I get that there are many things we need to pratice, 1000 hours or some such number someone made up to become an expert. I am however not so sure about that with lots of the things we teach at school and in particular mathematics. When I spat the dummy recently about homeschooling and feeling we had no direction and rhythm to our homeschool trip I set Helena old school maths activities, well problem solving problems. The first thing I thought was that she knew nothing but 3 weeks in I see how wrong I was, it’s just taken her that long to see the problems as a fun challenge and for her confidence in the format to happen. The problem that made her storm and rage on Monday was done on Friday with a comment on how she could do it, it was “easy” yet at the same time she was genuinely pleased with herself. I confess we have done no “real” formal mathematics, occasionally.. er to be more accurate I’d say “rarely” Helena picks up one of the books I’ve brought her and will do some addition like problems.
Today’s problem was 3x=24 what is 2x… not that it looked like that ..
She used the abacus. She knew she wanted 2 thirds of 24 and so she needed to work out what one third was and double it. Her first idea was to get 24 beads and divide into 3 then she realized it was so close to 30 = 3 tens. So she took away the 6, 2 from each 10.
The next problem had her inventing equipment to physically do it which then turned into a game.
We tried playing the game but couldn’t get very far up our trees so tried to calculate why… she lost some interest then but Dad and I were totally into it!
Helena solved the game problem by adding in another dice. She was then manipulating the dice numbers to make equations easier. E.g. If the takeaway dice was a 3 and if one of the plus dice was a 3 she just cancelled them out. If the takeaway dice was a 2, one of the plus dice a 5 and the other a 3 she could find the double 3. I.e. 5-2+3, and “doubles are easy”. We talked about the number to subtract being a negative number so that when we made our chart we added the negative numbers knowing that it meant more to take away. I know she knows that 3 x 4 is the same as 4 x 3 as she makes jokes about this, I can also make an assumption she knows 2 + 4 = 4 + 2. This is was all without practice. Her basic facts are slow but that’s just arithmetic not mathematical thinking. I don’t know how but she knows 50% is a half, something to do with shopping, she just works stuff out.
I imagine her at school with the drudgery of basic facts… then I imagine her failing some standardised test some place and making NZs maths skill slip down the ratings… I frankly don’t give a damn. There is nothing wrong with her mathematical thinking, sod basic facts (if she ever takes up role playing she’ll get quick) lets focus on fun and lots of maths (but not arithmetic) is fun, I’ll model that.