> On 24/05/2011 21:40, andrel wrote:
>
>> The whole point of learning multiplication tables by heart is that you
>> need them to do all other computations in base 10.
>
> Most people would consider that you need a calculator to do any
> computations in base 10, beyond really trivial ones.

Trivial, like multiplying 2 random phone numbers in your head? :P
I've done that several times, just for the /fun/...
Take some random 10 digits number, then another random 7 digit number. 
OK. Now, without paper, what is the product? Hint, it's 17 digit long, 
possibly 18. Your pocket calculator can't give you the exact result.

>
>> If you don't know them by heart a large part of our culture is
>> inaccessible to you.
>
> Such as?
>
>>>> If not, I weep for humanity.
>>
>> I'll join you.
>
> I fear for the future of society, but for many reasons in addition to
> this...

:P Alain

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>> Most people would consider that you need a calculator to do any
>> computations in base 10, beyond really trivial ones.
>
> Trivial, like multiplying 2 random phone numbers in your head? :P
> I've done that several times, just for the /fun/...
> Take some random 10 digits number, then another random 7 digit number.
> OK. Now, without paper, what is the product? Hint, it's 17 digit long,
> possibly 18. Your pocket calculator can't give you the exact result.

Now, personally, I can't even *remember* a 17 digit number without 
pencil and paper, never mind *compute* it. :-P

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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>>> Most people would consider that you need a calculator to do any
>>> computations in base 10, beyond really trivial ones.
>>
>> Trivial, like multiplying 2 random phone numbers in your head? :P
>> I've done that several times, just for the /fun/...
>> Take some random 10 digits number, then another random 7 digit number.
>> OK. Now, without paper, what is the product? Hint, it's 17 digit long,
>> possibly 18. Your pocket calculator can't give you the exact result.
>
> Now, personally, I can't even *remember* a 17 digit number without
> pencil and paper, never mind *compute* it. :-P
>

Remember the 10 digit number and the 7 digit number.
Multiply the first one by the first digit of the 7 digit one.
Remember that.
Repeat for all other 6 digits.
Shift and add the 7 intermediate results.
DONE!

It's a king of mental jogging :)

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>>> Most people would consider that you need a calculator to do any
>>> computations in base 10, beyond really trivial ones.
>>
>> Trivial, like multiplying 2 random phone numbers in your head? :P
>> I've done that several times, just for the /fun/...
>> Take some random 10 digits number, then another random 7 digit number.
>> OK. Now, without paper, what is the product? Hint, it's 17 digit long,
>> possibly 18. Your pocket calculator can't give you the exact result.
>
> Now, personally, I can't even *remember* a 17 digit number without
> pencil and paper, never mind *compute* it. :-P
>

I forgot to tel that you should do it while walking in the city. Please 
use secondary streets.

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On 5/25/2011 4:10 PM, Alain wrote:

>
> Remember the 10 digit number and the 7 digit number.
> Multiply the first one by the first digit of the 7 digit one.
> Remember that.
> Repeat for all other 6 digits.
> Shift and add the 7 intermediate results.
> DONE!
>
> It's a king of mental jogging :)

Crap! no way I could do that, my working memory does not have enough 
capacity!

-- 
~Mike

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On 25-5-2011 9:48, Invisible wrote:
> On 24/05/2011 21:40, andrel wrote:
>
>> If you don't know them by heart a large part of our culture is
>> inaccessible to you.
>
> Such as?

basically most of the mathematical knowledge.


-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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>>> If you don't know them by heart a large part of our culture is
>>> inaccessible to you.
>>
>> Such as?
>
> basically most of the mathematical knowledge.

I don't see why you need to memorise multiplication tables to understand 
mathematics.

Indeed, one of the most important things I learned at college is that 
mathematics is *not* just about memorising multiplication tables. 
There's actually far more to it than that. The fact that my school 
education completely failed to mention this is... rather worrying.

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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On 28-5-2011 14:36, Orchid XP v8 wrote:
>>>> If you don't know them by heart a large part of our culture is
>>>> inaccessible to you.
>>>
>>> Such as?
>>
>> basically most of the mathematical knowledge.
>
> I don't see why you need to memorise multiplication tables to understand
> mathematics.

You can not understand long division or long multiplication without 
those tables. That means that e.g. the whole concept of prime number 
becomes void. As will be most things in number theories. Not that you 
actually need them, but not having a feeling for numbers will reduce it 
to a collection of unrelated facts.
How to understand how to do long division with polynomials or binary 
numbers without knowing how to do it with base 10 infinite precision 
numbers?

What I am trying to say is not that the multiplication tables are 
important, but that they are needed for the next steps. Long 
multiplication and long division are among the first algorithms kids 
learn. Skip them and everything in maths and physics (and ...) that uses 
algorithms will suffer greatly.

> Indeed, one of the most important things I learned at college is that
> mathematics is *not* just about memorising multiplication tables.
> There's actually far more to it than that. The fact that my school
> education completely failed to mention this is... rather worrying.

And that relates to the other thing I want to get across: maths is part 
of our Culture. As a teacher your task is to get across how beautiful it 
can be.
ATM the problem is that some decades ago a process was started by which 
the teachers teachers were selected on other grounds than knowledge of 
the subject. Being taught by people who equated maths with boring sums 
and stupid tables, the next generation was even worse. With time the old 
teachers resigned and the young generation took over. In short: we are 
in a downward spiral.
At the same time also politicians were recruited more and more from the 
humanities departments (IIRC none of the politicians of our ruling 
parties have a degree in any science of technology subject. In the 
largest opposition party we have one real scientist (was professor in 
biology, became minister of education and lost the election). In total 
we have 150 members of parliament.) Culture is redefined as anything but 
science by these incompetents. Not understanding maths is now considered 
something to be proud of by those who think of themselves as the elite 
of this society. That spiral will make have to make a few more turns 
before it goes up again.
I hope Asia will be the guardian of this piece of human culture this 
time, like the Arabs in mediaeval times. In the western world science is 
on it's way to become extinct with very few changes of stopping the process.



-- 
Apparently you can afford your own dictator for less than 10 cents per 
citizen per day.

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andrel wrote:

> On 28-5-2011 14:36, Orchid XP v8 wrote:
> > > > > If you don't know them by heart a large part of our culture is
> > > > > inaccessible to you.
> > > > 
> > > > Such as?
> > > 
> > > basically most of the mathematical knowledge.
> > 
> > I don't see why you need to memorise multiplication tables to
> > understand mathematics.
> 
> You can not understand long division or long multiplication without
> those tables.

One note: I think people should know them by heart and also be able to
do simple calculations in their head, simply because it is not very
pragmatic not to know them. You can't and shouldn't, IMO, always revert
to a calculator for that. It keeps you fit, up there.

But knowing these tables by heart does not help in *understanding*
anything. The knowledge only helps in applying that understanding a
little more pragmatically.

I can understand long division and multiplication, prime numbers and
number theory principles very well without knowing the multiplication
tables by heart.
-- 
Rudy Velthuis

"Go away...I'm alright." -- H.G.Wells, dying words

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>> I don't see why you need to memorise multiplication tables to understand
>> mathematics.
>
> You can not understand long division or long multiplication without
> those tables.

You need to know what a multiplication table *is* in order to understand 
long multiplication and long division. However, you absolutely do *not* 
need to memorise the contents of said table to comprehend mathematics.

I have no idea what the corresponding tables are for octal. But I still 
understand how long division works in octal - i.e., THE EXACT SAME WAY 
AS IN DECIMAL!

The rest of your argument seems to follow from this flawed premis.

>> Indeed, one of the most important things I learned at college is that
>> mathematics is *not* just about memorising multiplication tables.
>> There's actually far more to it than that. The fact that my school
>> education completely failed to mention this is... rather worrying.
>
> And that relates to the other thing I want to get across: maths is part
> of our Culture. As a teacher your task is to get across how beautiful it
> can be.

Agreed.

FWIW, my teachers also utterly failed to demonstrate that literature can 
be enjoyable. The only literature we did was Shakespear and some dope 
addict named Coleridge...

> Not understanding maths is now considered
> something to be proud of by those who think of themselves as the elite
> of this society. That spiral will make have to make a few more turns
> before it goes up again.

I've often wondered how the hell we ended up in a society where being 
stupid is considered a virtue. Apparently a few centuries back, 
everybody who was anybody had to know and be able to debate the finer 
points of (say) Lord Kelvin's new theories about thermodynamics...

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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