Thanks! :)
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One thing I've learned recently, is that the world is no longer looking for people who can memorise things. We have computers now, hard disks capable of storing several gibabytes (now even tera bytes)... soon, the 'merit' for memorising things will not be as it was in the past. It will turn more towards thinking skills and problem solving skills. That's why I'm not too strict with the multiplication tables. I never myself learned them all to 12 (:o) but with practice, I came to know the tables on the tip of my fingers. I came to even know the tables of 13, 15, 16, 25 especially.
I've tutored enough math, and believe that knowing the times tables sure goes a long ways towards doing algebra, geometry, trig, etc. I always refused to allow my grade school and high school students have calculators until I was sure they knew the times tables and knew how to think through the various math problems.
It isn't so much as the memorization and regurgitating of the times tables, but having the discipline to learn them and know how the whole thing works together -- and not just be mindless calculations on a fancy little gadget with buttons.
In the same way, my mom had me and my siblings learn how to properly mop a tile floor on our hands and knees, so we'd understand how dirty the corner can get and where the fallen crumbs like to hide.
Lol...
actually, I've been thinking of a sticky for the mathematics forum, containing all the stuff that we learn from small classes, as from secondary studies... I feel somewhat lazy about it though. I might start one in my holidays, the true ones which are in six months time.
I think I'll include:
Algebra (solving, simplifying, factorising)
Trigonometry (solving, simplifying, identities)
Probability (conditional, independent)
Coordinate geometry (plotting, drawing lines, curves, gradients, trigo curves, area, volume, three dimensional coordinate geometry)
Linear law
Rates
Functions
Indices/Logarithm
Partial fractions
etc
I know what you are saying. I admit that calculators do make people lazier and make them take much time. I've seen that too many a times among some friends. They would use a calculator to do 13 times 3! I can work without a calculator if the problem involves 'round figures' (not going into endless decimals, and involving square roots of non-square numbers).
My point was memory will always be essential. However, it remains for the basics, the ones that you won't be assessed ever in your life. You would have course use them in most, if not all problems you encounter. I won't say either that it is useless to learn all the tables up to 1000, it is good, but you will not be asked to do 257 times 911. You apply your knowledge of multiplications to solve more complex problems. The world does not need a population of reciting parrots, but a thinking, innovative population which can take the best decisions.
It is in this respect that I'm directing my point.
I understand what you're saying, but if I had to solve 257 x 911, I'd jot it down on a piece of paper (keeping my columns nice and straight) and solve it forthwith, rather than dig around in the junk drawer for a calculator.
When I went to school (even college), calculators were unheard of for students. (I should check what years they WERE available.) The nerds used abaci, but the rest of us calculated on paper or in our heads. I remember physics homework that was pages long, and we had to show all our work. One mistake in a calculation, and the answer would be wrong (and we'd get a lower grade).
Another thread...
This one is about whether a person is too old to learn math.
Yes, same goes for me :). Even if it were a six digit long number, without a calculator, I'd do it on paper, using the knowledge of my 1 to 9 multiplications tables.
The table of 10 and 11 are just too simple.
And for the random number I said earlier, I would have 'improvised' because of the presence of the '11'.
Apart from that, I can say I don't have a 'super' memory, but I memorise things easily with practice. After so many multiplications, how can I not know the basic tables? :)
Oh, speaking of calculation mistakes, the exams we have now deduce little marks for such mistakes and they still give you marks for the working, your methodology to tackle the problem.
...
I think we are hi-jacking Clough's thread :eek:
Yes, see you on another thread WG :) Have a good sleep!
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