I've been tutoring maths at primary to A-level in the UK for more than ten years now. In that time, the most critical problem I've seen is when children (usual

I've been tutoring maths at primary to A-level in the UK for more than ten years now. In that time, the most critical problem I've seen is when children (usually in the 12-16 range) see mathematics as a plethora of small, arbitrary techniques to solve specific problems, and can't see that they all are related together under a few key concepts. This means they hit a brick wall when they are assumed to have mastered and internalised the previous techniques. For instance, many fail to connect multiplication, division, addition, subtraction, integers and scale in order to construct an intuitive sense of rational number. This makes further work with rationals an uphill struggle. I've found going back to the beginning and putting together whatever concepts are lacking using proof and demonstration creates an almost digital change in confidence and proficiency: before it's a mystery, after it's simple. I'm pretty sure that the way schools break down mathematics into tiny portions and call each one a separate topic is to blame here. While breaking things up into micro steps is the easiest way to solve a particular mathematical exercise (and important in solving problems), joining things up into a single overarching entity is how you actually understand the subject. So breaking stuff up is really useful within a problem, but on its own doesn't give you the long-term preparation you need, and is inappropriate over an entire curriculum. I think any mathematics curriculum needs to have both, but it's the joined-up approach that's more often lacking in schools. I haven't been able to get the JUMP curriculum (site down?), but I'd really like to see how it deals with these issues.