Sunday, January 23, 2011

Reforming Math 2

(Continuing from Reforming Math 1.)

Here's my second e-mail to the Head of School at Natural Friends:

In this e-mail I will describe some of the issues I've noticed with NF math.

Here's a  simple, and commonly agreed on, description of the goals of elementary school math: by the end of elementary school, students should be able to perform the basic operations (addition, subtraction, multiplication, division) on the basic types of numbers (whole numbers, fractions, decimals, percents.)  I've seen this as a description of what kids should know by the end of 5th grade, so NF actually has an extra year to get it done.

Does Natural Friends achieve this rock-bottom math education?  Not even close.

As an example, consider fractions.  When Older Daughter was attending NF fifth grade, I started tutoring her at home using Singapore Math.  I thought I would begin with something familiar to her, so we started with fractions.  The very first problem in Singapore Math was "write 7 divided by 4 as a fraction".  To my amazement, Older Daughter had no idea how to do this, after weeks of "covering" fractions at NF.

One of the basic operations is division.  The only reason Older Daughter knows how to divide one fraction by another is because I taught her myself.  The question was never even addressed at Natural Friends.  Again, this is considered a basic piece of elementary school math and it will be needed for 7th grade pre-algebra.  At Friends Omphalos, it's just assumed that 7th-graders know how to divide one fraction by another.

To oversimplify, the goal of progressive math education is that kids should like and be interested in learning about math.  The goal of traditional math education is that kids should have basic math skills.  Neither of these goals is being met at NF.  NF kids routinely say they don't like math, and they can't perform basic operations either.

I noticed when Older Daughter was at NF that math is taught with words rather than numbers.  That is, there's a lot of discussion about how to do things, and the homework often involved writing explanatory paragraphs (!).  But math is, among other things, a language, and it must be learned on its own terms.  You wouldn't teach a Spanish class entirely in English, right?  Similarly, you can't teach math without spending a great deal of time writing numbers, symbols, and equations.

Something must be done.  NF needs a coherent math curriculum, and then you need to follow through.  You need to make sure that kids at the end of each grade have attained the basic skills appropriate to that grade.

I have heard of several cases of families leaving NF because of the sorry math teaching.  If you want to increase enrollment at NF, you need to improve math.


  1. Great letters, FedUpMom. I can't wait to see what response you get.

    At the same time, though, part of me resists the idea that "they need to know this stuff because they'll be expected to know it next year." I agree that the skills you describe are important, and I understand that you're forced to deal with the expectations of the middle school choices that you have. But it seems a shame that so much math instruction is forced on kids, and so much math anxiety created, for no better reason than that "you'll need to know it next year."

    I've always been struck by the disparity between what we expect high school seniors to know about math and what adult Americans actually know about math. Virtually everyone in America gets taught the skills you describe (and much more), but I'd be reluctant to bet any money on whether most adults could divide a percentage by a percentage. And that's just the elementary school expectation -- never mind whether anyone can use the quadratic equation, or sines and cosines.

    I don't blame schools for that; I just think people are unlikely to retain skills that they are seldom called upon to use. But it does make me wonder about the degree to which we compel kids to spend huge chunks of their childhood learning those skills (or struggling with them), often at the expense of other subjects that are arguably just as important or more (like the humanities!).

    I'm not denying that a certain amount of "numeracy" is an important part of being well-educated. (If it were up to me, I'd put more emphasis on basic probability and statistics, and less on trigonometry and advanced algebra.) I just wish there was a more effective and less painful way of trying to get there than marching the kids lockstep through a pretty arbitrary set of year-by-year expectations. My impression is that this is an area where homeschooling has a real advantage, because of the opportunities it provides to treat each child individually. (Maybe you're demonstrating that with your use of Singapore Math!)

  2. Chris, in this case I really don't mind the expectations. They seem reasonable to me, and if the subject is taught well, it doesn't have to be a painful process at all. It can be enjoyable.

    Even if my kids don't go into a math-heavy career, they should at least be able to handle their finances intelligently. They'll need these math skills in order to do that.

  3. It's a bit similar to saying that kids should be reading fluently by 3d grade. It sounds arbitrary, and I guess it is, but I'm OK with it. It's a necessary skill.

  4. I can't argue with that very much, though I do think a third-grader is much more likely to use reading in her everyday life than a fifth-grader is to use division by fractions. But I agree that if it's taught well, it can be enjoyable and not painful. Unfortunately, that's a big "if," and keeping it enjoyable doesn't seem to be a high priority.

    I do agree, too, that constructivist math seems just as liable as old-fashioned math to make the kids miserable. I'd be curious to hear more about why the kids at your daughter's school don't like math. I see the same thing happening with my daughters, which is why I wonder whether they'd just be better off if they waited until they were a little older to take some of these concepts on.

    (I'm partly dreading the day when they start to read real literature for school, for similar reasons. I sometimes think cultural conservatives ought to strongly support sex education: you know the schools would find a way to make sex boring and aversive.)

  5. HA! I have often said to myself, "these people could turn a 14-year-old boy off to sex."

    With math, I don't think the problem is that the kids aren't old enough; I think it's just taught unbelievably badly. The curriculum stinks, the teachers don't like or understand math themselves, and the whole scene is just a mess.