In the study, a part of longitudinal research focused on the emergence of mathematical knowledge structures in a learner's mind is presented. It concentrates on the analysis of introspective data gained from the author's study of a non-standard arithmetic structure in terms of the model of abstraction in context (Hershkowitz, Schwarz and Dreyfus). Some episodes are described by factual and interpretative accounts. It is shown that the above model can be applied to introspective data and used for their interpretation. The parallel between the model and Duffin and Simpson's idea of understanding is discussed. (Contains 6 footnotes and 3 figures.) [For complete proceedings, see ED500860.]