I remember in one exam working out the answer including all the written working, but I could see it was the wrong answer although I couldn’t see where my logic had failed.
So I added to the working that the answer was incorrect and why I thought that. I have no idea whether that helped me or not. But I imagine so.
However, when you are in the real world your employer wants the correct answer. Not a long and well executed explanation as to how you got it wrong. Lol.
Yes that’s true.
As an engineer educated in the days of slide rules, one of the key skills one developed was that of quickly estimating the answer by mental reasoning in order to know where to put the decimal point in the answer obtained from one’s slide rule.
I noticed as calculators took over from slide rules that this skill was rarely seen in younger colleagues and I have often thought that part of the feel that an engineer gets as to the quality of a design comes from an understanding of how the approximate maths works for the design in question.
It might be a maths-physics distinction. The physics mark schemes I use habitually make the distinction I describe. Mathematicians might be less subtle!
Mark
I looked at that O level paper and, as it did over 50 years ago, my brain melted.
Mrs B on the other hand had the answer to part A in about 2 minutes. Then again, she did a very similar paper in 1963 and went on to gain top grade A levels in pure maths, applied maths and physics.
It’s handy being married to a human calculator when you’re as thick as I am.
Quite possibly. Though I suspect that people taking GCSE (especially foundation level) are not expected to notice or understand the distinction.
I haven’t kept up-to-date with the Maths syllabub, but when I was teaching it there were three levels - Foundation, Intermediate and Higher (or something - possibly Advanced, though I don’t think so). Now there are only two levels - Foundation and Higher.
I think that it is still the case that GCSE Grade C (the highest level you used to be able to get in the Intermediate paper) is the lowest ‘O’ level grade - effectively a ‘pass’ in ‘O’ level terms. When I took ‘O’ level maths, the pass grades were from 1 to 6, I think.
The problem is that they keep changing the grading systems. I believe that GCSE now goes from 9 (the highest grade) to 1 (the lowest) - so the opposite way round to anything else.
Just out of interest, I came across this ‘O’ level paper:
I don’t think any of my pupils would be able to do much with that paper. A hat, maybe, or a boat.
I recently watched the movie ‘the man who knew infinity’ and suspect that Srinivas Ramanujan would have made an exceptionally poor maths student!! Fascinating film.
Peter
There are two types of equation here, either implicit e.g 2x - 3y = 0, 3y - 2x = 0, 3y = 2x etc or explicit in the form y = mx + c, which would give y = 2x/3, when the original is re-arranged into this form. The explicit form gives the gradient = 2/3 and the y-intercept at (0,0). This equation has an infinite number of solutions, which can be shown via a linear graph, so it may just be that your son was required to find the smallest positive integer solutions, which would be at (3,2).
There is no one answer to the question as specified, but it may be an open-ended question where your son is required to “investigate” the equation given, thereby unearthing a deeper understanding of what the original information gives. This comes from a former teacher with over 30 years in the UK education system.
Sorry, just realised I should have replied to the original poster. Apologies.
Yes, that’s what was baffling me, and him in fairness. He was given some questions yesterday, but didn’t finish them all and he was going to go back to this one having written it down.
I think he’s either misread or skipped some additional detail which you’d need to know though he now wonders if x and y values might have related to some figures in a preceding question where their possible values might have been more tightly defined.
I did suggest that when he goes back to it that unless it’s obvious that he writes down why he can’t give definite answers without knowing other parameters.
And that’s why in engineering and many other enterprises, we arrange for our calculations to be independently checked.
Alternatively, the calculation has to be done in two different ways.
Either way, full exposure of the method and calculations is also needed.
If you have time, take look at the recent GCSE maths problem that Ravvie set in the Brain Teaser thread.
I knew I had a good method, but I also knew I had made a mistake, because a quick check calculation based on approximations revealed a completely different value.
Yes, I understand that. I used to work in high volume database marketing. I would ask programmers to produce mailing lists and a rough calculation of what I was expecting told me whether I had confidence in the outcome. The programmers quite often would make a mistake.
If there were some other constraints in an earlier part of the question then it may form a pair of simultaneous equations which normally, but not always, find a pair of solutions. Without that prior information, who knows? Depending on his age and ability level you’d usually not see simultaneous linear equations until Year 8 or 9.
My child recently started school and already, I break out in cold sweat when she asks me for help with homework. The day she brings home trigonometry I’m screwed.
OTOH when she asks the age old question we all did, “What is this useful for in everyday life?” I can quite honestly reply, “Darling, I’m in my mid forties, have been a graphic designer, a system engineer, a programmer, and designed my own home that passed planning permission. I’m fairly certain that unless you work for NASA, you’ll never need this again.”
Unless you go sailing in something larger than a dinghy, or fly etc., and there are time when it is useful in designing things (actual things, rather than graphics). But you are right - most people will never use it, and if they need it they could probably learn it then. I think the point, though, is not learning trigonometry itself, but the various bits of knowledge and way of thinking that it relies on. OTOH, mostly when it is taught, it is taught simply as a series of steps with no real feeling for the underlying ideas. For instance you (yes, you!) could construct trigonometric tables if you wish, and if you had been taught well then you would know how to do it. Most people who have done maths have no idea how to, though.
Yes this old saying tickles me, having suffered mathematics though out my education right up to my degree level, I was surprised that i could actually get to use my skills within my first year of working for a living.
Its a bit like having a good, full set of tools, if you know how to use them you find uses for them in life from time to time. I find it reassuring that I can prove some thing rather than accept, "There or there abouts or That’ll do! "
I’ve worked as both a pilot and a (civil) engineer and I can’t remember a day that went by without using trig or other elements of maths and physics.
Geography and history has come in useful, as indeed has English (we did Use of English during our A Levels). It helps if you can write clear instructions and decipher badly written ones.
When we started trig at school, I had no idea what I would do for a living, but maintaining HGVs was high on the list.
I’m glad I put a bit of effort into those seemingly pointless subjects.
I certainly don’t want to single out and imply I think trig is useless. But like many things, it has a niche use that the vast majority of people will never bump up against again in their lives. Most of the examples given sort of prove that. I mean, most people are not pilots, or civil engineers.
By the same token the same thing could be said about algebra or statistical functions. Personally, as a programmer I use algebra, algebra adjacent logic, and statistical functions every day. They put a roof over my head. But 99% of people won’t use them ever either. If I’m honest, I was probably rubbish at them at school because of how they were taught and got more proficient as I learned on the job.
My gifted daughter on the other hand, sits and does math questions for fun for hours on end.
Much of the problem with conveying mathematics is the poor teaching material. All the “Tom has 4 marbles, Jane has 6” rubbish or , “Two cars leave Tesco and Sainsbury in opposite directions travelling at 45Kph” crap just switches off the inspiration light for most children. I mean let’s be honest, the answer to most of the hypothetical questions in text books is “who cares?”/ If the whole syllabus was taught like engineering problems on the Starship Enterprise or the first manned mission to Mars, I suspect it would be vastly different.
Understanding how to really apply this stuff is critical. When I asked my teacher what algebra was for, her reply was , “Why does it have to be for anything? Why can’t it be for the beauty of mathematics. You certainly need it to do your homework.”
Buuzzzzzz! Sorry. That was the wrong answer. Ms. X just sent a 14 year old me to sleep.
I agree that appealing to the beauty of maths is, for most people, totally unhelpful. But algebra, if you understand it, can be very useful. Not, of course, things like quadratic equations, for most people, but algebra can help in everyday situations. Which is why the “Tom has 4 marbles…” way of asking algebraic questions. They want to take it from the purely abstract to the practical. But you are right - maths is often taught badly, without inspiring the kids.
I taught maths to people who had, for one reason or another, done badly at maths in school - and quite successfully (I had the highest success rate at the college where I taught). While there, I attended a course of some sort for teachers, where I was talking to a teacher from another school or college. She asked me what maths qualification I had, and I replied ‘O’ level. She was appalled - said that I should have at least degree-level maths in order to teach GCSE maths, which is a quite normal requirement. I disagree. People who attain degree-level maths often cannot understand the difficulties that ordinary people have with maths. I could.