>> 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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