On 29-5-2011 13:12, Rudy Velthuis wrote:
> 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.

You can in theory, but I am pretty sure you won't in practice. Or at 
least the vast majority of people won't. At the age you are normally 
learning it you need practical examples. Only much later on when you 
have mastered abstract thinking you can understand the process without 
being able to perform the process yourself.
That leaves open the question how much mastering abstract thinking is 
hampered by not learning long division at the appropriate age. Then 
again, I don't know what kind of games kids play nowadays, so abstract 
reasoning and the concept of algorithms may come in a totally different 
way than in my time. (Though my time as a teacher does not suggest that 
other way was very effective).


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On 29-5-2011 15:51, Orchid XP v8 wrote:
>>> 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!

My point exactly. Having learned it in one situation carries over to 
another. Proves how vital it was for you to learn at that point ;) See 
also my response to Rudy.

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

That you didn't think it through does not make it flawed ;)

>>> 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 Shakespeare and some dope
> addict named Coleridge...

Any relation with http://www.youtube.com/watch?v=JTD1QW3SM60 ?

>> 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.

It is not stupidity, they appreciate other things, like... like... whatever.

> 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...

Yes. Interesting isn't it.

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andrel wrote:

> On 29-5-2011 13:12, Rudy Velthuis wrote:
> > 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.
> 
> You can in theory, but I am pretty sure you won't in practice. Or at
> least the vast majority of people won't.

I'm not so sure. OK, I know lots of people who don't understand
fractions (I'm a dentist and most of my - especially younger -
assistants don't), and these usually don't know the tables very well
either, but I think that is because of a common cause: they hate maths.

I don't think knowing the tables is a prerequisite. It is just
correlated with an interest in maths, and that is probably a
prerequisite for the understanding (or vice versa).

-- 
Rudy Velthuis

"Computers make it easier to do a lot of things, but most of the 
 things they make it easier to do don't need to be done." 
 -- Andy Rooney.

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>> 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!
>
> My point exactly. Having learned it in one situation carries over to
> another. Proves how vital it was for you to learn at that point ;) See
> also my response to Rudy.
>
>> The rest of your argument seems to follow from this flawed premis.
>
> That you didn't think it through does not make it flawed ;)

You don't need to know the numerical value of pi to 40 decimal places in 
order to know how to use it. Similarly, you do not need to memorise 50 
figures of a multiplication table to understand how long division works.

>> I've often wondered how the hell we ended up in a society where being
>> stupid is considered a virtue.
>
> It is not stupidity, they appreciate other things, like... like...
> whatever.

 From what I can tell, "being rich enough to be able to afford stylists 
and makeup artists and photo editing staff to give you immaculate looks".

Either that or "being on TV".

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

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On 29-5-2011 22:58, Orchid XP v8 wrote:
>>> 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!
>>
>> My point exactly. Having learned it in one situation carries over to
>> another. Proves how vital it was for you to learn at that point ;) See
>> also my response to Rudy.
>>
>>> The rest of your argument seems to follow from this flawed premis.
>>
>> That you didn't think it through does not make it flawed ;)
>
> You don't need to know the numerical value of pi to 40 decimal places in
> order to know how to use it. Similarly, you do not need to memorise 50
> figures of a multiplication table to understand how long division works.

You do at the age you (or actually we, the old men in this group) 
learned long division.


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On 29/05/2011 10:03 PM, andrel wrote:
> You do at the age you (or actually we, the old men in this group)
> learned long division.

I never memorised the tables, as in being able to say 3 X 4 = 12. I had 
to recite them and stop at the right place.
Three nothings are nothing.
Three ones are three.
Three twos are six.
Three threes are nine.
Three fours are twelve.
Three fives are, oops!
Three fours are twelve.




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Regards
     Stephen

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On 29-5-2011 23:18, Stephen wrote:
> On 29/05/2011 10:03 PM, andrel wrote:
>> You do at the age you (or actually we, the old men in this group)
>> learned long division.
>
> I never memorised the tables, as in being able to say 3 X 4 = 12. I had
> to recite them and stop at the right place.
> Three nothings are nothing.
> Three ones are three.
> Three twos are six.
> Three threes are nine.
> Three fours are twelve.
> Three fives are, oops!
> Three fours are twelve.
>


Interesting, someone between old school and the calculator generation.
I think the most relevant question in this context is: Do you understand 
long division and if so at what age did you learn it?


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On 30/05/2011 11:49 PM, andrel wrote:
> Interesting, someone between old school and the calculator generation.
> I think the most relevant question in this context is: Do you understand
> long division and if so at what age did you learn it?

It depends what you mean by "Old" school. When I was at school, 
calculators were mechanical and you turned a handle to power them.

Yes I understand long division and I can generally divide by two digits 
in my head if the dividend is not too big. I really can't remember when 
I was taught it, at a guess I would say, about 9 years of age.

-- 
Regards
     Stephen

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On 5/25/2011 14:10, Alain wrote:
> It's a king of mental jogging :)

I used to be able to do 4 and 5 digit long division in my head, back in 
grade school.

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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On 5/29/2011 4:12, Rudy Velthuis wrote:
> simply because it is not very pragmatic not to know them.

Indeed. Actually, there was one event that eventually convinced my very 
smart wife that there are *actually* people in the world who are not very 
smart. She'd never actually encountered it as a gut feeling before.

We're in a store. We're buying something that's $20, but 60% off. The clerk 
is taking *minutes* to try to figure out the price. She finally digs out a 
calculator, figures out the answer is 12, and then hopelessly says "But is 
that the discount, or the price?" My wife finally snaps and goes "It's 60%! 
It's more than half!"

So, yeah, I think you must have at some point memorized the multiplication 
tables and used them a bit to get a feeling for such things.

Nowadays, I like to torture people when I buy $10.20 worth of stuff by 
giving the person a $20, waiting until they've rung it up, then handing them 
another $0.25 coin, and watch them struggle helplessly trying to figure out 
what the change should be on their own. (Actually, there's a dilbert about 
that that's pretty funny.)

-- 
Darren New, San Diego CA, USA (PST)
   "Coding without comments is like
    driving without turn signals."

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