The role of representations in promoting the quantitative reasoning - Serrazina, Maria De Lurdes (2018)
In this communication, we discuss the role of representations in the development of conceptual knowledge of 2nd grade students involved in additive quantitative reasoning through the analysis of the resolutions of two tasks that present transformation problems. Starting to discuss what is meant by additive quantitative reasoning and mathematical representation, we present after some empirical results in the context of a teaching experiment developed in a public school. The results show the difficulties with the inverse reasoning present in both situations proposed to students. Most students preferably use the symbolic representation, using also the written language as a way to express the meaning attributed to its resolution. The iconic representation was used only by a pair of students. Representations have assumed a dual role, that of being the means of understanding the students' thinking, and also supporting the development of their mathematical thinking.