I have been researching this for a couple of years and can recommend a couple of books that I thought were particularly good: * Good questions for math teachin

I have been researching this for a couple of years and can recommend a couple of books that I thought were particularly good: * Good questions for math teaching (http://amzn.com/0941355519 http://amzn.com/0941355519) * Young Mathematicians at Work (http://amzn.com/032500353X http://amzn.com/032500353X) * Number Sense Routines (http://amzn.com/1571107908 http://amzn.com/1571107908) * Dr Wright's Kitchen Table Math book (there are three) - http://amzn.com/0982921128 http://amzn.com/0982921128 I haven't finished these next two, but they look promising: * Fostering Geometric Thinking (http://amzn.com/0325011486 http://amzn.com/0325011486) * Fostering Algebraic Thinking (http://amzn.com/0325001545 http://amzn.com/0325001545) I also like the approach of the Art of Problem Solving curriculum, though it doesn't currently have elementary school material. I haven't used it on my own kids yet because they're still too young, but I did buy the set and I think it looks good. If you read "Good Questions for Math Teaching" you will probably modify the way the problems are presented to make them more open-ended, but I like that topics are introduced with a problem that is later explained, instead of explaining then drilling. http://www.artofproblemsolving.com/Store/curriculum.php http://www.artofproblemsolving.com/Store/curriculum.php Finally, I thought that this online course was a nice introduction to the approach. It's a pretty short course, but I just put the audio on an mp3 player so I could listen while working on other things and there were only a couple of places where I couldn't tell what was happening in the video. * https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about https://class.stanford.edu/courses/Education/EDUC115N/How_to... For a more general book about early childhood education, I really liked * "Engaging Children's Minds - the Project Approach" (http://amzn.com/1567505015 http://amzn.com/1567505015) * Making Thinking Visible (http://amzn.com/047091551X http://amzn.com/047091551X) * Learning Intelligence: Cognitive acceleration...(http://amzn.com/0335211364 http://amzn.com/0335211364) Sadly, most of these books are pretty pricey for the page count, but the material I thought was quite good. If you were to get only two, I'd say go with "Young Mathematicians at Work" and "Good Questions for Math Teaching" because they will probably give you the quickest jump start, especially if you can get the "How to Learn Math" course. If you're interested in where my evidence for the approach outlined here comes from, my main sources are the following books: * Effectiveness In Learning (cognitive load theory) http://amzn.com/0787977284 http://amzn.com/0787977284 * Visible Learning (synthesis of 800 meta-analyses) - http://amzn.com/0415476186 http://amzn.com/0415476186 Edited because I put some of them in the wrong spots and forgot links...