It feels strange watching Alex learn the basics of mathematics. So many solutions that come so naturally to me are a struggle for him, not through lack of intelligence on his part, but from their unfamiliarity as he tries to understand the basic concepts.
This morning it was money. When you think about it there's a lot of basic arithmetic stored in a piggy bank.
Alex wanted a milky pop from the canteen. That's 10 cents. Now he wants 5. For most of us that's easy, 5 x 10c = 50c. But he's barely touched on multiplication yet, so it's back to addition.
Fortunately, they've done counting on tens (a prelude to multiplication), otherwise the addition is very painful.
Okay, so we've got the first answer, now the problem is how to make it with coins. If you don't have a 50c coin then you need to make 50 from smaller denominations, say 2 x 20c and 1 x 10c. Again, we've got multiplications going on, or counting on twenties.
Then he wants to buy one for his friend. So now we have 5 + 1 = 6 milky pops. And we need to add 10c to the total cash required.
My spelling all that out was torturous, wasn't it? But that's the least level of detail required when you are starting out. For me now, I don't even have to consciously think about such sums. This level of mathematics is more of an emotional response than intellectual. Relationships between numbers have become intuitive feelings. Coins have shapes, you don't even have to think about the numbers on them, you just know how they fit together to make new numbers.
But I can see that developing in Alex. Sometimes he'll immediately pick the right answer to a mathematical question and it's only when he starts thinking about it too hard that he might struggle and get it wrong. It's fascinating to watch.