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Wednesday, August 07, 2013
Countdown to School: Middle School Math, Part Two (or, Getting there is half the fun; come share it with me.*)
Part One is here.
First, a bit of Charlotte Mason catechism.
Why was Charlotte Mason disappointed in the results of her early teaching experiences?
"The children, no doubt, 'got on'––a little; but each one of them had the makings in her of a noble character, of a fine mind, and where was the lever to lift each of these little worlds?"
Why didn't Charlotte Mason think much of just plugging away at long arithmetic problems (among other things)?
"If education is to secure the step-by-step progress of the individual and the race, it must mean something over and above the daily plodding at small tasks which goes by the name."
What should be done during lessons?
"This is the sort of thing that the children should go through, more or less, in every lesson––a tracing of effect from cause, or of cause from effect; a comparing of things to find out wherein they are alike, and wherein they differ; a conclusion as to causes or consequences from certain premises."
How is teaching math like French?
"Supposing, for instance, that by good teaching you secure the child's attention to the verb avoir, he will remember it; that is to say, some infinitely slight growth of brain tissue will record and retain that one French verb. But one verb is nothing; you want the child to learn French, and for this you must not only fix his attention upon each new lesson, but each must be so linked into the last that it is impossible for him to recall one without the other following in its train. The physical effect of such a method appears to be that each new growth of the brain tissue is, so to speak, laid upon the last; that is, to put it figuratively, a certain tract of the brain may be conceived of as being overlaid with French."
What was that again?
"Every Lesson must recall the Last.––Let every lesson gain the child's entire attention, and let each new lesson be so interlaced with the last that the one must recall the other; that again, recalls the one before it, and so on to the beginning."
Second, those who want to teach Charlotte Mason-style math should read "You don't need a composition program," a post at Higher Up and Further In. The subject is different, the principles are much the same. Not expecting more than is reasonable for a child's age, either in attention span or final output (hour-long grade one math, anyone?). Trusting the process through many weeks or months or years of faithful narration, copywork, and dictation from worthy books, and without undue interference (also known as classroom clutter or busywork).
Now ineffective and even harmful curriculums do exist in math, as well as in English and other subjects. We've run into a couple of them ourselves. The Deputy Headmistress recently mentioned a book that her teenager asked her to read aloud because she was having difficulty, but even reading it aloud could not make a good book out of a poor one, and they agreed to drop it. There is an important, but obviously difficult, distinction between needing to persevere with something, even when it's difficult or doesn't seem immediately rewarding, and deciding to modify it or even let it go.
And the testimonies of those who have "taught math Charlotte Mason-style," especially in the upper years when we all seem to turn to the same few textbook publishers, are fewer and farther between than those whose children have become excellent readers and writers. That is a fact. However, lack of recognition doesn't mean it doesn't exist. What of the way of the will and the way of the reason; the three instruments of education (environment, habit, living ideas)? What of students' ability to visualize, as they do in their spelling, their picture study, their narrations? What about simply having more doors opened? What about "not how much does he know, but how much does he care?"
Finally, in a world that is already too utilitarian, too unpoetical, too competitive, analytical and computer-driven, why and how should a "human curriculum" promote mathematics? And what kind of mathematics? Where do our middle-schoolers, somewhere in the transition between elementary mathematics and senior-high algebra and geometry, fit into that vision?
Those are the questions. Stay tuned for an attempt at some answers.
*Movin' Right Along, from The Muppet Movie. See Part One.