New Words and Concepts for Early Algebra Teaching: Sharing with Teachers Epistemological Issues in Early Algebra to Develop Students’ Early Algebraic Thinking

We present the ArAl project, conceived as an integrated system of teacher education and classroom innovation, aiming at renewing the teaching of arithmetic in an early algebra perspective, guiding pupils towards the discovery of letters to express generalities. We focus on some theoretical key points (KP) and on the main language constructs (LC). Through excerpts of class-discussions, we show the incidence of KP and LC on the progressive construction and refinement of pupils’ early algebraic thinking. Finally we discuss the difficulties met by teachers at the K–8 levels when they reflect upon their knowledge, beliefs, attitudes, and ways of relating with the pupils.