If you think primary and secondary school math education blows chunks, you’re not alone, and you wouldn’t have been 40 years ago either.  Improving basic mathematics education was a really hard problem, is a really hard problem, and will continue to be… a really hard problem.  And somewhat surprisingly the teachers and professors who lead reform have often lead us astray.  In the 60s, the fashionable reform was called the New Math, promising to modernize the curriculum for the nuclear age through early introduction of set theoretic terminology and organization around “unifying structures” a la Bourbaki.  Perhaps the most famous parody was Tom Lehrer’s song, New Math.

But without a doubt, the most important critique of the New Math was Morris Kline’s 1973 book Why Johnny Can’t Add, which is now available for free online.  In it, Kline eviscerates the New Math with razor sharp wit and then proceeds to expertly dissect the what, why, wherefore and hows of the movement.  His writing turns what could have been an exercise in dull litany into a bona fide page turner.  For instance,

If someone argues that the earth turns from east to west and another that the earth turns from west to east, one cannot compromise, however well-meaning one may be, by saying that the truth lies between these alternatives.

Kline makes (at least) three important arguments in his book.  First and most proximate, he explains why abstraction is a bad direction for reforming grade school mathematics.  Second, he pushes the discussion beyond a conservative reaction, equally condemning traditional practices of rote memorization.  Third, he pushes the discussion beyond curricular reform, emphasizing the lack of attention paid to pedagogy.  That is, Kline reminds us that the question is often not what to teach, but how.

Throughout the book Kline is a sharp critic of context-free mathematics, condemning the majority of professional mathematicians who have little knowledge of or interest in the applications and historical roots of mathematics.  From personal experience I know that his descriptions of some mathematicians’ open disdain for applications are not exaggerations or isolated cases.  Ultimately, Kline portrays a vision of scholarship at odds with the practices of modern research universities.

Moreover, the breadth and openness of mind desired of the ideal scholar would require that he also see mathematics from the nonmathematician’s point of view so that he can appreciate the attitudes and problems of young people.  To put the matter crudely, the proper mathematical scholar must not only know his stuff but also know whom he is stuffing.  We need, in other words, professors of broad scholarship and educational insight as opposed to the self-centered, narrow researcher.

(Kline further takes up the topic of college education in another book, Why the Professor Can’t Teach, which I’ve just started reading.)

The best quality of Kline’s book is the way in which it cuts to the essential issues, leaving the reader with more than just a topical critique.  His occasional lapse of judgement or silly stance viewed with 20/20 hindsight can more than be forgiven.  The core argument coheres, and never seems to require revision or update.  If you feel strongly about education, or teach for a living (wink, wink, nudge, nudge academics) then this is a must read.  “Those who cannot remember the past are condemned to repeat it.”