'Day number': a promoter routine of flexibility and conceptual understanding

This paper is part of the Project “Adaptive thinking and flexible computation: Critical issues”. In this paper we discuss different perspectives of flexibility and adaptive thinking in literature. We also discuss the idea of proceptual thinking and how this idea is important in our perspective of adaptive thinking. The paper analyses a situation developed with a first grade classroom and its teacher named the day number. It is a daily activity at the beginning of the school day. It consists on to look for the date number and to think about different ways of writing it using the four arithmetic operations. The analyzed activity was developed on March 19, so the challenge was to write 19 in several ways. The data show the pupils’ enthusiasm and their efforts to find different ways of writing the number. Some used large numbers and division, which they were just starting to learn. The pupils presented symbolic expressions of 19, decomposing and recomposing it in a flexible manner.