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.