The last decades brought about new challenges for teachers: we talk about
educating, not only instructing; educational goals contemplate contents
but also abilities, attitudes and values; compulsory schooling was increased,
students are heterogeneous and literacy is considered to be a desirable
competency for All.
These changes imply the need to modify classroom practices. Collaborative
work revealed a potential that was stressed by several authors (Cobb,
1994; Schubauer-Leoni and Perret-Clermont, 1997; van der Linden et al.,
in press) for it allows pupils to work in the proximal zone of development,
to create socio-cognitive conflicts, establish innovative didactic contracts
and develop mathematical and communicational competencies. Therefore,
the combination of the theories of Piaget and Vygotsky has been defended
as a useful conceptual tool for understanding knowledge construction (Tryphon
and Vonwche, 1996).
This study is part of a broader project called Interaction and Knowledge
whose main goal is to study and implement peer interactions in the Mathematics
classes as a way of promoting pupils' academic self-esteem, socio-cognitive
development and school achievement. The project Interaction and Knowledge
is divided into two levels: 1) - A micro-analysis level, in which we studied
different types of peers, their interactions, the tasks, the mistakes
pupils make and the progress that peer interactions are able to generate
in statistical contents and logical development; 2) - An action research
level, in which some Mathematics teachers implemented peer interactions
as a daily practice during at least a school year. The data we are going
to present are from level 1, related to the content of Statistics.
The sample had 533 subjects (25 classes) and it was gathered in two consecutive
school years. All subjects were attending the 7th grade. The subjects
were divided into an experimental group and a control group and the ones
from the experimental group worked in peers (136 dyads) during three sessions,
solving challenging problems. After that each class participated in a
general discussion that was videotaped and in which pupils discussed some
of the tasks they had solved in peers.
Detailed analysis of some episodes illustrates the role of the interactive
processes at stake. Knowing how social regulations take place, how solving
strategies are chosen, who leads, how and when this leadership is performed,
how stalling moments are overcome or mistakes are found, or when socio-cognitive
conflicts arise are all essential elements to understand the complexity
of any interactive process and the contributions it may make to the appropriation
of knowledge and the mobilization of competencies. At the same time, this
analysis allows us to understand how an inter-subjectivity is constructed
and the role it plays in attributing meaning to statistical tasks.
The facilitating character of collaborative work is undeniable in the
studies we have undertaken (Carvalho and Cesar, 2000; Carvalho and Cesar,
in press; Cesar, 1998, 2000a, 2000b, 2000c). However, it is essential
to identify and explain the mechanisms that generate subjects' progress
and explore the contributions of collaborative work to statistical literacy
and to the education of critical and participant citizens.
Carvalho, C. e Cesar, M. (2000). The Game of Social interactions in Statistics
Learning and in Cognitive Development. In T. Nakahara & M. Koyama
(Eds.), PME 24 Proceedings (vol. 2, pp. 153-160). Hiroshima: Hiroshima
Carvalho, C. & Cesar, M. (in press). Co-constructing Statistical Knowledge.
In S. Starkings (Ed) Papers on Statistical Education presented at ICME9.
Cesar, M. (1998). Social interactions and mathematics learning. Mathematics,
Education and Society - Proceedings of the MEAS 1 (pp. 110-119). Nottingham:
Universidade de Nottingham.
Cesar, M. (2000a). Interaction and Knowledge: Where are we going in the
21st century?. In M. A. Clements, H. H. Tairab & W. K. Yoong (Eds.),
Science, Mathematics and Technical Education in the 20th and 21st Centuries
(pp. 317-328). Bandar Seri Begawan: Universiti Brunei Darussalem.
Cesar, M. (2000b). Interaccoes sociais e apreensao de conhecimentos matematicos:
a investigacao contextualizada. Educacao Matematica em Portugal, Espanha
e Italia - Actas da Escola de Verao em Educacao Matematica - 1999 (pp.
5-46). Lisboa: SPCE - Seccao de Educacao Matematica.
Cesar, M. (2000c). Peer Interaction: A Way to Integrate Cultural Diversity
in Mathematics Education. In A. Ahmed, J. M. Kraemer & H. Williams
(Eds.), Cultural Diversity in Mathematics (Education:CIEAEM 51 (pp. 147-155).
Chichester: Horwood Publishing.
Cobb, P. (1994). A summary of four case studies of mathematical learning
and small group interaction. In J. P. Ponte & J. F. Matos (Eds.),
Proceedings PME18 (vol. 2, pp. 201-208). Lisboa: Universidade de Lisboa.
Schubauer-Leoni, M. L. & Perret-Clermont, A.-N. (1997). Social interactions
and mathematics learning. In T. Nunes & P. Bryant (Eds.), Learning
and teaching Mathematics. An international perspective (pp. 265-283).
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Tryphon, A. & Voneche, J. (1996). Piaget-Vygotsky - The Social Genesis
of Thought. Hove: Psychology Press.
van der Linden et al. (in press). Colaborative learning. In P. R. J. Simons,
J. L. van der Linden & T. Duffy (Eds.), New Learning. Dordrecht: Kluwer