School Maths: 12 divided by zero = 12?!

[WeBuiltThisBuffetOnSausageRoll]

My DS came home yesterday quite sad and frustrated because he other classmates had lost marks in a school maths (his best subject) test for not getting the 'correct' answer that '12 divided by zero = 12'.

His reaction, upon coming home, was to look up the expected result of dividing by zero on several reputable maths sites and, as expected, none of them gave the answer that 'X divided by zero = X'. They all backed up his (and my) reckoning that the only possible correct answers could be 'undefined/impossible', 'infinity' or (possibly, at a real outside semantic push) 'zero'.

Thankfully, the teacher raised it the following day (I don't know if she had looked into it herself - it was a centrally-set test - after seeing the pattern of usually-able children unexpectedly all getting it 'wrong') and re-instated all the lost marks; but I'm still baffled as to how anybody could arrive at that answer in the first place, and it's bugging me!

Suppose the sum had been the simpler '12/2=6', the reckoning process would mean that you could have 12 apples and remove 2 apples 6 times, thus ending up with zero apples afterwards (as a valid 'checksum'); equally with '12/12=1', you could remove 12 apples once and again end up with the sum-validating 0 apples; but if 12/0=12 were true, you could thus remove 0 apples 12 times and be left with 0 apples - but of course, you wouldn't have 0 apples left after that: you would have 12 apples left; indeed, just as you would have if you removed 0 apples a thousand billion times!

Was this just a brain-fart by a tired maths test-setter - and one that wasn't immediately obviously wrong to a maths teacher yearning for half-term, who initially insisted that it was right when it was queried - or is there some kind of maths/philosophy train of reasoning that any boffins out there know of by which you could legitimately justify/argue that 'X/0=X' can indeed be correct, the same as 'X-0=X' naturally would be?! It doesn't really matter, obviously, but it's still irritating me a bit!

I think physicality, i.e. apples, boxes, cutting up a pizza, etc., works at the very earliest of stages, i.e. the first few years of primary, when you're dealing with VERY simple numbers, fractions, etc. Like number lines which have a use at the most basic level for adding and subtracting. BUT, it seems that schools/teachers don't move on from them soon enough and try to use them for more complicated things. I.e. my son's primary tried to teach multiplication and division by using number lines! And as we've seen from earlier posters in this thread, the basics/simple ideas simply don't work when it comes to more complicated things, hence the dividing 12 apples by 0 conundrum. Teachers really shouldn't be dividing by zero in primary schools as it's simply not a concept that primary pupils (nor their teachers apparently) have the "tools" to cope with. Teaching a wrong answer at an early age helps pupils to develop the "I can't do Maths" mentality that causes so much damage - far better just to avoid the difficult areas and concentrate on the simpler/basic stuff at young ages.

😂

I'm definitely getting fatter on this thread with all the apples, sweets and pizzas I'm eating to get them to zero. I soon won't be understanding Rene's posts with dresses and wardrobes as they won't fit so be sent to charity...then there will be 0 dresses. Hmmmmm... both zero in the end 🤔

That's still ignoring the fact that some people really can't do more advanced maths simply because of how their brains work. Their brains just can't understand such abstract concepts. It's not a case of being taught badly or not wanting to "take a leap of faith". It's just their brains. I am an intelligent person. I'm also autistic, dyspraxia and have ADHD. One or all of those things has made it so that I just can't wrap my head around this stuff. I also can't do physics. Light, waves, radiation. Nope! How about space and the universe? Double nope. The universe is expanding. Into what? Into nothing. It just is. 😭

Ah but can you convert your weight from stones into centimetres then calculate the change in potatoes? Without using a calculator!

@BadNomad

That's still ignoring the fact that some people really can't do more advanced maths simply because of how their brains work.

Hence why I think that the basics/simplistic Maths needs to be concentrated on, especially in earlier years, with the more complicated/abstract stuff completely ignored until later years and only for those who have the capacity to learn and understand it.

I believe that a lot of the UK's problem with Maths is that it's taught at too high a level, too early. That just makes people think they're crap at Maths and stops them from even trying.

Whoever thought that setting a "divide by zero" question to primary pupils was a good idea shouldn't be anywhere near teaching Maths!

People can't move on to complex Maths until they've absolutely mastered the basics of numeracy and are confident with the simple stuff. It's like trying to teach algebra and simplifying/manipulating equations to people who don't know their times tables nor prime numbers - it's just setting pupils up for failure and complete loss of confidence.

Isn't there talk of making maths compulsory until 18-years-old? If they do that then they really will need to revamp what is taught and when. I barely scraped a pass at GCSE. I would have quit education complete if I'd been forced to do 2 more years of it.

People need to know functional maths. The stuff they will need to know in their day-to-day lives. Percentages. Distances. Weights. Scales.
Everything else should be optional.

Like number lines which have a use at the most basic level for adding and subtracting. BUT, it seems that schools/teachers don't move on from them soon enough and try to use them for more complicated things. I.e. my son's primary tried to teach multiplication and division by using number lines!

We had similar concerns with primary school teaching - number lines and numicon till Y6 even if like our kids they'd made the leap to abstraction and patterns.

We were also told DS didn't have a maths brain by early primary school teachers - he just sat GCSE maths early and got an A star ( we are in Wales where A star to G remains and early sitting still allowed). What he needed was less "fun" group activities and clear explanations and lots of practise - very like how DH and I were taught found thankfully via online site.

DD1 has a primary year when she was told maths was for boys and hard - she didn't do as well as previously - she also by Y2 hadn't really understood place value which was fine apparently which did lead to her transposing numbers incorrectly which may have been a sign she had dyscalculia we were told - it went away as an issue once she had firmly grasped place value.

We stepped in mainly with mathsfactor and they are all now apparently naturally talented at maths according to their teachers .

I agree. I've always thought the 11+ exam was set at a pretty good level, i.e. covering all the basics as you mention, plus fractions, and VERY simple algebra. I have often wondered whether we should concentrate towards something very similar as a "numeracy" qualification that pupils can take at various points during their school years when they're ready. And then, and ONLY then, move onto the more complex Maths i.e. trig, pythagoras, more complex algebra, matrices, etc. So if you pass your "numeracy" exam at, say, 12 or 13, you move onto "Higher" maths or similar description, but if you don't, you stay in "numeracy" lessons until you pass it, whether that's aged 12/3 or aged 15/6. There really is no point at all in trying to teach solving simultaneous equations to pupils who can't do basic equations etc.

I love this way of looking at it!

That's interesting. In Ireland, Maths is a compulsory subject for the entirety of secondary school, along with Irish & English. (But Leaving Cert (A level equivalent) is 6 subjects, most do 7, some do more - so not as in-depth as A level subjects)

So many people do hate Maths (and Irish - but that's a different conversation!). I think there's a lot of validity in ensuring Maths is taught the whole way through. I loved some areas, like calculus, and geometry. I struggled with others like probability.

I've really enjoyed reading the posts by people who love Maths & can explain it well eg with the use of equations.

I think the point that when we try to overuse practical examples it falls down for higher level concepts is a good one - I would have struggled with the concept of negative numbers, square roots and so on because they weren't 'real'.

There is a "numeracy" GCSE in wales - most pupils take numeracy and maths GCSE.

It's being scrapped next GCSE update in a few years and going back to just maths GCSE. Though they are doing same with English there will just be English not current language and Lit and much more controversially just Science GCSE and not option of triple science like now.

Infinity.

Sine, cosine and tangent do have physical correlates though. They are just ratios of one angle to another angle (more or less).

I was just listening to Rutherford & Fry's last episode of this series, which is about the impossible/imaginary square root of -1. This is apparently a useful tool for some purposes in maths, despite being non-existent. The OP's DS might enjoy it - and decide whether to become a mathematician or not. Or maybe just to use the information to taunt his teacher!

It's available on BBC Sounds here: www.bbc.co.uk/programmes/m001j432

Fractions get turned into pizza. I can understand trig in so far as I can visualise circles and can therefore visualise angles. But sine, cos and tan can fuck off. And take surds with them.

Take your pizza slice and cut it into a right angle triangle.

Sine Cos and Tan are all about the ratios of the lengths of the sides.

So if you take a personal pizza (small) and you have a triangle with the exact same size angles as an extra large pizza say 90 degrees and 2 45 degree angles as an example. The ratios of the lengths of the sides will always be the same.

Sine is the ratio of the side opposite the right angle with the longest side of your pizza for example.

This makes no sense at all. Multiplication works the same backwards ( eg 2x4=8 & 4x2=8) so if Xx0=0 0xX=0.

It's just pure common sense, surely?

If you have 1 bag of 12 apples you have 1x12=12 apples.
If you have no bags of 12 apples you have 0x12= 0 apples.

While we're at it...I have never understood why X x 0 = 0 ...
If you have 12 apples and multiply them by nothing, the 12 apples still exist don't they?

Again I think it helps if you have a more wordy understanding of what divide or times means.

I distinctly remember a maths teacher telling us that "times" means "lots of". So if you have 1 x 12, that's 1 lot of 12. 0 x 12 means 0 lots of 12, therefore, nothing. 0.

A bit like whoevers law of magical something that if you have some food you can make more of it, but you can't magic food out of nothing.

Sine is the ratio of the side opposite the right angle with the longest side of your pizza for example.

God my brain isn’t working today sine is the ratio of the side opposite one on the non right angles with the longest side gah!

Soh
Cah
Toa

That is burned into my brain, along with Meth, Eth, Prop, Bute.

You can have no lots of 12 apples, or 12 lots of no apples. Either way, no apples.

That's how I was taught. Those people saying it's split into 0 group, so the answer should be 12 is mixing up with splitting into one group. When there's no group, it's not meaningful. Certainly can't be 12.

Love a maths thread.

Dividing by fractions is fun. What are you actually doing in 'practical terms'?

So if I have 20 / (1/10) - you are effectively asking how many groups of 1/10 can you make from 20.

I think that division with fractions is always taught too abstratically. (not a word)

Where as - we are having a buffet. Each person needs 3/4 of a pizza. We have 20 pizzas. How many people can we feed?

They're confusing "it's impossible" with "not dividing".

The dresses/wardrobes thing probably illustrates this better than the sweets/children. It's easier to understand that you're not a wardrobe, and therefore holding 12 dresses doesn't mean you've hung 12 dresses in a wardrobe. Sweets and children can make you visualise standing there with sweets without understanding the point that you're not a child and therefore haven’t divided.

Lady Muck is shouting at you because holding on to the dresses isn't hanging them in wardrobes. You're not a wardrobe so holding them doesn't fulfil the task.