81–90 of 198 posts
I recently worked with a person who had to do her three times table using her hands, starting from 3. She would still struggle at about 6 or 7 times. We worked behind the counter in a builder's merchant. She is no longer working for us.
Why not?
Earlier quoted context omitted.
Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?) With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both…
decimals cause huge problems for computers. How do you represent 0.6 as a floating point? In the long run, the correct solution is for everything to be binary.
It's just that top to bottom very few people are willing to trade the loss of speed for the increase in accuracy (not that decimal is great either, you still run into plenty of repeating fractions)
Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…
Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?) With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both…
There's lots of questions thrown up by this. If people need to know times tables, do they also need to know powers of 2? They come up quite often if you deal with computers. What about squares? Anyone doing polynomials later on will be using them constantly. My sense is you will end up memorising the things that come up anyway, so why be so strict? You'll end up teaching kids that math is a memory game. So for fun, w…
You're right about 86400 and 1729. I know up to 2¹⁷=131072 and also the special cases 2²⁰=1048576 and 2²⁴=16777216 (the 7s in the middle make it easier to memorize, and it seems to come up a lot). I would really like to remember 2³²=4294967296 (I always just remember "4.2 billion") and should probably get around to that. I learned a lot of pi in middle school but even then I knew that it wouldn't be useful for anythi…
In the broader sense, I'd prefer that a lot more time be spent on number theory than on arithmetic. I am rarely without a smartphone to the point where its in my hands for even basic math that I could do in my head (but which, due to infrequent use, I would spend a few seconds questioning whether or not I really did get the right answer).
The schools start with algebra and other concepts much earlier, now (at least my district does), but I started teaching my children formulas and basic algebra from the point they started learning to add and subtract (kindergarten in my district) along with binary and hexadecimal positional numerical systems. I remember struggling with that in my teens when I started learning software development my entire exposure to numbers was in decimal (10 is the number after 9, always!). In the first grade, my kids didn't have that mental block and I found they grasped the idea far more quickly than I expected. As they've learned multiplication and division, I've shown them the same in binary and hexadecimal and illustrated how they relate to one another. Everyone struggled being introduced algebra so late when I was growing up. And it progressed so quickly, going from Algebra (2 yrs), Geometry (1 yr), Trigonometry (1 yr) and pre-calculus/calculus that students fell mostly into either "memorize the formulas/algorithms and regurgitate the test answers or struggle like crazy and never get to Trig/Calculus until college. I left with an understanding of math but that was mostly due to my taking up programming at that time and having to learn what it all really meant because I wanted to do things in code that required me to understand it.
[1] The British Metric Society "The Mess We're In" http://www.metric.org.uk/the-mess-we-are-in
[2] The reality is that you're only asking students to memorize one more number since 10 is "add a zero and multiply by one" and 11 is an obvious pattern with single digits.
Earlier quoted context omitted.
Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?) With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both…
I'd assume if we used base 12 for everything we'd also use it for writing numbers too. 1 2 3 4 5 6 7 8 9 a b so 10 would be 12
I did not otherwise specify, so I represented my numbers in base 10 everywhere even though I was talking about base 12.
Only in non-metric countries. Back in the British era of pounds, shillings, and pence, hardware had to be built to do arithmetic in that system. This resulted in one of the strangest, and most complex, purely mechanical computing devices ever built - the McClure Multiplying Punch [1], from Powers-Samas. This device came out in 1938. The comparable IBM machine was the IBM 602 Multiplying Punch, but IBM only did decima…
1. We have time. Days are 24 hours, a multiple of 12.
2. We still have time. Hours are 60 minutes, a multiple of 12.
3. Yet more time. Minutes are 60 seconds, a multiple of 12.
4. We have circles. There are 360 degrees in a circle, another multiple of 12.
5. The numbers 1, 2, 3, 4, 6 and 12 itself divide into 12 evenly. The next smallest number that has more factors than 12 is 24, which manages to be a multiple of 12.
They should probably learn HEX at age 9
"Every child in England will be expected to know their times tables before leaving primary school from next year.
Pupils will be tested against the clock on their tables up to 12x12 in new computer-based exams that the Department of Education (DfE) said were part of the government’s “war on innumeracy and illiteracy”." http://www.theguardian.com/education/2016/jan/03/pupils-face...
Gove is no longer the Education Secretary...he is now the Justice Secretary. God help us.
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This one I'm entirely unconvinced of. It is easier for the computer to adapt to us, rather than vice versa. And over time things get easier and easier for the computer, while staying the same for us. Which is why over time we wind up interacting with computers in ways that are more and more adapted to us rather than them. We already have acceptably good algorithms to convert to/from different representations, and rou…
you can't use exact fraction arithmetic to take a square root, which comes up, you know, just a little bit, in physics. Of course this is a problem for binary representations, too, but you might as well not start out with an input that is already imprecise.