Banca de DEFESA: PATRICIA FREITAS DO NASCIMENTO

Algebraic Thinking and the Game of Hopscotch: An Investigation from the Perspective of the Theory of Objectification

Algebraic thinking; early years; theory of objectification; recursive sequences; hopscotch game.

Discussions regarding algebraic thinking among early elementary school students in
Brazil have intensified following the introduction of the National Common Curricular
Base (BNCC), which presents a new thematic unit on algebra focused on the
development of algebraic thinking. This shift created new demands for educators,
highlighting challenges related to organizing pedagogical practice in mathematics
instruction. Against this backdrop, this research aims to investigate how algebraic
thinking manifests in 4th-grade students - based on the Theory of Objectification (TO)
- when engaging with tasks involving recursive sequences formed by multiples of a
natural number. We adopted the Theory of Objectification as our theoretical
framework; this theory offers a conception of algebraic thinking that accounts for
cultural and historical aspects while contributing to the organization of classroom
pedagogical practice by emphasizing collective work. According to the theory in
question, algebraic thinking is characterized by the presence of the vectors of
indeterminacy, denotation, and analyticity. Based on these considerations, this
qualitative study - grounded in both bibliographic and fieldwork - employs audio and
video recording as well as written records for data collection and multimodal analysis.
Accordingly, we conducted a teaching-learning activity with a 4th-grade class at the
Childhood Education Center - a laboratory school affiliated with the Federal
University of Rio Grande do Norte. To this end, we held sessions with the class in
which we explored multiples through the game of hopscotch. The results show that,
within the teaching-learning activity, processes of objectification were
evidenced—namely, the three vectors of algebraic thinking according to the Theory
of Objectification (TO), and the presence of elements characterizing the joint labor.