Early algebra: Repeating pattern and structural thinking at foundation phase

Abstract

Background: Working structurally with patterns at foundation phase (FP) enhances habits of mind that advance early algebra at this early stage of mathematical learning. The South African curriculum proposes that learners work with and understand the logic of a pattern, but this important idea has largely been neglected in classroom texts and in the supporting texts that guide teachers regarding curriculum implementation. At FP, most problems dealing with cyclical structure operate at a level of extending sequences by producing the next item that continues the order in which items are presented.

Aim: The purpose of this article is to examine the curriculum documents and teaching resources used by FP teachers to deal with repeating patterns. Across the elementary mathematical landscape, there are opportunities to work explicitly with structure in its various conceptual embodiments.

Setting: Six Grade 2 teachers in public schools participated in three workshops that foreground a structural approach to teaching pattern.

Methods: A thorough document study was conducted to ascertain what the curriculum and supporting texts make available for the teaching and learning of repeating pattern.

Results: A more structural approach fosters algebraic habits of mind that lead to more sophisticated forms of mathematical reasoning. A typology that summarises the relational features, intended skills development, complexity of sequences and the use of structural features on four levels is proposed to guide practice towards structural exploration.

Conclusion: Focusing on the cyclical structural aspects embedded in repeating patterns inducts the young learner into relational thinking that advance early algebra.