The mathematics curriculum in the United Kingdom (UK) has undergone radical changes, placing a particular focus on mental computation. Pupils are not taught written methods of computation until they are able to add and subtract any pair of two digit numbers mentally. Teacher education programmes in the UK have required adaptation to reflect these changes by developing beginning teachers' understanding of "connectedness" of mathematical thinking. Drawing on data from one institution in West London, this article explores the development of connected thinking. Results suggest that, without specific intervention geared to the development of such thinking, trainee teachers' mental mathematics understanding is likely to be at variance with connected mathematics thinking.