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Commognition

Theory · All theories
Evidence · 1 claim (1 for) · 1 study (1 qualitative), q3 · 0 of 1 report an effect size · 1 claim rests on one study

Description

Commognition (Sfard) treats mathematical thinking as a discursive activity: numbers and numerical relations are "discursive constructs generated in, and for the sake of, communication," not mental objects a learner comes to possess. This is a participationist rather than acquisitionist stance — a young child's spontaneous reaction to a change in quantity is a precursor to numerical thinking but not itself an instance of it, because only participation in the discourse (using number words, comparative language, and counting procedures in socially recognizable ways) counts as numerical thinking under this theory. Individual development is described through the individualization of pre-existing discourses that a child encounters through participation with more experienced others. Within this program, a routine (a stable task-procedure pairing) can be a ritual — performed for its own sake or for social approval, with no attention to whether it produces a meaningful outcome — or an exploration — performed because of what it accomplishes, with attention to the outcome ("product"). De-ritualization, the shift from ritual to exploration, proceeds through two kinds of bonding: vertical bonding, connecting a procedure's steps to its outcome, and horizontal bonding, recognizing that different procedures applied to the same task produce equivalent outcomes. Lavie & Sfard (2019) trace this process empirically in early numerical development, proposing a three-stage sequence — pre-quantitative/pre-numerical precursors, separate quantitative-non-numerical and numerical-non-quantitative "discourses of order," and a final discourse of cardinality where the two coalesce.

Implications

Context

  • Applies most directly to early numerical and mathematical development, where the theory was elaborated, but the general ritual/exploration and bonding constructs are proposed as general mechanisms of discursive development
  • Requires longitudinal, close observation (video-recorded teaching episodes) to trace routine and vocabulary development over time; not easily assessed with a single measurement

Target Learners

  • Young children (the source study: ages 2-4) in the earliest stages of numerical discourse participation

Target Learning Objectives

  • Moving from ritualized, imitative performance of a numerical routine toward flexible, outcome-sensitive use of that routine (exploration)
  • Coalescing separately-developed quantitative (comparison-based) and numerical (counting-based) discourses into a unified sense of cardinality

Claims

Examples

Key Sources

  • Lavie, I., & Sfard, A. (2019). How Children Individualize Numerical Routines: Elements of a Discursive Theory in Making. Journal of the Learning Sciences, 28(4-5), 419-461. https://doi.org/10.1080/10508406.2019.1646650
  • Sfard, A. (2008). Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing. Cambridge University Press.
Page metadata
Field Value
type theory
title Commognition
description A discursive theory of mathematical thinking (communication + cognition) holding that mathematical thinking is not a private mental process but a form of communication that develops through participation in mathematical discourse, so learning to think mathematically means individualizing that discourse rather than acquiring internal representations.
status review
canonical True
generated by claude/unspecified on 2026-08-29
trust unverified — no one has confirmed this page's content
sources 1 — lavie-sfard-2019

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