Algebraic thinking

Abstract

Algebra is one of the most extensively researched areas in mathematics education. Over the past 40 years, many researchers have addressed the problems associated with the learning and teaching of algebra in school and beyond. Hence, as Radford noted in his plenary lecture at CERME 6, this raises the question of “whether or not there is really something new to say about algebraic thinking” (p. XXXIV). Having reviewed the work on algebraic thinking at CERME, our answer to Radford’s question is most emphatically “yes”. While this body of work at CERME has extended our understandings of algebraic thinking, it also demonstrates how we have yet to reach a consensus on some of the fundamental questions associated with the teaching and learning of algebra. Like the discipline as a whole, the Algebraic Thinking Working Group has a long history. The group has featured at all CERME conferences except CERME 2. A total of 146 papers have been presented with authors representing 29 countries across the world. In this chapter, we cannot refer to all these papers individually. Rather, we highlight the main themes that have been discussed, highlighting what are, in our view, the key papers that contribute to these themes. We begin with a clarification of what algebraic thinking is. On this basis, various topics of algebra are described before the particular issues of their teaching and learning are discussed. We conclude with an evaluation and critique of CERME algebraic thinking research as a whole. Finally, we consider potential future avenues of work.