I think I kinda sorta get it, but what’s the point? If I have 5 piles of prunes, with 4 prunes in each pile, isn’t it a lot easier to announce, “5 times 4 is 20” than it is to do some kind temporary rearranging of the universe to try to make 4 the same as 10?
i learned that and still use it…
Doh:smack:
I didn’t think that was important, but yes, your exposition a small subset of people still use base 16 (and on occasion, base 8).
Fun fact - in some conventions the case of the “x” denotes the case of the A-F. For example 0x0a and 0X0A is correct while 0x0A or 0X0a technically isn’t (this isn’t universally accepted AFAIK though).
And Marlitharn - yeah, one of the, er, odd things about New Math was that it emphasized different bases for its own sake, while it’s somewhat noble to show that math isn’t limited to sets of 10, doing it without direction or application was part of the failure. Some bases are still used in computer science for reasons explained above, and I’d imagine (though this is wild guessing) that maybe some mathematicians use this for constructing sets with various applications that I couldn’t guess at. The only other way I’ve heard of other bases being used in a modern context is in Primary Math Education courses, where it’s used to illustrate to Education majors how difficult math is for some children to learn by stripping everything down and forcing them to learn new conventions, which I thought was a pretty clever use for it.
But as Derleth said, the reason it’s used in Comp Sci is that everything is a switch, on or off. Base 2 offered a good way to represent everything, since you needed an arbitrary convention to store numbers anyway you may as well use one that translates to our own number system. Base 8 and base 16 offered compacted ways to write them (trust me, being able to write 0x80000000 instead of 1000 0000 0000 0000 0000 0000 0000 0000 every time is a pretty nice luxury).
The important thing remember is that there is nothing magical about the base 10 we’re using, it’s just one of those arbitrary choices that was made long ago.
If characters from Disney had developed math from scratch they would probably have picked base 8 (they only have 8 fingers :)) and for them 5 times 4 would have been 24.
Sometimes, like in the case of computers Derleth talk about, some other base may simply be more natural or convenient to use rather than converting everything to base 10.
Er, put “is why” somewhere in that.
Yes, that’s right. “Little Twelvetoes”. It was made in 1973. By this time, TPTB had pretty much rejected New Math.
And then Bob Dorough (the singer/narrator) takes us through the old-fashioned times-table for twelve.
Anything times nine, the digits in the answer will add up to nine. So 54 must be 6x9. 5+4=9. That leaves 56 to be 7x8.
ETA: examples:
2x9 = 18 1+8=9
3x9 = 27 2+7= 9
4x9 = 36 3+6=9
etc.
3717x9 = 33453 3+3+4+5+3=18, 1+8=9
and so on.
It’s hardly new. I learned how to multiply with those methods & divide exactly like that in the early 80s. So that’s at the very least 25 years old. (And I think the textbooks we used were older.)
They relies on estimation & the distributive property, neither of which is all that complex. (The lovely youtube video doesn’t say what happens when you pick the wrong number when you’re doing traditional long division and have to erase over and over using the crappy erasers that are available to 4th graders Nor does it show the work needed for “traditional long division”).
I also use chisenbopping if I have to count on my fingers. Way more useful than being limited to adding two numbers under 5.
From what I can tell, the big problem is that it was taught by people who really didn’t understand what they were doing.
Okay, ignorance fought. I still don’t entirely understand it, but I’ll never use it, and I see how it’s used by people who do use it, so I’m content. Thanks!
The first edition of the Everyday Mathematics curriculum came out in 1998. However, I’m sure the methods in the curriculum come from various sources and are much older than that.
The main thing I remember about “New Math” was that before it came along we would have “problems” in our workbook that might look like this:
-
8 + 5 = ?
-
17 x 2 = ?
-
5 + 8 = ?
-
2 x 17 = ?
-
2 + (4 + 6) = ?
-
6 + (2 + 4) = ?
AFTER the “New Math” arrived, we were taught principles whose names we had to freaking memorize and the “problems” we had to answer in our worksheet looked more like this (answers filled in for the benefit of anyone who didn’t have to learn these terms): -
8 + 5 = 5 + 8; this is an example of the "Commutative Property of Addition"
-
17 x 2 = 2 x 17; this is an example of the "Commutative Property of Multiplication"
-
2 + (4 + 6) = (2 + 4) + 6; this is an example of the “Associative Property of Addition”.
Also on the list: Distributive Property of Multiplication over Addition.
My reaction then: We know that, yeesh, all those workbooks where they’d reverse the order, yeah we got it, doesn’t matter which comes first, yadda yadda. Why do we need to have a NAME for it?
Teachers’ reaction then: Yeah, like my 4th graders are going to latch right on to terms like “commutative”, “associative”, and “distributive”. Those will fit right in with the rest of their everyday vocabulary. Just to think that last year my biggest vocabulary concern in math class was getting the kids to say “multiply” instead of “times it by”.
[mostly irrelevant aside]
Ten years later in music composition class, they were forcing us to learn chord progressions, like the I chord can lead to the IV or the V, etc… and of course my ear knew all that (and could differentiate between the harmonic structures of old classical, later classical, and modern) but now I had to learn the stupid NAMES… “Aah, it’s ‘New Math’ all over again!”
[/aside]
Well, AHunter3, it looks like you learned it and understood what you learned well enough that all these years later you can still explain it. Regardless of whether it’s useful or not, they did a pretty good job of teaching it to you then.
All very well but once you get into matrices, A×B does not equal B×A. Those of us old enough to be brought up with old British measures are quite familiar with bases other than ten. Twelve in particular is much easier to work in sub-dividing measures. Ever tried cutting a cake into ten equal pieces? Now halving and finally estimating thirds is very easy.
It’s easy to count dozens as well, using the thumb against three segments of fingers on one hand. I’ve heard that this is still done in Iraq and if, instead of doing the same on the other hand you just tally each digit, you get the Sumerian-Babylonian base sixty still used for time and angles.
I think the reason ancient measures are often dozens or give a hint of binary is precisely because they were less interested in adding up than in dividing down and could do that easily in halves and thirds before they had regular standards to measure against.
This just proves my point about how ideas just become politically correct, especially in education. I was taught in no uncertain terms that “the research” heavily favored whole language. I didn’t believe it, as I have some idea of how studies can be skewed, but the professors weren’t unclear in their support of leaving phonics instruction for the most part.
Dumb.
Maybe this odd little fact will help: 56=7x8. 4 consecutive digits!
And 12=3x4. Also 4 consecutive digits! AFAIK, those are the only actual combinations for which that particular form of equation is true.
(underlining added)
“Very strong point”, indeed!
Indeed, those correspond to the only two solutions to the slightly more general quadratic equation 10d + (d+1) = (d+2) * (d+3). Not that this equation will help anything, mnemonic-wise; it just explains where those come from.