In this chapter I present an account of the Pilot Study. The presentation is in chronological order even though it is inevitable that particular emphasis is put retrospectively on certain aspects of the study that have turned out to be significant in the light of the Main Study. The observation period is described as well as the main phases of data processing. Findings are also briefly presented. The overall presentation is geared to sustaining the points made in the final section where the formative influence of the Pilot on the Main Study is reviewed.

Summary: From October 1992 to June 1993 ten first-year mathematics students were observed during tutorials given to pairs of them on Analysis, Topology and Linear Algebra. Fieldnotes were taken during observation. Coding and categorising the data followed. Subsequent focus was on the category constituted by the students' difficulties regarding mathematical understanding. Its contents were further processed and analysed. A triad of difficulties — topical, logical and symbolic — was used as a descriptive tool and provided the order of presentation in the analysis. The study exerted strong influence on determining the methodological and thematic structure of the Main Study.