concepts in the empirical sciences. On my reading, the constructs that she proposes (and they are numerous) do indeed satisfy these criteria. As Sfard [2008] notes, her commognitive approach is located squarely within the sociocultural tradition. However, rather than focusing on broad, ill-defined practices, she centers her attention on distinct forms or genres of human communication, analyzes them as patterned, collective forms of activity and argues that they are developmental prior to the activities of the individual. She also draws on Wittgenstein’s later philosophy by equating the meaning of a word with its use in language. Methodologically, this tenet implies that analyses of the meanings that particular words have for certain groups of people should focus on how they use the words of interest and tease out the rules according to which they do so. Sfard stresses that this requires the analyst to adopt an outsider’s perspective by suspending his or her familiarity with the discourse under investigation and thus with what is being spoken about. As she notes, this analytic stance is akin to that of an investigator of a virtual reality game who does not have access to the perceptual experiences of the players. It is important to emphasize that, for Sfard, a genre of communication or a discourse is not restricted to verbal utterances. For example, mathematics (viewed as a discourse) is distinguished from other forms of communication by the use of particular words, the rules that guide participants’ construction of their actions and reactions, the objects that are the focus of their attention (e.g., algebraic functions) and the perceptual mediators that they employ (e.g., tables, graphs, written notation). Sfard goes on to argue that any human society comprises a number of partially overlapping communities of discourse. Her commogitive perspective clearly makes contact with the work of James Gee [1997] in that both characterize learning as a process of becoming an increasingly substantial participant in specific discourses. Further, both contend that supportive interactions with people who are already full participants in those discourses are critical to the learning process. However, Sfard’s approach stands apart in terms of the precision with which she analyzes both the key
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features of particular discourses and the processes by which people become increasingly substantial participants. It should be clear that Sfard [2008] challenges the widely held assumption that we first formulate our thoughts and then express those thoughts in language. In doing so, she rejects the view that thinking precedes and can be separated from speaking and, more generally, from communication. This position might erroneously be dismissed as a variant of psychological behaviorism. However, this summary judgment would misrepresent her intent. Her goal is clearly to account for people’s actions rather than merely their observed behavior. As Taylor [1995] clarified, behavior is concerned with physical responses, including speaking, whereas actions are concerned with the intentionality of observed behavior2. This concern for intentionality immediately focuses attention on the very phenomena that were banished by psychological behaviorism, namely, meaning and understanding. Rorty [1979], also an admirer of Wittgenstein’s later philosophy, termed explanatory approaches of the type that Sfard proposes epistemological behaviorism precisely because she questioned the assumption of an internal cognitive process isolated from speaking and communicating. Sfard’s use of the term commogition serves to emphasize this epistemological behaviorist stance. Her proposal is radical not because she eschews a focus on meaning but because of the manner in which she attempts to account for meaning. For Sfard, investigating the history of a particular discourse such as mathematics and studying the developing mathematical discourse of a child are different facets of the same endeavor. In the second part of the book, she proposes specific constructs for analyzing discursive patterns across an entire mathematics community, in the mathematical discourse of newcomers, in particular mathematics classrooms, and in the activity of individual students. In doing so, she attends to the macro-level of historically established mathematical discourse, the meso-level of local discourse practices jointly established by the teacher and students in a classroom and the micro-level of individual students’ developing mathematical discourses. Sfard’s approach therefore instantiates Diane Vaughan’s [1992, 2002] argument about the importance of coordinating analyses across these 3 levels. From my perspective as a mathematics educator, Sfard’s focus on all 3 levels is an important contribution given that sociocultural theory has thus far been of limited use in formulating instructional designs for supporting students’ mathematical learning. It is in fact difficult to identify instances of influential research-based designs in mathematics education whose development has been primarily informed by sociocultural theory. In my view, this is because the notion of cultural practice typically employed by sociocultural theorists is located at the macro-level and refers to ways of talking and reasoning that have emerged during extended periods of human history. As a consequence, sociocultural theorists usually frame the task facing both the mathematics teacher and the instructional designer as that of mediating between the micro-level of specific students’ activity and the macro-level of institutionalized mathematical practices. This framing overlooks Vaughan’s [2002] empirically grounded arguments concerning the importance of the meso-level to theories of practical action. As Vaughan put it, the discourses of a local collective vary from institutionalized discourses ‘such that they become specifically tailored to practical activity in every2 As Searle [1983] demonstrated, intentionality is not limited to conscious intentions that are formed prior to action but can also involve what he terms intentions-in-action.
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day life, reproducing universalistic symbol systems in the environment, but elaborating them in locally particularistic ways’ [2002, p. 48]. As we know only too well, the forms of discourse jointly constituted by the teacher and students in different mathematics classrooms can differ significantly both from each other and from historically established mathematical discourse. The attention that Sfard gives to the mesolevel of the classrooms is critical in my view because the local discourse in which children participate constitutes the immediate social setting of their learning. In the later chapters of the book, Sfard [2008] develops the instructional implications of her analysis of mathematical learning as a process of inducting students into mathematical discourse. In doing so, she distinguishes between what she terms metalevel learning and object-level learning. Meta-level learning results in changes in the rules of students’ mathematical discourse. For example, the transition from whole number arithmetic to fractions is an instance of meta-learning because statements such as ‘multiplication makes bigger’ hold for whole numbers but not for fractions. In contrast, object-level learning expands the scope of students’ current mathematical discourse. For example, the construction of novel relationships between numbers by students who are relatively proficient in whole number arithmetic is an instance of object-level learning. This distinction is analogous to that which Gregory Bateson [1973] drew between first- and second-order learning that concern learning within an established context (e.g., whole number arithmetic) and about a new context (e.g., fractions) respectively. Sfard’s primary concern is with meta-learning and thus with scaffolding students’ induction into a novel form of mathematical discourse. As Sfard [2008] observes, it is unreasonable to expect children to reinvent a particular form of mathematical discourse such as fractions by relying exclusively on their own resources. Meta-learning is instead most likely to occur as students encounter the new form of discourse directly and their individualization of that discourse is supported by someone who can already participate substantially in the discourse. However, Sfard contends that students’ initial attempts to individualize the discourse almost inevitably result in rituals whose primary purpose is to create and sustain social bonds by gaining approval and becoming members of a group. She justifies this claim by arguing that there is an inherent circularity in meta-learning as a developmental process: students cannot appreciate the value of the new discourse until they are aware of its advantages, but this appreciation only emerges as they use the discourse before they are fully proficient. This insight leads Sfard to challenge instructional approaches that aim to promote ‘learning with understanding’ if this implies understanding before practice. She instead argues that practice makes $$$ meaningful. As Sfard’s remarks are open to misinterpretation, it is important to clarify that in speaking of practice, she is not referring to repetitious textbook exercises but to students’ supported participation in a discourse. Her analysis of what she terms rituals is generally consistent with a Vygotskian account of learning in which students’ activity is initially discourse for others and only later becomes discourse for oneself. Sfard discusses a number of processes that are involved in this transition. In doing so, she goes some way towards elucidating Vygotsky’s [1987] account of the formation of mind as a process of internalizing interpersonal processes. In discussing the instructional implications of her commognitive perspective, Sfard [2008] identifies 2 conditions that she contends are critical for meta-learning. The first is that the support provided to students give rise to what she terms commognitive conflicts between students’ current discourse and the new discourse.
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Sfard takes care to differentiate commognitive conflict from the more common notion of cognitive conflict by noting that it is an essential rather than an optional pedagogical move and that it originates from differences in ways of communicating rather than from discrepancies between beliefs and external evidence. She then indicates that both the students and the teacher have to be committed to overcoming the commognitive conflict if it is to be a gateway rather than a barrier to the new discourse. This leads Sfard to the second condition for meta-learning, namely that the students should be ready to follow the teacher even though aspects of the teacher’s discourse might initially appear arbitrary. For Sfard, this requires the establishment of a learning-teaching agreement about the leading discourse, the students’ and teacher’s respective roles, and the nature of the expected change. Taken together, the links between Sfard’s commognitive perspective and Vygotskian theory and her discussion of this learning-teaching agreement indicate that she is proposing an apprenticeship model of teaching that is broadly compatible with Lave and Wenger’s [1991] notion of legitimate peripheral participation. As Lave and Wenger have indicated, agreement about the nature of the expected change requires that students have access to the entire discourse from the outset. On my reading, the circularities that Sfard contends are inherent in meta-learning have potentially far-reaching implications for equity in students’ access to mathematical ideas. Sfard suggests that children’s willingness to cooperate with the teacher by participating in a new form of mathematical discourse is grounded in a desire for social acceptance. I would add that, for older students, the reasons for initially participating in mathematical discourse in a ritualized way might also include entry to college and future economic opportunities. D’Amato [1992] called rationales of this type, in which learning mathematics in school is a means of attaining other ends, structural significance. It has been well documented that not all students have access to a structural rationale. Gutiérrez [2004] observed, for example, that many students from traditionally underserved groups do not see themselves going to college, hold activist stances, have more pressing daily concerns (e.g., housing, safety, healthcare), or do not believe that hard work and effort will be rewarded in terms of future educational and economic opportunities. D’Amato [1992], Erickson [1992], and Mehan, Hubbard, and Villanueva [1994] all documented that students’ access to a structural rationale varies as a consequence of family history, race or ethnic history, class structure and caste structure within society. The immediate implication of Sfard’s analysis is therefore that there are inherent inequities in students’ motivation to learn mathematics in school that are associated with the extent to which they have access to a structural rationale. Given the disquieting nature of this conclusion, I hope that aspects of Sfard’s analysis might require modification. At a minimum, she highlights the importance of cultivating students’ mathematical interests as an explicit goal of both instructional design and teaching. In concluding this review, I want to reiterate that Sfard’s commognitional perspective has the potential to overcome some of the limitations of sociocultural theory. As she notes, the commognitional perspective is very much a work in progress. I consider this line of work to be one of the most important current developments in research on thinking and learning. The reader should be aware that Thinking as Communicating is a challenging book. If this reviewer’s experience is any guide, the constant stream of insights that Sfard provides through to the final pages of the last chapter are more than ample reward for the reader’s persistence.
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References Bateson, G. (1973). Steps to an ecology of mind. London: Paladin. D’Amato, J. (1992). Resistance and compliance in minority classrooms. In E. Jacob & C. Jordan (Eds.), Minority education: Anthropological perspectives (pp. 181–207). Norwood, NJ: Ablex. Erickson, F. (1992). Transformation and school success: The policies and culture of educational achievement. In E. Jacob & C. Jordan (Eds.), Minority education: Anthropological perspectives (pp. 27–51). Norwood, NJ: Ablex. Gee, J.P. (1997). Thinking, learning and reading: The situated sociocultural mind. In D. Kirshner & J.A. Whitson (Eds.), Situated cognition: Social, semiotic, and psychological perspectives (pp. 235–260). Mahwah, NJ: Erlbaum. Gutiérrez, R. (2004, August). The complex nature of practice for urban (mathematics) teachers. Paper presented at the Rockefeller Symposium on the Practice of School Improvement: Theory, Methodology, and Relevance, Bellagio, Italy. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge University Press. Mehan, H., Hubbard, L., & Villanueva, I. (1994). Forming academic identities: Accommodation without assimilation among involuntary minorities. Anthropology and Education Quarterly, 25, 91–117. Rorty, R. (1979). Philosophy and the mirror of nature. Princeton, NJ: Princeton University Press. Searle, J.R. (1983). Intentionality. Cambridge, UK: Cambridge University Press. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. New York: Cambridge University Press. Taylor, C. (1995). Philosophical arguments. Cambridge, MA: Harvard University Press. Vaughan, D. (1992). Theory elaboration: The heuristics of case analysis. In C.R.H. S. Becker (Ed.), What is a case? Exploring the foundations of social inquiry. New York: Cambridge University Press. Vaughan, D. (2002). Signals and interpretive work: The role of culture in a theory of practical action. In K.A. Cerulo (Ed.), Culture in mind: Towards a sociology of culture and cognition (pp. 28–54). New York: Routledge. Vygotsky, L.S. (1987). Thinking and speech. In R.W. Rieber & A.S. Carton (Eds.), The collected works of Vygotsky, L.S. Vol.1: Problems of general psychology. New York: Plenum.
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