Data collection was completed in March 1994. No withdrawals from the study occurred and at no instance was the observer asked to leave or pause recording. The general ambience between volunteers and observer can be described as growingly amicable. Amicability on the part of the participants is probably evidence that the researcher's presence is not seen as threatening or disrupting. Therefore it is reasonable to assume that the students' behaviour has been fairly natural during observation.

When participants expressed their interest in my findings during observation I generally referred to the course and to areas of the mathematical content with which the students appeared to have difficulty. My reluctance to be more specific was due to a methodological concern related to the presupposition that, in a minimally participant observation, the participants should not be influenced towards behaviour that interferes with the naturalistic character of the observation: in other words, I clearly avoided any statements that might have deterred the participants from openly discussing the problematic aspects of their mathematical learning. In this vein I was consistently repeating during observation that my presence was not of an evaluative nature and that I was interested more in their difficulties than in an impeccable demonstration of mathematical competence. The degree of openness that the students and tutors demonstrated during data collection as well as a remarkable pile of comments according to which the experience of participating in the study is seen as very positive — the comments on my presence in the tutorials and the interviews vary from 'definitely not obtrusive' to cathartic and relieving 'confession' — indicate that the participants were convinced and that they welcomed such an investigation.

I was very willing to reveal the details of my work after data collection was completed. This resulted in a number of informal discussions with the participants and also in an invitation by one of the participating colleges to a seminar in which I presented some data and analysis. I also accepted a similar invitation by the Mathematical Institute at Oxford. All participants declared their willingness to provide me with any feedback that would turn out to be necessary in the course of data analysis.

In sum the above outlined ambience had a positive influence on the quality of the data in the sense that the students did not appear intimidated and at times were willing to elaborate further on their thinking knowing that I found it interesting — especially towards the end of the observation period.