You bring up an interesting issue. My opinion is that your son needs to acquire problem-solving skills as well as a foundation of 'math facts' that come from memorization. In this same vein, I use an approach to teaching reading that draws on both the whole language approach and phonics. Both are valuable and neither should be used to the exclusion of the other.

The child who has not memorized the basic math facts is going to take longer and be bogged down unnecessarily as soon as trading(previously called "borrowing") is necessary. I don't want my students to have to stop to figure out every simple addition or subtraction problem that comes up.

For example, I think that all students should memorize their doubles, i.e.,4+4, 5+5,6+6, etc. From here it is an easy leap to a double plus one (4+5) or a double plus two (6+8). Another rote skill I like every student to have on hand is the one for combinations that make ten; this is particularly helpful when they move on to adding columns of numbers.

Of course, there is the argument that in today's world electronic calculators are more accurate and faster than humans. This is true, for complex math problems, but we still want to bring up children who have some framework for judging whether or not an answer is reasonable. After all, we all make mistakes punching in numbers, and we all have to be able to make quick mental calculations.