Primary teachers' semiotic praxis

windows into the handling of division tasks

Corin Mathews

Hamsa Venkat

Mike Askew

pp. 257-274

in: Norma Presmeg, Luis Radford, Wolff-Michael Roth, Gert Kadunz (eds), Signs of signification, Berlin, Springer, 2018

Abstract

The teaching of division is a complex task: division is difficult to teach in a connected and coherent way, given the diversity of models of division, and differences in their associated actions and utterances. This chapter focuses on the signs produced by teachers in their attempts to explain division. The signs produced follow from unifications between signifiers and signifieds located within what we are calling signification pathways. Our focus is on signification pathways that are co-produced by teachers and learners, and endorsed by the teacher. The data presented in this chapter exemplify categories within an emerging analytical framework of signification pathways when teaching division, which vary in the coherence of the signs that are involved. In this chapter we consider the possibilities and constraints of these signification pathways in relation to the semiotic system related to division from a mathematical interpretant perspective. The analysis makes visible limitations, ambiguity and incoherence across the signification pathways. The conclusion examines how the production of signs and the connection of signs in the signification pathway may lead to certain meanings about division that the teacher endorses as valuable in the teaching of division.