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  #21  
Old 15.06.2012, 13:47
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Re: Math instructions at school: good or not?

I don't recall the rule of 3 either...at least not so termed! but show me the equation and I can solve it, no problem

Those differences in long division are interesting! I guess I will relearn it all with my kids...
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  #22  
Old 15.06.2012, 13:58
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Re: Math instructions at school: good or not?

Interesting read, but fundamentally flawed, in my view. The idea that learning how to, for example, manipulate number representations of a page before being able to actually use them in a real context seems perfectly appropriate to me. and the triangle in a square can actually be proved very simply by a tiny bit of trig if you've already learnt the rules. The writer seems to think that demonstrating something by looking at a picture is as good as being able to produce a proper proof, which is surely counter to the very concepts of mathemetics.
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Old 15.06.2012, 14:01
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Re: Math instructions at school: good or not?

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I had a comprehensive scientific education in the UK and never heard this called the "rule of three". We simply didn't distinguish it in any way - we just learnt how to generally rearrange algebraic equations.

I just googled it, and think I now know why - this is how the "rule of three" used to be described in the most popular UK maths textbook in the 19th Century (Cocker's Arithmetick):


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Again, observe, that of the three given numbers, those two that are of the same kind, one of them must be the first, and the other the third, and that which is of the same kind with the number sought, must be the second number in the rule of three; and that you may know which of the said numbers to make your first, and which your third, know this, that to one of those two numbers there is always affixed a demand, and that number upon which the demand lieth must always be reckoned the third number
Clear?
Sounds like "Three shalt be the number thou shalt count, and the number of thy counting shalt be three. Four shalt thou not count, nor either count thou two, excepting that thou then proceed to three. Five is right out. "
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  #24  
Old 15.06.2012, 14:13
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Re: Math instructions at school: good or not?

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Interesting read, but fundamentally flawed, in my view. The idea that learning how to, for example, manipulate number representations of a page before being able to actually use them in a real context seems perfectly appropriate to me. and the triangle in a square can actually be proved very simply by a tiny bit of trig if you've already learnt the rules. The writer seems to think that demonstrating something by looking at a picture is as good as being able to produce a proper proof, which is surely counter to the very concepts of mathemetics.
Concur. Interesting thing that the writer equates math with "painting genius and creativity" and brings Michelangelo in the discussion - yet I am sure even Michelangelo was given a bit of basic instruction one way or the other as opposed to being told "here's some paint and canvas - go play with it".

The whole idea of letting kids "discover" mathematical concepts (which permeates current teaching dogma - at least on this side of the Roestigraben) is great from a "let's let the child play and discover" point of view - but seriously, are we really as a civilisation spend endless amounts of time rediscovering 2'000 year old theorems instead of building on them?
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  #25  
Old 15.06.2012, 14:18
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Re: Math instructions at school: good or not?

I have also never heard of rule of three. If it is what is mentioned here:
http://en.wikipedia.org/wiki/Rule_of...#Rule_of_Three

then to me it looks like it simply a rote-learned rule, useful for only a specific example, so pretty useless in general.

If I wanted to evaluate x from the example given: a/b = c/x

then i'd just rearrange the equations using any valid (and more generic) rules.

ie. if you move something from one side to the other side then if it was on the bottom it goes on top, and vice versa. Or i'd probably start by flipping both sides of the equation upside down, so it becomes b/a = x/c then move c to other side so it goes on the top side.

So, don't really see the point of the rule of three I'm afraid.
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Old 15.06.2012, 14:26
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Re: Math instructions at school: good or not?

I am planning to start a course in speed maths - more of a basic maths course for kids ( age 8-14).

Primarily focus on fast calculations techniques simple maths ( Add, subtract, Divison, multiplication, squaring, square roots,fraction handling etc):
Eg. 11 x 15 = ( they should be able to answer this easily in less than 5 seconds ,without using a paper and pen)
This is done via simple technique ( when a two digit number is multiplied by 11 , sum the digits and put it in between )
i.e. 1+5=6
so 11 x 15 = 1 6 5

Prerequisite to enter the course:
Tables ( 1X10 to 5X10)
Medium of instruction = English

Details to follow - will post on forum
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  #27  
Old 15.06.2012, 14:37
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Re: Math instructions at school: good or not?

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So, don't really see the point of the rule of three I'm afraid.
The point? To do it faster instead of actually start flipping around with the equations - and to make it more palatable to less mathematically inclined people

You know, like knowing the relative sizes of the sides of a square triangle when the two other angles are 30 and 60. You can go the long way, or the short way
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  #28  
Old 15.06.2012, 14:39
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Re: Math instructions at school: good or not?

In all honestly, I've stopped dealing with rearranging/rule of three/whathaveyou methods decades ago---my calculator takes care of that now and everyone is happier.
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  #29  
Old 15.06.2012, 14:42
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Re: Math instructions at school: good or not?

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You had to google "rule of three" and you teach math?
I have a maths degree from a UK university, and I've never heard of it. As others have pointed out - it's basic algebraic manipulation.

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In my background and upbringing, 'maths' is the improper use. Hearing the term 'maths' irritates me, but I understand that is how it is used other places in the world.
Maths is short for mathematics. Do you call statistics "stat" or "stats"?

In answer to the OP, I've not noticed a particular problem with the mechanics of maths, but rather that since the Swiss system is geared toward rote learning, students who've done well previously find maths difficult, because it involves reasoning.
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  #30  
Old 15.06.2012, 14:49
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Re: Math instructions at school: good or not?

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I have a maths degree from a UK university, and I've never heard of it. As others have pointed out - it's basic algebraic manipulation.
Yeh, probably because it is never taught at university level... . Anyway.

Let's agree that it is used frequently in teaching throughout Continental Europe and apparently not in the Anglo-Saxon curriculum... deal?
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  #31  
Old 15.06.2012, 14:51
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Re: Math instructions at school: good or not?

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Maths is short for mathematics. Do you call statistics "stat" or "stats"?
Well, I don't think we have to argue as to who is right or wrong. In the US we say math and not maths. Just different.

But to answer your question, if I was talking about the class I would say "stat class". If I was talking about a set of numbers or results, I would call them stats. But that could just be me
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  #32  
Old 15.06.2012, 15:01
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Re: Math instructions at school: good or not?

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Yeh, probably because it is never taught at university level... . Anyway.
Well, I did go to UK university after spending 14 years in the UK school system, and it was never mentioned there either.

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Let's agree that it is used frequently in teaching throughout Continental Europe and apparently not in the Anglo-Saxon curriculum... deal?
That's for sure. And it wasn't taught to my kids either in the Swiss system - though given other teaching practices, I wouldn't have been surprised.

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...But to answer your question, if I was talking about the class I would say "stat class". ...
*shudder*
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  #33  
Old 15.06.2012, 15:09
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Re: Math instructions at school: good or not?

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That's for sure. And it wasn't taught to my kids either in the Swiss system - though given other teaching practices, I wouldn't have been surprised.

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  #34  
Old 15.06.2012, 15:14
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Re: Math instructions at school: good or not?

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The point? To do it faster instead of actually start flipping around with the equations - and to make it more palatable to less mathematically inclined people
How is it faster?

How is it even any different?

Tom
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  #35  
Old 15.06.2012, 15:34
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Re: Math instructions at school: good or not?

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I have a maths degree from a UK university, and I've never heard of it. As others have pointed out - it's basic algebraic manipulation.

Maths is short for mathematics. Do you call statistics "stat" or "stats"?
....
This is a simple language difference based on geographics. In North America it is know as Math, in other places in the world the use the term Maths. If you look at the top Mathematics Universities, they will be using the term Math, not Maths (albeit they are American Schools, but nevertheless).

a quick search gave this:

"“Math” as a colloquial short form of “mathematics” first appeared in print quite a while ago, in 1847, although that “math” sported a period (“It rained so that we had a math. lesson indoors.”) and was thus clearly a simple informal abbreviation. “Math” unadorned appeared by the 1870s. “Maths” is a bit newer, first appearing in print in 1911."
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Old 15.06.2012, 15:49
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Re: Math instructions at school: good or not?

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If I wanted to evaluate x from the example given: a/b = c/x

then i'd just rearrange the equations using any valid (and more generic) rules.
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How is it faster?

How is it even any different?

Tom
From the example above: I for one (based on the automatism ingrained in me by the famous rule) I automatically multiply the known opposites, and divide by the remaining known figure without rearranging anything nor caring where x actually is in the equation.

It is not different in any way (the mathematical result post-rearranging and solving for x is similar).

The teaching rationale was that for folks lesser mathematically inclined it was thought to be easier to do the rote "multiply the opposites, divide by what remains" rather than master "solving an equation system".

Whether that was timed and demonstrated to be faster I do not know.

But the return of the French system to the rule after having abandoned it in the 70es must say something about its effectiveness in my opinion.
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  #37  
Old 15.06.2012, 15:58
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Re: Math instructions at school: good or not?

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The whole idea of letting kids "discover" mathematical concepts (which permeates current teaching dogma - at least on this side of the Roestigraben) is great from a "let's let the child play and discover" point of view - but seriously, are we really as a civilisation spend endless amounts of time rediscovering 2'000 year old theorems instead of building on them?
I agree. To horribly paraphrase Newton, we don't want the next generations saying:
"if I haven't seen further, it is because I spent my life trying to grow into a giant (instead of climbing on the nearest giant's shoulders)"
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  #38  
Old 15.06.2012, 16:41
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Re: Math instructions at school: good or not?

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This is a simple language difference based on geographics.
What, really?

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If you look at the top Mathematics Universities, they will be using the term Math, not Maths (albeit they are American Schools, but nevertheless).
Not quite sure what your point is here. That they use "math" because they're American, or because they're top, and you're trying to imbue some kind of authority?

Maths is clearly better, since the pun "math debates" doesn't really work. Unless you have a lisp.
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  #39  
Old 15.06.2012, 16:49
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Re: Math instructions at school: good or not?

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From the example above: I for one (based on the automatism ingrained in me by the famous rule) I automatically multiply the known opposites, and divide by the remaining known figure without rearranging anything nor caring where x actually is in the equation.

It is not different in any way (the mathematical result post-rearranging and solving for x is similar).

The teaching rationale was that for folks lesser mathematically inclined it was thought to be easier to do the rote "multiply the opposites, divide by what remains" rather than master "solving an equation system".

Whether that was timed and demonstrated to be faster I do not know.

But the return of the French system to the rule after having abandoned it in the 70es must say something about its effectiveness in my opinion.
You still have to find a,b,c, and x. Second, depending on the question asked the equation could be in the form of b/a = x/c and erroneously think of a/b = x/c. You still have to form the equation in your head.

Sally has a little business and works 5 days a week she makes 4 skirts any given workday. If she takes one day of, how many skirts will she make that week?

James has an orchard with 8 trees. He wants to expand he orchard with two additional trees. How many apples less does he collect right now when he will collect 500 kg in the future.

Miss Daisy is on the road for 4 hours. She is driving from Montgomery where she started to New Orleans which 310 miles away. So far she drove 240 km. How much longer will it take?

Snowball paint one nice and shiny doll every 5 minutes. Minstix on the other and paints 5 clowns in the time Snowball paints 4 dolls. How long so it take Minstix to paint three fire trucks?
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  #40  
Old 15.06.2012, 16:50
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Re: Math instructions at school: good or not?

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What, really?

Not quite sure what your point is here. That they use "math" because they're American, or because they're top, and you're trying to imbue some kind of authority?

Maths is clearly better, since the pun "math debates" doesn't really work. Unless you have a lisp.
...just supporting notes that 'math' is an acceptable term and not considered incorrect. If I was studying in the UK I would probably switch to the term 'maths' as well for seamless assimilation.

I still think the term "maths" sounds horrible, however the "maths debates" example is definitely an amusing superior application. I will switch the use for this case from now on.
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