There are two main arguments underlying the claims for the value of interactive computer programming used by students to model mathematical ideas. One is concerned with mathematical content, i.e. with mathematics as an object of study. The other is concerned with mathematical activity, i.e. doing mathematics, or ‘Mathematicking’ [1]. Both content and activity include processes and these provide the main links with programming. Examples of processes in the content of mathematics are addition, transformation and integration, and these can be described by instructions in a computer program. Examples of process in the activity are problem‐solving, proof generation and pattern finding which can be described by analogy to program building and debugging. We assess the arguments for programming, in relation to the training of teachers, and describe a pilot‐study in which student teachers with mathematical difficulties were taught the programming language LOGO. Observation of the students, learning the language and using it to manipulate computer models of mathematical ideas, which they had not understood previously, highlights both advantages and disadvantages in this approach. The problem of the representation of mathematical ideas within programming projects is discussed.