The transition from arithmetic to algebraic in mathematics teaching at the Collège
Part two: Curricular perspectives: the notion of modeling
DOI:
https://doi.org/10.23925/1983-3156.2023v25i1p556-596Keywords:
Curricular reform, Arithmetic, Algebra, Didactic transposition, Mathematical modelingAbstract
The objective of the article is to discuss the epistemological and didactic dimensions of the curriculum reforms carried out in the 1960s. Among them, the Chevènement reform that aimed to rescue the arithmetic to the detriment of the algebraic. This look at the numerical was seen as something destabilizing of the curriculum in the French education system in the late 1960s. This reform understood the numerical as something practical and coming from reality, that did not need such abstract ideas, as algebra demanded. The Chevènement reform relegates the algebraic aspects in second place but does not exclude them; the use of letters is seen as a preceding generalization of the studies of numerical calculations. The problems posed in the teaching of arithmetic and algebra in the French education system are revealed, they involved the process of didactic transposition established in the official college program. The didactic transposition, which modifies the operation of the objects of knowledge, gives a certain specificity to the official program that the prodigal school proposes to the student. This official program engenders in the student a personal program that, as it is in the official program, will enjoy limited adequacy as the said object of knowledge, which will no longer be a pure didactic stake, will only be a tool of the student's didactic-mathematical activity: for example, the factoring of an algebraic expression may no longer be the goal of his activity, becoming the means to solve a third degree equation, knowing one of its roots.
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