The Form in Algebra: reflecting with Peacock, on Upper Secondary School Teaching

After the first two years of upper secondary school the aim of learning algebra is not to be able to "do" algebraic calculations of ever increasing difficulty, but to be able to apply with certainty what has been learnt so far. As part of educational research then we must ask ourselves what kind of "control" of algebraic operations is acquired by the students: checking by substitution, the recognition of known "forms", or mastering and recognising the rules of syntax. The author prefers to get the students into the habit of using the last two methods of control, i.e. she thinks that it is better, at a certain level, to underline explicitly the "leap" from arithmetical algebra to symbolic algebra, giving a major attention to "form". To do this she takes a step back into the past, to the time when the basis for modern algebra was being laid and George Peacock underlined the two separate aspects of algebra, distinguishing between independent science on the one hand and "instrumental" science for discovery and investigation on the other.