If learning involves wiring changes in the brain perhaps the question is what is the best learning environment for facilitating brain changes? http://www.smh.com.au/tv/show/brain-fitness/brain-fitness-for-kids-20111028-... Stuart
Kerry>
I'm a bit of two minds about drilling. I get how over-drilling can kill any creative spark a student may have for the beauty of math. Having taught it at the undergraduate level (which too often means, "at the middle-school/high-school level"), I've had to endure the scowls and sneers of those who didn't care a lick about math but had to do their calculations anyway, because that was part of the syllabus. However, I can also see how it certain facility with numbers and arithmetic operations is necessary to even begin to deal with math at anything more than a pure computational level. I had a buddy who also taught and was quite proficient in martial arts. In his class, he approached arithmetic drills as he would repetitive practice/warm-up in the martial arts context--do something relatively mundane so often that it becomes automatic, then move on to more sophisticated stuff.
If there is an answer, it's probably the same one that it's always been--adjust the material with the level and goals of the student in mind.
Kerry -- lkmitch@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=lkmitch%40gmail.com>www.kerrymitchellart.com