A geometric interpretation of the effects of anxiety on test performance

Abstract

Teachers, at various levels, are frequently confronted with the problem of test anxiety; there can be very few amongst us who have not had students explain their difficulties on the grounds of stress or panic in examination situations. Psychologists have carried out extensive research in this area. Important questions include the investigation of connections between variables such as test anxiety, task difficulty and performance, the former concept being f requent ly broken down into two components, namely worry and a physiological component emotionality. The complexity of human behaviour and the problems inherent in careful experimental investigation have led to a situation in which a broad synthesis, using the language of mathematics to link key variables, is conspicuous by its absence. In this article we pu t forward a number of hypotheses concerning the above variables together with reasons which, in the author's view, make them seem likely. These conjectures, viewed in geometric terms, are synthesized to give a sequence of increasingly complex geometric models predicting the combined effects of test anxiety, task difficulty and stamina on performance. It turns out that these models can all be viewed as either cross-sections of, or as examples of, the lip catastrophe of Wasserman (1975). The author would emphasize that this viewpoint arises on a step-by-step basis, out of consideration of specific aspects of particular situations; it is not introduced a priori. Our account includes predictions from the models on three topics: (i) the comparative behaviour of highand low-test-anxious individuals in testing situations, (ii) the relative merits of treatments of test anxiety that concentrate on worry, as opposed to those that focus on emotionality, and (iii) the existence of a hysteresis loop in the relationship between task difficulty and performance. In each case our predictions agree with experimental results. This is not, of course, a full justification of the theories. However, even if some specific details are incorrect, the models are relatively flexible and open to suitable adjustment. The author w o u l d like to thank Don Bass for drawing his attention to the similarity be tween his