The Pirie-Kieren theory

Lyndon C. Martin has written an article called Folding back and the dynamical growth of mathematical understanding: Elaborating the Pirie–Kieren Theory. The article is going to be published in The Journal of Mathematical Behavior, and it was available online yesterday at ScienceDirect. Here is the abstract:
The study reported here extends the work of Pirie and Kieren on the nature and growth of mathematical understanding. The research examines in detail a key aspect of their theory, the process of ‘folding back’, and develops a theoretical framework of categories and sub-categories that more fully describe the phenomenon. This paper presents an overview of this ‘framework for folding back’, illustrates it with extracts of video data and elaborates on its key features. The paper also considers the implications of the study for the teaching and learning of mathematics, and for future research in the field.
For another article discussing the Pirie-Kieren theory and related theories, you might want to take a look at this article by Droujkova et al. from PME29.