To give the earlier comments posted here their due, I think Keith Devlin's argument in the interesting article kindly submitted here is incoherent enough that it is possible even for people who largely agree with Devlin's conclusions to disagree with how he presented his argument. I really like to talk about mathematics education here on Hacker News, because I am a (part-time) mathematics teacher by occupation.[1] It's plain that mathematics education is better if it is really education ("drawing out," by word origin) rather than teaching in the sense of speaking out words that maybe no pupil is listening to. Mathematicians are fond of saying that mathematics is like swimming--you can only learn it by doing.

I can cheerfully damn the Common Core State Standards in Mathematics with the faint praise that they are generally better than the previously existing curriculum frameworks in most states of the United States.[2] I have lived in other countries, and I know that mathematics education can be done far better than it is done in the United States.[3] Keith Devlin is certainly correct that young mathematics learners must learn to work exploratively with challenging problems that cause them to think and wonder about what they are doing rather than merely memorizing thoughtless procedures.

It is also crucially important that elementary school teachers be trained and equipped to teach mathematics well, as lousy mathematics instruction in early childhood is an especially strong factor that keeps many American pupils poor.[4] Right now many families are doomed to low incomes and thus low upward social mobility by how their children are instructed in mathematics in elementary school.

[1] The nonprofit organization that organizes the classes I teach provides some details about the classes.

http://ecae.net/math1/

http://ecae.net/math2/

http://ecae.net/math1/orientation/

[2] http://educationnext.org/files/ednext_20123_Forum.pdf

[3] "Good intentions are not enough" by Richard Askey

http://www.math.wisc.edu/~askey/ask-gian.pdf

Review by Roger Howe of Knowing and Teaching Elementary Mathematics by Liping Ma

http://www.ams.org/notices/199908/rev-howe.pdf

"Word Problems in Russian and America" by Andrei Toom

http://toomandre.com/travel/sweden05/WP-SWEDEN-NEW.pdf

[4] "Racial Equity Requires Teaching Elementary School Teachers More Mathematics" by Patricia Clark Kenschaft

http://www.ams.org/notices/200502/fea-kenschaft.pdf