Resumen

We report an analysis of data from an experimental replication of “Object-Process Linking and Embedding” (OPLE) in the case of integer arithmetic instruction originally developed by Linchevski and Williams (1999) in the realistic mathematics education (RME) tradition. Our analysis applies Radford’s theory of semiotic objectification to reveal new insights into how reification is achieved. In particular the method of analysis shows how the factual generalization of the so-called compensation strategy encapsulates the notion that “adding to one side is the same as subtracting from the other side”: a vital grounding for symbolic integer operations later. Other aspects of objectification are discussed that are considered likely to be important to the semiotic chaining that students achieve in the OPLE sequence that can lead to an intuitive grounding of integer operations. We argue that semiotic theory needs to be elaborated to understand the vital role of models and modelling in leveraging reifications in RME.