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

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verbal spatial organisation, which helped to master the hierarchy between dynamical and static elements (either as data or as parts of the sketched plants); and calculations that helped finding and fixing intermediate elements, but which could have been mastered abstractly and independently from the particular situation. Confusion due to the insufficient everyday conceptualisation of increase was overcome thanks to a sufficient mastery of the additive situation and related external representations (numerical, verbal, schematic). This made the situation challenging and attainable at the same time. We can conjecture that such conditions made the scientific/everyday concept dialectics effective. Argumentation was the way by which that dialectics enhanced students conceptualisation. It also allowed some students to appropriate elaborate verbal expression reflecting refined understanding of the situation. We heard sentences such as: “the plant that increased the most is the one which was in the dark although the highest was the one in the light.” At the end of Phase 1, all students could distinguish and calculate increases and heights; 9 expressed the relation between them as in the excerpt mentioned above. Phase 2: comparison activity and collective discussion This text was distributed for individual comparison, before collective discussion: JESSICA : the plant in the dark increased the most because it increased 3 cm, on the contrary the plant in the warm place increased 2 cm. I say that the one in the dark increased the most because the centimetres of the part of the plant that increased are the most. GIUSEPPE : the plant that increased the most since Friday, December 3 is the one in the dark, because it increased 3 cm, but the one in the warm increased 2 cm and so 3 are more than 2. But in fact the plant which is the tallest is the one that makes 28 cm, and it is the one in the warm. Questions : 1) In which way did Giuseppe and Jessica reason ? 2) In Giuseppe’s text there is a consideration we cannot find in Jessica’s. Which one is it? This metacognitive reflection about their problem solving led students to share the reasoning and stabilise it within the class, as well as to deepen, for some students, and to pursue, for the others, the effort of clarification and interpretation of the situation. At the beginning of the collective discussion, the weak everyday conceptualisation of increase appeared again: many students mixed it up with height in their reasoning, even though they had been able to discriminate them during their interaction with the teacher. But once some students referred to the bit that increased, the evoked spatial situation helped to restore the “right” argument. However, the drawing was not needed anymore. A new example given by a student established another criteria to distinguish increase from height in relation to time: a child’s height is his/her increase since birth (note that this is rigorously true for plants, not for children…); while increase is determined in relation to two dates. All along the discussion the
arguments to interpret and compare the texts concerned “reality” (the known development of the plants), spatial organisation, and calculations, with their hierarchical organisation. Phase 3: Individual synthesis The teacher brought the students to a synthesis by the following question: Is it the same to say “which plant increased the most” and to say “which plant is the tallest”? Why? The generality of this question aims a more scientific handling of the involved concepts. 12 students out of 20 produced a general and valid synthesis, most gave examples (and some of them were creative in doing it). 14 students referred to time. 6 out of these 14 had produced a drawing in Phase 1. A CHARACTERISATION OF SCIENTIFIC CONCEPTUALISATION IN SCHOOL CONTEXT Let us now describe scientific conceptualisation as we consider it pertinent in school context, and present a characterisation that allows to evaluate its evolution. We will use it to analyse the effect of Vgotsky’s everyday concepts/ scientific concepts dialectics on conceptualisation, as well as the conditions that helped this dialectic to take place. This characterisation captures two entangled aspects: the epistemological construction, and the development of cognitive activities. Vygotsky (1986; cf Vergnaud, 2000) helps us to recognise the quality of the use of the concept, and its evolution. Vergnaud (1990) helps us to recognise explicit links with experienced “reality” through reference situations and external representation; and with subject’s activity interpreted through operational invariants 1 . External representation, in coherence with the experience field didactical theory, includes gesture and language in the broadest way (cf Radford, 2003). We consider two characters of conceptualisation and at the same time we try to describe how to detect them: - The evolution of systemic links of concepts. Linked objects can be reference situations, external representations, other concepts, or components of concepts (according to Vergnaud’s definition). Links can be propositions about the objects (e.g. propositions that express properties, characteristics, analogies or differences or hierarchies), metaphors, examples, etc. Operational invariants or generalisations can underlie these links. - Students’ awareness in handling the concept, its components or its systemic links: it consists in the mastery of the concept, and the intentional recourse to it or to some of its components, that can be detected specifically in using and expressing operational invariants and through using its external representations. AN ANALYSIS OF CONCEPTUALISATION IN OUR EXAMPLE 1 Vergnaud defined a concept as composed by the set of its reference situations, the set of its operational invariants ('schemes', theorems in actions, etc.) and the set of its symbolic representations (see Vergnaud, 1990).
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