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Innumeracy of note

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Innumeracy of note

Old 23rd Aug 2020, 16:15
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Grrr Innumeracy of note

Back in the good old days, the average person used to take pride in having a robust grasp of basic maths: enough mental arithmetic not to be overcharged at the shops, enough skill with pen and paper to make more complex calculations. *
I observed this event nearly twenty five years ago, on public transport.

Three people walk onto the bus and one person asks for,
"Three nineties."
After a long pregnant pause, the person asked,
"How much is that ?".
Fortunately, the bus driver twigged.
This person didn't know how much to give the driver.
"That's two dollars seventy, please."

At a dinner party that evening, I related this tale. and a property manager of a real estate agency said,"I don't know that, I'd use a calculator."

A few years after this I went back to University to do math. The lecturers were quite clear about developing a skill with pen and paper to make more complex calculations. This was the skill needed to do the exams. Write out the equations and cancel if applicable. The questions were formed in such a way that if you had developed simple numeracy using pencil, or biro, it all canceled out simplifying the answer. However, if you hadn't developed that skill, you had a difficult data entry problem. You'd have to keep entering the same number, or multiples thereof, into both top and bottom of the fractions in the equation.
You can get the answer using a calculator. Sure made the poor mutts sweat.
Awful lot of key tapping going on. Also, you couldn't get away with a pre-programmed calculator. The question would have had to be known in order to pre-progam the calculator. The lecturers knew how to confound a calculator.
Wait, there's more.
Recently, a millennial Lab Manager of a large company showed me a simple equation to model reactant / product. X is reactant and Y is product.
Y = X / ( 1 - X ).

The question was, "How do I work out what X is?"
Well, I felt like the bus driver. You just have to wince and then write it out.

Y*( 1 - X ) = X.
Y - X*Y = X.
Y = X + X*Y = X*( 1 + Y ).
And so,
X = Y / ( 1 + Y ).

If I couldn't do that by the age of twelve, in an era when social promotion had not been thought of. I would have been told that I would be going to the local Technical College next term. There was a consensus among the other boys that it was one step removed from Borstal.
"Make your choice, punk."
A threat that motivated me, and the others, to acquire the necessary skills.

There are young people today who have been cheated in their education. No number of laptops or calculators can give you simple numeracy.

I thought that it might add humor to the pages of PPRuNe if people posted their own examples of innumeracy. Schadenfreude is always funny. Like the journalist who said how much he enjoyed buying a politician's autobiography from the seconds table outside a book store.
"It's alright. I'll wait till it's a dollar. Even more enjoyable."

*Shamelessly pinched from another post.
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Old 24th Aug 2020, 08:51
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When were the 'good old days'?
Not at one of the schools I attended in the '60s where you would be shouted at (or insulted) in some classes for having difficulty in understanding or performing tasks. I've got a grip of arithmetic but come up against a firewall with the likes of algebra, equations, formulas, logs etc. I've never needed to use them as a hands-on engineer anyway. The eggheads found them child's play but I seem to remember a lot of them being very clumsy at art, woodwork and metalwork.
There's a little of Brave New World in Nature - (almost) everyone has a role. No point in brilliant inventions if there's no one to build or repair the products.
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Old 24th Aug 2020, 09:21
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Anyone remember being taught binary? What a pretty pointless exercise. 1+1 = 10, I think? I was taught it as an eleven year old and never saw or heard of it again.

The columns being 16, 8, 4, 2, 1 instead of being tens thousands, thousands, hundreds, tens, units.

1010 = 2+8 (10)
1001+ = 1+8 ( 9)
——— ———
10011 = 16 + 2+1 (19)
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Old 24th Aug 2020, 09:26
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When I left school one "good" career option for the more numerate was to become a bank teller, from which one could expect a job for life and reasonable prospects of eventually becoming the middle-class stalwart of society - a bank manger! Roll-on a few years and I suffered the indignity of applying for a mortgage. The mortgage specialist in the bank was obviously innumerate, struggling with numbers of zeros in spoken numbers that I wrote a complaint to the bank (who seemed utterly unconcerned). The same bank later tried to get me to pay Ł10/month for the privilege of my custom; while explaining the annual benefits I had the jaw-dropping experience of seeing the adviser get a calculator out to work out how much the annual fee would be. Obviously banking jobs are based more on nepotism than numeracy these days.
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Old 24th Aug 2020, 09:41
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Originally Posted by BehindBlueEyes View Post
Anyone remember being taught binary? What a pretty pointless exercise. 1+1 = 10, I think? I was taught it as an eleven year old and never saw or heard of it again.
There are only 10 types of people in the world: Those who understand binary, and those who don't

PDR

PS - please understand that most of what is being discussed here is arithmetic - not mathematics.
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Old 24th Aug 2020, 10:31
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Binary is actually quite important in the world of digital electronics!

One big issue with maths is the quality of teaching. My partner's brother had difficulty with maths at school. He gained an Engineering degree at Southampton but did not enjoy engineering. He is now a school maths teacher! With his nature and personal experience I believe him to probably be a very good maths teacher.

When I was at at my junior school we had an inspiring headmaster. If he was teaching us he would often give us some simple mental arithmetic questions at the beginning of our lesson. He made it fun. I am lucky that I have always been able to do many calculations in my head, it is very useful for gross error checks. These days I am often bemused that a calculator is needed for reltively simple addition!
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Old 24th Aug 2020, 10:41
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When No. 1 daughter had just started school, for fun I taught her to count in binary on her fingers. I wonder if that's why she's now a software engineer.

I had a couple of reasonably good maths teachers at school, but by far the best ones were the practising surveyors later at tech college, who were teaching part time.
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Old 24th Aug 2020, 11:05
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It all depends on the context in which you use the values you are calculating. Good mental arithmetic is very useful, I totally agree.

​​​​​For non-critical numbers, mental arithmetic or scribbling on paper is fine.
For critical calculations, why not use a calculator?
I am an automation engineer in a pharmaceutical company. We simply must avoid at all cost any chance of errors as lives deoend upon it...literally.
So we not only eliminate - as far as possible - human error, we also have all calculations checked by a second person.

This isn't dumbing down, it's making sure we don't kill anyone.

Horses for courses.
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Old 24th Aug 2020, 11:09
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Originally Posted by M.Mouse View Post
Binary is actually quite important in the world of digital electronics!

When I was at at my junior school we had an inspiring headmaster. If he was teaching us he would often give us some simple mental arithmetic questions at the beginning of our lesson. He made it fun.
Unfortunately, there are not enough teachers who inspire or make it fun. Even the less gifted will learn something useful from teaches who do have those attributes.

The other thing that some teaches fail to do is give practical reasons for understanding arithmetic. For example, if you told kids that if they knew the difference between say 10% off, or two for Ł10 on a certain item, you could compare and see which one is the best value. If they can see that they could save money, some of them will be more inclined to learn. Sadly there are a lot of lower income adults who never learnt that and do not know the difference, but had they, if could have had quite an impact on their finances.
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Old 24th Aug 2020, 11:20
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I was never a fan of arithmetic and maths, but learnt it as instructed.
I was, however, allergic to Chemistry and Biology, with an additional dislike of Physics.

So I told skool that I would not do them as O levels.

Their revenge was to make me do 3 maths O levels. - Maths, Add Maths and Statistics.

The real value of Statistics was pointing out to various Uni lecturers/lechers how bad their Statistics were. Bad use of Stats is endemic in the UK. I guess Trump didn't study it, either.
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Old 24th Aug 2020, 11:20
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I repeatedly fall down when it comes to arithmetic.
I'll generally sail through all assessments or aptitude tests until it comes to anything involving numbers and there I'll fall flat on my arse.
I'm particularly bad under pressure which made my performance in the 'individual problem' at OASC a sight to behold. Shame because again, I'd passed all the aptitude tests.
I've often wondered if I have some form of numerical dyslexia?
I blame my teacher in primary who left me in tears after I couldn't recite the 0 times table. Scarred me she did.
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Old 24th Aug 2020, 11:24
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Originally Posted by PDR1 View Post
PS - please understand that most of what is being discussed here is arithmetic - not mathematics.
You mean it's arithmetic, rather than other branches of mathematics.
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Old 24th Aug 2020, 11:46
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Arithmetic or mathematics, I'll leave you pedants to fight it out.

I was always useless at both, but by far the most important thing that was ever hammered into me at school was the 10x table. Learnt by rote in junior school.

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Old 24th Aug 2020, 12:00
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Originally Posted by M.Mouse View Post
Binary is actually quite important in the world of digital electronics!

One big issue with maths is the quality of teaching. My partner's brother had difficulty with maths at school. He gained an Engineering degree at Southampton but did not enjoy engineering. He is now a school maths teacher! With his nature and personal experience I believe him to probably be a very good maths teacher.

When I was at at my junior school we had an inspiring headmaster. If he was teaching us he would often give us some simple mental arithmetic questions at the beginning of our lesson. He made it fun. I am lucky that I have always been able to do many calculations in my head, it is very useful for gross error checks. These days I am often bemused that a calculator is needed for reltively simple addition!
To be fair, that might be why despite never using it, I can still remember how to do it after all these years. My teacher must have done a pretty good job as I think we only had a handful of lesson on binary.

I’m enough of an old fart to still believe that multiplication should still be taught by rote. My mental maths has always been very quick because of it. Quite often, I can have something worked out in my head before my adult children have even written it down. Not because I’m clever, just because it’s so embedded.

Quite often I’m surprised that techniques with maths aren’t taught. I’ve watched people trying to work out 90% of something when to me it’s easier to take the 10% option and take it away. Same with adding ‘awkward numbers’ Surely it’s more straightforward to round them up and then take away the (smaller and less complicated ) difference?

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Old 24th Aug 2020, 12:06
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By complete coincidence, I ran into a binary problem this morning. I was playing with some code to transmit electricity usage via an RF link, and was getting really odd data at the receiving end. Turned out I was transmitting in big endian and receiving in little endian. The data was a 16 bit binary value representing power, in Watts, being transmitted as two 8 bit bytes, a high byte and a low byte. I had the two byte values swapped over in a couple of variables at one end, relative to the other end. Years ago I'd have spotted that error in seconds, but it took me around half an hour to see what I'd done wrong. Kept looking at the variable labels and still not seeing they were swapped over.
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Old 24th Aug 2020, 12:26
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Same with adding ‘awkward numbers’ Surely it’s more straightforward to round them up and then take away the (smaller and less complicated ) difference?
Exactly what I've aleays done. Make whatever the calculation is easy by rounding up or down. Then take the bits and pieces off afterwards, if you need to. Also gives you a ballpark figure so you can tell very quickly if you've made a mistake.

Handy for me because I often do.
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Old 24th Aug 2020, 12:44
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Maffs??? I struggled with that at skool. Before my eyesight went south, my career choice was airline pilot, which would have required a BEA or British Caledonian sponsorship and to get one of those at that time, apart from perfect eyesight, one needed pure and applied mathematics at O level. At school I was taught these subjects by two ex university lecturers and it all went over my head. My cousin, a teacher with an MSc in physics was wheeled in at weekends to help, but to no avail, it was meaningless to me. 4% in the mocks and probably less in the actual exam. It was soon after starting these subjects that my eyesight fell below the minimum required, which didn't help with motivation.

Move on a few years and I'm doing an HNC in Construction Management on day release, in the final year we had a subject called structures which involved applied mathematics, my heart sank as I knew I did not stand a chance of passing. Our lecturer was a young wiz kid structural engineer with his own practice and was doing a bit of teaching while he built this up. Problem written up on the board, answer worked out in his head (instantly) and written next to it, followed by (at lightning speed) the steps to get from question to answer. None of us (class of 20), could grasp any of this. So we raised this issue with the course tutor at the end of the first half term passing this exam was essential to obtain the HNC; he was not happy, "how dare you complain about one of my staff" etc, etc etc. When we returned after half term, in walks the head of the plumbing department, the college trained a lot gas fitters for British Gas and says "I don't know why they have given me you lot to teach structures, I don't know a thing about it", he had been a plumber before becoming a college lecturer. You could have heard a pin drop in the room, as the thought, we're doomed, all doomed, went through our collective heads.

Now as it happens, this bloke could teach and I mean really teach and as far as I am aware, we all passed that structures exam, I certainly did. He explained things at a level that class could understand, something that no one else who had ever taught me complicated maffs had ever manged to do.

To this day, I always tell people that I was taught applied mathematics by a plumber and I will always be grateful to that man.

My Dad b1923, could add up a column of numbers of any length and no of digits in his head, I never figured out how he managed that and could always do it quicker than someone using a calculator or adding machine as they had before calculators.
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Old 24th Aug 2020, 13:00
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Like others I learned the tables 1 to 12 by rote which seemed to have worked for me over the years. What I and many others struggled with at school was the mental arithmetic tests which were sprung on the class quite frequently but over time my ability improved so it was not such an ordeal. After school and when I started frequenting the local pubs, as you do, I started to play darts and in those days you had to put your name on the list of pending players and were expected score the game before you played. This really did sharpen up your addition, subtraction and multiplication skills because if you were slow or got the results wrong you were subject to insults and derision from all of those present!

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Old 24th Aug 2020, 13:00
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Teachers were the reason I got a phobia about numbers. Started when marched into a room with multiplication tables pasted all round the walls and having to repeat them parrot fashion for the whole lesson. No reason given as to what they were, or what use they had. Result, never kept them in memory. Forward to next school. Teacher of the only speak when spoken to variety, probably a hang over from recent service in WW2. Put tasks on blackboard and left pupils to get on with it. Called individuals up to have their book marked, starting on front row. I was at back so didn't get called up until one day he changed routine and up I went, carrying a blank book as I didn't understand any of the work on the board, maybe because I lost the whole of winter 1947 classes through catching measles and whooping cough. Anyway, teacher took one look at my book, pulled me over his lap and gave me six of the best, then sent me back to my place. No questioning as to why I hadn't done any work. My parents didn't believe in corporal punishment, so I had never been hit before, and for it to happen with no query as to my "sin" left me with a fear of teachers which was unresolved until my parents, worried at my total lack of advance at school, moved me to an independent day school where, unbelievably, teachers actually spoke to you and listened to what you said. Too late for my numeracy though, as I lacked the basics. Got on all right with algebra and trigonometry (Log tables, only adding)..Always felt a bit inferior for not having the ability of others with numbers, but have been fortunate in life.
When made redundant, had to go to job seekers, and use a primitive computer to suggest future occupation based on input knowledge and hobbies. Came up with "Airline Pilot". Er, no way.
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Old 24th Aug 2020, 13:10
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Originally Posted by BehindBlueEyes View Post
Anyone remember being taught binary? What a pretty pointless exercise. 1+1 = 10, I think? I was taught it as an eleven year old and never saw or heard of it again.

The columns being 16, 8, 4, 2, 1 instead of being tens thousands, thousands, hundreds, tens, units.

1010 = 2+8 (10)
1001+ = 1+8 ( 9)
——— ———
10011 = 16 + 2+1 (19)

Lift the lid on most “computer” based stuff and you will find it full of binary, you could say it’s what makes the world go round!
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