Commognition is a theory of thinking and learning in learning sciences research, introduced by Anna Sfard in 2008 book. It is a portmanteau of communication and cognition as if thinking is a person's communication with themselves. As if individual cognition and interpersonal communication are two forms of a single phenomenon rather than distinct processes. She claims that mathematics, as any other domain of knowing, is a historically established discourse, and learning mathematics is the process of becoming a participant in that discourse. Commognition developed from Sfard's 1998 distinction between "acquisition" and "participation" metaphors for learning, an article that became one of the most cited in educational research. The framework has been taken up and extended by mathematics education researchers, but also in chemistry, physics, science, statistics and teacher education, and a 2025 synthesis of Scopus-indexed studies reported that its use has grown since 2020.
Development The framework's immediate precursor is Sfard's 1998 article "On two metaphors for learning and the dangers of choosing just one", in which she argued that theories of learning divide between an acquisition metaphor, in which learning is the accumulation of possessions such as concepts and schemes, and a participation metaphor, in which it is a matter of becoming a member of a community, and that neither metaphor can be relied on alone. The article circulated widely outside mathematics education, and Sfard returned to its distinction in 2025 to assess what the participation metaphor had yielded over the intervening four decades. Sfard developed commognition in response to what she described as weaknesses in twentieth-century theories of human development. In her account, "acquisitionist" schools such as behaviorism and cognitivism conceptualized learning as the acquisition of entities (behaviors, concepts, mental schemes) and, because they attended only to the individual, could not explain historical change in human ways of acting. "Participationist" thinkers following Lev Vygotsky instead described human learning as growing participation in historically established forms of activity. Commognition, Sfard wrote, took this line one step further by treating domains of knowing, mathematics among them, as discursive activities — a move she traced to two sources: the arguments of Vygotsky and Ludwig Wittgenstein against separating thought from its expression, and postmodern philosophers, among them Lyotard, Foucault and Rorty, who described science and knowledge-building as discourse.
The term appeared in Sfard's publications in the early 2000s and was fully outlined in Thinking as Communicating (2008). In the book's introduction, Sfard located the project's beginnings in puzzles from her research on mathematics learning: systematic student errors, young children's non-standard handling of numbers, and the failure of decades of reform to improve mathematics learning in any lasting way. She argued that such puzzles could not be resolved without operationally defined concepts to replace the ambiguous everyday vocabulary of thinking and learning. The first part of the book presents the general theory of thinking as communicating. The second applies it to mathematics.
Sfard continued developing the approach after 2008. In a 2018 chapter, she framed commognition as a research discourse defined by its keywords, its data, its methods of analysis and its endorsed claims, and summarized the storylines that commognitive research had by then produced, including accounts of how numerical, algebraic and functional discourses develop in learners and of how identity-building talk interacts with mathematical activity. With Man Ching Esther Chan, she later compared problem-solving dialogues recorded twenty-five years apart in Montreal and Melbourne, using the comparison to develop commognitive methods for analyzing why opportunities to learn are sometimes not taken up.
In a 2025 article, Sfard returned to the distinction with which the project had begun — the contrast she had drawn in 1998 between the acquisition and participation metaphors for learning — and set out the vocabulary her group had arrived at after almost three decades of work. The paper replaced the noun "activity" with "practice", defined as a network of interconnected routines together with the range of situations in which they apply, and presented routines and practices as the framework's units of analysis, in place of the "knowledge" and "concepts" of acquisitionist research. It also proposed a hypothetical five-step action cycle — recognize, simulate, select, interpret, perform — that connects the framework to neuroscientific research on prediction and simulation and is intended to explain why human performance varies from one situation to another.
Sfard wrote the entry on commognition in the second edition of the Encyclopedia of Mathematics Education, and the International Commission on Mathematical Instruction devoted a unit of its Awardees Multimedia Online Resources project, created and recorded by Sfard, to "Learning, Commognition and Mathematics".
Framework The theory's point of departure is a definition: thinking is "the individualized version of interpersonal communication," a communicative interaction in which one person plays the parts of all interlocutors, and which need not proceed in words. Sfard presented this as a non-dualist position that rejects the form-content dichotomy and the Cartesian split between the bodily and the mental. She derived it from Vygotsky's claim that uniquely human capacities originate in historically established collective activities: if thinking is such a capacity, its collective predecessor must be interpersonal communication. Because thinking and communicating are taken to be one kind of process, the theory holds that both can be investigated with a single set of analytic tools.
Within this vocabulary, mathematics is a discourse: a form of communication made distinct by four characteristics. These are its keywords, such as "three", "set" or "function"; its visual mediators, such as numerals, algebraic symbols and graphs; its routines, the patterned ways in which characteristic tasks such as defining or proving are performed; and its endorsed narratives, the theorems, definitions and computational rules that the community of the discourse accepts as true. Learning mathematics is accordingly defined as individualizing mathematical discourse: gradually becoming able to use the discourse agentively, in response to one's own needs.
The model sets mathematics apart from most other discourses in one respect: Sfard described it as autopoietic, a discourse that creates the very objects its participants talk about. New mathematical objects arise, on this account, through objectification, the introduction of nouns that come to be understood as names for new discourse-independent objects. Sfard identified three discursive devices at work: saming, giving a common name to things previously seen as unrelated; encapsulating, replacing talk about many objects with talk about a single entity such as a set; and reifying, turning talk about a process (adding 5 to 7) into talk about an object (the sum of 5 and 7). A new noun then undergoes what she called alienation: it comes to be used in impersonal statements, as if its referent existed independently of the discourse.
Routines occupy a central place in the theory. Sfard analyzed a routine as a pair consisting of a task (the performer's vision of what must be repeated from precedent situations, where a precedent is a past event deemed similar to the present one) and a procedure (the prescription for action, deduced from what was done in the precedent events). The same procedure can ground different kinds of routines depending on how the performer sees the task: in explorations, the goal is producing an endorsed narrative; in rituals, the performer recapitulates others' actions for the sake of social approval rather than for any product. Most routines, Sfard held, fall between the two poles, and learning often takes the form of deritualization, in which the performer's attention gradually shifts from the performance itself to its outcome and the routine becomes more flexible and better connected to other routines.
The theory distinguishes two kinds of discursive change. Object-level learning extends the stock of endorsed narratives about existing objects. Meta-level learning changes the meta-rules of the discourse itself, as happens when the integers are extended to rational numbers, and some old truths, such as "multiplication makes bigger", cease to hold. The new discourse may be incommensurable with its predecessor, and encounters between incommensurable discourses produce what Sfard termed commognitive conflict. Such a conflict becomes an opportunity for learning, she proposed, only under a "learning-teaching agreement" in which participants concur on which discourse leads, who teaches and who learns, and what the process should look like. Because newcomers cannot yet judge the outcomes of the new discourse, meta-level learning is, on this account, bound to begin with rituals.
Commognitive research takes discourse, rather than the individual mind, as the object of inquiry. Its data are recordings and verbatim transcripts of interaction, and the analyst is required to alternate between an insider's and an outsider's perspective on the discourse under study.
Subjectifying and identity Alongside mathematizing (talking about mathematical objects) participants in a mathematics classroom are engaged in subjectifying, an overt or covert talk about the participants themselves. Where subjectifying takes the form of stories about a learner's enduring properties rather than about her actions, Sfard calls it identifying. With Anna Prusak she operationalized identity as a set of "reifying, significant, endorsable stories about a person", and cast learning as an effort to close the gap between a current identity and a designated identity.
Because this definition makes identity a species of discursive construct, it brings the social and emotional dimensions of learning within reach of the same analytic tools the framework applies to cognition, rather than leaving them to a separate theory. Sfard and Einat Heyd-Metzuyanim accordingly described learning mathematics as an interplay of mathematizing and identifying, and argued that identity-constituting narratives (labelling a student "weak", for instance) tend to function as self-fulfilling prophecies with long-term effects on learning. Heyd-Metzuyanim used the framework to trace how a "disabled mathematical identity" is co-constructed in teacher–student interaction, and how cycles of identifying and mathematizing can reinforce one another into mathematical failure. Sfard set out the position at length in 2019, defending stories as the appropriate unit for identity research.
Mellony Graven and Heyd-Metzuyanim called the 2005 article "incredibly influential in the field of mathematics education", but reminded that comparatively few of the many papers citing it actually adopt its operationalization of identity as reifying, endorsable and significant stories. The two later surveyed the strand in the Fourth International Handbook of Mathematics Education.
Culture, language and practical activity