socially constructed continually challenges learners’ thinking and emphasises the
personal meaning individuals make.Socio-cultural perspectives
Socio-culturalism provides a theory of learning within which the cognitive, social,
motivational, physical and emotional combine. The belief is that all higher-order
functions such as learning grow out of social interactions. This view of cognition
moves ‘beyond the idea that development consists of acquiring skills. Rather, a
person develops through participationin an activity, changingto be involved in the
situation at hand in ways that contribute both to the ongoing event and to the
person’s preparation for involvement in other similar events’ (Rogoff, 2003, p. 254).
This allows individuals and groups to make generalisations across a range of experi-
ences which Hatano (1988) terms adaptive experience.Wood and Atfield (2005)
emphasise that Vygotsky ‘did not claim that social interaction automatically leads
learning and development: it is more the means used in social interaction, particu-
larly language, that are taken over and internalisedby the child’ (p. 92).Mathematical graphics as cultural tools
Vygotsky emphasised the significance of cultural(symbolic) toolsin assisting the
learning process within socio-cultural contexts and, as van Oers argues ‘mathemat-
ics as a subject is really a matter of problem solving with symbolic tools’ (Oers,
2001a, p. 63).
The cultural (symbolic) tools described by Vygotsky include ‘language, various
systems for counting ... algebraic symbol systems, writing, diagrams, maps, techni-
cal drawings and all sorts of conventional signs’ (Wertsch, 1985, in Wood and
Atfield, 2005, p. 92). Used in specific ways and contexts within a culture, such tools
are used and adapted over time and in the process, new ones are created (Rogoff,
2003). Self-inventedcultural toolsare key to learning symbolic languages and are
central to our work on mathematical graphics. Drawing on the work of Jordan
(2004), Wood and Atfield stress that the children’s role in this process is one of active
and mutual engagement that allows them to transform what is internalised through
guided reinvention and co-construction (Wood and Attfield , 2005, p. 93).
In this way, an individual’s mathematical graphics becomes a ‘social product that
may develop into still higher levels of abstraction and constantly feed back into the
community’ (Oers, 2001a, p. 65). Studies by Wenger (1988) of different communities
of practiceshow that people who come together in a community such as a social
group, school or within a particular work context, focus on joint enterprises.Through
shared experiences of mathematical graphics in nursery or school, children explore,
discuss, adapt, internalise, reinvent and co-construct their understandings of the
written language of mathematics. Bakhtin (1981, 1986) has extended our under-
standing of the importance of creating knowledge together through talk. The belief
is that higher-order functions such as learning grow out of social interactions.Making marks, making meaning 238657part 1b.qxd 04/07/2006 18:06 Page 23