Analysis of justification and generalization processes of the rectangle area formula by primary school students

Resumen

In this paper, we describe a research developed with prospective elementary teachers in the University of Valladolid. The study is based on the analysis of a task about the justification and generalization of the formula to calculate areas of rectangles when its base and height are rational numbers. The analysis of students’ productions was carried out from two different perspectives. On one hand, we consider Harel & Sowder’s proof schemes (1998) and Van Asch’s (1993) pre-formal proofs to try to discover the intentions of generalization in these students and their outcomes. On the other hand, we use content analysis (Bardin, 1996) to identify the mistakes made by students. The most notable conclusions are the lack of intention to generalize in a majority of students and the abundance of errors related to the concept of unit of area measurement.