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..

Based at the University of
Haifa, Israel, I am also
affiliated with

BOOKS

Sfard, A.
& McClain, K., Eds. (2002). *Learning tools: Perspectives on the
role of
designed artifacts in mathematics learning.* Mahwah, NJ: Laurence
Erlbaum
Associates [also publishes as special issue of *Journal of Learning
Sciences,
11(2,3)*.]

Kieran,
C., Forman, E., and Sfard, A., Eds. (2003). *Learning discourse:
Bridging the
individual and the social: discursive approaches to research in
mathematics
education.* Dodrecht, TheNetherlands: Kluwer Academic Press [also
published
as the special issue of *Educational Studies in Mathematics*, *46(1-3)*]

Sfard, A. (in press).
Thinking as
communicating:
Human development, the growth of discourses, and mathematizing.
Cambridge, UK:
Cambridge University Press. (to appear: January 08 in US, March 08 in
UK) [Table
of contents + introduction ] [more
about the book] [amazon]

**SELECTED
JOURNAL ARTICLES AND BOOK
CHAPTERS **

Sfard,
A.(1991). On the dual nature of mathematical conceptions: reflections
on
processes and objects as different sides of the same coin.*
Educational
Studies in Mathematics*, *22*, 1-36. [download]

Sfard, A.
& Linchevski, L. (1994)^{ }. The gains and the
pitfalls of
reification: The case of algebra. *Educational Studies in
Mathematics ,
26*, 191-228. Reprinted in P. Cobb (ed.),

Sfard, A.
(1994). Reification as a birth of a metaphor. *For the
Learning of
Mathematics*, ** 14**(1), 44-55.

Sfard, A.
(1995). The development of algebra: Confronting historical and
psychological perspectives. *Journal of Mathematical Behavior, * ** 14**,
15-39.

Sfard, A.
(1997). On metaphorical roots of conceptual growth (A commentary). In
English,
L. (ed.), *Mathematical reasoning: Analogies, metaphors, and images*.
pp.
339-371.

Sfard, A.
(1998). On two metaphors for learning and the dangers of choosing just
one.*
Educational Researcher, 27(2), *pp. 4-13. [English] [Hebrew]

Sfard, A.
(2000a). Symbolizing mathematical reality into being: How mathematical
discourse and mathematical objects create each other. In P. Cobb,K. E.
Yackel,
& K. McClain (Eds), *Symbolizing and communicating: perspectives
on
Mathematical Discourse, Tools, and Instructional Design *(pp.
37-98).

Sfard, A.
(2000b). On reform movement and the limits of mathematical discourse. *Mathematical
Thinking and Learning, 2(3)*, 157-189. [download]

Sfard, A.
(2000 c). Steering (dis)course between metaphor and rigor: Using focal
analysis
to investigate the emergence of mathematical objects. *Journal for
Research
in Mathematics Education, 31(3)*, 296-327*.
*

Sfard, A. & Kieran, C.^{
} (2001). Cognition as communication: Rethinking
learning-by-talking
through multi-faceted analysis of students’ mathematical interactions. *Mind,
Culture, and Activity, 8(1), *42-76.

Sfard, A.
(2001a). On the gains and dilemmas of calling different things the same
name. *Quarterly
of Cognitive Science, 1(3/4)*, 359-388.

Sfard, A. (
2001b). Learning mathematics as developing a discourse. In R. Speiser,
C.
Maher, C. Walter (Eds), Proceedings of 21^{st} Conference of
PME-NA
(pp. 23-44).

Sfard, A.
(2001c). Communicating to learn or learning to communicate? Mathematics
education in quest for new answers to old questions. (Book review). *Zenralblatt
fur Didiaktik Mathematik / International Reviews on Mathematical
Education,
33(1)*, 1-9.

Sfard, A.
(2001d). There is More to Discourse than Meets the Ears: Learning from
mathematical communication things that we have not known before. *Educational
Studies in Mathematics*, 46(1/3), 13-57.

Sfard, A.,
Forman, E. & Kieran, K. (2001). Learning discourse: Sociocultural
approaches to research in mathematics education. *Educational
Studies in
Mathematics*. *46(1/3)*, 1-12.

Sfard, A.
(2002) The interplay of intimations and implementations: Generating new
discourse with new symbolic tools. *The Journal of Learning
Sciences, 11(2,3)*,
319-358.

Sfard, A.,
& Kay McClain, Eds. (2002). Analyzing tools: Perspectives on the
Role of
Designed Artifacts in Mathematics Learning. *Journal for Learning
Sciences
11(2&3), *153-161.

Sfard,
A. (2003). Balancing the unbalanceable: The NCTM Standards in the light
of
theories of learning mathematics. In J. Kilpatrick, Martin, G.,
&
Schifter, D. (Eds.), *A Research Companion for NCTM Standards *(pp.
353-392).

Ben-Yehuda, M.,
Lavy, *The Journal for Research in Mathemtics Education*, *36(3)*,
176 – 247. [download]

Sfard, A. & Lavi, *Cognition
and Instruction*, *23(2)*, 237-309. [download]

Sfard, A.
& Prusak, A. (2005). Telling identities: In search of an analytic
tool for
investigating learning as a culturally shaped activity. *Educational
Researcher, 34(4)*, 14-22* .*[download the article] [download
Mary Juzwik's critique] [download
my rejoinder]** **

Sfard, A.
& Prusak, A. (2005). Identity that makes a difference: Substantial
learning
as closing the gap between actual and designated identities. In H.L.
Chick
& J.L. Vincent (Eds.) *Proceedings of the Twenty-ninth Meeting
of the
International Group for the Psychology of Mathematics Education*
(Vol. 1,
pp. 37-52), Department of Science and Mathematics Education, University
of
Melbourne, Victoria, Australia.

Sfard, A.
(2005). What could be more practical than good research? On mutual
relations
between research and practice of mathematics education. *Educational
Studies
in Mathematics, 58(3)*, 393 – 413.

Sfard,
A. (2005). What changes when learning goes to school: The
communicational version, the case of mathematics. *European Journal
of School
Psychology, 3(1),* 301-326* *.

Sfard, A.
(2005). Challenging discourse. A commentary. In A. Chronaki & *Challenging
Perpsectives on
Mathematics Classroom*, 323 - 338. Communication.

Sfard, A.
(2005). Discourse in flux - Commentary to *Cognition in flux* by
Geoffrey
Saxe. *Mind, Culture, and Activity, 12(3&4)*,* *233-250.

Sfard, A.
(2005). Essential dialogue. Review essay on “Dialogicality and social
representations”
by Ivana Markova. *Human Development, 48(6) *, 363 - 370*.*

Sfard, A.
(2007). When the rules of discourse change, but nobody tells you -
making sense
of mathematics learning from commognitive standpoint. *Journal
of
Learning Sciences, 16(4)*, 567–615.

Ben-Zvi, D., & Sfard, A. (2007). Ariadne’s Thread, Deadalus’ Wings, and the Learner’s Autonomy. Education and Didactics, 1(3), 123 - 141. [download]