Aprendizagem de frações no 6° ano do Ensino Fundamental na perspectiva de medição: um enfoque Fenomenológico.

Abstract

The teaching and learning of fractions are important and recurring subjects in Mathematics Education researches and undergo numerous approaches or methods of teaching and learning fractional numbers. The focus on the part-whole perspective is predominant in both documents and researches. Faced with this, it is understood that there is a need to invest in researches on another perspective, in this case, that of measurement, which has historic-epistemological characteristics for the comprehension and construction of a fractional number. This viewpoint was investigated under the research’s questioning: What shows about the learning of fractions taught from the measurement perspective, with emphasis on the idea of magnitude and unit construction? The qualitative research took on a phenomenological approach. For this purpose, this paper’s data was gathered from the lived experience of the teacher in her mathematics classes. The activities based on the perspective of measurement were implemented in a class of the 6th grade at Elementary School. All of the material produced, dialogs (between the teacher and the students or between students) and symbolic records or non symbolic (figurative representations) of the students or of the teacher were recorded, transcribed and, later on, analyzed. In this analysis, the qualitative analysis software, Atlas.ti, was used as a facilitating instrument and we proceeded according to the phenomenological perspective, highlighting the Meaningful Scenarios and, starting from them, through successive reductions, got to the Meaning Units. Seeking what was being demonstrated, the converging units were articulated and, from them, the categories were elaborated. The research culminated in seven open categories: C1) Inicial understandings about fractions; C2) Common unit of measurement relationship with multiplicative relationship; C3) The unit and its relativism; C4) The necessity and recognition of the unit; C5) Demonstration of the equivalent meaning; C6) Symbolization and/or representation of the fractions; and C7) Comprehension of fractions without rods. These categories were interpreted hermeneutically and emphasized the unit’s meaning as a central aspect for the understanding of fractional numbers. This unit is not fixed, it is chosen, elected in the context of its own measurement. Furthermore, the comparison revealed itself as the most recurrent action and deserves a spotlight, once the understanding of the common unit was maintained in the various arrangement possibilities between the rods.