Abstract

VIDAL-SZABO, Pedro; PARRAGUEZ, Marcela; BONILLA, Daniela  and  CAMPOS, Samuel. Modes of thinking the set Z 4 in teachers who teach algebra in the first years of school. Educ. mat. [online]. 2023, vol.35, n.2, pp.170-195.  Epub Jan 19, 2024. ISSN 2448-8089.  https://doi.org/10.24844/em3502.07.

Abstract: To link arithmetic with the practical and theoretical thinking of algebra, this exploratory research framed in the Modes of Thinking Theory conducted a case study to characterize modes of thinking about the set ${\mathbb{Z}}_4$ and its interactions in Chilean primary school teachers. For this purpose, the answers given by 30 in-service teachers to an online questionnaire were analyzed, based on a proposed cognitive model that defines the modes of thinking about the set ${\mathbb{Z}}_4$ with its articulators. The results show that these teachers, generally adhere to the cognitive model and evidence more articulation between synthetic-geometric and analytic-arithmetic modes than between analytic-arithmetic and analytic-structural modes, which shows less privileged theoretical thinking. In conclusion, the algebra of primary teachers can be activated by conceiving the set ${\mathbb{Z}}_4$ as a mathematical fragment with 4 elements constructed. Each one is considered a distinct set of congruent numbers modulo 4 that partition the set ℤ, making the concept of equivalence class contribute to the cognitive construction of the set ${\mathbb{Z}}_4$ as a cyclic graph of order 4.

Keywords : Modes of Thinking Theory; Cognitive Model of the set ℤ ₄; Mathematical fragment; Primary teachers; Modular arithmetic.