Sunday, April 06, 2008

Backwards 9's

This is a page of math Fiona did not too long ago. I love it for a few reasons. First of all, I'm proud of what she understands about math. I'm delighted that she enjoys putting it down on paper and has no hangups about workbooks -- they're just fun the way crossword puzzles might be for adults. But I also love this example because it puts an unschooling spin on what could be a pretty conventional schoolish program.

I mean, look at this ... here she is doing addition and subtraction easily and correctly, with an understanding of place value, but she's still writing 9's backwards. And about half of her 3's too, and occasional 6's and 4's as well, though you don't see those here. For Fiona a solid vibrant foundation in math has nothing to do with knowing how to make tidy numerals that point in the right direction.

I remember Sophie at age 7, doing multi-digit multiplication, and incorporating fantastic mental math shortcuts that demonstrated a firm mastery of place value, but still occasionally writing "13" as "31" and other such incongruous mistakes.

Fortunately my kids don't read curriculum-writers' scope and sequence. They don't know that multi-digit multiplication shouldn't be taught until they've sorted out whether twenty-four is written as 24 or 42. They don't know that work with parentheses and multiplication should wait until after you have learned to print a numeral 9 correctly.

I love these little incongruities. They're like the little stories I can sometimes read outside, the ones made of a bicycle left near a copse of trees, a discarded jacket, a pile of special stones, a stick in the ground. And one sandal. How odd. Where is the other one? What happened here?

These little trails of clues are evidence of my kids charting their own unique course, led by interest, veering off in unexpected directions, finding unusual ways of looking at things and moving where they decide they should. The backwards 9's are evidence that my kids are going at things their own way, according to their agenda.


  1. I love that page you posted, too. For the same reasons you listed... It seems that children in school are stunted by largely irrelevant details (like getting those nines turned around) so that meaningful learning doesn't even have room to occur. Fiona knows it's a nine, so it's a nine, that's how I look at it. Occasionally William (when he writes) still turns b's and d's around. But he knows what he means, so I leave them alone. Or he seems them later himself and laughs -- pronouncing them as they're written is usually good for a chuckle.

    That looks suspiciously like the typeface in Singapore Math -- did Fiona manage to rope you into getting her some Singapore? lol

  2. Your easy and acceptance is inspiring and comforting for those of us still uptight about so much of our approach to home education!

  3. Yes, Karen, I was cleaning up the piano last week and uncovered a 2B workbook that one of the older kids skipped past. Fiona grabbed it and dived in. She worked like crazy in it, even though some of it was obviously beyond her, so I relented and ordered the preceding one. Now she's alternating Singapore and Miquon, which is slowing her down a bit -- a good thing, I think.

  4. Beccy6:35 am

    I tried these sums on DS, for fun, with interesting concurring results. I wrote the questions out on a piece of paper, so the print was probably bigger than your book, but he still took up 2 lines for each answer. When writing 80 he said a little rhyme for remembering how to write 8 and seemed far more satisfied with successfully writing 8 than doing the sum correctly! I guess that shows which skill is harder for him.

  5. Wow, she is a good mathematician! And an eager beaver too :)

  6. I'm so glad to see this! I was actually to write you a question on that matter.... and you answered it without even having to ask! :D

    Thank you SO MUCH!


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