... and other things I was never taught that might have kept me interested in number theory at school.
God, my maths teachers were really just phoning it in.
I only just discovered this trick reading an Arthur C Clarke (RIP) novel this afternoon, where (as usual with Arthur C Clarke) the main plot of the book is all about some malevolent race of space aliens coming to kill us all, while another more benevolent one comes in and saves us - he was a bit of an obsessive, Arthur C, I fancy, in that respect.
But the peasant multiplication thing, it's great. I'm going to show it to my girls tomorrow - they'll be fascinated, having just (at 6 and 7) have had to go through the torturous process we all remember, of learning, by rote, all the "times tables" up to 12 to be able to "do" multiplication. Of course, learning by rote is an ultimately quicker method, but I don't think it teaches them the nature of numbers, or of maths. I know I was turned off maths for similar reasons - no-one in the English education system I grew up in (and I ended up with an "A" Level in Maths) ever showed me this, though, and it's the kind of thing that would have made me far more interested in numbers, and how they work.
I expect you know what I'm on about by "peasant multiplication", but I'll quickly reiterate anyway - the thing where you just double and halve (chucking the odd half away each time) the numbers on each side, then add up only the ones that still have an odd counterpart, so for example
13 x 27
becomes
13 x 27
26 x 13
52 x 6
104 x 3
208 x 1
and then add 13 + 26 + 104 + 208 = 351.
351 = 13 x 27.
This should be on the maths syllabus at 8-year-old level, if it's not. Yes, I know, you get to a stage where you insticntively look at a multiplication like that and know it's 100ab+10(bc)+10(ad)+cd, or whatever, but tricks like this are fun, to learn, along the way.
God, my maths teachers were really just phoning it in.
I only just discovered this trick reading an Arthur C Clarke (RIP) novel this afternoon, where (as usual with Arthur C Clarke) the main plot of the book is all about some malevolent race of space aliens coming to kill us all, while another more benevolent one comes in and saves us - he was a bit of an obsessive, Arthur C, I fancy, in that respect.
But the peasant multiplication thing, it's great. I'm going to show it to my girls tomorrow - they'll be fascinated, having just (at 6 and 7) have had to go through the torturous process we all remember, of learning, by rote, all the "times tables" up to 12 to be able to "do" multiplication. Of course, learning by rote is an ultimately quicker method, but I don't think it teaches them the nature of numbers, or of maths. I know I was turned off maths for similar reasons - no-one in the English education system I grew up in (and I ended up with an "A" Level in Maths) ever showed me this, though, and it's the kind of thing that would have made me far more interested in numbers, and how they work.
I expect you know what I'm on about by "peasant multiplication", but I'll quickly reiterate anyway - the thing where you just double and halve (chucking the odd half away each time) the numbers on each side, then add up only the ones that still have an odd counterpart, so for example
13 x 27
becomes
13 x 27
26 x 13
52 x 6
104 x 3
208 x 1
and then add 13 + 26 + 104 + 208 = 351.
351 = 13 x 27.
This should be on the maths syllabus at 8-year-old level, if it's not. Yes, I know, you get to a stage where you insticntively look at a multiplication like that and know it's 100ab+10(bc)+10(ad)+cd, or whatever, but tricks like this are fun, to learn, along the way.
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