Writing at a Psychology Today blog, Peter Gray describes a study conducted in the late 1920s:

At the beginning of their sixth grade year, the children in the experimental classes, who had not been taught any arithmetic, performed much better than those in the traditional classes on story problems that could be solved by common sense and a general understanding of numbers and measurement. Of course, at the beginning of sixth grade, those in the experimental classes performed worse on the standard school arithmetic tests, where the problems were set up in the usual school manner and could be solved simply by applying the rote-learned algorithms. But

by the end of sixth grade those in the experimental classes had completely caught up on this and were still way ahead of the others on story problems.(emphasis mine.)

Barring significant interest and fascination by a young child in formal,
on-paper, abstractly-worked mathematics study, in which case I'd be in favor of letting the child study as much and as fast as they wanted to, there seems to be evidence that *waiting* with text-book-based arithmetic study may be a better way to go.

Anecdotal evidence from friends of mine bears this out. One friend, a mathematics major herself, has shared with me that all the basic math necessary for success in Algebra can be taught within a year or two by an interested and attentive student. (She'll correct me in the comments if I've gotten that anecdote wrong.) Another friend does no formal math with her children until the middle school years, when they start right in with Algebra.

I'm seeing signs of this with Sparkle Kitty (age 7 as of this writing). We don't do much paper math yet.* But she knows how many quarters go into a dollar, and how many dimes. We play with fractions in the kitchen. She *conceptually* understands multiplication, addition, subtraction, and division. She is not scared of numbers; they are useful tools to her.

Contrast her experience with mine at the same age. At age seven, I was terrified of math. I got sick to my stomach when faced with the dreaded "timed tests" of second grade.** I often froze up and didn't finish my sheet. I developed a "*I can't*" attitude towards math, something that continued to haunt me well into my third year of college. It wasn't until Middle School that I eventually did learn most of my basic math facts. It wasn't until I was working in a Architecture office that I figured out that I'm perfectly capable of *thinking mathematically, *and I learned *that* by using math in a real-world, immediately-useful, on-the-job setting, not in a classroom.

A couple of you are saying, "But my kid is 9 and he *loves* math!" Go back to the first paragraph after the indented quote from the article: if a kid loves it, let them at it. But I'm becoming convinced that, just as is the case with reading instruction, there's absolutely no developmental magic to starting formal, structured, sequenced instruction in Kindergarten or First Grade. For some kids, maybe even many kids, there is much benefit to simply *waiting*.

I'd rather have a kid who didn't do a single math problem on paper until they were eleven years old than one who spends a lifetime thinking they are mentally deficient and are incapable of mathematical work because of early failures in symbolic thinking.

*I'm lying. We don't do *any* paper math yet.

**In which circle of Hell do timed tests belong?

I don't know in which Circle of Hell timed math tests belong, but it could be fun to think up a good contrapasso for the people who administer them.

Posted by: Bethany | 25 March 2010 at 01:30 PM

Jenny I couldn't agree more and I was a kid who loved math, math problems and actually even like timed tests but that's cause I was good at them and really the pits with other stuff. In my head I go back and forth with this idea about most/all academic subjects and wonder if I will ever figure out what is the right thing to do.

Posted by: Ageena Hass | 25 March 2010 at 02:13 PM

Hello Elephant's Child:

It's true that children will "do math" without using a formal curriculum. Just like some children learn how to read without being "taught how to read."

(Mostly because the parents read aloud to them.)

I would rather introduce Math at a later age, when the child knows how to read well.

Now if only I could learn how not to hate long division. . .

Posted by: Otherjane | 25 March 2010 at 03:10 PM

This is really great news, and I thank you for it. :) There's so much good news on the blogosphere this week! :D

I had a conversation just this morning with my 8-year-old about arithmetic. She says she doesn't like it, then she turns around and uses it--none too badly--for her computer game. I think we'll leave the book sit on the end of the school table for awhile, and let off on the "work." :P

As for timed tests: I think they were actually the teeth in the mouth around Cassius. Wow. I hate timed tests so much.

Posted by: Gauntlets | 25 March 2010 at 03:33 PM

EC, if I remember correctly, the claim was that all arithmetic could be taught in 120 hours, assuming you've got a 12- or 14-yr-old kid who's lived with real math, measured things, tells time, uses money, played board games, baked, etc. I think it would be unreasonable to expect that the 120 hours could be jammed into one month of math instruction.

Mrs Gauntlet, my girls (like yours) "didn't like math." They were BAD at it, doncha know. And yet, for all their moaning about math and their claims of ineptitude, they would go out into the real world for part-time jobs or volunteer work (oh, at age 14-17, say) and come home grousing to no end about the stupidheaded kids who worked with them. They couldn't make change. They couldn't figure up how much four 75-cent pops and three $3 hamburgers cost unless they hauled out the calculator. And when my girls would complain and complain and complain to me about these dunderheads who were getting A's at the public school, it was more than I could do to sympathize with my daughters over the sad state of public education. I just laughed at them for not realizing that they (not their co-workers) were the ones who were GOOD at math.

Posted by: Susan G | 25 March 2010 at 04:26 PM

I have so enjoyed reading these posts on your blog today and Jane's blog the past few days.

BTW-- I finally realized just this afternoon why the name of your blog is what it is. Duh. I can't believe I'd never READ Kipling before!

Posted by: Cate Olson | 25 March 2010 at 04:50 PM