This paper presents aspects of a study that investigates the development of an instrument, a reference framework, to analyse students' written responses to non-routine problems in a first year calculus course in order to describe the complexities of their understanding and to assess their understanding of particular mathematical concepts. Consistent with methodological procedures of grounded theory, the constructed reference framework, which contains six categories, is an amalgam of established instruments founded in the mathematics education literature and based on emergent categories of understanding founded in the empirical data collected for the study. Results of the study, which also implements a fuzzy measure of the level of students' understanding, are based on the inscriptions in the form of student mathematical texts that participants produced.