I've seen this posted so many places so many times that surely there's a market for materials and support for it. Where are they?
http://mathoverflow.net/questions/5074/are-there-elementary-...
...but I too would like to see what you are looking for, at an elementary school age level.
... and I'd also like a pony :-)
It's entirely problem-based; each night the students are assigned a set of about ten problems, and they do the best they can with them. The next day, they meet in groups of twelve with a teacher (more like a facilitator) who leads them in a discussion of how they approached the problems and their solutions. Although the problems themselves are often quite practical, they are designed to illustrate and reveal over time the abstract concepts behind them, and they lead the students towards finding abstractions and generalities as they go.
It's free and publicly available; I recommend downloading them and reading through a few problem sets to see what I mean.
At undergrad level, I love Axler but I haven't found a similar calculus book.
As an example, here's a summary of research-based best practices for teaching Calculus: https://edtechdev.wordpress.com/2014/06/03/calculus/
This sounds suspicious, and I imagine there are differing goals and motivations here. For example, much of math education research also centers around standards and testing.
http://math.stackexchange.com/questions/1040232/can-you-reco...