Third graders’ functional thinking: an early algebra study

Abstract

This paper qualitatively explores how third-year primary school students (8-9 years old) approach questions about a generalization problem that involves a pictorially presented functional relationship ( i(m)=3m+2 ). Using the Grounded Theory, the strategies, relationships, and representations used by 11 students are examined through the analysis of their written productions in response to a paper-based task. The results obtained show the variety and combined use of strategies by students as well as the use of covariation and correspondence relationships, occasionally, under a proportional reasoning that accounts for an illusion of linearity . Likewise, particularization and contextual generalization are observed when it comes to answering a general question. We can see the influence of geometric aspects of the pictorial representation that presents the functional relationship in the students’ resolutions. The importance of the problem context, of the numerical relations between the quantities involved, of their size, and of their determinate/indeterminate character to promote functional thinking is manifested. As a consequence of the study, implications are derived in the design of tasks to this end in the first grades.

Functional thinking; Strategies; Representation systems; Primary education; Early algebra