Don Ellicott <ellicott@swnebr.NET> wrote us as follows:
"... By the way, both of my children have or will learn the times tables
I don't think they memorized them by rote. Every so often the older one will explain some concept behind his understanding of the times tables to the other.
" After some reflection I think that is true of most of my "good" math students. Very few of them rely on rote learning. They have many facts memorized
they have retained them and use them because they have some understanding of the why behind the fact"
[RAR now:] As you see, I have made use of some technology to display this message a bit unusually. The occurrence of "but" in these statements lends a flavor to memorization that ought not to be there, as if some excuse were needed when an (otherwise) sensible person memorizes something.
Of course we have all memorized many thousands of English words, even though the technology that in some sense makes this unnecessary has been in place a long time, with Gutenberg's invention, and Noah Webster's, only two of the achievements in this development.
I have known many actors, fine actors whose understanding of their roles on stage will move you to tears, and who have played dozens of parts in their time, and who with each new role -- and even a repeat of an old one played before -- have to spend hours memorizing their parts, parts which they already understand pretty well, but which they will understand even better once they get on stage and are able to try them with the book no longer in their hands.
Nobody has ever asked an actor to memorize a part without understanding it. Nobody has ever asked an actor not to memorize his part. Nobody should ever ask a child to memorize a fact without understanding it. Nobody should ever ask a child not to memorize something.
In all my life I have never had occasion to be sorry I learned something, whether a memorized fact or an intricate theory. With better discipline, self-discipline included but not exclusively, how much more could I have learned, and how much happier could I have been!