Here are some key findings from the NMP:
- When students understand that the brain can change and that effort can make you smarter, they perform better. This is directly at odds with the "either you got it or you don't" attitude toward math ability. Everyone needs to embrace this different way of looking at math. Every teacher and parent should read Intelligence vs. Effort: Stop Reading, Start Trying!
- Procedural fluency, conceptual understanding, and problem solving all buttress each other. Recent "math wars" have pitted those old-school math folks who want to emphasize algorithms and rules against new-age math folks who want to emphasize conceptual understanding. They are both right and wrong. You need to have it all intertwined. It's not a matter of either/or.
- Arguments about whether a classroom should be student centered versus teacher centered lack any foundation in real research. The differences between teacher effectiveness are all about the skill of the teacher--not about the type of classroom she runs.
- There is a tremendous lack of solid research for many aspects of math education. We don't know what really works.