id: 06617743
dt: j
an: 2016e.00535
au: Barwell, Richard
ti: Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue
and dialectic.
so: Educ. Stud. Math. 92, No. 3, 331-345 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht
la: EN
cc: E40 C50 D20
ut: mathematical language; mathematical discourse; dialogue; dialectic;
Bakhtin; Vygotsky
ci:
li: doi:10.1007/s10649-015-9641-z
ab: Summary: The importance of the role of language/discourse in the learning
and teaching of mathematics is noted in many mathematics curricula and
standards documents. In the research literature, this role has been
widely theorised from a Vygotskian perspective. This perspective is
limited by some of its underlying assumptions, including an
instrumental and systemic view of language as tool and its basis in
dialectic. In this paper, I propose a Bakhtinian, dialogic perspective
as an alternative. I focus my discussion on the long-standing issue of
the relationship between formal and informal mathematical language in
the learning and teaching of mathematics. I illustrate this discussion
with an examination of interaction in an elementary school mathematics
classroom in Québec, Canada. Based on Bakhtin’s ideas, I argue that
mathematical meaning emerges through locally produced, situated
dialogic relations between multiple discourses, voices and languages in
mathematics classroom interaction. From this perspective, students do
not follow a linear path from informal to formal mathematical
discourse; rather, they work with the teacher to expand the repertoire
of possible ways to make meaning in mathematics.
rv: