Emma’s Negotiation of Number: Implicit Intensive Intervention

Abstract

We investigated the extent to which one elementary school child with ­working-memory differences made sense of number as a composite unit and advanced her reasoning. Through ongoing and retrospective analysis of eight teaching-experiment sessions, we uncovered four shifts in the child’s real-time negotiation of number over time: (a) initial “2s” and symmetry to consider counting on, (b) participatory awareness of 10 and use of algorithmic knowledge, (c) break apart and growing anticipation of tacit counting, and (d) advanced participatory tacit double counting. The results suggest a possible link between the child’s participatory knowledge and the extent to which her enacted activity met her goals for solving the problem more than her current “knowing.” The implications regarding a possible proof of concept toward implicit, intensive instruction are shared.