Is this how they teach maths today?

i like this from wikipedia - catchy

PEMDAS (Parentheses, Exponentiation, Multiplication/Division, Addition/Subtraction, alternatively "Picking Eminem Made Dre A Star" or "Please Excuse My Dear Aunt Sally")

well 4+xy is obviously the same as 4+x*y as xy=x*y

so either 4+xy=14 or it equals 30,

I can't believe anyone with qualifications in maths would put it at 30. Except maybe teachers.

Al, even if you ignore BODMAS, there are 2 different answers to what is in front of you. Can't be dogmatic about it.

If you have four oranges and two lots of five apples, how many fruits do you have?

Yes, i guess you would never say 'I've got 4 of something, and 2 more, and i've got five lots of it'

That's not how you say that when you read it out loud though. You maths it like you speaks it.

ha, try this (from the wikipedia page)

4+2*5 on windows calc (simple mode) gives 30

4+2*5 on windows calc (scientific mode) gives 14

:)

:^0

We will agree to disagree. Brackets were invented to get rid of the confusion so why set questions that can be read in two different ways resulting in two different answers?

Was my time at school wasted? Maybe I learnt what I wanted to learn and blocked off all the rubbish taht they try and fill your heads with. The maths I learnt was good enough for use on Betfair - that's the important bit!

hahahha

Maybe Betfair just tried to change some code based on this thread and blew the site up?

I must confess to always using way too many brackets, but that's my inherent trust of other people at work

its obvious when you start writing algebraic equations isn't it

z+xy always means z + (x * y), never (z + x) * y

the question is obviously specifically designed to test the student's understanding of order of operations.

Hi Al, I think i was wrong to say there's two ways to read it. Why would anyone ever say 4+2 instead of 6? Thats how you have to read it to get the answer to be 30

the real problem I have with it is that it's teachers who didn't know this.

Surely at some point at teacher teaching school, they get taught to look out for potentially difficult or trappy looking questions that their classes might be able to make a mess of. It can't all be about putting cones on your head and pretending to be the solar system surely?

Is that what they do at teaching school?? That figures

those who can and all that lori.

primary school teacher with 1-4 years experience gets about the same as an assistant manager at mcdonalds.

although you don't get a minimum of 13 weeks holiday a year.

but surely there is a minimum level of qualification? don't you need to have passed some kind of mathematical qualification to teach maths?

grade c gcse if i remember correctly from the channel 4 program on on monday night.

Is that the grade they get with a 20% mark?

GCSEs are terrifying, I remember the first year they came in someone showed me their biology paper and one of the questions had 100 creatures drawn on the page and the question was "count how many of these bugs have wings"

Since then, the word is they've got easier :0

lower than i'd have thought.

to be honest though - the question was obviously designed to cause someone to slip up. It's a bit pedantic. They are probably taught to use brackets, and encourage kids to use them.

as i said on the other page i don't agree monkfish.

that question has been deliberately set to test the candidate's knowledge of order of operations.

Anyone who hasn't been taught BODMAS, hasn't been taught Maths, it's that simple. The Victorians knew of the principle and it's one of the things that separates Mathematics from simple Arithmetic. Maths includes Algebra and the equation given is algebraic.

and with a little bit of googling order of operations is taught in year 6 (10-11 apparently). most worksheets contain loads of question like the one asked deliberately testing BIDMAS/BODMAS/PEDMAS

agreed gallivanter, like much of what is taught (especially at A level which i did a while ago) it can be argued that it's not that useful in a day to day situation but the answer IS 14. mathematics follows an order of operations, BODMAS, which was still being taught (at least in the school i went to) in the 90s

Just for interest here are the other questions they asked:

1. 2 x 5 - 4 = (97% correct)

2 1/2 divided by 1/4 = (47% correct)

3. 1.4 divived by 0.1 = (34% correct)



Answers below:












1. 6
2. 2
3. 14

i am aware of that DStyle but the hope was to show up teacher's inability to teach maths.

They asked 188 primary teachers in the whole of England and use that to produce tv programmes and newspaper headlines about the state of the education system. I'm sure the mathematicians amongst us can comment on the legitimacy of that sample.

DStyle 17 Feb 11:06
and with a little bit of googling order of operations is taught in year 6 (10-11 apparently)

Do many teachers concentrate on lower age groups and others on the older ones? If they asked 100 primary one teachers this and none of them knew the answer then it wouldn't matter at all would it?

I'm not saying it shouldn't be a concern that teachers don't know maths but i'm not sure how big a deal this is

just thinking the same myself actually. i imagine that each teacher is assigned a year group and sticks to it so they'll probably be a lot of them that don't teach this topic.

as for the state of the education, having watched that channel 4 program, the problem really didn't appear to be with the teachers' knowledge of the entire syllabus; rather it appears that children get left behind because the teachers are unable to help all children conceptualise abstract mathmatical ideas.

along with the idea that you can either "do" maths or you can't.

the japanese have a very very different attitude.

It's a big deal because we expect primary school teachers to be at least slightly above average in intelligence and to have at least an average education. A grade C GCSE isn't too much to ask. What if a child asks a question? I still remember the teacher who assured us that the world wasn't anything near a million years old. She wasn't being religious, she really didn't know.

it's one thing complaining that they can't teach the syllabus but do you think they should be there to answer random questions thrown at them from the pupils on any subject?

When i used the phrase "big deal" it was in relation to who teaches what. I don't expect a Physics teacher to be able to teach me French - and i suspect there are some teachers in this study who never have to teach this year 6 level maths.

There are probably kids coming out of school who can't even do the 2 x 5 bit of the question even if they knew the order in which to do it.

i think that 2. and 3. are even scarier, especially 1.4 divided by 0.1 which is basically trivial with no traps, tricks or anything

the fact that more of them get question 2 than question 3 is something i find quite strange.

Does anyone know if this was a written test? Was it done over the phone?

I agree with that Monkfish, I'd have thought that dividing fractions in your head was harder than decimals.... I'm sure racing for change would agree :D

especially if they were asked in that order. if you got that one right you would have surely have been aware of being asked to divide by less than 1

In fact, were people possibly asked one question each?

I should maybe look into this myself instead of asking haha

I bet if you asked them what 10% off their sofa was, they'd all get it right.

do you think they should be there to answer random questions thrown at them from the pupils on any subject?

Yes, if the subject at the level of the question is taught in primary school.

These are primary school teachers. They should be competent enough to answer any questions that primary school children are expected to answer.

Isn't that like saying that a football coach should be as good a striker as Wayne Rooney? You don't have to be Wayne Rooney to be a good coach.

ok Gallivanter - but if the worst thing you can remember in your education was that your teacher didn't know the age of the planet then i wouldn't get too worried.

We're not talking about games where innate skill is often required, we're talking about simple things that ALL 11-year-olds are expected to master. If the teachers aren't educated enough or able enough to masterr them then they are in the wrong job.

Someone can teach a physical skill without being able to do it themselves. But how does a teacher teach knowledge without having the knowledge themselves?

For example, how can the the 53% that couldn't divide 1/2 by 1/4 teach children to do it if they don't know how to do it themselves?

actually are they all "expected to master" them?

Wayne Rooney: Hey boss, where do I kick the ball to score a goal?
Coach: Buggered if I know mate, do 20 more pushups.

never mind BODMAS do you remember silly old harry chasing a horse through our attic. eh those were the days

Do you really want this guy teaching your kids?

Enter Richard Dunne, an author and consultant who specialises in making basic maths calculations more tangible. Using paper cups to represent units, Richard asks children to model addition, subtraction, multiplication and division calculations (or

Oh deary f*cking me :(

Eek!

he was also referred to as potentially the Jamie Oliver of Maths? hahahha

Blackadder: You have two beans. If I give you two more beans, what do you have?
Baldrick: A casserole.

are they all "expected to master" them?

They're all taught how to multiply and divide using both vulgar and decimal fractions. All of the questions are deliberately set at a basic level so that all the pupils are capable of understanding and answering them.

what does that make
a very small casserole

http://www.guardian.co.uk/education/2010/feb/14/primary-teachers-fail-maths-tests

More about the results there.

Only 4% knew that 2 divided by zero is infinity???
It doesn't matter if its not a representative or significant sample. I'd be shocked that there's 149 teachers in the whole country who didnt know that, let alone in a group of 155

I wish they'd asked the pupils the same questions.

Certainly never heard of BODMAS, but multiplication and divsion certainly take priority over + and -. And I got a grade A in O level maths.

It breaks your heart that all these kids will never be able to understand their bets.

But they will be good casserole chefs.

:^0

I was shocked at times when I helped my kids with their GCSE maths revision...and they ended up with an A and an B !

You only need a C to be a teacher!!

Lori 17 Feb 10:45
the real problem I have with it is that it's teachers who didn't know this.

A disgrace, BODMAS is the next thing you learn after being taught the basic operations

Lori 17 Feb 11:48
I agree with that Monkfish, I'd have thought that dividing fractions in your head was harder than decimals.... I'm sure racing for change would agree

------------------------------------------

How many quarters go into a half? Surely not very difficult! You jus' need to understand what a quarter is and a half is.

I'm not claiming it was hard, just that multiplying by ten is trivial

Wonder how they got on with the Monty Hall puzzle?

Some sharp minds around

I wish they'd asked the pupils the same questions.

They did this was all on dispatches i think the other night, the kids just guessed numbers 12 or 6 or whatever. they were asked to explain how they got the number and they were bit sheepish :)

Probably discarded all the prizes and went to the pub brendan.

In engineering the answer is 14, no doubt.

However if you put it in a normal calculator I'd guess it might be actually doing:

4+2 = Y then 5*Y

which a scientific calculator will not do, it can accumulate (nest) multiple operations. The reason brackets are implemented is (partly) to alter the order of operations, if say you wish to +/- prior to * or /

I can understand why people might say 30 though, its not such a big deal but teachers thats another matter....on the other hand engineers can't spell or talk to woman.

most calculators should, and will, do the multiplication first

Honest Al 17 Feb 09:22
From this week's Sunday Times;

"Primary school maths teachers are failing to attain the standard of arithmetic expected of 11-year olds, new research has claimed".

They went on to ask a few straight forward questions, and this one caused the most problem;
What is 4 + 2 x 5 ?

"Only 20% of the teachers tested for a Channel 4 television documentary were able to work out the solution of 4+2x5 = 14, NOT 30 - multipication takes priority over addition".


Is this a wind-up? Since when did multipication take priority? I make the answer 30, and will always make the answer 30. No wonder the kids today can't add up.

Would you also say that 4 + 2 ^ 2 = 36
Or would you agree that it is 8?

Division by zero is an illegal operation btw. :D

Moonlight 18 Feb 00:19
Division by zero is an illegal operation btw. :D

from http://www.math.utah.edu/~pa/math/0by0.html:

" The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction.

To begin with, how do we define division? The ratio r of two numbers a and b:
r=a/b

is that number r that satisfies
a=r*b.

Well, if b=0, i.e., we are trying to divide by zero, we have to find a number r such that
r*0=a. (1)
But
r*0=0

for all numbers r, and so unless a=0 there is no solution of equation (1).

Now you could say that r=infinity satisfies (1). That's a common way of putting things, but what's infinity? It is not a number! Why not? Because if we treated it like a number we'd run into contradictions. Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity. If that's so, then
infinity = infinity+1 = infinity + 2

which would imply that 1 equals 2 if infinity was a number. That in turn would imply that all integers are equal, for example, and our whole number system would collapse. "

"Ask for example what we obtain when adding a number to infinity. The common perception is that infinity plus any number is still infinity. If that's so, then
infinity = infinity+1 = infinity + 2"

An infinite quantity of something cannot coexist with a finite quantity. Therefore adding a number to infinity is impossible (as is subtracting a number from it).

To give an example, say you construct a regular polygon with 5 sides, then with 6 sides, 7 sides etc. When you take a regular polygon with an infinite number of sides, you have a circle. You cannot add a side to a circle, to create a polygon with infinity+1 sides, nor can you take away any amount of sides to create a regular polygon with a finite number of sides.

Infinity is all encompassing. If 'everything' is contained by infinity nothing can be added to it.
Conversely nothing can be removed, as if this was possible, it could also be added again.

I can't prove any of the above, but it makes intuitive sense to me :D

BODMAS

Excuse my ignorance but how do you get a normal cheap calculator to give you an answer of 14 if you key in the following:

4
+
2
x
5

Not trying to be clever, but if that is how the question is written you would expect a primary school kid to follows what is in front of him/her.

An incredible haul, because you MUST be fishing.

get a better calculator

Definitely not fishing - just astounded that after 50'odd years being told that my maths is wrong. And everybody I ask thinks that this very simple sum adds up to 30.

Ask outside the staffroom Al ;)

I blame countdown

Not trying to be clever, but if that is how the question is written you would expect a primary school kid to follows what is in front of him/her.

definitely fishing after that one.

not really sure how relevent this is as i have no idea what profession the person who answered it was but on the weakest link this evening one of the questions was

Q: express 0.25 as a percentage
and the bloke answered: one quarter

thats pretty stupid. was like a 50 yr old man, should know better.

Q: express 0.25 as a percentage

as a percentage of what??

110

Wow

Either this thread is a massive wind up or the education system in the UK is horribly inadequate

Or both

Tracy has been given this maths question

4+2*5

Tracys answer is 30

Why is Tracys answer wrong?

Top answers ~

1. Tracy is a woman.
2. Tracy is a Teacher.
3. Tracy used a cheap calculator.

Honest Al, try it on a calculator, you will see the anwser if 14.

OMG!!The windows calculator gets it wrong. Even Microsort can't add up it seems.

slayerofthe'kins 19 Feb 13:59
OMG!!The windows calculator gets it wrong. Even Microsort can't add up it seems.

It gets it right on scientific setting though.

* and / take priority over + and -

tracy is a cross dresser .

Let x=y

Then x^2 = xy [multiplied by x both sides]

Then x^2-y^2 = xy-y^2 [subtracted y^2 both sides]

Then (x+y)(x-y) = y(x-y) [factored each side]

Then x+y = y [cancelled (x-y) both sides]

Then x+x = x [substitute x in for y]

Then 2 = 1 [divide both sides by x]

A little induction on the above result shows that any natural number is equal to any other natural number

So there's no need to be arguing over the different answers given, as they are really just the same

a=0
b=1
c=2

a*b = a*c
b=c

Proof that women are evil

Women require time and money

Women = Time x Money

and we know that time is money, so Time = Money...

Women = Money x Money = Money^2

And we know that money is the root of all evil

Money = Sqrt (evil)

Therefore

Women = (Sqrt(evil^2))

So we conclude that

Women = Evil

i solved it without calc... its 22

Eldrick:
Then x+y = y [cancelled (x-y) both sides]

Implicitly this is dividing by (x-y) but as you've stated that x=y then this is tantamount to dividing by 0 - which is not allowed. Anything divided by 0 is considered Not Defined (this is not the same as infinity) - as another poster pointed out, it is an illegal operation.

Same argument holds for the post that followed that one, where the initial statement was a=0.

There are any number of supposed 'proofs' that 1=2 or 1=whatever, they almost all hinge on performing this illegal operation in some form or other which is usually dressed up algebraically to disguise the tactic.

As to the main point, BODMAS rules the order of operations, nowadays it is taught as BIDMAS (the I stands for Indices).

Hence 4+2x5 is 14, and brackets are not necessary to arrive at that - but they may help clarify things for people. When using a calculator you should be aware of these BODMAS rules as not all calculators automaticaly adhere to them. It's traditionally the cheapo calculators that use the simpler algorithm, no excuse for Microsoft though.

Other good ones that trip people up:
What's the square root of 1/4?
What's the first prime number?

Eldrick:
Then x+y = y [cancelled (x-y) both sides]

Implicitly this is dividing by (x-y) but as you've stated that x=y then this is tantamount to dividing by 0 - which is not allowed. Anything divided by 0 is considered Not Defined (this is not the same as infinity) - as another poster pointed out, it is an illegal operation.

Same argument holds for the post that followed that one, where the initial statement was a=0.

There are any number of supposed 'proofs' that 1=2 or 1=whatever, they almost all hinge on performing this illegal operation in some form or other which is usually dressed up algebraically to disguise the tactic.

As to the main point, BODMAS rules the order of operations, nowadays it is taught as BIDMAS (the I stands for Indices).

Hence 4+2x5 is 14, and brackets are not necessary to arrive at that - but they may help clarify things for people. When using a calculator you should be aware of these BODMAS rules as not all calculators automaticaly adhere to them. It's traditionally the cheapo calculators that use the simpler algorithm, no excuse for Microsoft though.

Other good ones that trip people up:
What's the square root of 1/4?
What's the first prime number?

correct moonshiner, the post from investor after was basically restating the argument in far fewer lines, but the division by 0 was a little more in your face then

why is the first prime number question tricky? i can only guess that some people like to bicker about whether 1 is a prime, i have it in my head that it isn't but it will just come down to a convention rather than any illuminating logical argument

Moonshiner 20 Feb 13:11

[...]
Anything divided by 0 is considered Not Defined (this is not the same as infinity) - as another poster pointed out, it is an illegal operation.
[...]

It is considered undefined because accepting the answer infinity leads to an apparent contradiction. However the underlying assumptions can easily be challenged.

I was taught that 2 is the first prime because, for reasons I've forgotten, 1 isn't a prime.