A Possible Learning Trajectory for Young Children’s Experiences of the Evolution of the Base-10 Positional Numeral System

Abstract

This chapter discusses teaching and learning of addition in early years under the mathematization framework. Addition-by-counting and the principle of Break-Apart-and-Make-Ten (BAMT) are used as examples to illustrate theoretical constructs in the process of mathematization: guided re-invention, horizontal and vertical mathematizations and the emergent modelling. The mathematizing process of addition is interpreted as progressive refinement of discourse mixing the gestural, verbal, iconic and symbolic registers. Subitizing is discussed under the interplay between mathematization and a materialist approach to mathematics