vygotsky's everyday concepts/scientific concepts dialectics in school ...

they can be identified through the relationship established between comparison of
transformations and a “real” dynamical situation, as well as through schematic (direct
or mental) treatments of the static visible aspects and the dynamical, only thinkable,
aspects. Hierarchic organisation between the various additive calculations, in relation
to their interpretation as static or dynamical, was an operational invariant, as well as
the arithmetic theorems in action underlying the numerical treatment.
Concerning students awareness:
at the beginning of the sequence one part of the students mastered the additive
situation only through calculations. At the end, though, all of them were able to
interpret calculations in relation to the reference situation and give examples of
comparable additive situations. They revealed then a conscious mastery of this
additive situation and an ability to relate it or compare it to other situations (as
comparing increases of children by comparing increases between two dates, and
heights as increases since “birth”).
CONDITIONS THAT ALLOWED THE VYGOSTKIAN DIALECTICS TO
WORK
The analysis of the didactical situation put into evidence two main conditions that
favoured the setting of this dialectics and its functioning.
- The important use of the “reality”, the development of various expression about it
and the development of everyday concepts in school context. This comes from the
experience fields didactical setting, which implies making sure that students are
sufficiently involved in some activities related to this “reality”, and important
everyday concepts are explicitly shared, and enriched with verbal and other external
representation through observations and discussions. In fact, everyday concepts do
not quite correspond to spontaneous ones, though they remain in the everyday stream
of conceptualisation (cf Vygotsky, 1985, Chapt. 6).
- Argumentative activity managed by the teacher allowed students to interpret the
situation, express and discuss their views, handle and compare various (verbal,
schematic, numerical) external representations. It helped students to assimilate the
new construction, because they had to express themselves in a variety of ways to
answer to a variety of detailed questions. Argumentation played a dynamical role so
that the dialectic could evolve.
CONCLUSION
Vygotsky’s scientific concepts/everyday concepts dialectics works as a powerful
model for conceptualisation in teaching and learning contexts. But through
observation of examples such as the one reported here, I found that it can turn out to
be also an efficient tool to plan teaching situations in order to achieve some important
educational aims in mathematics. The "experience fields" didactical setting does use
this dialectics as one of the levers to develop conceptualisation, with some specific
favourable conditions: