Is mathematical knowledge constructed? A cultural-historical critique of object oriented conceptions of learning activity
Palavras-chave:
Activity Theory, Contradiction, Learning Paradox, Leading Activity, Mediation, Zone of Proximal Development, ProlepsisResumo
It has become a truism (ideology) to state that mathematical knowledge is constructed collectively, in communities of practice, and individually, on the part of students whileengaging in mathematical tasks. However, construction implies an image of the end result of the labor process, which allows people to build a house and compare each step to the plan. Students, on the other hand, do not know the end product of their learning process, the new knowledge. This knowledge, therefore, cannot be the transitive object towards which construction is oriented. In this study, I provide a cultural-historical critique of objectoriented notions of learning activity. Using classroom episodes as examples, I propose an alternative based on L. S. Vygotsky’s commitment to the primacy of the social, whereby any higher psychological function was a social relation first. This allows the final product to be available in the present, as relation, without the learner’s conscious awareness, and thereby determine learning and development. The idea of the future acting in the present is captured in M. Cole’s notion of prolepsis. Implications are discussed with respect to curriculum design in mathematics classrooms.
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