Monday, February 04, 2008

Multiplication without vexation (CM and Math)

Multiplication is vexation,
Division is as bad,
The rule of three doth puzzle me,
And fractions drive me mad.
- Author unidentified

Last weekend a few of us (Coffeemamma, PirateMum, Birdie and I) got together and talked some CM--mostly math. How do we apply Charlotte Mason's ideas to our math teaching?--especially when "what Charlotte said" ranges from saying that she had no special insight into teaching mathematics, to making very pointed comments about the overemphasis on pure mathematics in the English public school system, to setting out bean exercises, and recommending domino games for flittery little girls.

I mentioned how the first chapter of Galileo and the Magic Numbers has such a wonderful description of Galileo being taught about triangle numbers by his new tutor, using a bag of white pebbles; and how (when we read the book, usually in about grade 3) I try to incorporate the Miquon Math lessons on triangle numbers into our Galileo readings. That's one connection I've found between "everyday math" and people who've done wonderful things with numbers and equations--and the fact that this part of the story is about a young boy makes it even more relevant. But I wish there were more opportunities like that...

Afterwards I had time to think about some of what we talked about, and it occurred to me that Charlotte Mason herself--and I could have this wrong, I'm just positing something here--may not have been that different from many of us in her attitude toward mathematics. That is, although we know she was very well versed in literature, history, and botany, she may have been limited either by education or simply by a slight lack of interest in things mathematical.

That is not to say that I don't think she had some excellent insights about math teaching: for instance stressing problem-solving skills rather than doing rows of repetitive sums; and having children work through things themselves (such as writing out their own times table chart) rather than giving them pre-made manipulatives and charts that take the teeth out of the learning experience. However, doesn't this still apply mostly to arithmetic rather than to the larger world/universe of mathematics?

We know that she enjoyed keeping up with the latest scientific and archaelogical discoveries (and encouraged her students in those areas), but is there any evidence that she had as much enthusiasm for mathematics (and, by extension, physics)? Was she interested in what Einstein was doing during her lifetime?

And if Charlotte Mason felt like this, must this then be typical of a CM education?

Some might say yes: you can't be everything, and one must admit that the classical loop into which CM fits seems to encourage literature and history majors (or perhaps entomologists and ornithologists) rather than future mathematicians and physicists. Perhaps parents whose own bent is in those directions will naturally find themselves drawn more to other styles of homeschooling. Don't forget, though, that CM's own high school students studied three branches of mathematics at once--the subject was not neglected, although it would be interesting to see whether it was handled with as much imagination and insight as the other courses were. It would be worthwhile to search through the online Parent's Review articles from that time (mostly written by CM's colleagues) and see what their collective approach was.

On the other hand...I would say no. The sense of wonder that Charlotte Mason encouraged can be brought into mathematics as well; and a CM education in general can benefit "non-typical" CM students whose first love is not history. I say that because I have such a student. The education that she received at home benefitted her by teaching her that the world is "so full of a number of things" and that she was capable of learning about whatever interested her. Unfortunately, that doesn't particularly include history; but it does include chemistry and aesthetics and computer systems and a number of other things.

If we want to teach mathematics or at least arithmetic CM-style, are we limited to either picture-book-math or Victorian arithmetic textbooks? No, I wouldn't want to put such limits on what CM math teaching is when there are so many good approaches out there (besides some of the public-school math mess). I would say that any approach claiming to be CM-friendly must balance the fun picture book side of things with a cumulative teaching of solid arithmetic skills, not too heavy on re-inventing every wheel but still allowing students to reason things out. I would definitely recommend what my own school days missed completely: books of math history and biographies of mathematicians; true accounts of significant developments; readable, interesting stories for younger children comparable to the wonderful books that are out there about Marie Curie, Thomas Edison and Galileo. And for the upper years, not just puzzles, which mostly just irritate the less mathematical of us; but any kind of "popular mathematics" writing that would give us a sense of what and why it's all about. The weekend newspaper book sections often review such books--the kind written for the general public. Good libraries will have a shelf of them too, or can get them for you. There really are books out there that are written to make what happened (and what's happening) in mathematics accessible and even interesting for the masses of us who graduated feeling rather clueless about higher math (and not caring much if we did).

Maybe I'm wrong about Charlotte Mason's interest (or disinterest) in what mathematicians were up to. I wouldn't have blamed her, either, if all she ever heard about in math class was theorems! But I think we can use her larger philosophy, and her methods, to open up an even bigger world for today's students. And perhaps we'll have a little less vexation for the next generation.


Lisa said...

I love and think CM would have approved of many of the great resources listed there. Maybe if she would have had these kinds of materials available she would have developed more of a passion for the subject and written more about it.

Betty Canuck said...

It was a pleasure to meet with you and the other ladies. A really encouraging meeting for me.

You've done some good thinking on the subject. I still feel to 'new' to speak with any authority on the "What would Charlotte say" questions.

I chuckled out loud because... well, I'm a History, English and Psychology triple major and so I felt 'pegged' by your one thought about the appeal of Charlotte Mason style.

Anyways, I don't have any more to add on topic but thanks again for the meeting. And your grammatical post just had me giggling!

Katie said...

13yodd and I have been having math conversations for the last few weeks, trying to figure out what she wants in the way of math, and what you said fits into her thoughts exactly. She has read many of the books recommended at, and she told me that the reason she keeps plodding along in the math textbook (we used Scott Foresman and now she has gone into the first University of Chicago Mathematics Project textbook) is because of the promise of "exciting math" down the road. Even as I tell her it is not necessary in her father's and my eyes that she make it to calculus by her senior year of high school, she still has that goal. And she doesn't have as much precision in math as she probably should, but she finds it exciting to think of the exploration possible at the higher levels. That keeps her motivated. (No one has ever relegated her to the "regular classes," so she supposes she can go as far as her interest takes her.) I can't wait to see how this pans out in the next several years. She is going to have to work really hard and make herself attend in order to get through the levels she wants to get through. And she might do it, too.

But she will be doing it without me. I am completely un-math-oriented, and have reached the limit of what I can teach. Now I am pointing her to tutors and classes!

(Sorry for writing a book in your comments section! Your post really lined up with some thoughts I have been having-- a sort of wonder at the effectiveness of living math. Who knew?)