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My research is devoted to study of human thinking in general and of mathematical thinking in particular. Inspired by the critique of the traditional divide between thinking and speaking issued, among others, by Wittgenstein and Vygotsky, I define thinking as individualized form of interpersonal communication. The disappearance of the time-honored dichotomy is epitomized in the term commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication, with its distinctive property of recursive self-reference, may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another.
In my empirical research I follow the development of mathematical discourses, with the word development referring to the growth of these discourses both throughout individual lives and in the course of history. The focus of many of my studies is on the issue of objectification, that is, on those discursive mechanisms that bring about the emergence of new mathematical objects. In a series of studies in Israel, Canada, and US, most of them conducted together with PhD students, I have been investigating such topics as the development of algebraic discourse, the discourse on negative numbers, early numerical discourse, the mathematical discourse of students diagnosed with learning disabilities and those regarded as high-achievers, and the professional discourse of high-school mathematics teachers. Results of these studies have been published in a series of journal articles and book chapters (some of them in books I co-edited with others), and they have now been summarized in a book due to appear in the beginning of 2008..
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Sfard, Anna, Thompson, Patrick W. (1994): Problems of reification: Representations and mathematical objects. In Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education North America Plenary Sessions, 1 (0) pp. .
Sfard, Anna (1994): Reification as the birth of metaphor. In For the Learning of Mathematics, 14 (1) pp. 44-55.
Thompson, Patrick W., Sfard, Anna (1994): Problems of reification: Representation and Mathematical objects. In: Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education - North America , 1994, Baton Rouge, USA.