I've seen some surveys where mathematics ranks as the favourite subject of a plurality of primary school children, ahead even of art, and I'm starting to see how that could be. Even arithmetic is very much an experimental, hands-on subject at this age. Helen still wants to count even familiar collections of objects, and hasn't twigged yet to the persistence of cardinality. But she's taken to counting collections in different orders, including quite convoluted ones (sometimes reverting to simple side-to-side when she gets lost), as if curious that she gets the same result. And last night she lined up her six bath ducks (which stick onto the wall) and counted twelve eyes, and then said something like "what happens if we take one duck away" and counted ten eyes, all without any prompting. And now I'm getting a barrage of questions, all of which I answer as best I can. "What's nine and nine?" - "Eighteen". "What's nine and nine and nine and nine and nine and ... and nine?" - "Uh... 126, I think"...
Mathematics is the ultimate general-purpose toy. Some of you no doubt think it's unnatural, but for me not playing with mathematics with Helen would be as strange as not reading with her (and writing is just as "unnatural" as mathematics, if you think about it).
So what happens? All young children seem to love stories - so far having them read to them, rather than reading them themselves - but only a small fraction of them go on to regularly read novels as adults (or teenagers). Similarly, children may find mathematics fascinating at six, but by sixteen most of them have lost all interest in it, if they don't actually dislike it. Is this some natural progression, an inability to cope with longer texts or higher levels of abstraction, or is it a by-product of formal schooling, where reading has been narrowed to specific ways of approaching specific texts and become a chore that has to be rewarded with stickers, while mathematics has been reduced to arithmetic and algebra and calculus and turned into a competition only a few can win?