An analysis of the representation's production when solving early algebra problems in elementary school

Abstract

The study of external representations in early algebra usually focuses on formal symbolic aspects. Therefore, little is known about the role those other representations might play in the development of algebraic thinking. This article analyses representations like drawings, schemes, and idiosyncratic symbols spontaneously produced by third-grade elementary students (n=27) during an early algebra program with generalized arithmetic and functional thinking components. The program was evaluated through a pre-test, posttest design. There was a significant increase in the students’ generalized arithmetic and functional thinking performance. The sophistication of the representations produced by the students increased for the functional problems but not for the generalized arithmetic problems. During the program, the levels of representations remained stable. It was found that the production of more sophisticated representations was associated with a better performance in functional problems but not on generalized arithmetic problems. The notion of how the production of external representations can support the acquisition of algebraic ideas is discussed. Conclusions are drawn by highlighting some theoretical and practical implications of the study.