Using seeds of algebraic thinking to identify moments of algebraic potential -

Abstract

Early years (5 to 7 years) and middle years (8 to 11 years)

In this workshop, we will collaboratively think with grades K to 3 about some activities and tasks that can be traced to early algebraic thinking. Our goal is to present grades K to 3 teachers with the concept of algebraic seeds to support them in viewing algebraic thinking as something that emerges from students’ everyday experiences, both in and outside of school. Build on these seeds to develop more sophisticated mathematical thinking.

During our interactive workshop, teachers will play a game that will support them in understanding the elements of a new framework – seeds of algebraic thinking. This framework supports teachers in noticing how and when to build on students’ algebraic ideas, known as moments of algebraic potential. During the game, we will discuss the different strategies used by the teachers and through group discussion, look for links with early algebraic thinking using the seeds framework. We will then conceptualise the seeds, sharing examples that illustrate each that emerged from the workshop discussion, our studies’ classroom teaching experiments and prior research. Examples of seeds from prior research include classifying and structuring – comparing balance, covariation, and what you see is what you get. We will discuss possible strategies for noticing these seeds and what this might mean for elementary-level algebra instruction. We will then present teachers with instructional resources that build on algebraic seeds, including books, practitioner articles, lessons, websites, and three research-based lessons for ages 6 to 9 students from our classroom teaching experiments about algebraic representations.

We will close by discussing what this might mean for students’ learning of school algebra. Aligning with the aim of IGPME, our overall goal for this workshop is to rethink what it means to teach algebra at the elementary level.