Reddit mentions of Visible Learning

Piaget has a good theory for cognitive development which proves to be quite valid when applied to learning. Visible learning and their further publications ground that up nicely in science. People who are 'good at math' often have developed up to their "formal operational stage" earlier than others, quite simply, and teaching maths that are at the appropriate level of cognitive development will yield the best results. Not everyone develops the same, so just like walking and talking, ease in doing higher maths might set in later on.

This means that some people, who only get to that stage in their late teens and truly develop it in their early 20's, will have been a bit worse at math than others - often identifying themselves with being bad at it, feeling sorry for themselves over it, and overall despising the stuff. This in turn leads to less interest in developing this part of their mind, making them even worse off. To a similar extent, this is true at every step of Piaget's cognitive ladder, so those who skipped early, well... even if only one stage was late, the rest might feel sluggish and forced, like an old injury nagging at your pride.

TL;DR Good news/bad news: in their 20's, everyone is on equal footing, very capable of learning it all, but few are still in school and most have willingly locked themselves out of learning math.

If you're interested in quant stuff, there's a researcher here in Aus/NZ named John Hattie who published a compilation of meta-analyses (http://www.amazon.com/Visible-Learning-Synthesis-Meta-Analyses-Achievement/dp/0415476186) related to educational achievement. There are certain strategies (as well as factors outside the teacher's control, e.g. SES) that are shown with robust evidence to be more effective at advancing the student's learning. His website and supplementary resources also show you how to calculate effect sizes for your own classroom interventions.

I realise this isn't as touchy-feely as some of the other answers OP is getting, but I saw the words quantitative and "good teacher" and immediately thought some of you might be in to this.

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These are all good books to start with ^^

In terms of just educational reforms Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement may be a jumping off point for you. It's fairly US-centric but there is information from a lot of other countries (in particular, I believe, New Zealand).