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scentless_apprentice:

bgy1mm:

The decimal place value system isn't maths - in fact the vast majority of numbers are no longer represented that way.

 

Explain.

We use base ten for representing number because we have ten fingers, a biological rather than a mathematical fact. There's nothing special about base ten numbers from the mathematical point of view, therefore nothing special about the 10x10 multiplication table.

The two logical place-value systems are base 2 and base phi. Virtually all modern computers use base 2 (a few use binary-coded decimal, a sort of hybrid of base 2 and base 10). Since most numbers are represented electronically, there are many many binary numbers for every decimal number - for instance the machine I'm typing this in now has about 4 trillion binary numbers in its memory, and shows maybe 20 decimal numbers on the screen at present. Reals are usually represented in IEEE floating point format. No base phi computer is currently in mass production, but base phi has theoretical advantages and the idea is often discussed.

Obviously, understanding the way your culture represents numbers is fundamental, but it isn't. strictly, mathematics. A person from another culture could do the same mathematics with a different representation. 

bgy1mm:

scentless_apprentice:

bgy1mm:

The decimal place value system isn't maths - in fact the vast majority of numbers are no longer represented that way.

 

Explain.

 

 

We use base ten for representing number because we have ten fingers, a biological rather than a mathematical fact. There's nothing special about base ten numbers from the mathematical point of view, therefore nothing special about the 10x10 multiplication table.

The two logical place-value systems are base 2 and base phi. Virtually all modern computers use base 2 (a few use binary-coded decimal, a sort of hybrid of base 2 and base 10). Since most numbers are represented electronically, there are many many binary numbers for every decimal number - for instance the machine I'm typing this in now has about 4 trillion binary numbers in its memory, and shows maybe 20 decimal numbers on the screen at present. Reals are usually represented in IEEE floating point format. No base phi computer is currently in mass production, but base phi has theoretical advantages and the idea is often discussed.

Obviously, understanding the way your culture represents numbers is fundamental, but it isn't. strictly, mathematics. A person from another culture could do the same mathematics with a different representation. 

 

Hey bgy1mm, why are you posting on the Sabbath?

Won't that other theoretical construct - what do you call him/her/it... god? - get theoretically upset with you and send you to a theoretical hell?

 Over the last 5 or 6 years I have taught kids from the Dutch educational system - both public and private - and the results have not been positive.

Not one student has had the technical ability to cope with a high level mathematics course. Understanding of mathematics, maybe, but technical ability, no. Without this they cannot get anywhere.

So something is going wrong, somewhere along the lines in many countries of the world when it comes to mathematics teaching. 

The only countries that appeared immune from this were China and South Korea, however even now we are beginning to see the odd student from those countries lacking in technical ability. The common denominator seems to be that they were educated in an international school following the English National Curriculum.

On the surface of it, the NC seems to be ok. Yet the implementation of it, or at least how the implementation of it is taught in Teacher Training Colleges is severely hindering mathematical learning and understanding.

 Do you actually read what people write?

OH DEAR!

This can of Oxbridge academics approach to the teaching and learning of mathematics and debates using words and langauge that the majority of adults (let alone children) dont understand leaves me cold to be honest.

Curriculum - dictated teaching methods - APP - test etc etc all count for very little IMHO.

What matters (and yes there is plenty of academic reaserch to support this to keep the boffs happy) is the realtionship between the pupil and the class.  Without it everything else is destined to fail.

So if I need to be a bit imaginiatve in what topics I teach , creative in the way they are presented or if I need just to rote learn some basics or do some consolidation excercises - all will be successful if the students are behaved well and set expectations that they will engage with the lesson.

If they spend more time throwing paper pellets and listening to Itunes then all of the above debate becomes irrelevant.