Research on how to teach math to children - what schools of thought are there about teaching math? Firstly, I'm not sure if this is the best place to post this question because there isn't quite one answer, but in my opinion what proves to be the "best" answer would be a well supported one with lots of information on different approaches. 
I've been tasked with helping to redesign a math curriculum for an enrichment program and I have very few restrictions on what the curriculum should include or how it should flow. The curriculum is meant to be an enrichment curriculum (supplementary to the existing one here in Ontario). 
I wanted to find some resources on proven and effective ways to design and teach math so that students have a deeper, more rigorous and more intuitive understanding of math - an approach that prepares them to tackle math abstractly and ultimately prepares them for higher level math. The curriculum starts at grade 4 and continues on to grade 11.

I would design a curriculum where you teach students to love math and realize its potential. Show them early on where it hides in nature and how it describes the world around us. Don't make it seem like the chore and burden most schools do
For some useful techniques, there is an article on how to improve teaching methods so that kids learn better and it sticks with them. Here
