4 ms·

I confess I found it dismal that the first problem was to learn the multiplication tables. If I'm looking for a book to excite anyone, that's not where I start

by lcuff 5y ago

I confess I found it dismal that the first problem was to learn the multiplication tables. If I'm looking for a book to excite anyone, that's not where I start. I get that those operations quickly become important in algebra and number theory, but that's hardly the essence of mathematics. All that said, I'm not sure where I'd start for secondary students, but the interest generated by watching _ideas_ emerge in 3blue1brown videos is a stark contrast to this kind of start.

svat 5y ago
Note that the first problem is not actually to learn the multiplication tables! Problem 1 is to calculate a few things like 0.004×0.02 and 1.08÷1.2 in one's head; it's just that these real questions are placed in 1(b), with a precursor 1(a), purely to indicate prerequisites, that states "Compute for yourself, and learn by heart, the times tables up to 9×9." (Incidentally, even here the "compute for yourself" part is the real heart of the matter, though of course knowing the times table up to 9×9 is something very useful. You'll see a lot more connections once there's some "fuel", as mentioned in the preface and the introduction to the chapter.) In any case, don't let a cursory look at Problem 1 decide the nature of the book for you. There's more than meets the eye. I don't know much about Tony Gardiner but the other author, Alexandre Borovik, has a wonderful blog called "Mathematics under the Microscope" (https://micromath.wordpress.com/ https://micromath.wordpress.com/) (and also a book of that name); to everything he brings a profound perspective with a light touch, a unique combination. A couple of memorable posts I still remember from over a decade ago: • “Psychophysiology of blackboard teaching” https://micromath.wordpress.com/2010/09/24/psychophysiology-of-blackboard-teaching-2/ https://micromath.wordpress.com/2010/09/24/psychophysiology-... • “Achilles, Tortoise and Yessenin-Volpin” https://micromath.wordpress.com/2009/02/16/achilles-tortoise-and-yessenin-volpin/ https://micromath.wordpress.com/2009/02/16/achilles-tortoise... • All the posts about "a childhood story". Anyway, I haven't gone through this book so far, but skimming through some chapters and how they are put together, there is a lot of gold here. See for instance Problem 78, which is simply twenty opportunities to think about "3 - 1 = 2".
- jvvw 5y ago
  Tony Gardiner was in charge of the maths olympiad training in the UK for many years - he produced some very good material for that including a book on maths olympiad preparation and the fact that he was one of the authors made me definitely interested in having a look at this.
throwaway67114 5y ago
Mathematician's Delight by W. W. Sawyer seems a good book.
parenthesis 5y ago
I like to point out to people that to learn the times tables up to 10, there are only really 36 facts to learn, since anything times 1 or 10 is trivial, and multiplication is commutative. (That's already a nice little problem to look at, to show that it is 36.) And then there are many interesting tricks to approach those 36. For example, the 'fingers' trick for the 9 times table. (Which leads to consideration of why do the digits of a multiple of 9 always add up to a multiple of 9?) Muliplying by 5 is half of multiplying by 10. Multiplying by 4 is doubling twice, etc. Before you know it, you just have to drill the ones most common to choke on (like 7x7, 7x8).

by lcuff 5y ago

svat 5y ago

Note that the first problem is not actually to learn the multiplication tables! Problem 1 is to calculate a few things like 0.004×0.02 and 1.08÷1.2 in one's head; it's just that these real questions are placed in 1(b), with a precursor 1(a), purely to indicate prerequisites, that states "Compute for yourself, and learn by heart, the times tables up to 9×9." (Incidentally, even here the "compute for yourself" part is the real heart of the matter, though of course knowing the times table up to 9×9 is something very useful. You'll see a lot more connections once there's some "fuel", as mentioned in the preface and the introduction to the chapter.) In any case, don't let a cursory look at Problem 1 decide the nature of the book for you. There's more than meets the eye. I don't know much about Tony Gardiner but the other author, Alexandre Borovik, has a wonderful blog called "Mathematics under the Microscope" (https://micromath.wordpress.com/ https://micromath.wordpress.com/) (and also a book of that name); to everything he brings a profound perspective with a light touch, a unique combination. A couple of memorable posts I still remember from over a decade ago: • “Psychophysiology of blackboard teaching” https://micromath.wordpress.com/2010/09/24/psychophysiology-of-blackboard-teaching-2/ https://micromath.wordpress.com/2010/09/24/psychophysiology-... • “Achilles, Tortoise and Yessenin-Volpin” https://micromath.wordpress.com/2009/02/16/achilles-tortoise-and-yessenin-volpin/ https://micromath.wordpress.com/2009/02/16/achilles-tortoise... • All the posts about "a childhood story". Anyway, I haven't gone through this book so far, but skimming through some chapters and how they are put together, there is a lot of gold here. See for instance Problem 78, which is simply twenty opportunities to think about "3 - 1 = 2".

jvvw 5y ago
Tony Gardiner was in charge of the maths olympiad training in the UK for many years - he produced some very good material for that including a book on maths olympiad preparation and the fact that he was one of the authors made me definitely interested in having a look at this.

throwaway67114 5y ago

Mathematician's Delight by W. W. Sawyer seems a good book.

parenthesis 5y ago

I like to point out to people that to learn the times tables up to 10, there are only really 36 facts to learn, since anything times 1 or 10 is trivial, and multiplication is commutative. (That's already a nice little problem to look at, to show that it is 36.) And then there are many interesting tricks to approach those 36. For example, the 'fingers' trick for the 9 times table. (Which leads to consideration of why do the digits of a multiple of 9 always add up to a multiple of 9?) Muliplying by 5 is half of multiplying by 10. Multiplying by 4 is doubling twice, etc. Before you know it, you just have to drill the ones most common to choke on (like 7x7, 7x8).