Numerical scoring of assessment performance is extremely widespread within education, and yet the use of numbers in this context requires theoretical assumptions which are rarely articulated or tested. Traditional marking systems use numerals in a way that is equivalent to psychological measurement, and hence encounter all of the same problems associated with psychological measurement in terms of the meaning of the numerals used. This paper outlines the theoretical relationship between measurement and marking, and presents an overview of the problems of psychological measurement and their relevance to assessment in education. In particular, the problems associated with aggregating marks to form a final score are discussed. These problems are illustrated by the assessment of a first-year psychology course of 17 components and 1039 students. Simulations based on this case-study show the substantial problems of determining final marks when the issues previously discussed are taken into account. Some alternative approaches to traditional marking procedures are considered, including the involvement of students in pre- and post-test decisions about assessment of performance, and the need for frank discussion with students of the problems of aggregated final scores.