Author |
Message |
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Fri Dec 07, 2007 2:49 pm Post subject:
About Math... |
|
|
Which one is correct, now-a-days?
2+3x6=20
or
2+3x6=30
?????
Wout |
|
Back to top
|
|
|
blue hell
Site Admin
Joined: Apr 03, 2004 Posts: 24081 Location: The Netherlands, Enschede
Audio files: 278
G2 patch files: 320
|
Posted: Fri Dec 07, 2007 2:52 pm Post subject:
|
|
|
What do you mean "nowadays", multiplication has priority over addition of course. You're not trying to tell us that is too hard that way for the kiddies these days are you? _________________ Jan
also .. could someone please turn down the thermostat a bit.
|
|
Back to top
|
|
|
Fozzie
Joined: Jun 04, 2004 Posts: 875 Location: Near Wageningen, the Netherlands
Audio files: 8
G2 patch files: 49
|
Posted: Fri Dec 07, 2007 2:54 pm Post subject:
|
|
|
I don't think "meneer van dalen wacht op antwoord" ever changed. Why would it? It is 20. Why would you think otherwise (or am I missing something here)?
Edit: Jan types two minutes faster than I do _________________ Spinning at ~0.0000115740740741 Hz |
|
Back to top
|
|
|
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Fri Dec 07, 2007 3:28 pm Post subject:
|
|
|
Yes, it changed in 'Meneer Wacht - van Dalen - op antwoord, and, lets take a look at multiplying and dividing, which are done in order of their appearance in line, so no multiplying first per definition.
Wout |
|
Back to top
|
|
|
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Fri Dec 07, 2007 3:33 pm Post subject:
|
|
|
It was
4:2x2=1,
now it is
4:2x2=4
Wout |
|
Back to top
|
|
|
blue hell
Site Admin
Joined: Apr 03, 2004 Posts: 24081 Location: The Netherlands, Enschede
Audio files: 278
G2 patch files: 320
|
Posted: Fri Dec 07, 2007 3:37 pm Post subject:
|
|
|
Wout, are you saying that the 2nd example you posted is considered to be correct in modern education?
It's all just a matter of agreement of course, and I don't really care how to notate things 2 3 + 5 x works just as well as x 6 + 2 3 after all (depending on conventions), but I'd certainly like to stay informed about these matters _________________ Jan
also .. could someone please turn down the thermostat a bit.
|
|
Back to top
|
|
|
blue hell
Site Admin
Joined: Apr 03, 2004 Posts: 24081 Location: The Netherlands, Enschede
Audio files: 278
G2 patch files: 320
|
Posted: Fri Dec 07, 2007 3:38 pm Post subject:
|
|
|
Wout Blommers wrote: | It was
4:2x2=1,
now it is
4:2x2=4
Wout |
Ah, is that what you mean - multiplication and division always have had the same priority, so nothing changed there. _________________ Jan
also .. could someone please turn down the thermostat a bit.
|
|
Back to top
|
|
|
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Fri Dec 07, 2007 3:44 pm Post subject:
|
|
|
What was really meant is there is always a relation about the real world and the abstact formula on the blackboard. The formula has to represent something else, in which all is clear. If the multiplication has to been taken first, it has to be in front of the other calculations.
Wout |
|
Back to top
|
|
|
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Fri Dec 07, 2007 3:46 pm Post subject:
|
|
|
Blue Hell wrote: | Wout Blommers wrote: | It was
4:2x2=1,
now it is
4:2x2=4
Wout |
Ah, is that what you mean - multiplication and division always have had the same priority, so nothing changed there. |
Well it changed for me, because I had to do it like the first example. Only adding and substraction were perfomed in order of the formula.
Wout |
|
Back to top
|
|
|
Kassen
Janitor
Joined: Jul 06, 2004 Posts: 7678 Location: The Hague, NL
G2 patch files: 3
|
Posted: Fri Dec 07, 2007 3:48 pm Post subject:
|
|
|
Isn't writing just "2+3*6" asking for trouble in any case?
If we meant to add first we'd write the factors very differently, probably like;
6(2+3)
If I meant to multiply first I'd at least write;
6*3 + 2
As the 2 is clearly some sort of constant and I tend to drop those at the end, if you don't higher order equations start looking quite odd.
2 + 3³ + 4²
looks decidedly odd to me
3³ + 4² +2
sorts the terms by magnitude, much cleaner and so we better already do that for simpler ones because if we don't we'll have to shuffle them around when simplifying or merging factors which will lead to errors.
Anyway, I'd add brackets to that example regardless of what order the school or syntax or whatever says as it's just asking for trouble. _________________ Kassen |
|
Back to top
|
|
|
Kassen
Janitor
Joined: Jul 06, 2004 Posts: 7678 Location: The Hague, NL
G2 patch files: 3
|
Posted: Fri Dec 07, 2007 3:57 pm Post subject:
|
|
|
Wout Blommers wrote: |
Well it changed for me, because I had to do it like the first example. Only adding and substraction were perfomed in order of the formula.
Wout |
Isn't that dangerous?
If we have this;
4 - 2
I'm perfectly entitled to rewrite that as
4 + -2
However, as I understand these new rules rewriting things in such a way now potentially means also having to change the order of the whole thing.
Isn't this new rule harming the reflexivity of the addition (x + y == y + x) which is one of the foundations of math? Is this new idea actually any good for anything? _________________ Kassen |
|
Back to top
|
|
|
bachus
Joined: Feb 29, 2004 Posts: 2922 Location: Up in that tree over there.
Audio files: 5
|
Posted: Sat Dec 08, 2007 6:12 am Post subject:
|
|
|
All I know is that on this side of the pond we do it this way.
http://en.wikipedia.org/wiki/Order_of_operations _________________ The question is not whether they can talk or reason, but whether they can suffer. -- Jeremy Bentham |
|
Back to top
|
|
|
Oskar
Joined: Jul 29, 2004 Posts: 1751 Location: Norway
|
Posted: Sat Dec 08, 2007 7:48 am Post subject:
|
|
|
Me, I teach English and I have papers to prove I'm useless at Maths, but shouldn't one stick those numbers in brackets to avoid confusion? _________________ Where there are too many policemen, there is no liberty. Where there are too many soldiers, there is no peace. Where there are too many lawyers, there is no justice.
Lin Yutang (1895-1976) |
|
Back to top
|
|
|
blue hell
Site Admin
Joined: Apr 03, 2004 Posts: 24081 Location: The Netherlands, Enschede
Audio files: 278
G2 patch files: 320
|
Posted: Sat Dec 08, 2007 7:51 am Post subject:
|
|
|
It's the same here.
Usually one won't write stuff like 2x3/4 but explicit grouping is used instead:
Or simply (2x3)/4 in typed-up text
Only fractions can be a bit confusing, as sometimes multiplication is assumed to be implicit and other times addition is.
could be 4x(2/3) or (4)+(2/3) depending on the context it is used in - usually it's clear what is meant. _________________ Jan
also .. could someone please turn down the thermostat a bit.
|
|
Back to top
|
|
|
blue hell
Site Admin
Joined: Apr 03, 2004 Posts: 24081 Location: The Netherlands, Enschede
Audio files: 278
G2 patch files: 320
|
Posted: Sat Dec 08, 2007 7:55 am Post subject:
|
|
|
Oskar wrote: | but shouldn't one stick those numbers in brackets to avoid confusion? |
That would be the thing to do whenever confusion is possible, people are lazy though ... and they seem to get pleasure from making things more complex than necessary _________________ Jan
also .. could someone please turn down the thermostat a bit.
|
|
Back to top
|
|
|
Kassen
Janitor
Joined: Jul 06, 2004 Posts: 7678 Location: The Hague, NL
G2 patch files: 3
|
Posted: Sat Dec 08, 2007 10:40 am Post subject:
|
|
|
I tend to add brackets as though the compiler were actually a mischievous imp actively trying to subvert the outcome if give then chance.
For a while I thought this would make it all more messy when read back but in practice I find it turns out it makes it easier to recognise where the terms have gone and so easier to replace them with something else when updating the code.
That said, I don't think it's smart for Dutch educators to unilaterally change stuff like this. There's no harm done if people just calculate their budget this way for themselves but it could lead to trouble when talking about the process of calculating a budget with others from a different country or generation. This whole thing is asking for confusion and I don't see what we are getting back for it. _________________ Kassen |
|
Back to top
|
|
|
bachus
Joined: Feb 29, 2004 Posts: 2922 Location: Up in that tree over there.
Audio files: 5
|
Posted: Sat Dec 08, 2007 4:51 pm Post subject:
|
|
|
Kassen wrote: | I tend to add brackets as though the compiler were actually a mischievous imp actively trying to subvert the outcome if give then chance. |
I use parentheses liberally as though I might forget what I was thinking three minutes after I write it down _________________ The question is not whether they can talk or reason, but whether they can suffer. -- Jeremy Bentham |
|
Back to top
|
|
|
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Sat Dec 08, 2007 5:06 pm Post subject:
|
|
|
Kassen wrote: | ... That said, I don't think it's smart for Dutch educators to unilaterally change stuff like this. ... | Of course it isn't smart and it is not in the books, but there is confusion. In primary school it isn't taught at all, now-a-days. And I know there was a conference somewhere, on international level, were this was all debated. But is there something decided yet?
Wout |
|
Back to top
|
|
|
Kassen
Janitor
Joined: Jul 06, 2004 Posts: 7678 Location: The Hague, NL
G2 patch files: 3
|
Posted: Sat Dec 08, 2007 6:44 pm Post subject:
|
|
|
What do you mean it's not taught? Are they stuffing everything in brackets or simply limiting calculations to two terms max? And where did this confusion coming from at all?
Maybe the preference towards evaluating left to right comes from the use of more basic calculators? _________________ Kassen |
|
Back to top
|
|
|
blue hell
Site Admin
Joined: Apr 03, 2004 Posts: 24081 Location: The Netherlands, Enschede
Audio files: 278
G2 patch files: 320
|
Posted: Sat Dec 08, 2007 6:47 pm Post subject:
|
|
|
Kassen wrote: | Maybe the preference towards evaluating left to right comes from the use of more basic calculators? |
No it's older _________________ Jan
also .. could someone please turn down the thermostat a bit.
|
|
Back to top
|
|
|
Kassen
Janitor
Joined: Jul 06, 2004 Posts: 7678 Location: The Hague, NL
G2 patch files: 3
|
Posted: Sat Dec 08, 2007 7:07 pm Post subject:
|
|
|
Well, *I* don't remember anything about evaluating things left to right from when I went to school.
I find all of this quite odd, I think they should outfit kids with programmable calculators. They'll use those as it's faster then paper but you won't get anything into them without understanding how it all works. At least that's what I did though admittedly the fact that programmable calculators were strictly forbidden was a strong incentive as well. _________________ Kassen |
|
Back to top
|
|
|
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Sun Dec 09, 2007 1:54 am Post subject:
|
|
|
My point is somewhere on the line since I left primary school the 'rule' was changed, as Dutch spoken people will remember, 'M-V-D-W-O/A' became 'M-W-V-D-O/A' and maybe even 'M/W-V/D-O/A', which implies Dividing doesn't have to wait until Multiplying had its thing...
The thing is I can't find anything about the subject anywhere, only what people 'assume'...
Wout |
|
Back to top
|
|
|
Kassen
Janitor
Joined: Jul 06, 2004 Posts: 7678 Location: The Hague, NL
G2 patch files: 3
|
Posted: Sun Dec 09, 2007 3:57 am Post subject:
|
|
|
Wait, I was thrown off by your first example.
Now that I re-read the rules change the only thing that changed is that roots got put next to the powers which makes perfect sense as they *are* in fact powers (or at least can be re-written as powers). never noticed how odd that sentence was as the notation of roots inherently makes their scope clear so by the time you get to roots nobody cares about the sentence any more.
Fortunately nobody is proposing that we can do multiplication and addition in any order we like or find convenient at the moment like I thought you were saying at first.
M/W-V/D-O/A is perfectly fine as the pair can be re-written as each other;
the square root of x == x to the power of a half
x divided by y == x multiplied by one-y-th
and
x minus y == x plus minus-y
Makes perfect sense and that sentence was just demonstrably wrong on account of the priority of roots but that doesn't mean everything about it that was right can now also be swapped around liberally, cut to pieces, glued down creatively and contrasted with crayons. Also; the sky isn't falling.
If it's still hard to deal with the now inconvenient sentence you can memorise;
Meneer Wout Verstrekt Dagenlijks Onze Alcohol
It's more correct and I'm sure it will be more popular with your classes as well.
;¬) _________________ Kassen |
|
Back to top
|
|
|
Wout Blommers
Joined: Sep 07, 2003 Posts: 4529 Location: The Hague - The Netherlands
Audio files: 123
G2 patch files: 12
|
Posted: Sun Dec 09, 2007 5:14 am Post subject:
|
|
|
|
|
Back to top
|
|
|
Oskar
Joined: Jul 29, 2004 Posts: 1751 Location: Norway
|
Posted: Sun Dec 09, 2007 6:46 am Post subject:
|
|
|
Wout Blommers wrote: | My point is somewhere on the line since I left primary school the 'rule' was changed, as Dutch spoken people will remember, 'M-V-D-W-O/A' became 'M-W-V-D-O/A' and maybe even 'M/W-V/D-O/A', which implies Dividing doesn't have to wait until Multiplying had its thing...
The thing is I can't find anything about the subject anywhere, only what people 'assume'...
Wout |
Whatevr you do, DON'T ask a Maths teacher! _________________ Where there are too many policemen, there is no liberty. Where there are too many soldiers, there is no peace. Where there are too many lawyers, there is no justice.
Lin Yutang (1895-1976) |
|
Back to top
|
|
|
|