Another one of those story-thus-fars that regular readers can skip.
- I'm working on a book called Singapore Math Figured Out ForParents.
- Singapore Math is the system of math teaching used in that small nation since 1981, in most of the top-performing-in-international-comparison Asian nations, and increasingly in many other countries.
- For about ten years it's leaking slowly into the United States via charter schools (especially for the gifted), homeschoolers, and some of the "college academy" schools that aim at increasing the college enrollment and success of low-income, first generation, and people of color.
- Singapore Math has been partially included in the Common Core standards, and many public school systems are considering moving to it as a way to meet those standards.
- Singapore math is genuinely better than other ways ofteaching math, but it absolutely requires teachers who really know what they're doing, which requires them to be adequately prepared and trained, which, historically, the United States has screwed up nearly every chance it got. So my guess is that my country is going to miss its best chance to become better at math, and this point in history is a spectacularly bad time to do that.
- As part of Singapore Math Figured Out for Parents, I've had to study a great deal of the history of math instruction, especially in the U.S. The main track of the book will be about how parents can make Singapore Math work out for their kids, but for a variety of reasons it seems like a good idea to have a section about how we got into this mess in the first place.
- And so I've been blogging that history, about one sizable chunk per week.
New Math: the first try to fix math instead of avoiding it.
I simply stared. "Why, I'll graduate from high school, Dad. That'll get me into college."
"So it will. Into our State University, or the State Aggie, or State Normal. But, Kip, do you know that they are flunking out 40 per cent of each freshman class?"
"I wouldn't flunk!"
"Perhaps not. But you will if you tackle any serious subject—engineering, or science, or pre-med. You would, that is to say, if your preparation were based on this." He waved a hand at the curriculum.
I felt shocked. "Why, Dad, Center is a swell school." I remembered things they had told us in P.T.A. Auxiliary. "It's run along the latest, most scientific lines, approved by psychologists, and-"
"-and paying excellent salaries," he interrupted, "for a staff highly trained in modern pedagogy. Study projects emphasize practical human problems to orient the child in democratic social living, to fit him for the vital, meaningful tests of adult life in our complex modern culture. Excuse me, son; I've talked with Mr. Hanley. Mr. Hanley is sincere—and to achieve these noble purposes we are spending more per student than is any other state save California and New York."
"Well . . .what's wrong with that?"
"What's a dangling participle?"
I didn't answer. He went on, "Why did Van Buren fail of re-election? How do you extract the cube root of eighty-seven?"
Van Buren had been a president; that was all I remembered. But I could answer the other one. "If you want a cube root, you look in a table in the back of the book."
New Math and Old Myth: Scraping off some of the accumulated barnacles of self-justification
For want of a kindergarten teacher, algebra was lost ...
If the cardinality of the set of stools=2 and is restricted to integers, how do we define the location that is between two stools?
- a rigorous structure in which math would be built up from fundamental axioms, via logic, into complex deep concepts, thus ensuring that mathematically talented students would arrive into university classrooms with a deep understanding of the basis of math itself.
- a mind-broadening freewheeling experience of the many exciting faces of modern mathematics, of how much there was yet to be discovered just for the sheer joy of knowing it, and applied to sciences and human affairs in ways not yet dreamt of.
Standing between two stools is even harder when there's no support
- What no one did: Retrain or replace most of the teachers in the lower grades, at a large cost, and begin New Math with the incoming first, second, and third graders, working your way upward into the higher grades as you obtained more teachers who really understood it. It would also have helped to supply supplementary material and sessions to explain things to parents so that they could stay involved and learn along with their children. This would have cost a great deal, but probably would have worked as well as anything could, given the damage already caused by split focus and developmental mistakes.
- What the SMSG recommended: since the hard way was clearly out of the question, the SMSG suggested that school districts should begin by introducing New Math via high school advanced classes, where bright students could quickly catch up on the pieces they were missing, and where teachers tended to be more mathematically proficient, so that retraining would be easier and quicker. This would allow time to introduce New Math into teacher training curricula in the teacher's colleges. Then the schools could gradually spread the concepts downward (from Grades 10-12 through junior high, middle grades, and primary grads) and outward (from advanced to standard academic to general and remedial classes) as older teachers retired and better-prepared ones moved in. This meant a more or less constant retraining budget for about ten years, working down from 12 to K, giving the maximum time to the less math-oriented lower grade teachers (and allowing some graduates to come back around the cycle and enter the system in elementary education). The estimate was that in about ten years the whole school system could be converted to the new way, with most of the (large) expense falling in years 4-7 of the process.
- What they actually did: For just the cost of replacing the textbooks (and remember, that's money for kickbacks and new football uniforms), hand all the teachers at all levels the new textbooks in the last couple weeks of summer break and tell them to look these over and try to stay a chapter ahead of the students. If any teacher absolutely insists, send them to one of the cheap or free SMSG summer math seminars, from which they can return either as confused wet blankets, or as unpopular know-it-alls, either way helping to ensure nobody else would want to go (and ask for travel money) the next year.