Abstract

BLOCK SEVILLA, David. “The jumps of the frogs.” Study of a didactic sequence on proportionality, with ratio comparison tasks, in fifth grade of primary school. Educ. mat. [online]. 2021, vol.33, n.2, pp.115-146.  Epub Dec 06, 2021. ISSN 2448-8089.  https://doi.org/10.24844/em3302.05.

This paper is about a didactical study on comparison of ratios in fifth grade of primary school. A sequence of situations was designed and applied in the context of frogs that, with a certain number of jumps, advance a certain number of meters; it’s about figuring out which jumps are bigger. The measure of a jump is not a whole number, but it is not necessary to make this number explicit, the comparisons are made at the level of ratios between natural numbers. A computer program was used to allow students to detect errors in their anticipations. The sequence seeks to favor the learning of the notion of ratio and, more generally, the development of proportional thinking. The results confirm the adequacy of the problems to move in that direction and reveal an unforeseen achievement: the development of the capacity for argumentation, to formulate and debate general rules.

Keywords : Teaching of Mathematics; Basic Education; Proportionality; Ratios; Rational Numbers.