Mental calculations with rational numbers: strategies' range and strategy selection

International audienceIn this paper primary and secondary school students are followed while they try to perform operations with rational numbers first mentally and then in paper-and-pencil. The same tasks were given to the participants of both groups. The findings give evidence that no matter the context (mental or written calculations) the dominance of the mental form of the written algorithm is unquestionable for both groups. Moreover, most of the student were not able to explain their decision to use the algorithm in their mental calculations. The students who were able to justify their choice claimed that their criterion was the accuracy, speed and easiness provided by the algorithm which creates a paradox since for all the items on the study the algorithm is the most time-consuming strategy