An article by Skemp (1976) on mathematical understanding describes two different types of "understanding", "relational" understanding which he initially describes simply as "knowing both what to do and why", and "instrumental" understanding which he describes in the first instance as "rules without reasons". In this article, the author highlights the differences in the types of learning by using Skemp's language to make the classifications. She used Skemp's formulation to see whether she would be able to distinguish two types of pupil-learning in practice in order to contrast the behaviour of an instrumental and relational learner in the classroom. (Contains 1 table.)