An understanding is not directly accessible to others and we cannot rely completely on the owner’s judgement. Instead, we usually have to rely on what can be inferred from their responses and behaviour. What counts as understanding depends on the context so the assessor needs to be clear about what is to be evaluated. A starting point would be to seek evidence of a relevant, coherent mental structure. This structure can often vary in richness according to the degree of integration of its elements and their relationships with other knowledge. Beyond that is what understanding may enable. It may, for instance, produce an explanation, make a prediction, justify or criticize an argument, evaluate a situation or position, or solve a problem. Each of these applications of understanding could be in areas close to or remote from one the student knows. This generative capacity is often the reason for understanding in the first place so testing for capability in application could be a central feature of assessment (Perkins, 1994b). The differences described above are largely of a qualitative kind and could be arranged

hierarchically. For instance, the revision of the popular Bloom taxonomy by Anderson and Krathwohl (2001) provides a hierarchy ranging from reproductive thought to understanding, application, analysis, evaluation and creative thinking. Such hierarchies, however, can obscure important fine structure. Understanding is not an indivisible product, an all or nothing, but varies in degree. At some given time, someone may understand something to some extent and, later, understand it better. Similarly, they may be able to apply the initial understanding in limited ways but, later, may apply it more widely. At the same time, hierarchies can tempt us to overlook an iterative process in thinking. Applying a partial understanding may lead to a revision of mental structures which amount to a more coherent or wider understanding. This process may be seen in a novice’s developing grasp of a subject. As engagement continues, more or less isolated and relatively small mental structures are integrated so that a greater coherence develops. Principles, rather than the surface features of situations, begin to govern

the novice’s responses. The conditions which determine the legitimate application of knowledge are learned and, as experience accumulates, it plays an increasing part in achieving goals (Glaser, 1990). Collis and Biggs (1989) devised the SOLO taxonomy which captures something of this by classifying a response according to the evidence it gives about the nature of the mental structure. The taxonomy ranges from no relevant response, through simple structures to relationships and wider connections of the relationship. These could be seen as various levels of understanding. Conceptions of this kind are useful in that they may suggest what constitutes shades of understanding. Evidence of higher degrees of integration and of widening capabilities in application is generally taken to indicate the quality of understanding. This means that assessment should provide opportunities for a student to show different degrees of integration of knowledge and different breadths of capability. Simply increasing the number of questions is not enough if they only assess one level.