Just to chime in on the subject of drill and rote memorization, the most effective method may well depend on the preferred learning style of the particular child. According to Silverman's theory of visual-spatial learners (which, by her estimate, are about 30% of the student population), VSLs do not learn by drill and repetition, or rote memorization, but by seeing relationships, whereas auditory-sequential learners may need some repetition to reinforce learning and fare much better with rote memorization.
http://www.visualspatial.org/Articles/appendc.pdf (or for a fuller discussion of VSLs and math, see
http://www.visualspatial.org/Articles/mthstrat.pdf and *especially*
http://www.visualspatial.org/Articles/algebra.pdf )
Incidentally, on the local evening news the other night there was a segment about recent improvements in math in a particular local school. The school had switched to Singapore math, which, according to the news story, required less drill and used more visual representations. I know I've seen discussions of that curriculum on these boards, and I admit I don't know anything about it, but I did find the news story interesting.
just my two cents--
