This relationship between the themes under analysis in the chapter by Corcoran and Pepperell, and the dimensions of MKT is clear and to be expected in any study into learning to teach mathematics. Furthermore, the authors provide a new perspective on implementing the KQ. They note how participants felt somewhat constrained by a perceived linearity of the four dimensions, and so resequenced the components in a way that was more consistent with their experience of Lesson Study. Hence, taking the pupils’ learning as their starting point, they first gave prominence to Contingency. This naturally led on to the Connection dimension as they reflected on particular cases, and ultimately to the Transformation and Foundation dimensions. The point is not to advocate one particular sequence over another, but to illustrate the legitimacy of reordering of the KQ dimensions in order to focus on and improve MKT.