Elementary school teachers’ understanding of unit fractions

Resumo

Teachers’ mathematical knowledge is critical for their teaching of mathematics. We investigated whether elementary teachers believe that a unit fraction, , results only from a whole equipartitioned into 1/n parts. We adapted Ciosek and Samborska’s (2016) Frame Task, presenting a frame consisting of three unequal segmented squared rings, with one squared ring shaded. In semi-structured interviews, 19 teachers engaged the task and reasoned whether the shaded portion equals 1/3 of the frame. Our findings indicate that about three-quarters of the participants believe that either (1) to have one-third of a quantity, a section needs to be one of three parts, or (2) a section cannot be 1/3 of an object if the object is partitioned into three unequal sections. Finally, we hypothesize how an iterative perspective of unit fractions may mitigate against the false beliefs that Ciosek and Samborska (2016) and our study document.