Summary and Looking Ahead

Abstract

This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this document reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student. Mathematical relations, patterns, and arithmetical structures lie at the heart of early algebraic activity, with processes such as noticing, conjecturing, generalizing, representing, justifying, and communicating being central to students’ engagement.

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This topical survey, with its sketch of the history and evolution of the field of early algebra, has highlighted research related to the nature of early algebra, its learning, and its teaching. We have noted, in particular, that early algebraic thinking does not develop on its own without appropriate instructional support. And so, as we look ahead to the future, we recommend that further research be carried out in the following areas:

• The nature of classroom culture and the role of the teacher in fostering early algebraic reasoning.

• The forms of curricular activity that support early algebraic thinking.

• The nature of professional development that supports teachers’ capacity to foster early algebraic thinking in the classroom.

• Theorizing about the study of number, operations, and properties in the context of early algebra.

• The use of neuroimaging techniques to inform the learning and teaching of early algebra.

• The development and use of digital tools to facilitate the teaching and learning of early algebra.

• The impact of early algebraic thinking on students’ later study of algebra.