Communication XIV CIAEM-IACME, Chiapas, México, 2015. Fractions in teaching practice with fifth graders

Studies of learning processes about fractions are mostly based in individual responses to standardized tests. From the results, supposedly replicable, researchers statistically establish tendencies in the evolution of students ’ thinking. However students learn in different environments compared to those designed by researchers. While researching inside classrooms for instance it seems that the findings cannot be replicated given the environmental unique features. Contrasting the findings from researches focused on classroom events to others based on tests, one can ask if it is possible to build a bridge between the two perspectives, which seem mutually excludable. We propose an answer to this question giving to each perspective its value for teaching. Therefore we propose an approach that depicts the differences in schooling between what can be generalized and what cannot. We present an episode about teaching and learning fractions and decimals to illustrate our attempt to reconcile the two perspectives. Key words: teaching fractions, learning paradigms, generalizations of knowledge