Free At LastAugust 21, 2010
If you want to see someone really committed to freedom in education, check out Free At Last: The Sudbury Valley School, which you can read online at the link, if you want. I went there for the first chapter, on teaching arithmetic, but stayed for the later chapters.
But read that first chapter, with the surprise at the end. Consider how amazing it is that students could learn six years of arithmetic in twenty contact hours, and then consider how it’s not so surprising after all. In fact, consider the research (both these quotes from a larger article, available here):
… early childhood may simply be an inefficient period in which to try to teach skills that can be relatively quickly learned in adolescence.
— Prime Time for Education: Early Childhood or Adolescence? by William D. Rohwer, Jr., Harvard Educational Review, Vol. 41, No. 3, August 1971, page 316, from the summary.
Several groups of important investigations on the teaching of arithmetic have contributed findings that have led schools to make changes in the organization of the curriculum. One group of studies dealt with the effect of postponing or deferring the teaching of arithmetic in the primary grades. Included in this group are the studies by Ballard in 1912, Taylor in 1916, Wilson in 1930, and Benezet in 1935-36. In these studies formal arithmetic instruction was withheld in one group and administered as usual in another group. At the end of the experimental period, the comparative achievements of the two groups were measured. In each case the experimenter recommended the postponement of “formal” arithmetic – Ballard for two years or the age of seven, Taylor for one year, Wilson for two years, and Benezet until grade 5.
On the basis of these and other studies the plan of eliminating formal arithmetic instruction from grades one and two, sometimes also grade three, has been adopted by a considerable number of school systems. In some systems there is not even an approved plan of informal or incidental arithmetic. Such a procedure fails to recognize certain very important facts about the studies referred to above. A careful reading of the reports of these four experiments shows that while formal practice on computational processes was postponed in the experimental groups, there was a great deal of use made in these classes of various kinds of activities, games, projects, and social situations through which the child was brought into contact with numbers and given the opportunity to use them informally in meaningful ways. It is especially clear in the studies by Wilson and Benezet that arithmetic was not in fact postponed at all. It is evident that what happened in these two studies was that computational arithmetic was replaced by what I called earlier in this paper, social arithmetic. In each study the plan was to emphasize number meanings, to develop an understanding of the ways in which number functions in the daily lives of children both in and out of school, and to develop what is called number “readiness” for the more formal work to follow …
— Mathematics Teacher, Volume 31, October, 1938, pages 287-292, article “Deferred Arithmetic” by Leo J. Brueckner, from a paper read at the annual meeting of the National Council of Teachers of Mathematics in Atlantic City, J. J., Feb. 26, 1938.
[1938! We’ve been working on this problem of how to teach math for so long, and there have been so many examples of places that have solved it (check out UCDS or PSCS if you live in Seattle. They have solved the problem, as far as I’m concerned), and we can’t as a whole, get it together!]
Notice that those kids who learned arithmetic at Sudbury Valley probably already had a wide experience with non-formal arithmetic. When they wanted it, they learned the formal part in a flash. And indeed, that’s the way it should go: exposure, play, experience, “number readiness,” with formality following when the child is ready. According to most research I’ve seen, [for example], this is usually around 9-12 years of age, though it can come a few years earlier or later.
And that, as I read chapters following, is the amazing, courageous thing about Sudbury Valley: they let the motivation come from the students, and when it comes, they take it seriously. It’s an amazing thing to really trust in people like this. And there are ways to mess it up. If you go in naively and say, “let’s just let kids do their thing,” and do nothing else, it can fail pretty dramatically. There’s more happening: the deal-making, the environment. This is artfully artless teaching. They make it look easy, when really it’s simple. Not the same thing.