Fair sharing in learning rational numbers in a 5th grade class - Hélia Pinto; Neuza Carlos; Nicole Duarte (European Teacher Education Network, 2023)
Rational numbers are considered a difficult set to teach and learn, and these difficulties are identified in the literature as related to the nature of the set itself, as well as to its teaching. Thus, one of the difficulties relates to the fact that the more traditional teaching does not take into account the different meanings of fractions and the diversity of units. Thus, it is important to carry out studies that promote opportunities for students to work on those ideas. This study aimed to understand the implications of fair sharing tasks in the learning of rational numbers in an exploratory teaching context, in a 5th grade class. To achieve this goal a didactic sequence composed by 7 tasks was implemented, but in this article only the results of 4 tasks shall be analysed. To carry out the study the interpretative paradigm was used, with essentially qualitative approach, case study design, and the sequence of tasks implemented. Data were collected through participant observation and student productions. From the results emanates, in an initial phase, the use of iconic representation and informal language, that is, the use of informal strategies. However, these culminated with the symbolic representation, namely, the fractional representation, so the students seem to have managed to connect their intuitive strategies with the symbolic representation, in a meaningful way. Thus, the context of fair sharing seems to have promoted an informal approach to situations and therefore the connection between informal and formal ideas in a meaningful learning process.