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Wout Blommers



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PostPosted: Fri Dec 07, 2007 2:49 pm    Post subject: About Math... Reply with quote  Mark this post and the followings unread

Which one is correct, now-a-days?

2+3x6=20
or
2+3x6=30

?????

Wout
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Blue Hell
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PostPosted: Fri Dec 07, 2007 2:52 pm    Post subject: Reply with quote  Mark this post and the followings unread

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?
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PostPosted: Fri Dec 07, 2007 2:54 pm    Post subject: Reply with quote  Mark this post and the followings unread

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 Smile

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Wout Blommers



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PostPosted: Fri Dec 07, 2007 3:28 pm    Post subject: Reply with quote  Mark this post and the followings unread

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
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Wout Blommers



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PostPosted: Fri Dec 07, 2007 3:33 pm    Post subject: Reply with quote  Mark this post and the followings unread

It was
4:2x2=1,
now it is
4:2x2=4

Wout
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PostPosted: Fri Dec 07, 2007 3:37 pm    Post subject: Reply with quote  Mark this post and the followings unread

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 Very Happy

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PostPosted: Fri Dec 07, 2007 3:38 pm    Post subject: Reply with quote  Mark this post and the followings unread

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.

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Wout Blommers



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PostPosted: Fri Dec 07, 2007 3:44 pm    Post subject: Reply with quote  Mark this post and the followings unread

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
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Wout Blommers



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PostPosted: Fri Dec 07, 2007 3:46 pm    Post subject: Reply with quote  Mark this post and the followings unread

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
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PostPosted: Fri Dec 07, 2007 3:48 pm    Post subject: Reply with quote  Mark this post and the followings unread

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.

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PostPosted: Fri Dec 07, 2007 3:57 pm    Post subject: Reply with quote  Mark this post and the followings unread

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?

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PostPosted: Sat Dec 08, 2007 6:12 am    Post subject: Reply with quote  Mark this post and the followings unread

All I know is that on this side of the pond we do it this way.

http://en.wikipedia.org/wiki/Order_of_operations

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Oskar



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PostPosted: Sat Dec 08, 2007 7:48 am    Post subject: Reply with quote  Mark this post and the followings unread

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?
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PostPosted: Sat Dec 08, 2007 7:51 am    Post subject: Reply with quote  Mark this post and the followings unread

bachus wrote:
All I know is that on this side of the pond we do it this way.

http://en.wikipedia.org/wiki/Order_of_operations


It's the same here.

Usually one won't write stuff like 2x3/4 but explicit grouping is used instead:
Code:
2x3
---
 4
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.
Code:
 2
4-
 3


could be 4x(2/3) or (4)+(2/3) depending on the context it is used in - usually it's clear what is meant.

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PostPosted: Sat Dec 08, 2007 7:55 am    Post subject: Reply with quote  Mark this post and the followings unread

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 Very Happy

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PostPosted: Sat Dec 08, 2007 10:40 am    Post subject: Reply with quote  Mark this post and the followings unread

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.

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PostPosted: Sat Dec 08, 2007 4:51 pm    Post subject: Reply with quote  Mark this post and the followings unread

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 Shocked

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PostPosted: Sat Dec 08, 2007 5:06 pm    Post subject: Reply with quote  Mark this post and the followings unread

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?

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PostPosted: Sat Dec 08, 2007 6:44 pm    Post subject: Reply with quote  Mark this post and the followings unread

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?

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PostPosted: Sat Dec 08, 2007 6:47 pm    Post subject: Reply with quote  Mark this post and the followings unread

Kassen wrote:
Maybe the preference towards evaluating left to right comes from the use of more basic calculators?


No it's older Very Happy

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PostPosted: Sat Dec 08, 2007 7:07 pm    Post subject: Reply with quote  Mark this post and the followings unread

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.

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PostPosted: Sun Dec 09, 2007 1:54 am    Post subject: Reply with quote  Mark this post and the followings unread

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'...

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PostPosted: Sun Dec 09, 2007 3:57 am    Post subject: Reply with quote  Mark this post and the followings unread

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.

;¬)

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PostPosted: Sun Dec 09, 2007 5:14 am    Post subject: Reply with quote  Mark this post and the followings unread

Very Happy
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Oskar



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PostPosted: Sun Dec 09, 2007 6:46 am    Post subject: Reply with quote  Mark this post and the followings unread

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! Shocked Cool Wink

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