@Matt "Your argument of “Well, that is the way the tests are, like it or not†seems to not get at this. Yes, the tests are this way, whether I like it or not. But that is no argument ...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151955
@Marvin I don't understand then what you are driving at. The argument here is "memorization of multiplication facts and memorizing the division algorithm is not a prerequisite to mathematical und...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151596
@Daniel What is your experience teaching at the K-12 level? Also, what markup is allowed in the comments? ----- Your fixation on scalene triangles has caused you again to miss my point. Let me qu...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151521
@Matt Stating that Daniel never ran into scalene triangles in his various geometry courses is a valid comment. Saying he met Coxeter is not and Daniel acknowledges that. You may not like what's t...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151515
@Marvin Perfectly valid algorithm, but horribly inefficient. Using this "horribly inefficient algorithm", I can compute quickly 6 times x in my head for a wide range of x values. Granted...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151505
@Marvin, How do you discount an appeal to authority in one line, and in the very next one, justify polynomial division by appeal to authority ("A typical AP Calculus test problem involves integra...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151501
@Daniel "What do you do for 6 times 8 … subtract 12 from 60? In this instance, my brain wants to use the fact that 5 times 8 is 40 (since 10 times 8 is 80), and then just add 8, to get 48."...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151496
@Peter I teach math to my boys using puzzle books for kids. I have not yet used Garner's, but the idea is the same. I choose neat problems and I ask them to work it out... when they get stuck, I ...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151439
@Marvin What do you do for 6 times 8 … subtract 12 from 60? In this instance, my brain wants to use the fact that 5 times 8 is 40 (since 10 times 8 is 80), and then just add 8, to ...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151438
"To this day, to compute 6 times 9, I do… 6 times 10 minus 6." What do you do for 6 times 8 (resp. 6 times 7) ... subtract 12 (resp. 18) from 60? ----- "Who cares about what a scalene trian...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151333
Benoit was never taught the alphabet and never learned multiplication tables past fives. Even today he claims not to know the alphabet, so that it is difficult for him to use a telephone book. St...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151303
I would teach kids math by basing lessons on Martin Gardner's Mathematical Games column from old issues of Scientific American. That's how I learned to love math, in spite of the tremendous effor...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151340
@Ben The grades he gets when he is 13 are important? Might it keep him from getting into college later? Even assuming that they are important, on the long run, the best thing you can do for your ...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151272
The ability to multiply small numbers in your head needs to be learnt, and the multiplication table is a key part of that, but it's to show the patterns that make many of the entries easy to lear...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151203
My 13-year-old wholeheartedly agrees with you. I find, however, that I cannot encourage him to skip the pointless rote memorization as I still think it's important that he get good grades. Oh wel...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151268
If we look at the great mathematicians of the past we find a considerable number that had extraordinary mental powers in the field of memory and mental arithmetic. (Gauss, e.g., just to cite a si...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151197
Funny enough, I was reading opinions on math education I really agree with from Bill Thurston in 1990 here last night: http://arxiv.org/pdf/math/0503081.pdf His introductory remarks here are also...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151196
I think learning multiplication table is important, it makes life easier. Absolutely agree with the rest of the article.
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151097
There is a reason why you would make someone go through dividing 115.5 by 24.21. It is an un-natural process. It requires you to actually make an effort to solve it. Of course you will never be d...
https://lemire.me/blog/2015/03/09/the-mathematics-we-teach-our-kids/#comment-151036