Abstract:

This study presents a teaching experience focused on the development of early algebraic thinking in the first year of basic education in Portugal, within the context of a continuous professional development program for in-service teachers. The work emerges from recent curricular guidelines that emphasize the introduction of algebraic thinking from the beginning of schooling, particularly through the exploration of patterns and sequences.

Adopting a design research methodology, the study involved a collaborative process of lesson planning, implementation, and reflection carried out by a group of four teachers. The task designed focused on a pictorial repeating pattern and aimed to promote students’ abilities to identify regularities, determine repeating groups, extend sequences, and establish relationships between terms. Special attention was given to anticipating students’ difficulties and defining purposeful teacher actions aligned with an exploratory teaching approach.

The task was implemented in four classrooms with students aged six to seven. Data were collected from teachers’ planning documents, classroom observations, and students’ productions. The results show that students were highly engaged and able to successfully identify repeating patterns and determine near terms using counting and representation strategies. Some students demonstrated emerging generalization processes, particularly through the identification of recursive relationships between terms and the organization of data in tables. The use of multiple representations, including pictorial, manipulative, and tabular forms, proved to be a key factor in supporting understanding.

The study also highlights the role of exploratory teaching in fostering meaningful mathematical discussions and promoting students’ reasoning. Furthermore, the collaborative work among teachers was identified as a critical element for professional development, enhancing their ability to design rich tasks, anticipate student thinking, and manage classroom discourse effectively.

Overall, the findings suggest that carefully designed pattern-based tasks, implemented through an exploratory approach and supported by collaborative teacher practices, can effectively promote early algebraic thinking. This work reinforces the importance of sustained teacher training aligned with curricular innovation and focused on students’ mathematical reasoning.

Keywords:

Teacher Professional Development, Early Algebraic Thinking, Exploratory Teaching, Mathematics education.