Interpreting graphically displayed data is an important life skill. This thesis examines some of the problems that 14 and 15 year olds encounter when interpreting trends in cartesian graphs. A survey of errors made by 144 pupils is discussed, which shows that two of the most difficult aspects of graph work are interpreting changes in gradients, and inter-relating the graph with its context. A detailed analysis of individual pupils interpretations of changes in gradients shows that pupils conceptions of gradient can be classified according to whether they have an 'iconic' or an 'analytical' origin. iconic descriptions are concerned with the structure, shape or position of the curve, whereas analytical descriptions are concerned with more abstract notions, such as the angle or steepness of the curve, and rate of increase. The results indicate that the occurrence of different kinds of conceptions is influenced by both the form of the graph and its context. In another study, the pupils were given two structurally isomorphic graph interpretation tasks. The results of this investigation also show that the context of a graph in relation to its structural form, has a profound influence upon the way that pupils interpret it. Interpretations are described, in which the influence of metaphors, knowledge from everyday life experience and anthropomorphic reactions can be seen. Pictorial accounts show how conceptions from some of these sources are brought into the pupils interpretations.