In this chapter I am going to focus on the pre-cursors to understanding in these two subject domains by drawing on my own work on a programme called Cognitive Acceleration through Science Education at Key Stage 1 ([email protected]). This programme is part of a growing family of cognitive acceleration (CA) programmes developed by Philip Adey and Michael Shayer. The original Cognitive Acceleration through Science Education programme was designed to work with secondary school students and was embedded in the science curriculum. See the book Really Raising Standards (Adey & Shayer, 1994) for full details of that programme and the underlying theory to all their CA programmes.