A possible learning trajectory for young children’s experiences of the evolution of the base-10 positional numeral system

The concept of base-10 numeral system is fundamental to other mathematical concepts such as decimal numbers and exponents, and yet for a variety of reasons, including differences in number naming language, many children in the early years of school find the concept of place value difficult. Renowned mathematics educator Freudenthal (Mathematics as an educational task. Reidel, Dordrecht, Holland, 1973) was critical of the way that mathematical content knowledge is often simplistically identified as the learning of ready-made mathematical objects, leaving the evolution and refinement process of mathematics unattended. It seems, therefore, that children’s experience of the evolution and construction of the base-10 numeral system should gain a position in young children’s mathematical experiences. This chapter outlines a possible learning trajectory for children in the early years of school for this purpose, together with a brief elaboration of its theoretical underpinnings. The ultimate goal is to open up possibility for young children to connect to the evolution of the base-10 number system, and so deepen their understanding of the concept of place value.