OT Teaching Math from the 50's to Today

They usually added "assume pi to be 22/7"

Your answer is wordy, but you don't actually explain why it works, any more than I did.

I was using E(E(Y|X)) = E(Y) which I think is called the tower property. Would students be expected to prove that? It's a long time since I was at school.

Yeah, I guessed you were hinting at that, but I couldn't see how a calculator would give that result.

I usually preferred 355/113 as being accurate to 6 decimal places.

I used Brian's method - I think it's clear enough. Here it is again: 'Mean' = total score / no. of pupils So total score = mean x no. of pupils = 60 x 30 = 1800 For the girls, total score = 54 x 20 = 1080 The boys' total must be 1800 - 1080 = 720 The boys' mean is 720 /10 = 72

If you say so.

I recognised your method.

If you used it, you would be expected to state: E(E(Y|X)) = E(Y) first then drop the numbers in.

Other than in the very simple questions, candidates are expected to show more than numbers which happen to arrive at the right answer.

I think one of the criticisms over here are that they do not focus on the real world use of maths, In your example they did at the start, by the end it is assumed everyone does it on calculators or similar, and need not know the workings. I blame the Greeks myself.

Maths was far better before they got involved.

As for social comment. No I've never actually heard of those later ones, since that world not be in Maths, but something else. I also don't see how you can attribute human emotions to animals when you really do not know if they have a sense of self in the first place. Certainly some do, like dogs, Elephants, and many Whales and Dolphins, but that is mainly developed due to their way of life over the millions of years and generations. Does a bumble bee have a sense of self? Brian

Well, you didn't mention boys and girls partition the class.

Not just mine, I copied Fredxx's method. Even though he did it wrong, it was obvious what he did wrong.

So yes, it was pretty obvious what was being done.

On the other hand, none of us stated that we assumed boys and girls partitioned the class. None of us gave a formula for mean.

Well, fine, but that is rather arbitrary. I see it used all the time without explanation. It is about the most basic rule of conditional expectation.

The rules of arithmetic can be used without mention?

Yes, but what are they supposed to show? I'm reasonably proficient, and yet had no idea what, you say, the examiner wanted.

The National Curriculum has an emphasis on mental maths, method ( showing working), and practical applications.

These are carried through to GCSE maths.

OFSTED expect to see evidence of, for example, mental maths during inspections. I?d imagine it would be serious if they didn?t see it.

Both GCSE and KS3 NATS ( SATS as they used to be) have calculator and non- calculator papers.

Certainly the A levels did until I retired. They may have changed since. That said, there isn?t much actual calculation in A level maths.

Perhaps you should read it again?..

"I blame the Greeks myself"

Bloody Xi :-)

Andrew

Yeah, I can't see it. That is what I found hardest about O'level Maths, trying to guess what was actually meant. A'level was a little better, but it wasn't until degree that the language became more precise and hence easier to understand.

Along a similar vein, car manufacturers owner manuals in the 1960/70's used to advise on how minor maintenance tasks could be performed by the owner, the latest one's are full of warnings not to drink the battery acid and the like, makes you wonder what happened to common sense.

Lawyers and the nanny state

Often power tools now come with a warning booklet full of safety do nots that is larger than the instruction manual. I suspect that the first thing in the box discarded is the safety instructions full of petty warnings. People reading the instructions are unlikely to find the one or two real safety concerns when using the equipment - the warnings will have been carefully hidden in the bit about not using your angle grinder when taking a bath!

I forgot all maths I ever learnt after a couple of years.....

My problem with this is that it's an artificial problem of the sort that would never occur in the real world. Who would have only the information given and would want to know the answer to the question? No wonder pupils hate maths if they can't see any benefit.

Well are you saying that 71.9999 (9 recurring) is not 72 or is 72?

Not sure what the comma at the end meant? I assumed it was supposed to be the dot at the top and like me you have no way of doing that on a computer on the newsgroup.

Cheers

Adam