Giancarlo Navarra

Theoretical Issues and Educational Strategies for Encouraging Teachers to Promote a Linguistic and Metacognitive Approach to Early Algebra

After an overview of the studies which led to the rise of the study of early algebra, we sketch our vision of this disciplinary area and of its teaching from a linguistic and socio-constructive point of view. We take into account the teacher’s role in the socio-constructive teaching process and stress the importance of reflecting upon the teaching and learning processes in order to reshape the teacher’s ways of being in the classroom. We dwell upon the strategies enacted and describe the tools we have shaped: theoretical, for the enculturation of early algebra teachers, and methodological, which aim at promoting their awareness and control of their action. We conclude with some considerations about the value of the tools and modalities we have used, as well as on the factors which determine their efficacy.

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.