Thursday, June 07, 2007

A mathematical year

Noah has completed the Singapore Primary Math program. Since he looked up from playing with blocks at 39 months of age and told me "1, 4, 9 and 16 are all square numbers" I've known this kid has a math brain. Thinking back even earlier, he was a very late talker, and I distinctly remember him counting at 18 or 19 months of age by looking at a group of objects and saying "na, na, na, na, na, na, NAH!" in a rising vocal cadence. He was working out one-to-one correspondence, and the rhythm of mathematical patterns, long before he could talk.

He balked at formal math and basic arithmetic, though. I offered Miquon Math to him at age 5. He was keen for about a week and did two or three dozen pages. That was that. At age 6 he picked up the Miquon Red (2nd) Book and did most of that over the course of a couple of months. Then he ran out of steam in the Blue (3rd) Book. At age 7 1/2 he decided he might like to try Singapore Math. I had him do the placement test and he scored "ready for 2B." I didn't believe the test, ordered 2A, and realized that the test was right, he could do much more than I thought he could -- he was definitely ready for 2B. I ordered it. He dived in ... and was rather underwhelmed. Over the next couple of years he would occasionally get out the 2B or 3A books and do an exercise or two but he wasn't really getting anywhere. He had a lot of perfectionistic anxiety over his formal math work. He would miss the obvious, assuming the questions were complicated, and get angry at himself over his struggles. He clearly had a great mathematical mind but the arithmetic would send him into a tailspin.

I wasn't terribly happy about Noah's relationship with math. Our family has always steered clear of anything grade-levelled, with the sole exception of Singapore Primary Math, because I don't want my kids comparing themselves to external benchmarks. But I really like the Primary Math program and figured I could always explain to the kids that the numerical levels referred to something Singaporean that bore no relationship to Canadian grades. Noah didn't buy it. I knew he was brilliant at math, but he thought he was 'behind,' and even when he felt like doing some math work, he invariably ended up anxious and upset. And the more I just let him be, the 'behinder' he got, and the more demoralized.

Last fall we had an optimistic heart-to-heart about things, and he decided he'd like to do some math to sort of "catch up to the interesting stuff." It's not something I would have encouraged him to commit to, but once again I'm grateful to the SelfDesign program that we were put in a situation where discussing his educational needs and desires in an somewhat organized way was expected. Did he want to do any math bookwork? If so, what? At that point he was technically working in 3B. He wrote into his SelfDesign Learning Plan that he would like to finish the Grade 4 and 5 Singapore levels this academic year. A lofty goal, but I figured if he wanted to do it, he could.

And so, in October he and I settled into a routine of spending 15-20 minutes working on math together most evenings. During the first two or three months there were regular perfectionistic meltdowns. It was obvious the mathematical concepts were easy for him, because when he was relaxed and optimistic, he would blow me away, doing complex multi-step calculations in his head. But there were many many days when something would trigger those perfectionistic meltdowns -- and once he reached that point even the simplest of math was confusing for him. Still, he didn't want to adjust his learning plan. We just kept giving things a fresh start each night. A lot of evenings were fine, but during those first couple of months, there were many that were a struggle. I wondered whether supporting him in this was really the right thing to be doing.

But by December he had covered a lot of material, and meltdowns were becoming less frequent. By February, they'd almost entirely become a thing of the past. He was learning easily and retaining it very well indeed. I can only assume that this is because he has such a rich pre-existing understanding of the basic sense of math and mathematical relationships. Conceptually he was light-years beyond his level of arithmetical ability. By April he had completed his goal for the year. I thought he'd decide to stop doing regular math, but no, he carried on into level 6. "Because the books are purple," he said. "That's the viola colour. I have to do those books." And now he's finished level 6 (Canadian/U.S. Grade 7, more or less). And his favourite part of math is Algebra, so we're moving right on to the Algebra 1 program from Teaching Textbooks. I'm a little concerned about the simplicity of the problems in this program in comparison with Singapore Math, but we're giving it a whirl. So ... from Singapore 3B (Grade 4?) to Grade 8 level math in just over 8 months.

What amazes me is how much easier math has become for him as he's worked through to considerably "harder" levels. What he has gained is not so much arithmetical skill, though he has certainly gained a lot of that. What he's most importantly gained is confidence and optimism, and a wonderful object lesson in the value of plugging away at the mundane in order to gain an affirming and motivating sense of mastery and a launch into more interesting work.


  1. Anonymous5:50 am

    I would get him a "scientific calculator" (if he doesn't already have one) just to play around with. I read on another blog where an unschooled girl simply spent hours on one, just doing her own thing.

  2. That's great!

    And is always so reaffirming to finally see how those glimpses of their understanding as babies actually materialize and become who they truly are as beings.

  3. I think I should print out this post and shove it in the hands of the next moron who, upon hearing we're unschooling, mutters "but what about math??".


  4. I read your blog occasionally. Got the link from some group - I'm not sure if it's the Suzuki Chat group or another. I'm from Singapore. Have 3 children, 13y, 10, 8 .

    Noah is 11 this year? I saw 1996. So did he finish until the 6B showed in your photo?

    6A/B is for 11/12yr old children here in Singapore.

    Why do you find that grade-levelled Singapore Math is acceptable compared to other types of Math?


  5. Hi SAM. The Asian approach to math is something I've come to see a lot of value in. In the west the focus seems to be mostly on memorization of "math facts" and alogrithms at the expense of understanding the mathematical logic beneath those operations. Then occasionally North American curricula will swing wildly towards creative conceptual math, at the expense of computational facility. So there is a "memorization" focus with occasional forays into "creative concepts" but no meeting of the two in a balanced fashion. American children tend to score quite poorly on internationally-normed tests of mathematical skill, and I'm sure the primary math curriculum approach used here is a large part of the cause. Most of the homeschooling math programs available to us here in Canada are American.

    I wanted a math program for my children that took the Asian path. Singapore's old Primary Math 3rd edition program from the 90's is widely available in North America for the homeschool market because I'm not alone in seeing the value in this balanced approach. Because the language of instruction in Singapore is English, of all the Asian curricula, your nation's program was ideal for importing to North America. There are North American publishers of these materials now, since they're no longer in common use in Singapore, but we actually ordered ours around 2000 direct from Singapore, because it was very much less expensive that way.

    I realize that Noah has got well "ahead" in maths. That was not really my intention, but he has been motivated and has found the material more and more interesting as it became more challenging. He finished 6B last month.

    I have enjoyed looking through your blog just now. Thanks for dropping in and leaving a comment!

  6. Yes, I took a look at the book prices - so expensive compared to our local book stores. *hehe*

    The actual Math exams do tend to be more difficult than what those textbooks show though.

    Ah... if we talk about Asian as in the traditional Chinese way, the rote-learning bit would be THE way to learn. *haha* Not so creative. These days, students from China are top scorers in Singapore, and they come not knowing English. You know how they learn? By memorising the English dictionary and by memorising textbooks and essays and good phrases and they score distinctions. And it's easy to them to memorise because they have been trained from very young to memorise lots & lots of classic phrases & Chinese classical peotry. There's probably some good in memorising, yah? Altho' to us, it seems like drudgery. Probably it does train the mind in some way.

    Great that Noah finished the Math syllabus ! Amazing. Most local children finish it around the 1st term of their 6th year in Primary school because the rest of the year would then be used to prepare for the PSLE exams.

    If you need any material from our local bookstore, let me know if I can help!

    I know a homeschooling family friend that uses the local textbooks too. I suppose that's inevitable since even tho they are homeschooled, they have to take the national exams at the end of 6 years.


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