The Story of an Experiment is another interesting story from Perla (see previous post), which she posted to support her contention that children should not be taught arithmetic, except as connected with real life experiences, until they are at least ten years old. I write about it here, not because I agree with her, since I most emphatically do not, but because the story nonetheless makes some excellent points.
In the early 1930s the superintendent of schools for Manchester, New Hampshire tried an experiment—several experiments, actually. Essentially, he abandoned math as it was taught in the elementary schools, and concentrated instead on language and logic: reading, reasoning, and speaking, with arithmetic introduced only as it came up in the course of the rest of the studies. The results, as he reports them, were spectacular, with the "new curriculum" students far exceeding the abilities of their traditionally-taught age-mates, even in mathematical reasoning, and where they were behind (in basic arithmetic manipulation) they caught up quickly when formal study was introduced in sixth grade.I don't believe for a minute that the secret of their success was in what the students didn't learn, but what they did. Reasoning is a skill, and those who have been taught to think logically can be expected to out-perform those who have not. Before considering that the early teaching of mathematics will "dull and almost chloroform the child's reasoning faculties," one would have to see the accomplishments of those who learned both reasoning and the multiplication tables.
What I suspect is going on here, besides the laudable emphasis on logic and language, and the deliberate connections made between learning and real life, is that the old curriculum was teaching math as if mathematics comprised rote arithmetic skills alone, and these were taught—most likely by teachers with no understanding of the math themselves—with no context, no grounding in real life. Thus the children learned nothing about math, but only how to plug numbers into formulas, and that poorly.
Real learning does not paralyze the brain, but fear does. The errors described in this article are of the same kind and degree as those made by the bright fifth graders John Holt describes in How Children Fail, which he attributes primarily to the fear that comes of seeing math as irrational and incomprehensible—just a collection of magic formulas into which one casts numbers and hopes for the best. In my own experience, I remember being taught what seemed to be a dizzying array of disconnected formulas for finding surface areas and volumes of various solids, none of which would stick in my mind even long enough to make it through a test. Only later, when I made the monumental discovery that math actually could be expected to make sense, did I discover that one could derive most of the formulas with a little thought; then the fear went away and I could even remember most of them. :) Similar fears assailed me in the conversion of temperatures between Fahrenheit and Celsius; I could never keep the formulas straight. Again, a little logic (and the knowledge of a few data points, such as 32°F = 0°C) fixed that problem—but I had been taught not to think, but to apply formulas blindly.
So I'm sure the superintendent's experiment helped the children's mathematical reasoning, not by keeping them away from harmful knowledge, but giving them reasoning skills and by taking away the fear engendered by long hours spent in rote learning. That doesn't mean rote learning is bad, especially at an age when children memorize things as a matter of course. Can it possibly be more harmful to memorize subtraction facts or historical dates than Star Wars characters and commercial jingles? It does mean that memorization should be done in short, frequent doses—that's more effective, as well as more enjoyable—perhaps a few minutes every day, and should be only one small part of the total mathematical experience.
Jonathan is memorizing Scripture; not just short verses, but entire psalms, and when his mother gets around to posting his recitation of Psalm 1 I'll include a link. :) What's more, he's learning the King James Version, full of words and verb forms no longer in his everyday language experience. Not that I have any complaint, because whatever one might say about the KJV's comprehensibility and the accuracy of some of the translation, it's still the most poetic version we have. If he were merely memorizing words it would be of limited value, though even "just words" would establish a foundation he could build on as he matured. But he's not merely memorizing words; he's learning what they mean, and of course it's all in the context of a family life in which the truths are worked out in practical, daily living. In this situation, I find it hard to imagine the learning is harming his developing brain. :)
Frequency, consistency, and context are powerful keys to learning, whatever the subject. So are delight and the absence of fear. If I could teach elementary-age students only arithmetic or logic, I would choose logic, but that's a false dichotomy.
Take time to read the article, it really is enlightening. Note also the shadier side of the superintendent's experiment. Not wanting to deal with complaints from his more articulate, educated parents, he chose for most of his experimental classrooms those "located in districts where not one parent in ten spoke English as his mother tongue. I sent home a notice to the parents and told them about the experiment that we were going to try, and asked any of them who objected to it to speak to me about it. I had no protests."
