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