Monday, January 14, 2013

From the archives: Multiplication Without Vexation, or, Charlotte Mason and Math

First posted February 2008.

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

Last weekend some local CMers (Coffeemamma, Birdy, PirateMum and I) got together and talked shop--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 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. She's also developing a good writer's voice.

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.

4 comments:

Jeanne said...

So how do we come up with a list of these books? Not 'Living maths' books, but books like the ones you're describing here? I really like Clifford Pickover's books, but I don't like his worldview. Which ones do you particularly recommend?

Mama Squirrel said...

Wow, Pickover sure has a lot of interesting titles! Reminds me of that song, "Why should the devil have all the good music?"--you could redo it as "Why should the atheists write all the good math books?"

But no, I'm not going to be the one to come up with a list. I'm still too much on the learning end.

Jeanne said...

How about a favourite one or two then? Apart from the Gallileo book? Science bios are much easier to list, I think.

Mama Squirrel said...

Well, I like the Cwiklik bio of Einstein that Ambleside uses in Year 6; it's a bit repetitive in some places, but it does try to communicate an idea of what Einstein was actually studying, and that's not easy to do. The book actually points that out, that even when he got really popular, most people still didn't have a clue why his work was important, so the media tried to focus on his personality quirks rather than his discoveries.

There's also a little book by Isaac Asimov called How Did We Find Out About Electricity? I read it with my oldest years ago, and I remember being impressed by the way that Asimov worked the different scientists' stories together.

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