I doubt that anyone would deny that there is a need for math facts to be memorized. The question is by which means and by what time.
David Ritchie writes: >E.g, a person memorizes their times tables in 5th grade. Assuming the intervening years continue to involve math which calls upon the recall of the memorized facts, I think by 7th grade it has become intuitive.> However, he does not describe the process whereby the memorization took place in 5th grade. I think that Mark Houghton's insight in an earlier post is worth keeping in mind. Mark Houghton wrote: >To stick my own oar in, I think that in a debate about "rote memorization", the focus to the debate should be on the little word "rote", and not the strawman "memorization".> I would say the question is not whether multiplication tables ought to be memorized, but how. It's possible to achieve memorization by different routes. I know my son memorized his times tables by the end of 4th grade. I also know he did that by the process similar to the one described by Kevin Karplus for addition, that is, building on facts already known, rather than by attempting to memorize new facts in isolation., e.g., learning 6x7 by remembering that 6x6=36, and 36+6+42. Eventually, that scaffolding is no longer necessary and it is possible to say 7x6+42 without going through the intermediary steps.
Some seem to argue that memorization works better than understanding for students who are not blessed with high math aptitude. I do not think that it is encroaching old age alone that makes me trust less and less on my memory. How many of us have seen students staring at blue books with a look of panic on their faces because their minds have gone as blank as the pages in their blue books? It's the knowledge that, even if they cannot recall the answer to a specific question right now, they can proceed by retracing some of the steps that calms them down. Those who cannot break down their thought processes into manageable and recallable stages, on the other hand, have the look of people trying to squeeze their memory as if it were a lemon.