ultimately I want a context where my son can have the freedom to discover his own methods and traditional math isn't it.
I think this is a good point, depending on what "traditional" means. Still, I loathe EM as implemented in our district. It's extremely dumbed down, and I see a lot of the failings discussed in the video and mentioned by Val.
I think Singapore Math has a lot of strengths, and if it is fully implemented there is a fair amount of self-directed investigation that happens, even though it is also a straightforward mastery curriculum overall. SM supplies plenty of problem solving practice, including many problems that are not at all cookie-cutter in design and require some thought.
I think that a focus on investigating number relationships and arithmetical methods can be excessive, and that's part of what I see wrong with Everyday Math for a math-gifted student. For instance, DS was forced to "explore" number bonds ad infinitum, and didn't get anything at all from it. I certainly wouldn't want him taught rote, inflexible problem-solving skills, but for some of the basic arithmetic I don't see the harm in building a strong skill-based foundation and moving on to the good stuff.
In addition, I had the sad experience of having to tell DS7 to ignore all attempts to teach him mental math strategies at school. He has always been good at mental math, and SM honed that further with an almost uniformly straightforward approach. Attempts to teach mental math strategies the EM way at his school really messed him up and slowed him down at one point.
Maybe these programs are good for more average children, but I can't recommend EM to anyone for use with a talented math student.
