What is mathematics, and why should we teach it ?  And perhaps as we consider these questions, we could begin to understand how we should teach it.  First, I’ll summarise where we were at as few as five years ago and the strong evidence that a serious change in direction was absolutely necessary.   Pedagogies based around slogans, however appealing, misunderstanding of what little research literature of quality there is, and severely misguided strategies for improvement led to a system that was increasing inequity while driving lower performance across the board.  As a nation, albeit in the face of serious social change,  we abandoned things that had worked well enough for many generations.  Now,  informed by a ‘science of learning’ framework we (you!) are (evidently) reversing this decline and moving towards a more robust and fair system with an understanding of why and how people learn.