I found the biggest difference between British and American school exams
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- Опубліковано 9 гру 2023
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*edit*
Also hey sorry for the false upload there! If you were one of the quick few thousand that saw it, I had a lil editing error in the original version of this video I wanted to reupload to fix! The video needed loudness normalisation and I had an effect fail on me. First time that's ever happened to me! There's a first time for everything :)
Don’t worry Evan, false uploads happen to a lot of guys… I’ve been told.
Your video is about the English and Welsh education systems but you keep saying "UK system". Scottish Education is not the same and, at least in the past, used to be better. Regarding the losing points for the method. In Scotland if your answer is correct you get all of the points. If you go wrong on your journey to get the answer but still use a method that should have worked you will get points for everything up to the stage where it went wrong, so the English system sounds ridiculous to my Scottish ears. Interestingly, you then describe, what I've just said about the Scottish system for the US system. Which brings to mind my Physics teacher saying that he had been to a conference (1980s) and teachers and officials from the US were there looking to adopt our system. Yeh!
i was about to mention that
@@Thurgosh_OG
people talking about method marks is bullshit btw at gcse you get full marks for correct answers no matter what, at alevel theres method dependant marks but thats because the question is like a proof question where the method is the answer in a way, some schools teach that you loose method marks at gcse but thats just becasue if you get the wrong answer you can still get method marks so it is good practice to write out a method, but tehres no wrong method if it works it works and the people who mark the exams are just other schools maths teachers so they will know if it works
i will say tho y=mx+b is gross, c is the standard for an unknown constant from integration so it makes sense to use it in general for lines, b shows up more as an unknown coefficient for diffeential equations so it feels off to see +b, like writing F(x) instead of f(x), like its the same thing but because of other contexts those are used in it feels like an insane thing to do
The lying to students because it's too complex happens all the time. GCSE Biology and Chemistry are basically debunked in A levels and it's so annoying to be told everything you knew is wrong.
I remember in GCSE maths someone once said 'but we covered this last year. We're just going round in circles'
And the teacher, who was one of the best teachers in the entire school, made the analogy that education is like a spiral staircase
You're not just going round over the same topics again, but learning it at a deeper level
It's kinda no good just being told the most modern accurate take. You have to learn how we got to that knowledge too
Einstein didn't just come up with relativity. He had to know Newtonian physics first. And so do we. And actually Newtonian formula for gravity is still used for most things happening on earth even though it's 'debunked' and Einsteins calculations are more accurate. But they're also over-kill for applications on earth
Same with things like the model of an atom with a nucleus and electrons orbiting... It's near impossible to go straight into learning about atoms as fuzzy non-localised ball of potential. You have to learn the more basic version first in order to then get your head around the more complex
Multiplication is really just addition. But you need to have addition down solidly before you can multiply.
I think it depends on how you are told it was wrong, if it is explained, why it was 'good enough' but this is better, with the implication this will be wrong too, but is also good enough. The best teachers, I found, do this.
@jgreen2015 Not really, that's kinda the problem, teachers acting patronizing like that, instead of just trying to teach it. Anyone who watches PBS SpaceTime can understand the things you're saying with ease, hungry minds don't need to be told the content is hard, they need to be given that hard content so they can chew on it.
@@lexruptor people watching PBS space time have already been through education. People aren't going there without any foundational knowledge before hand
The same thing happens in New Zealand, but I don't really see it as "lying". I mean after all it's way easier to teach basic chemistry to 13 year-olds with an oversimplified model of an atom, than trying to explain what electrons actually are....
As a UK maths teacher, I have to say there is a lot of misinformation or 'urban legends' surrounding a lot of what people told you about how papers are marked. You don't have to write on the answer line. You don't lose marks if there is no working or method shown (unless the question specifically says "You must show your working"). There isn't some singular method that must be followed to be awarded marks, or be penalised if you don't.
Taken from some of the mark schemes we use:
"If the correct answer is seen in the body of working but the answer line is blank, allow full marks. Place the annotation ✓ next to the
correct answer."
"Questions where working is not required: In general, the correct answer should be given full marks."
"If a student uses a method which is not explicitly covered by the mark scheme the same principles of
marking should be applied. Credit should be given to any valid methods."
Yes we generally tell our students to do those things, but that is just so they stand the best chance of getting marks. You don't need to show working, but if you get an answer wrong you may only lose 1-2 marks, rather than 3-5. You don't need to put an answer on the line, but an examiner who has thousands of papers to mark in a short space of time is less likely to make a mistake if you do. There isn't one method you have to use, but the ones we are teaching we believe to be the best for our students. Etc.
We do lose points for that on our A-levels sometimes tho ¯\_(ツ)_/¯ There's a key that says e.g. "5 points total: 1 for writing out proper domain and arguments, 2 for proper method used 2 for proper result" ¯\_(ツ)_/¯
Don’t worry, Teach. I always write it on the line *and* place a box around it.
I may be wrong but in the US don't papers get marked locally rather than (more) centrally - so they'd be looking at a hundred or so papers to mark rather a few thousand. I guess anything done to help an invigilator see you got the right answer has to be good for both of you!
In my head my teacher basically taught these things (maths and English PEEL) to ‘keep the marker happy’. Make it easy for them and make them ‘like you’. A happy marker is more likely to give you marks where there could be contention and mark more generously. That’s how I’ve always looked at it anyway
For GCSE this is the case but at A level decent worked solutions are required, just writing down a number happens to be correct even though your method is nonsense will no gain marks
You automatically get method marks in Maths as long as you have the right answer. It's actually meant to be a form of marking that can forgive students for silly mistakes, as even if they didn't get the final answer they may still demonstrate knowledge eg: writing speed=distance/time and get some marks. If you are getting questions correct then you aren't dropping the method marks, however during exam pressure there is always the chance that you could mess up, therefore teachers tell us to write our methods down, so we can still demonstrate skills to the examiner.
Exactly - this is why teachers tell us to dumb it down, to make sure that if you get it wrong then they can give as many method marks as possible. You can still get 3/3 on a question with no working, it's just riskier as if you get that wrong you get 0, as opposed to possibly getting 1 or 2 with working out written
Mathematics isn't plural. Singular math.
@@MinorLGyou don’t have the top of a coat attached to your car.
@@TheDrumstickEmpire it just doesn't have the final gloss. The bumper is plastic anyways.
The only exception to this is when a question says "You must show your working". Unsurprisingly, you must show your working for those questions to get marks.
On the x vs multiplication point discussion. In Germany we not only use the point too (and I think I learned it from the start in elementary school), but we also use a comma to show the decimal part of a number. So an American 5.6 would be 5,6 in Germany. This way we never confuse the multiplication symbol with a decimal point, because we don't use that one.
I was about to comment that (for Austria though)!
And where English native speakers would write the comma (e.g. 1,000) we use a dot. So e.g. instead of 1,000.25 in German speaking countries we would write 1.000,25 although the dot is not necessary, as far as I know.
@@TheresiaKofficialInternational convention is to leave a space between thousands, millions etc, which is what I teach to kids but don't penalise them for using a comma whilst they get used to it
Same in the Lithuania!
Wait til you find out than in some countries a billion isn't a thousand million-it is instead a million million, with this long-scale term being the original definition.
im having trouble with this in union talks
As an examiner for Maths papers, as long as your answer is clear you will gain full credit for it. Also we go through rigourous training on marking several different methods for each questions and have to pass marking on each different question. In the GCSE you do not lose marks if the answer is correct regardless of showing all your working. In A Level it is examined different. The exam is more focused how to answer the question rather than the answer so you will lose marks for not showing a method if the answer is correct. Also in terms of the multiplication symbol you can use any.
I think it has changed so much over the years, education is such a political football, they won't leave it alone.
Maths? Norman, it's Mathematics. Haven't you seen the video?
Alright, imma go now, I'm late for my sport class. Tschüs.
the key issue with 'method marks' for this question I think would have been that if the method was unclear (as in, couldn't be followed) and the answer was incorrect/unclear, then you wouldn't be able to 'pick up' marks for having got at least part-way to the answer.
Usually mark-schemes for harder questions have multiple things written in them as potential methods (+ how to mark them if people have gone wrong at different stages) + a disclaimer for 'any other method', it just makes it harder to mark
@@victoriab8186 We have to rigourously go through each stage of the working to see where marks can be applied for any method given as long as it is correct. Even the A Level schemes do not cover every possible method. I have encountered many that have used varying methods to the mark scheme. It's the reason for the level of scrutiny we have as examiners. You also have to multiple years experience teaching at the relevant level in order to become a marker.
I was saying that it doesn't actually matter if the answer is on the line as long as your intended answer is clearly indicated such as putting it in a box. And for the GCSE as long as your answer is correct then working doesn't matter
This seems to have changed in the 24 years since i did my GCSE's then, as when i did my maths exams i didnt put any working out on the paper, but got every question right and only got a C. I didnt put working out down cause im dyslexic, and when i was growing up i hated writing things down, numbers came alot easier to me, so most of my GCSE exam was just done in my head, hence no working out required. It was wrong not to put the working out down, but hey-ho, i got a C so i was ok with that.
I personally really liked the PEEL system for writing. I really hated english/essay subjects and was terrible at them. I just didn't understand how to write essays. PEEL gave me a structure for my very logical brain to work around instead of just putting random thoughts onto a page without any actual substance behind them.
Jeez looks like this has changed I did my GCSE's in 2015 and it was (PEED) point, evidence, explanation and develop with a justification and conclusion at the end of the question or assessment linking it back to the original question. Unless it was changed because incredibly young gen Z's and generation alpha are way too immature
@@Nekogal21Hun I did my GCSEs in 2017. there's 2 year difference between us, I can guarantee you that those 2 years did not mean shit in terms of being "more mature' for people in your Year 11 laughing at "PEED" and my Year 9 for laughing at "PEED". Year 11s are 15 and 16 years old, they are children, of course they're going to find PEED the funniest thing on earth. changing it to PEEL doesn't matter cos it's the exact same thing
be realistic with yourself, you're not a beacon of maturity.
Sameee except its peezl in my school
@@Nekogal21odd, I also did them in 2015 and it was PEEL. Must be your school
@@JasperCasper24 I believe it was like it for all the schools in my particular region put on our specific curriculum for the group of schools idk
In Germany, we have BBB, which stands for Behauptung, Beleg, Beispiel (Claim, piece of evidence, example)
A valid Argument encapsulates all three points, and I found this always to be a good guideline whether someone was just populistic or actually had a point.
Without ‘Beleg’ an argument is without foundation, without ‘Beispiel’ an argument is not as easy to grasp.
This is much more logical than PEEL or 5-para structure. Simpler and more natural. My daughter is in an “American” school in Portugal taught mostly by English teachers… and Singapore math. She is brilliant, but her teachers adhere to absurd and arbitrary structures instead of teaching you to learn and understand…This happens in English and math. Idiotic in my opinion to learn rules for the sake of rules which do not enhance understanding.
PEEL has been really useful for me. We were never taught you *have* to do it, just that its a useful fallback, and I still use it in my 30s. I don't hold myself to using P, E, E, L in literally that order or that religiously, but it's really useful to review and make sure you have all of these elements somewhere in your writing.
Huh I never learned this but it sounds useful
Yeah, it's a really simple method for teaching students to structure an argument (as opposed to just making a load of points). Evan's American "equivalent" just sounds like an overly rigid version of intro, body, conclusion: what if you want to make a different number of points than 3?
Can confirm from german highschool literary class: we had been taught for years how to spot alliterations and hyperbels and whatnot, but all it took for me to deeply understand literature analysis was that ONE teacher in training who taught us something similar to the PEEL method. You know why? Because it finally told me WHY THE HECK WE WERE DOING THIS BULLSH*T over the last couple of years! Still makes me a better writer and reader to this day.
I agree. Unless you are doing creative writing, your writing needs to have some structure. Otherwise, it's going to be difficult to read and understand. It's not true that you will never use PEEL after you graduate. Trust me, if you don't use it, your writing is going to be BAD.
@@hannahk1306I think specifying 3 paragraphs was for three reasons. First and foremost, it limits how much a teacher has to read to grade the submission (though I strongly suspect they only skim the intro, conclusion and one of the other paragraphs anyway). Secondly it forces the student to have at _least_ three points to make. Thirdly, it forces the student to choose the points that best support their conclusion rather than drowning the reader in points to distract from a weak conclusion. Also, it probably helps to triage the papers, if there are less than five paragraphs, it goes in the "probably gonna fail" pile and, if there are more than five paragraphs, it goes in the "insufferable overachiever" pile, if exactly five it goes in the "conforming future capitalist drones" pile.
the reason people are calling rishi 'out of touch with reality' for wanting to change a-levels, is it is basically a non-issue. There are far more important things to focus on in the UK education system that could use the massive amount of funding that it would take to change over what is a whole new curriculum for sixth formers.
This may well be true but you have to start somewhere.
@@007knick then start at the bottom not in the middle/end
Yeah I'm praying for future generations that Rishi's proposed changes don't go through
Indeed, and the new one is not going to end up any better. It isn't like Rishi actually has any more of a clue, it'll still be farmed out to the same exam boards in the end. EdExcel will end up deciding as they always have done.
What UK education system is this? We have several! And '6th formers' isn't a thing UK-wide!
Think this video is based on a flawed premise. It primarily uses comments from GCSE or A-Level students who don't really know what they're talking about. I will say that we are taught to fill in exams in a very prescriptive way and it is often phrased as "do this or you will lose marks" but that's generally because that's the only way you can get kids to do anything they deem unnecessary. The truth is that you don't need to answer on the line, or underline instead of circle, or use PEAL, or write out the entire method. These are just handy lies given to children.
The real reason that teachers tell their students to follow these strategies is I think because of one of the greatest differences between the US and the UK. Exams are sent out to be marked by other anonymous teachers across the country. They will often have a large pile of exams to mark and not a lot of time to do it. If you don't follow the exact exam instructions of putting your answer in the right place, or explictly outlining every minor method step, they should still give you the marks. But if they are rushing, they may easily scan across the page, not understand what you were trying to do, fail to find the answer and not give you marks for it. If you've used a maths method they've never seen they should mark you for it, but if that method takes them 5 minutes to understand, they might not bother.
The truth is that these exam techniques are just to ensure that you can't possibly have points unfairly taken from you by rushed examiners. You should still get the marks, but why risk it? Also, exam technique normally only takes 1 or 2 lessons a year to cover, unless you count doing mock exams and practice papers, which I don't. So not sure why the one commenter suggests it takes up a majority of teaching time. That's kind of an absurd statement to me.
This deserves to be a top comment
I think you’ve just hi-lighted the issue here; it’s to do with overworking teachers with exam marking. The papers are flawed to begin with, when both my GCSE paper in mathematics had to be recalled and psychology A level paper had to be recalled due to an error in marking from the questions being unclear, clearly there’s issues with marking these papers. I thrived in coursework based subjects, due to the nature of how I was able to learn, and it was much later after getting a first in my uni degree that I realised how I learnt, and how people learn differently. I think the point of the video isn’t flawed, it emphasises the struggles, and flaws in our teaching system we have today. If students believe the only way to answer a question is to use PEEL or underline an answer which by the way is true for mental maths exam because it’s scanned by a computer, then yes, the video highlights the issue.
@@Ben-gm3tb I believe that GCSEs and A Levels have real problems in how they are structured and who they best serve. And there are absolutely massive problems with how exams are marked, but Evan didn't really talk about the real problems. He talked primarily about how we mark people based on stupid conventions, which is untrue and not the problem. If you're going to make a video about the "biggest difference between American and British exams" then you would hope that that difference was real. As you point out, overworked examiners is a real problem and it would've been great to highlight that issue.
I also disagree with this idea that teaching PEAL is a problem. I think most students understand that it is a framework for exams and not how to answer every question in life. But I also do think that PEAL is a very good framework for writing essays. Whilst at the top levels of education PEAL is perhaps a bit too prescriptive, at middle and lower sets, this framework is very important. The fact is that any good essay should always at its core remember to give evidence for its points, analyse that evidence and then link it back to the central thesis of the essay. So many students write essays that go off on tangents, or don't properly evidence points. Yes, you don't always have to write a paragraph that does every single one of these things, but it is generally a useful framework to follow. It of course can depend on teacher quality, but a lot of English teachers will point out to higher sets that there are instances where deviating from the structure can be useful, but it is a useful framework for all students to have in the back of their mind.
Again, there are many legitimate problems with our form of assessment, would've been great if any of them were mentioned in the video. It's much easier to point at a system and say that it's flawed. It's much more difficult to recognise the problems, not to mention the solutions.
Thank you. I feel there is some poor research in this video.
exactly this
The basis of P-E-E-L paragraphs are to teach students who struggle to dive fluently into a written answer (a structure to make it easier). Personally, I find these strategies extremely useful for subjects like RE and geography where you have to write masses of text in such a short space of time.
"Tell them what you're going to tell them, tell them and finally tell them what you told them" an easier way of remembering it. Still used basically for writing scientific papers etc
@@gillfox9899 exactly ref your last point.
If you have to write something, its structure is important. It's not as if you can't choose the vocabulary, or the framing of a sentence, but the overall structure of a paragraph should have a consistent logical order: make a statement, back it up, explain the link between both, then conclude.
I also find it a little difficult to accept the suggestion that we should follow the US path on this, given their rampant levels of illiteracy.
Evan, in every country, the study of the native language is about how to formulate arguments, writing unambiguous text, and in general clear communication. How well you know the language is different subject called "[native language] as a second language ". There is also often separate "creative writing" courses.
I think it is worth mentioning that GCSES and A levels are not always marked by teachers, and definitely not the pupils teacher. They are marked using a very narrow markscheme so particular words must be used in answers. I used to teach science and a lot of time was spent making sure pupils knew how to take tests.
I think even back in 1971 when I did the 11+ they told us the marking was partly done by machine. It was just multiple choice IQ type questions, there was no actual writing.
Not true. I've been teaching for decades and an examiner for almost as long. I have never known a teacher to teach 'how to take tests'. What we do is teach 'how to not throw away marks to questions you know the answers to'.
There is a difference.
I don't want a student to lose 5 marks on a graph because they're using a blunt pencil that means the accuracy of the mark can't be measured. I don't want a student to lose marks because they forgot to label a cell. I don't want students to lose marks because they forgot to say to sterilise the loop in a microbio prac, or forgot to add electrons to the inner shell on a diagram. All things they can do. All things they lose pointless marks on due to lazy thinking. All things that cost them grades.
If I want a dog to be good at sniffing out drugs, I'd best expose him to all the different types (subject content) AND teach him where to look for them (understanding the question), how they will be different to the smells from perfumes and bombs (understanding why one type of answer would get the marks when another wouldn't)... So if we would be expected to do that with a sniffer dog, why would you expect to do any less for children sitting multiple complex exams across multiple subjects which test not just their ability in Science knowledge but also COMMUNICATION, mathematics, pattern recognition, analysis, debate... ?
The mark schemes are not narrow. They are what the answers should be. They are all put through RIGOROUS standardisation by examiners prior to publication. And CORRECT words must be used. If I need to know specifically that a student knows, understands, and can use the term Neurone, it's no good if they bloodywell write 'cell'.
Science is all about communication. Using the correct terminology MATTERS. Or would you rather your doctor said you had lung cancer when they actually mean you have a harmless lung nodule, because you don't want for people in science fields to need to use 'particular' words?
@@hellfirepictures100% some of the comments I see people writing here I feel miss the point.
@@hellfirepictures as someone who took GCSEs this year, structuring your answers and remembering key words is incredibly important, particularly in English literature and language.
@@hellfirepictures I am a former A level biology student who is now studying for my undergraduate degree in biology. At A level I loved learning the biology content but absolutely hated taking the exams and going through exam questions because you had to know how to answer the questions correctly, not just the content. If I just answered the questions as they were written on the page, I would lose out on many or all of the marks because I didn't answer what the question was actually asking, which was whether I could demonstrate that I knew the part of the specification they were asking about. The best strategy was essentially to learn the spec off by heart so I knew when a topic came up in a question that they were probably asking about these things on the spec related to topic rather than what was stated in the actual question, and in response I would regurgitate the same statements that I had memorised that I knew covered the most common marking points on similar questions with maybe a bit of modification depending on the question. Much of my revision time was spent drilling key phrases into my head. I think the sniffer dog analogy actually works well to illustrate my point. The sniffer dog is given tasks to simulate what they would actually encounter in the real world whereas the student is given tasks that would simulate what they would encounter in (in my case) AQA A level biology exams.
If a question is written in such a way that a student can write an answer using the term cell rather than neurone and it be a correct answer, they should get the marks. They have answered the question and a neurone is a cell so they have not said anything incorrect. If the thing to be examined is whether or not the student can correctly use the term neurone, the question should make that clear. On the other hand if a doctor says you have lung cancer when you actually have a harmless lung nodule, the doctor is saying something that is factually incorrect rather than just not as precise as possible.
Science communication is a different set of skills where there is no one correct way of saying things and which requires you to tailor your wording and explanation to your intended audience. This is not examined in an A level exam where if you do not use the specific terminology on your exam boards specification you do not get the marks, even when other terminology is commonly used in the real world, including in scientific contexts. I do think its important to use correct and specific vocabulary, but the way exams are structured with their rigid mark schemes completely misses the way that people actually communicate (as well as meaning that correct answers that are not part of the specification content don't get marks (except for on the essay in AQA)). I'm sure you've seen answers where its clear the student knows what they're talking about but perhaps they used the word "digest" instead of "hydrolyse" and so you can't give them the marks. I've had to unlearn such a rigid way of thinking for my university exams because there isn't such a sure fire way of getting the marks, nor is that really what matters as long as I understand the content and can demonstrate that.
Thanks for reading all of this, I mean no disrespect and I hope this comment doesn't come across that way. Its a long comment that's kind of all over the place but I hope you can understand what I mean. I just would like you to be able to sympathise with me and perhaps any of your students who feel/felt the same way.
One of the lessons I really value from British exams is RTFI (Read The Fucking Instructions). It's the sort of skill that has saved me multiple times from hours of misery, all from just reading instructions carefully.
Yeah, was kind of surprised he got confused with the wording element when it teaches you to be more observational and not just assume what is wanted.
Which is great if the person/organisation actually Writes The Fucking Instructions, correctly, they often don't.
I know you (and Evan) are right,but - life's too short!
Yes, I think the point of the first comment mentioned (re best lesson ever learned) really went over his head. It's not about obeying authority etc (& frankly if you're taking a public exam, you're in the system by default), it's about paying attention and reading instructions. Or listening to them, in other contexts.
This is a huge advantage throughout life; it teaches you to pay attention to detail, not to be entirely wrapped up in yourself, to be calm and read the situation.
So many people, even as adults, don't listen to or hear others, but plough ahead with their assumptions, which can impact not just work but relationships. Learning to pay attention is one step towards mitigating this.
‘Curly x’ was always only normal ‘x’ to me, because we were only ever allowed to write in cursive in school, and so my letter x has always naturally looked ‘curly’. The multiplication symbol was not a letter, but a different thing entirely, that looks clearly different (two crossing straight lines).
As many British schools nowadays are increasingly de-emphasising the importance of proper cursive, or sometimes not even teaching it, I can see how this might be a growing problem, but traditionally, you could not confuse these in British handwriting.
Not sure why you think UK schools are not teaching 'proper cursive', it is expected that all 5 year pupils can write legible cursive. Until a few years ago, some schools only taught cursive, even when pupils were first learning to write. But it was realised it made it harder for those who struggled with learning to write.
I found my 1976 Maths GCE exam paper in the loft and showed it to one of my kids, who now teaches up to 'A' level Maths. Any doubters out there - it WAS harder then!!
But…. the two crossing straight lines that you use as the multiplication symbol (the one Evan shows in the video)… that‘s the symbol for the cross product (vector product/ cartesian product), isn‘t it? How would you write that then?
Here in Switzerland, I use x (no curls needed) for the variable x, the dot in the middle for multiplication and this kind of rotated cross for the cross product (Plus of course a comma instead of a point for decimals to make it extra confusing when looking at mathematics from other countries 😂), and under the answer I put a double line.
But then also my teacher writes very ugly and we sometimes have to ask him whether something is a figure or a letter (and if letter, is it u, n, h …? Looks all the same) so he is also very forgiving in our exams. 😅
I think the real problem is the use of computers for writing. Using the curly x (without having a curly x) is just a total pain when typing. Then there's the lack of a plus minus symbol, a root symbol, an infinity symbol, pie, etc. Maybe there's a specialist maths keyboard out there somewhere.
My x is *, my powers is ^, my plus minus is +-.. 😄
Not sure about Britain, but in Germany, the use of traditional cursive has definitely decreased. Even when I went to school, some schools were teaching a supposedly simplified style of cursive, which usually resulted in illegible handwriting because it was constructed without regard for fluent movements. Nowadays, a lot of schools seem to be transitioning to "Grundschrift" (basic script), which is basically print letters, but optimized for fluent handwriting.
The way I remember my British education twenty years ago, the use of dot for multiply was an A level thing. That’s when we were taught the dot and cross product, so we just wouldn’t have been expected to know what it meant at GCSE.
Wow you did matrices during A-Level? They removed that for us...
@@dugebuwembo I did matrices at A-level in 2011-2013 and learnt the dot notation then
@@hannahk1306 Wow they left it out when I was doing my A-Levels, I learned it at University.
@@dugebuwembo It might depend on what modules you did and which exam board, I don't think everyone on my degree course (computer science) had studied them but lots of us had.
@@hannahk1306 OK my exam board was Ed Excel and I did Pure and Stats for A-Level Mathematics.
My British teachers did sometimes emphasise that you have to answer the actual question, and that you do have to game the system and answer questions in a specific way. I remember this particularly for A level biology. Scientific but still very wordy. It was a bit annoying. Maths was easier for me because as long as you get the answer it doesn't matter too much how you got there.
Oh boy, I am may not be from the UK but from Poland and I took what we call "extended biology" course and then I had to take an "extended biology" exam for my graduating exams and the way we had to LITERALLY learn and were given little pamphlets explaining what the task ACTUALLY means depending how the sentence was structured. If you answered any of it the wrong way, you had zero points. Same if you used colloquial speech instead of scientific term even tho it was technically correct. It was a nightmare.
That wasn't a great maths exam then, everyone I have ever took had most of the points for that question related to how you got there and representing everything completely accurately.
Your workings in maths are really important if you get the answer wrong - you could get say 3/4 marks for a correct approach, but a slight mistake in your calculations.
@@hannahk1306 this is true. Though at least if you're confident enough with maths you can get full marks. I think it's easier to get full marks on a maths paper than a biology one
@@wyterabitt2149 many questions give points for working if you don't have the right answer but as far as I can remember the correct answer always just gave full marks
From my experience as a UK maths teacher, generally you would get full marks for the correct answer. You would only lose "method marks" if the method used does not imply the answer you got (i.e. you made errors that cancelled each other by chance). I've not marked proper GCSE exams but markschemes I've used (mock papers etc.) usually have an "other valid method" category that validates unsual methods that are correct. This was just my impression from exam marking anyways. I think teachers (especially during exam prep) will tell students to write down everything as students tend to show less rather than more working out. But I agree that teaching to an exam isn't a great way of getting students engaged but is unfortunately the reality for most year 10/11s (and A-Level).
One moment that cemented the end of my time in education was a GCSE maths exam. I can't remember whether it wanted an angle or length or something, but I couldn't remember the equation. So I drew the triangle out to scale and measured it.
I got the answer correct (I remember that for some reason, it was 42.7) and was marked wrong because I didn't work it out the way they wanted.
I left school pretty soon after that and now do maths for a living in finance, but without all these arbitrary requirements.
i think method marks are really helpful!!! if you get half the working out right but mess up the 2nd half, you should still get marks
@@andyp743 If it didn't explicitly say to use a mathematical approach, then I'm pretty sure that shouldve been marked correct. Though who knows, perhaps they've become less restrictive in the years since
@@andyp743 if the question said "calculate" then you're not allowed to do that and you have to work it out with calculations (or at least i think so and maybe it was different when you took it). goofy thing is in physics you have to do the exact opposite when working out resultant forces and you have to draw out to scale vectors representing the force and measure it, and calculating it with say pythagoras' theorem for example wont get you any marks.
@Plasmacticus the trauma of having to draw scale diagrams. As a current A-Level physics student, drawing scale diagrams and counting squares under a graph, instead of doing some simple trig and calculus, is my biggest pet peeve 😅
As an engineer, structure in writing English reports is very much a life skill. It's not PEEL, but rather IMRAC (Introduction, Methodology, Results, Analysis, Conclusion) which is very helpful both when committing knowledge to paper (PDF more likely nowadays) AND when reading other people's reports.
You can use STAR (Situation Task Action Result) for applying for jobs as well. Plenty of situations where a structured writing style comes in handy.
PEEL can still be useful within sections or paragraphs in a scientific or engineering report.
Actually, @@sunway1374 , PEAL puts the cart before the horse. It concludes before you've introduced your topic. It's terribad in every way imaginable and it teaches students the dishonest practice of jumping to conclusions (P), then cherry-picking the "evidence" as if what they're saying is true (E+A) then repeat the preconceived idea is if it were some kind of conclusion (L). While I understand it to be the heart and soul of an argument, arguments are the tools of politicians, litigants, and hostile divorcees - not honest professionals. Moreover, PEAL subtly communicates to the audience that you're lying to them.
@@Mercurio-Morat-Goes-Bughunting You are misunderstanding and distorting what PEAL means.
@@sunway1374 You're not making any sense. Can you be more specific?
In point of fact, PEAL begins with the point (i.e. a conclusion) instead of exclusively finishing on the point. That's not a distortion nor does what that means, in practice, constitute any form of misunderstanding. If anything, the statistically predominant outcome of choices in expression is the ultimate understanding.
Generally, anything which begins with a conclusion is not to be trusted. And you can count 100 PEAL arguments chosen at random versus 100 IMRAC essays for real-world accuracy in terms of conclusion and find this for yourself.
Moreover, the sheer absurdity of expecting the reader to read the mind of the writer places the onus of clarity squarely and exclusively on the shoulders of the writer. So the onus is solely on the writer to make what he or she expresses clear enough for the reader to fully understand on the first pass. PEAL doesn't do this because it reduces an otherwise useful exploration of a question to an mere argument and it does so by communicating to the reader, loud and clear, that the writer is merely justifying a preconceived idea. Whether or not that is the intention of PEAL is irrelevant because it's on the writer to be clear, precise and unambiguous - not on the reader to read the writer's mind.
IMRAC achieves this clarity by laying out the necessary structural elements (method being a primary point of reference for everything else) although I think the "introduction" bit would be clearer under the heading "background" because that's where you put the literature review which raises the question you're addressing.
Even in a work of fiction, starting with your grand finale is a very poor choice of structure.
When I did O-level and A-level maths in the early seventies, we were taught to use the multiplication sign, the dot and just placing symbols next to each other interchangeably, depending on what made things clearer. We were also taught to write the decimal point at mid height, because all our work was hand written on lined paper, so it could be missed if it was written on the line. We used the "curly x", too, to distinguish it from the multiplication symbol. I might also add, none of our exams (in any subject) were multiple choice, we actually had to provide the answers ourselves.
Totally agree. I always put the decimal point in the middle even to this day. I also did my O and A levels in the 1970s
one more argument against the decimal dot ... Using a decimal comma (which is clearly recognizable on lined paper even in it's proper place and cannot be confused for any other mathematical symbol) you can easily use dot's (where necessary) for multiplication. And you keep a central × free for the relatively rare cases that you need to write a cross product.
American here. We always put the decimal point down low (on the line). It seems to me that raising it up and putting it in the middle ("half-high") is a recipe for disaster! Does 3•6 mean three point six (three and six tenths), or 18? Crikey! 😄
(For what it's worth, ISO 80000-1 directs that the decimal marker [whether a point or a comma] should be "on the line".)
I honestly had NO IDEA that there was an alt for the multiplication symbol outside of * used IRL!
I took O levels - the predecessor to GCSEs. We weren't taught how to take the exams or even how to revise. It was a real eye-opener to see how my son was taught to answer the English paper. So many structures and strategies to remember rather than actually the language itself.
Which is what posh schools do and what the parents pay for. The payment is not to stuff your kids brain with actual information,you're paying to have your kid trained to NEGOTIATE THE SYSTEM. And your kid is going into employment at management level so he or she will have educated minions to do all the actual getting it right.
I also took O’levels and as I have no children was surprised by this video. The only exam I remember having a technique for was German. I did it as a correspondence course and took it at the same time as my younger brother. He told me that their teacher recommended that for essays they learn an essay off by heart and twist the set introduction round until they could use it.
Yes, all that was new to me, I took my school exams in 1976.
It's due to the results based nature of education. It's more time efficient to teach children how to get more marks from every bit of the exam than to spend time teaching the small sections that may not show up.
Its to teach children to prepare for the workplace and academia. That type of learning is exactly how you learn to write technical writing in workplaces and formal academic writing at university.
Haha, I'm doing a masters at the moment, and they keep having to remind all of the Chinese students that a 70% and above is the top band. My Vietnamese wife was very unimpressed when I told her that I got a 72 on my last assignment. The top mark in the whole cohort was 75.
Asian parents' high expectations have entirely fucked up their children's sense of achievement. I hope they keep being reminded of it because holy hell these kids are dealing with the mentality where only #1 is accepted. Which is why that one Korean guy who is like an astronaut and a doctor is basically the dream child. It's all just sad tbh.
In Czechia for example, we say "y=ax+b", "y=ax^2+bx+c", etc. We also use "," as a decimal instead of ".", which we use for multiplication. Oh and we use "(a;b)" for open intervals and "" for closed intervals.
Cool, in Switzerland, we also say y=ax+b and we also use commas for decimals instead of points. For multiplication we use the dot in the middle, like Evan. And the x he shows as the symbol for multiplication (which isn’t an x, but rather a rotated cross) is the symbol for a cross product (vector/ cartesian product).
How do you in Czechia visually structure large numbers? We either leave a space or use an apostrophe. (50 000 000 or 50‘000‘000 for fifty millions for example).
I personally mostly use square brackets for intervals. ]a;b[ for an open interval and [a;b] for a closed one, but I was taught there are multiple options to write it, also depending on whether you‘re using it in informatics, which I‘m interested to study, so maybe I’ll have to change how I write it. 😅
@@MischMagnifique In Czechia we use dot in the middle (it is just easier to write "." in a comment on YT) for multiplication.
For the large number structure... We may not structure them at all (mainly informal), we may leave a space between triplets and we can also use a "." (this time I mean exactly full stop though it's called ). We have the meaning of "," and "." switched from the US convention and that can be really confusing when sifting through different sources. I think nowadays the space is the most common with the dot not being used much (probably thanks to the clash caused by the spread of internet).
Example 1234567,89 or 1 234 567,89 or 1.234.567,89
One case I encounter the full stop as a thousands separator on daily basis is on my Canon F-788dx calculator (it can also output in the US format).
Marking the answer with a tick vs cross / underline, circle etc.
The answer papers are frequently machine marked. If you don't use the requested marking style, the computer doesn't recognise your mark. Hence the emphasis on reading the question thoroughly, and conforming to the answer style requested.
I agree with you that British exams reward learning how to do well on the exam in the rigid way they want you to, but I think PEEL is a bad example of this. Read any published academic essay and you will pretty much find all four of those features in every paragraph. They don't have to be really obviously signposted or in that specific order, but as a checklist to follow when you're 14 and have never had to structure an argument before, it's not too bad. A better example of this rigidity in English exams is the AOs (assessment objectives) you have to follow eg. AO3 - show understanding of the relationships between texts and the contexts they were written in. You have to show the examiner that you're doing each one, and know how to weigh them for the specific question you're answering. At that point you're not learning how to read and analyse, or how to write a well-structured essay, you're learning how to pass a particular exam.
My experience of doing maths in the UK was that once you start using x as a variable you stop using any sort of multiplication symbol on the whole e.g. 3x + 2 or 4(x+1). I can see how using a dot could lead to confusion as people can be a bit sloppy with writing things out, but I can also see how having two different x’s is confusing
Also, a dot on a piece of paper could be just a speck of dirt or blob of ink or something else that happened to get there by accident. So a good strategy for paperwork might be to minimise the use of dots as much as possible, and reserve them only for decimal numbers. Leave dots to decimals, and get rid of multipliers where you can. Especially algebraic stuff.
@@fredbear3915Not a problem if you got a comma as your decimal separator, like most of the world, lol..
YES! I'd forgotten this but I knew the sum he put up with algebra x and x looked really wrong to me for some reason. Of course - we just use brackets. (Feeling silly now for not figuring that out, I was drumming that into year sixes only a few months ago!)
@@markoturkhr But then you end up using the dot to separate thousands which makes less sense taking in to account the grammatical meaning of the comma and the dot (In English at least). The comma separates the list of thousands as it would a list in text and the dot acts as a full stop finalising the whole number.
For me I've evolved my handwriting significantly for the x variant as my decimal dots are often quite high up (they look wierd too far under so I tend to stick slightly higher than usual) and my algebra x's often have the two halves completely separate (like ↄc )
To show even more options, in Brazil we use y = ax + b (though I've seen y = mx + b in some books) and about the x thing, we use a dot for multiplication, but you can't confuse it with decimals because we use a comma for decimals. So 5x5 = 25 is fine, but 5.5 is 25 and 5,5 is five and a half.
As a professional pedant, I get triggered by people using x when they mean × (alt+0215, at least on UK keyboards, I don't know if it's the same in the US) ... I don't reckon more than 1 person in 100 knows that there even _is_ a multiplication symbol that is distinct from the 24th letter of the alphabet.
@@stevieinselby Worse still is the American desire to call the hash symbol # anything other than hash - it's "gates" for those that hadn't progressed past infant school, "pound" for those that have yet to learn that the pound symbol is £ and then we can the abhorrent mess where the likes of Microsoft call C# not C-hash, or C-pound, but instead call it C-sharp instead. A gate is a door equivalent in a fence, £ is the pound symbol, ♯ is the sharp symbol and # is hash, as used correctly in hash tag.
@@stevieinselby Well if I whant to be even more pedantic the dot should be 5 ⋅ 5=25 and the equation should be 𝓎 = 𝒶𝓍 + 𝒸 and yeah obiously 𝓍 ≠ x ≠ × ≠ 𝓍
@@nickryan3417 the word you're looking for is number sign, or octothorpe.
in Austria we use y = kx + d
Just had fun watching your transatlantic take on US vs UK math(s) education. I am a Brit in my 8th decade having been born just after WWII. I went to a highly academic school with a nightmarish Dickensian ethic. I learnt despite the environment but not because of it. I am a mathematician. I tutor A-Level maths students for Oxbridge entrance and some undergraduates. I am also writing a novel. English and maths thus play a part in my everyday life. A lot of the obsession with the form as opposed to the function of mathematics comes from people who do not have a conceptual understanding of the subject. If I ask, “What is Maths?”, I usually hear that it is something about numbers whereas to me, it is fundamentally about the principle of abstraction. We do study number sets and number theory, but that is far from the whole subject. I tutor students in the concepts, coming only later to examination technique but, yes, it is an annoying requirement in examination. For me, enlightened student understanding is key. As for fatuous arguments about variables or symbols, these are conventions where consistency and communicability are what is important. So, I have had students from 11+ all the way to university. I am not a schoolteacher and so select my students to be the brightest and best since I can. I build on fundamental concepts of set theory so addition and multiplication are binary operations mapping from the Cartesian product of a set with itself to itself. For these functions, we usually write +(a,b) in infix notation as a + b, and x(a,b) in juxtaposition notation as ab. Whether one writes ab as a.b or a x b or a*b is irrelevant so long as the symbols used are used consistently and for that single purpose to avoid confusion. My youngest students understand this and we build on it. I explain infinity and notions of discrete vs continuous to young children and they get it. These days, my students are all A-Level or higher, so I have to rebuild the foundations and correct misperceptions. Learning should be fun and this makes teaching fun. I love mathematics enjoy sharing that love with young and agile minds.
I’m 62 and really wish I’d had teachers like you.
I have to jump in defense of PEEL. It came in very handy throughout my degree. Sure, for high school english it's not super relevant, but if you have to write a few thousand word essay it's a godsend to have a framework to build it with. We use it in Australian curriculum too and if you do any sort of humanities degree where you're writing a lot of research essays you realise it just works.
Also useful if you work in any field where you write for influence.
The method thing for maths is wrong. If you used a valid method that was not listed in the MS you'd get the marks. So like as long as you haven't broken the rules of mathematics, you'd get all the methods marks if your answer was right.
Which is exactly what actually happens in the UK. Unless you are explicitly asked to use a specific method (eg "by completing the square") you won't be marked down for using a valid alternative method in a real exam.
This is the problem with Evan making all of these judgements based on UA-cam comments
The "mark the question" bit where you need to do a specific action depends on the exam board and how they input the test through print copying online, their machines or whatever will be able to determine where the answers are for each question that way
I teach ESL. One group I have taught frequently are foreign students studying abroad for the first time. Individual classes tend to be dominated by single national groups as different countries have different traditional times to take a semester overseas. I gave a super-majority Japanese class an in-class persuasive essay at the end of their three month stay. On the handout I gave them a selection of three topics with a blank to be filled in as the students pleased. One topic was: It is important to learn _______.
Of seventeen essays, twelve were nearly word for word identical: It is important to learn English because it will let you get a better job and help you meet people from other countries. (A few students substituted "cultures" for "countries".) The full essays were nearly interchangeable from first word to last. I had told the students that if the marker is bored they will get a lower mark. It's human nature.
I've been doing this for a fair while. Give me a paragraph length writing sample and I can generally spot the students who have taken IELTS or TOEFL or EPE--or been through the Japanese or Korean or Brazilian school system. They all have distinct one true way styles.
I tell my students there is always more than one way to say something or structure a longer piece. I also tell them that if they are going to be different, they have to be good. Really good.
The reason why PEAL/ PEEL has such a big emphasis placed on it is more so to make writing essays easier. Instead of going off on tangents, it helps you get straight to the point. For example, here in Scotland if you were to take a higher (equivalent of just below A levels) exam in history, you can get a maximum of 8 marks for knowledge and understanding and 6 marks for analysis. A PEEL structure ensures that students gain the maximum amount of marks in the least amount of time as you only have an hour and a half I believe for two essays. Less of an emphasis is placed on it even at Advanced Higher level (equivalent of just above A levels), where using history as my example again you are given no structure whatsoever and are told to "find your own writing style".
Oddly, I went to school in Scotland and did History and was never taught "PEEL" (though I realise we were taught that structure, which I never deliberately used, just without the acronym).
What I do remember (though not what all the letters stand for) is PADD CABLE for analysing sources.
As a Gen X Scotsman, we were not taught Peal/Peel. And in my time 'O'Grades', were recognised (within the UK) as being at a slightly higher level of achievement, than English 'O Levels', Highers were at a slightly higher level of achievement, than 'A Levels' and Sixth Year Studies, well above A Levels, were not even offered in England or Wales but could get you out of doing the first year of a Degree because you were already 'qualified' to that level of education. By your comment it seems that Scottish education has fallen further than I'd realised.
@@Thurgosh_OG I did some O Grades and some Standard Grades as I was at the transition point between the two.
O Grades were considered the same as English O Levels, Standard Grades the same as GCSEs, England changed from O Levels to GCSEs at around the same time. Highers were one year of study beyond Standard Grades / O Grades and there was at the time no English equivalent. AS Levels were later modified to be equivalent to Highers. Sixth Year Studies were considered equivalent to A Levels, but probably less common in Scotland than actual English A Levels.
I think you have to remember that the teacher is teaching to a class where 16 year olds will either love or hate the subject, and can get an A or a U, so their strategies (like PEEL and the 5 paragraph essay) tend to focus on the lowest common denominator in a class.
That thing I said before
@@conormurphy4328 you said "So you’re teaching people who have no interest in the subject something that they will probably never use in their future after education. And also teaching people who have an interest in the subject a strict and lesser way that restricts them moving forward in their development in the subject."
To that I say "Yes, you've perfectly summed up compulsory education"
@@beng6044 "Yes, you've perfectly summed up compulsory education" is so stupid, compulsery education is objectively amazing, not in its current frame but education is literally the most important thing in humanity and compulsery education is a crucial part of it. what i said isnt subjective or anecdotal there is a direct link with health, wealth, crime rate, satisfaction, happiness and basically all that is important with education, and thats excluding the evolution of humanity, which can only happen with further education(except progidies but to specific), and id say those things are the most important things to an individual and the collective. you are objectively wrong with that statement, summing up doesnt only include the negatives, summing up such a broad topic includes the generality of it not the current state of it; that includes the non-fixable cons, the benefits, the reasoning and what is actually compulsory education.
Yea as a higher achieving students I found I didn’t need to use those strategies and my teachers in top sets didn’t tend to teach them, those methods are really for people who are really struggling :/
@Ryan-mm1oj that explains why my school (private with entrance exams) never taught us this.
We actually had a mock exam where the last question was "write your name on the front on the exam paper and do not answer any of the questions". The thought behind it was to teach student to read through the paper before starting and identify the questions that were easy to answer and concentrate on those first. I guess also trying to get us to really understand the questions first / identify instructions and 'conform' to them.
When i was at school i did get the impression that we were mostly taught how to take tests rather than to learn the subjects. I was a straight D student, but have since learned to love learning and have taught myself many subjects including chemistry, electronics and some programming. Not to high levels, but certainly higher than GCSE.
I remember being given this test in the 6th grade (I was 11 years old). I started, and then read through the test to see what was going on, discovered the "gotcha" and erased my first written answers. While taking the test, I was about midway through the timed allowed, when I heard "OH KNOW" from another student. They frantically erased all the "wrong" answers (got a C for a grade). Those of us that did things properly got an A grade. Then there were the rest. It didn't count for much, but it was an interesting test. It was given by several teachers (different classes) on the same day probably do we wouldn't gossip about it after school. It was a long time ago!
I agree so much about the lying about stuff, like sqrt(-1) I had wonderful teachers, pretty much across the board. Any "wrong" things we were taught were always flagged as "this is wrong, but accept it's good enough for now. If you take A Level maths, you'll find out how and why you *can* do this!" The best teachers ignite interest in the subject. Even better, as long as it wasn't going to be confusing, sometimes they'd just quickly show us the highlights of the A-Level stuff.
The point of method marks for maths is that if you get it wrong, the market can see if you at least understood the question enough to have tried to get to an answer. As long as the method should work, it doesn't matter what method you use.
I remember doing O level maths and having one paper where we weren't allowed to use a calculator. This tended to mean that the answers would often be a whole number and therefore could perhaps be guessed correctly. If the correct answer is 7, I don't think it's unreasonable for someone who shows their working, but makes an arithmetical error to get more points for doing this and giving the answer of 6 than someone who just writes 7.
@@trickygoose2You also have the situation where calculators are allowed. Anyone can plug in the question in the calculator and get the correct answer.
Showing all the steps is how you prove you understand it.
Hi Evan,
14:48 The people up voting the comment, aren't (necessarily) up voting that you should get zero marks for not writing the answer on a line, but that it is likely that you will.
I think most of your respondents are giving you the advice they have been given.
It is difficult to mark papers fairly without some rules/expectations of 'correct' formatting.
It is specially difficult if the people marking have only a medium understanding of the topic and very little time to check your answers.
The American essay writing system you mentioned was actually how my history teacher taught us to formulate our gcse essays.
I was used to university exams in another European country and then moved to the UK. I found that exams in the UK were easier, but that they also relied much more on one's ability to memorise, because they are all closed book. The exams I was used to were open book, and accordingly far more difficult. Once I learned how to memorise well (never been good at it), I started getting good grades in the UK.
I think a lot of people's comments are coming out of a misconception about how maths exams are marked in the UK
1) If a question doesn't explicitly ask for working, full marks are awarded for a correct answer
2) If a question does explicitly ask for working, any mathematically plausible approach is acceptable - marks are only removed if it is beyond doubt the answer came from an incorrect method. (Like you did 2+2 to solve 2 squared, you would be wrong even though the answer is 4 either way)
3) Errors are typically carried forward and full marks awarded except for the arithmetic error provided the working is correct
4) Your answer should be on the line for clarity but if it isn't the examiner should look at the working to find the answer
In general people are confusing good practice - always show your working with clear steps and write answers on the line etc - with absolute rules. Mock exams might be marked more harshly to enforce these habits. But in actual exams there is a lot of benefit of the doubt given.
As a side-note, I agree using a dot for multiplying would not be sensible to do in a UK exam because it's just not a recognised way of writing multiplication and would cause confusion. You would never do 3 x y to mean 3*y you'd just write 3y so there's no scope for confusion with the variable x, especially as the use of curly x is basically universal and ingrained from the moment you learn algebra. In regular arithmetic you would use x though (3x5=15) and in my mind 3·5 far too similar to 3.5 but I guess it's what you're used to.
This applies to PEEL as well (not that I ever learnt it like that at school, though the same principles were taught). It's a good way to teach kids how to structure an argument, but it's not required. I quite like it to be honest, it helps to structure your thoughts and present them in a logical way. While we'd all love to be able to pull off some avant-garde alternative essay format to blow your examiner's socks off (and such a thing is perfectly legitimate and could get very good marks), it's much harder to do this in the pressured environment of an exam with a question you've thought about for 2 minutes before writing.
Yeah I absolutely agree. When I heard that, I was sure that my teachers told me that as long as the method is correct, no matter what method, you'll get the marks.
Good points. This correlates with what we were told.
I find with multiplication, it's easier to bracket the second term, e.g. 3(5)=15, that way there is no confusion with x or x.
In my experience, I found the dot notation became more common the higher the level of maths I studied. You certainly don't tend to see it at school much.
@@susannahdrazin220 Yes I think it does get used a bit more in university contexts.
Hi Evan,
As a GCSE student I have watched your video and found it really interesting , there are a lot of truths but also some misconceptions in the video.
We do spend half of the time on exam preparation and skill. There are a lot of specific you need: the very specific mark scheme and words you need for science, the exact timings for RE and English.
However, there are some misconceptions in the video too. The main one is the one about math. I don’t know if it is specific exam boards (I take Edexcel) and I don’t think I need to put the answer on the line. Also for GCSE you will never get marked done for the “wrong method” you will be marked done on your method if you haven’t shown you workings. (As my maths teacher says “it is the game we play” you must show your working for maximum marks) They do advise to use the specific method as it will be the one in the mark scheme.
For the dot instead of x, they do this so that it will be scanned into the scanner. Our GCSE are now all digitally marked and scanned. If you use a dot there is a slight chance that the scanner could not pick it up. Therefore using an x to make it clear
Hope this helps!!
I think half of the time doing exam skill/technique stuff is way higher than the avergage. But as we don't have coursework, it makes sense to ensure people don't make silly mistakes under pressure & go in knowing exactly what they're doing as best they can.
I love this. I took my exams before the advent of the pocket calculator, this is why you had to show all of your working out, that and the fact that mental arithmetic was a dark art meaning they couldn't see it. Fun fact: University education was free and politicians had civil debates on one of the 3 channels your black and white telly had.
Oh. This so reminds me of when I switched from a private school to a public one going from 7th to 8th grade. The math placement exam was so ridiculously basic for me that I simply wrote the answers because I could easily solve all of the problems in my head. Apparently because of this the counselor decided that I had cheated and placed me in remedial math. It took a month and my dad taking a day off of work to browbeat the counselor into dragging the teacher that taught the advanced math classes in and doing a verbal exam on the spot to get her to admit I hadn't cheated. After the teacher started to figure out where I should have been placed, he went and got a copy of his Algebra2 final exam. I then took that and only missed 2 of the problems because I hadn't learned about Sigma functions yet. The teacher then flat told the counselor that the school didn't have a math course that would be appropriate for me, as I was already beyond what he taught in his most advanced class (sans the sigma functions). He did explain them to me in the hall while my dad chewed the counselor out in "private" (at the top of his lungs so the entire office heard every word).
My dad was exceedingly irritated with the idea that anyone would think that I might cheat on a math exam since he regularly brought home some of his calculations from work so we could solve them together as a fun quality time activity. He was an aerospace engineer with Lockheed Martin at the time.
seems like also a lesson on schools or curricula in schools might be teaching math badly.
And well, in classes the average student is also quite discouraged to "ask questions or ask for something to be explained again"
Even though every teacher likes to say that they welcome questions. But as soon as something isn't understood or needs to be explained again, it's like "did you not listen? did you talk to your neighbor too much?"
@@ayoCC both of these seem like misunderstandings though, at least partly on the student's side:
Having to write down the process of how you arrived at your results is a standard requirement in most school systems, for one so teachers can grade you more fairly, but also in preparation for actual real world arguments and scientific papers, where you'd have to do the same on a larger scale. How finely detailed you need to write this down obviously depends on your target audience. In school i would consider the other students part of this audience, you need to explain your process so that most of them could follow.
Losing marks for missing explanations and the suspicion(!) of cheating are therefore totally understandable. Just deciding that it was cheating and placing a student in remedial maths without ever checking (via verbal exam or otherwise) whether they know the stuff is obviously too much, though.
Similarly "did you not listen?" is a valid rebuke to a very general question which would be answered by a complete repetition of the lesson. Asking a detail question on a specific point should get a proper answer.
@@lukasr5867 Well if someone wants to get something explained again even if they didn't pay attention before shouldn't be so bad.
I think we can still do a lot to improve the delivery of math knowledge without a crisis of student integrity.
The original commenter talked about their experience with their father learning math like puzzles and games and being far ahead of their peers.
It made me think, how much back and forth communication did it take to get to that level?
Also in terms of asking questions and repeat, repeat, repeat questions, there's never going to be any pushback like "ok why did you just ask that again? did you not pay attention? well you lost your one and only chance"
I can immediately think of one way we should be adding to how math is taught... Excel. break down every formula and algorythm into excel tables that can be used to plug in numbers. And they'll be using excel later anyway instead of ti-84
@@ayoCC If you didn't pay attention for five minutes, you should be able to formulate a precise question to ask (and get an answer). If you didn't pay attention the whole lesson and ask for a repeat of that, you are in somewhat of the wrong place. Then it's really on you to sit down at home and try to understand the material from the book or other sources. And if you truely have some large understanding issues with the material, despite paying attention, sure, it's fine to ask once or twice, and a good teacher shouldn't immediately jump down your throat for it. But if the same student asks for large repeats all the time, that will appear to the teacher like they never pay attention or really need some private tutoring.
The example of working with the father really just supports that point, it's essentially private tutoring on advanced topics. And 1-on-1 you can adjust very precisely to the needs and wants of your student, in a way that's just impossible in the classroom.
And please leave Excel out of this. If you really think math is about plugging in different numbers, you've missed quite a lot of it. It's about understanding exactly the part that excel would take away from you. And believe it or not, just like with open book exams, you still need to understand the material to a large extend, otherwise you'll spend all your exam time looking up stuff and not get anything done. Same with math and calculators or other tools.
Regarding the method point you've made: In Germany you also have to show the "Rechenweg"/ method how you came to your conclusion. It doesn't have to be the exact way you learned when getting in higher grades, but since the point of a test is to show what you've learned in class it is important to write down every step of the method. The teacher can't look into your brain and see that you've multiplied everything by 6 so it is important to write it down. Especially if you get to the wrong result in the end, the teacher can see where it's gone wrong, and if it is a mistake that happens a lot of pupils he/she can cover it again in class to make sure everyone has the same understanding before going on to a more complex topic. So I get why you think, that it is an easy step you do in your head so you don't have to write down, but with the teaching logic behind it, it is bad for showing what you've done.
Writing down the steps isn't just useful for teachers, it's also useful if you want to program a mathematical function or do more complex calculations, mental math won't really help if you're balancing 20 equasions for a mechanics problem.
I'm from the US, but I also had to write all of the work out in a math/maths problem in school.
I agree fully, I just want to add: in the Netherlands we don't use y=mx + b/c, we use y=ax + b. We just go through the alphabet when adding more letters so y=ax^2 + bx + c is next.
First of all I think it is useful to show the steps you took in your calculation. But insisting on Just one method to calculate something, when there are multiple correct ways of solving the problem is just plain stupid.
And concering the y = mx + b/y = ax +b and so in thing: god, am I upset with how many people cannot grasp the concept of variables (often because they are tought one "correct" formula at school). I teach fist/second Semester maths for engineers and I cannot count the times I had to explain that you can write the pythagorean Theorem with a, b and c or with x, y and z or If you Like with l, m and n. It still will Tell you "the square of the hypotenuse is equal to the sum of the squares of the Others two Sides"
@@Rincy42 while I did not see the messages Evan refers to when saying that his method precludes obtaining marks, it is worth noting that you can get the right answer from the wrong method quite frequently. One tactic I've seen my physics students employ, rather than learning and using an equation, is just to write out every permutation using the numbers in the question stem (X x Y, X/Y, Y/X) and pick one. Do they deserve a mark if they luck out of 3, when really they've no idea what they were doing or why?
The highly structured nature of English was why I enjoyed Advanced Higher so much - you completely abandon these strategies to more of the wayside. Personally, PEEL (or rather PEAR at my school) structured paragraphs did help me formulate arguments and I do use remnants of them later on, but they mainly serve the purpose of allowing you to complete the exam within the allotted time - which was the majority of the struggle in English. I am Scottish however, and our school system is slightly different.
i think that evan should talk about the difference between our school system and the rest of the uk cause we dont even have gcses 😭
I'd say the Scottish system is more than slightly different. I've had to explain it to confused english people multiple times before.
You nailed it though - they helped you to learn how to formulate arguments. That's the whole point. These are young children learning not adults.
what did PEAR stand for
In Ireland, we’re told to show all your workings because even if you get the final answer wrong you’ll get marks on everything you did correctly before you’re mistake. You can access the Leaving Cert marking schemes online and it shows it on basically each question, if I’m not misremembering.
Edit:
I definitely think you should look at the Junior Cert and Leaving Cert maths papers too.
I remember the Junior Cert English exam from the mid 2000s. Essay writing was primarily about volume.
Peel is a template to help people do analysis paragraphs, but a lot of teachers say that if you know what you’re talking about then you should just write in your own style of analysis
as a scottish person i love watching this cause the education system in scotland is almost entirely different from the rest of the uk, we dont have gcses or a levels. we have national 5 (in s4), higher (in s5) and advanced higher (in s6) and in english we use pcqa paragraphs (point context quotation analysis but this varies across areas apparently). i think it would be cool for you to look at the differences between scotland, america, and the rest of the uk!
I use peel paragraphs in Scotland? Maybe it’s just a individual teacher thing
@willross212 probably a school thing cause me and my two siblings all went to 3 different high school and all got taught pcqa
PCQA is the same as PEEL, just different phrasing :) it will look exactly the same on the page.
Wales is also slightly different
I'm scottish and I was taught a different variation of peel called 'pear' which was point evidence analysis refer to task but aside from that I'm also noticing so many differences between English exams and scottish exams alones
I took school and university exams in the UK over 50 years ago. Things have clearly changed since then. Back then, there was much less emphasis on examination technique. Education was seen as a way to acquire skills and knowledge rather than exclusively a preparation for passing a test. Yes, examination results were important, but not to the exclusion of everything else. If a class showed an interest in some area that was not strictly on the exam syllabus, there was latitude for a teacher to get students enthusiastic about a subject by diverging into topics that they will not be tested on. We were encouraged to 'read around the subject' and see things from multiple angles. Having a deeper structure of knowledge leads to better retention of new learning because there are more mental links to anchor new things into memory.
I don't think teaching a simplified version of a topic is 'lying to students'. Newtonian mechanics for instance is perfectly good for all practical purposes. Man walked on the moon thanks to Newtonian mechanics. Relativity and relativistic effects are a minor adjustment that only applies in extreme circumstances. I think it's perfectly OK to leave things like Relativity and imaginary numbers out of elementary science and mathematics, then later on explain that there is another, and slightly more nuanced way to look at things.
Education now is for providing competent minions who can operate systems and the management level is predetermined
Yes, the main purpose of state education is to produce compliant economic drones, but I would disagree that 'management level' is predetermined. Someone in a salaried management position is also a worker. The 'predetermined' class is those with inherited wealth who don't need to work. They choose to work. @@janebaker966
Marking exams is not an exam marker's job. In the UK, exam markers are teachers who sign up to mark some exams in the summer for a bit of extra cash.
As a math instructor, I make a point of writing algebra problems that don't use x, n, u, I or l, as they can be mistaken for other letters, numbers, or symbols.
No, the lesson wasn't "listen to authority", it was "pay attention". The lesson was that the tiny minutia do matter and it does actually count in real life too. I think you've just explained why every hotel where I've had check-in agents mistype my name into their system (having read it on my ID!) and try to give me the wrong room (or even succeed in doing so in one case!) have been in America.
The dumb-arses have never learned to pay attention to details and that does matter and it dramatically affects their work performance.
I am starting to see why science in this country is going downhill, when I see so many comments supporting some of the nonsense in the video.
Yeah, but HOW important is it really. Again, the education system we have today is still the archaic Prussian system designed to create obedient factory workers and soldiers who could shut up and get on with highly regimented tasks - this isn't just isn't the world we live in anymore. Businesses are increasingly looking for soft skills and creativity, and yes at times, they're okay with being a bit rough around the edges. Not to mention that this is essentially just speculation on your part, we were not taught WHY we needed to follow these stupid rules apart from the fact you had to.
@@dog-ez2nu The time when I was given the room key for another person's hotel room, that person was one of the most famous writers in the world and there was an unfinished manuscript in the room. If I'd been unscrupulous and stolen something like that, I imagine the hotel would have been sued for millions.
@@dog-ez2nu You do know that most of the tests he is refering to don't matter. 11+ and GCSEs have very little importance, so why not punish kids for doing sloppy mistakes when things don't matter so that they learn to not do those when things do matter
I actually really like the way PEEL (or in our school PETER) paragraphs are taught because it forces the majority of Britain to be drummed into them at a young age how to write/formulate a convincing argument and ensuring that they are able to review, critique and understand texts in a substantiated way. Most people won't use it past high school so they don't need to learn when to use exceptions and more fancy structures but you definitely won't lose marks for writing using a different structure as long as you are still making reasonable and substantiated claims about the given text
PEEL is basically how you're supposed to answer job interview questions too, so most people will use it throughout their working life!
What is the R for? Point, evidence, technique, explain...
@@grassytramtracks "Reflection". As in reflect back to the original question or reflect on this point in context with the rest of the text.
As someone who went through a literature/philosophy section in my secondary education, arguments can be structured in any way that works - but they must be structured, and that's not as natural or spontaneous in everybody's mind. We were taught an even more detailed, particularly stringent version of the 5 paragraph system, which if you did it correctly would always yield very professional and clear, pleasant results. It was a good method. But we weren't taught it because it was the only, or even the best, way to structure something. We were taught it so that the principle of structuring our arguments into a perfect architecture was the centre of our thought process when writing an essay or conceiving of an answer, and that is one of the best intellectual habits I was ever given, because without even writing, it brings structure and clarity to your ideas themselves. It's about changing how the students even think about the writing, debating, or planning process. Then, they can diversify.
I think one of the problems with the UK exam system etc is League Tables. I don't know how they do it in the US, but the quality of a school is judged on how many of their students are reaching the highest grades and so on. The problem with this is that it doesn't factor in (for want of a better phrase) 'natural ability'. I knew someone years ago who would get an A* on all his exams despite never putting in any work, and I've always argued that theoretically you could have a school full of students like this guy and according to the league table situation would be deemed a successful school, but the teachers haven't really done anything. However, across town there could be a school where the students were only getting middling grades but in another environment they would have failed outright. To me this second school deserves recognition because they are growing and developing their students, but because none of them are getting the higher grades they don't get said recognition. If the league tables were based on a grade increase (say a student was getting F's when they join the school, but C's when they leave.) it would be a far better.
Thank you. I was looking for a comment that would mention this point. League tables being used as a primary measurement of quality are highly detrimental because principals and teachers will inevitably focus on grades, rather than instilling curiosity and love of learning.
I found it really interesting that you said about the placement of the dot - because (I could be wrong here), I think most Brits use the centre placement of a dot in a decimal if we hand write it. Since most operating systems for computers originate from the US, it will automatically place them where you said and sure, we'll understand it. I'd be interested to hear from younger Brits on this, since it's a good few decades since I was taking exams. I've tried to explain the pernickitiness of the UK marking system (style marks, method marks, spelling marks, presentation marks) previously to US people that don't understand how our outstanding results are at the level of 75%, where US are expecting to have grade point averages that equate to high 90s. Do I think it's sensible? No! But an interesting side point is that we learn to 'play the game' which whilst you might not use the things to pass exams in future life, are remarkably good at setting you up for office politics and making sure you suss out the culture in terms of 'what are the things that I need to pay attention to for this company'.
Excellent comment!
I used a bottom-placed dot in GCSE but the centre was standard in A-Level and university, I did see the centre dot as a multiplier in legacy papers and in a few specific topics (vectors is the only one that springs to mind) but I agree - centre dot was the norm for decimals in my experience
I finished school in 2009, we always tended to place the decimal point at the bottom, but weren't particularly specific with it. It could be anywhere between the bottom and middle
Though, added to that, the only time I saw a dot intentionally in the centre was when I got to uni and we were doing the dot product of vectors and matrices
i was always under the assumption that because all students would have different handwriting, it may confuse the marker if you're handwriting is a bit messier, or you are just trying to be quick and can't tell where its supposed to go. i guess you could argue that the teacher could use common sense but as we know maths is a very yes or no subject its either right or its wrong, so they'll take everything as if it were intentional, rather than saying 'they probably meant to this so i'll give them the mark'
additionally (pun not intended, but noted), i think if Evan put a space between the numbers and multiply on that website it would have recognised it. 5x5 is 5x multiplied by 5. whereas 5 x 5 is five times five. or 5x squared is 5x x 5x. still confusing without a typeset i know. but you can always tell the difference with handwritten as you do the subject 'x' like 2 brackets ' )('
In my british school, (currently in gcse) when you times two unknown variables you just put the letters directly against eachother with no notation in between.
For example,
A×B = AB
Or
A•B+45=AB+45
This makes total sense to me now just because ive used it for so long now.
So you could write x³ as xxx.
@@Matlalcueitl yes you could, exactly.
@@jelly4393 In Poland we never use 'x' for multiplication, we always use dots. But… we use commas as decimal separators.
Yeah, I mean E=mc²
@@Matlalcueitlyou could but we wouldn’t because it’s the same variable
When it came to math in high-school, ms spinny for my 11-12 ap math, and calculus. She litteraly was one of the authors of the textbooks we used where i live. I absolutely loved her class, because she loved teaching it. Same with my physics, and chemistry teachers. A good teacher makes a massive difference.
As someone who's never been subject to either British or US school systems, PEEL make a LOT of sense.
When you're learning English (any native language, really), the goal is a lot less about proper grammar (once you're past the first few years of schooling) and far more about how to effectively communicate. That's the point of PEEL - at least as someone who hadn't heard about it until this video.
PEEL teaches you to be a more effective communicator, even outside of the language subjects. If you're writing a paper, regardless of subject, having a structure of "point, evidence, explanation/analysis, link" makes your arguments much more effective, because you're not weaving all over the place.
It's even useful outside of academia - look through comments on social media and notice how rarely people are capable of making coherent and convincing arguments.
Exam techniques get weirder after university in professional education. After I did my master's degree in maths, but wasn't accepted to carry on for a PhD (yes, still a massive chip on my shoulder) I became a chartered accountant. Which was 3 more years of study while holding down a full time job. But there, the commercial sector education firms pretty much taught you about exam technique only, with the subject matter coming as a side matter. And there was some dodgy stuff in there. For example, if a question was worth 8 marks, you had to make 8 separate bullet points to make it easier for the examiner and make sure they are numbered (fair enough), but if you couldn't think of 8, spread them across a page break so that on page one you have points 1, 2 and 3; then on page two you conclude the list with points 6, 7 and 8. The idea is that the examiner is so rushed that they don't bother to count them and if every point is correct they'll see you numbered up to 8 and so give you 8 marks when you only made 6 points. Not the best thing to teach to trainee accountants, in my humble opinion.
I was an English teacher here many years ago. I feel that you have missed out one important point in this interesting video. You are a highly intelligent man, well-qualified and very able to push your thinking on all this education while there are many ordinary middle of the road people who have neither the time nor the inclination to question as you have. Most of them needed the structure you are deriding to get by from day to day. I specialised in working with the middle groups and they were always overlooked in favour of the top or the bottom ones.
In the uk we use • and x for multiplying it's especially important in vectors where they do different types of multiplication
I am from the UK and have never seen anyone use a dot for multiplication sign
I was an English professor at community college in the US. I’m an actual expert at teaching students how to write arguments. I now live in the UK and can only find work as a supply teacher because, reasons. This video is giving me extreme anxiety but you have hit on something I feel in my bones every day. I see now why my experience is considered absolutely worthless in this country try. They cannot even understand what I’m saying when I say what I do. They can only see the thin side of the paper. It has destroyed my soul.
The situation with a primary teacher saying that you can't square root a negative number was almost certainly because that teacher was not a maths specialist. There are very few primary teachers with maths beyond GCSE and you don't do complex numbers unless you do double maths at A level. When I was a secondary teacher I often had to get kids to unlearn something a primary teacher had taught wrong. I don't want to diss primary teachers - I think it's a really hard job but it's simlly a fact that most do not have good enough maths skills to get things consistently right. The same thing would happen if I tried to teach French.
I think when they say you can't take the square root of a negative, it's not so much "you can't" as "don't try". At that stage of your education, it isn't useful because it doesn't involve real numbers, or at an earlier stage still, it isn't useful because you can't see or touch minus one of anything.
After that, as you advance, they tell you "now let's expand your minds by introducing you to imaginary numbers." If a pupil is avanced enough to handle 'i', they are intelligent enough to know, without being told, that you didn't lie to them back in the day but taught you something that was true in the context.
Exactly; each teacher is inidivdual, and how they'll answer a student's question about a maths' concept they're not going to learn in primary school will vary wildly, and isn't a systematic nationwide approach.
Yeah, it's the same principle in physics and chemistry, you start by being taught a simple system then every level of study you throw that out and start again with a more complex one - seems pretty standard. To suggest you were being taught something incorrect (or at least incomplete) would really get some students hung up and unable to progress.
I think a common difference that keeps arising between the two is in the British system they want you to show what you know in a smaller space of time so you can properly time your answers to the exam length given. Like with the essay structure, you still have freedom to elaborate and delve deeper into the question ONCE you’ve covered everything you’re supposed to. There’s nothing worse than going off on a tangent and realising you spent too long on one section and either rushing the conclusion or forgetting to add in important things you meant to add. Similarly with maths, they can appreciate you understand the maths but wouldn’t using a more streamlined method rather than a longer one prove even more so your knowledge of the question? I went to school in Ireland so it’s not the exact same but from watching your vids and hearing my friends experiences the specifics for maths answers and essay structure seems very similar. Also because we kept X as the multiplication symbol and a . Was only used for decimals we didn’t have to put the dot at the bottom we often had it in the middle between numbers as it was more visible when written. At a glance it may have been missed if it was too close to the line or on the line by mistake.
Overall neither seem interested in what you know, only what you can parrot back.
In the olden days when I did maths GCSE (1988), the questions would either require a particular method because it's testing knowledge of that specific thing, or strongly suggest the method with an "(or otherwise)" on the end to permit any valid method. The "or otherwise" allowed the top maths stream, who had already learned differential calculus, to solve area-under-a-curve questions by just integrating the equation between the limits to get their answer - which was way more accurate and considerably faster than fiddling around drawing lines and counting squares.
I believe most of Europe uses the dot as a multiplication sign once you hit algebra. Also, y = mx + q /math teacher, PhD
I thought it was y= mx + c so when you use the discriminant and the quadratic formula ect the letters match up better with y= ax^2 + bx + c, yk alphabetically
@@paigethompson5575 My point was that it just depends (many countries use different forms, e.g. in Greece it's ψ = αχ + β in Japan y = mx + d, etc.). Point being: it doesn't matter - it's a variable x and a constant denoted by whatever. This is why rote memorization should not be encouraged, but actually understanding is fundamental.
@@paigethompson5575 The y-intercept is b because in point-slope form you can use the point (a,b). (y-b)=m(x-a)
@@PurpleAlienPlanet I fully agree I was legit only saying something I noticed it makes no sense if people actually got annoyed by it, I think the commenter in the vid was saying it in a satirical way anyway aha x
3:10 that's why so many students who have since graduated say "do the past papers!" because the wording to the questions will always be way more complex and confusing in the real papers than they are in the textbooks which teach you the bare minimum.
i for one still struggled to answer essay questions in my psychology A Level because while I knew the content, i didn't know how to word it in a way that would get me the marks - my teacher even said this to me and said if it were possible, she would love to record me during class and send that video off to the unis i was applying to because i knew everything and was passionate about the subject but just couldn't get it down on paper
luckily i passed all my subjects and got into my first choice but i'm not lying to you when i say i still got a D in my year 13 March mock for Psych, it was a hard process to fix
You reminded me of the training I was given in how to make an effective presentation (in the world of work); “tell them what you are going to tell them, tell them, and then finally tell them what you have told them”. That way you have half a chance of people actually remembering what you have told them!
So interesting! I found UK maths exams so much more flexible than Austrian ones! For instance, in Austria (before there were nationally standardised exams) I had to use 5 rulers and things and draw perfect graphs on graph paper, and in the UK they wanted you to show the shape (could draw by hand) and note the important points, which showed you’d understood without having to draw and erase perfect smooth lines.
The skill here is 'following instructions'. It demonstrates your attention to detail, efficiency in doing tasks, critical thinking, etc. All these skills are used in everyday life.
12:19 I think this may be a key thing that you've missed Evan, unless I am very much mistaken, exam grading isn't a job, it's a thing some people get paid to do a couple of times a year as a side-gig to their job. Then they have to mark a number of papers quickly, so teachers have caught on to this and are teaching kids to "PEEL" on their work so that the markers can quickly see where marks should be awarded.
In much the same way that answering job adverts these days, in order to get through the sift you have to answer each point on the person spec clearly and deliberately, ideally right under a bullet point of said person spec
Couple of things:
1. I only have knowledge of the British education system, but i have partaken personally most of my life, and now as a parent get to see its continued evolution. More and more teaching is geared towards passing exams - on top of a large amount of time being spent in each subject being focused on how to approach the exam rather than actually covering the subject, the subject covered was focused on what is likely to be asked in the exam! I even had one teacher tell me it was more important to learn something verbatim than to understand it!?!
2. As a manager in an engineering workshop, let me tell you, "minutiae" do matter. RTFI is so important, half of our scrap comes from people ploughing into a job before fully understanding what's required and while the end result might look OK, it doesn't meet to customer's tolerances. The point is, there are times in life where someone doesn't have the time to explain the why (we'd need to at least triple the number of designers we have if they needed to convey all the why) and so you should read the instructions correctly and follow them to the letter. This isn't about "following authority" but being accurate in your work.
I think this applies in most jobs. Lack of attention to detail and failure to follow a process (instructions) wastes everyone’s time and gives a poor result. I have to train people in office processes, and I’m sick of having to give explanations of why every single step is the way it is, when the person could just follow it and we could all go home on time.
Even worse is unravelling all the problems caused by them later deciding that they still won’t follow the steps. For example they don’t follow the given naming format, we can’t work with the data they produce because we can’t sort,filter or search on it. Because they thought it didn’t matter, shouldn’t matter, they knew better, they forgot all about it etc.
If only someone had made them circle the answers like their tests said, or lose the marks.
Regarding more and more teaching being geared towards passing exams, in the early 80s the great bulk of my Maths homework in my second year was doing past exam papers. That meant *all* the Maths and Further Maths past papers, and most of the Special Maths/Special Further Maths papers from the previous 20+ years.
As I was lucky enough to have a talent for maths, that did mean that when exam time came around, I spent almost half the time just sitting and looking at a finished paper fairly confident that I'd got all the right answers and waiting until I could leave, but I happily forgot much of it within a few months.
I don't recall having meaningful teaching in how to *approach* the exam, but it was certainly teaching biased hugely towards getting the best grades, and that was over 40 years ago.
As a sidenote, I did feel a little guilty that as a Further Maths student, I was taught (and could legitimately use in the regular Maths exam) a calculus method I can't remember the name of, but which was essentially "I know the answer is basically pretty much *this*, so I'll just write it down with a few variables and then work backwards to work out what the values of the variables are" which the regular Maths-only students weren't taught, which made some questions incredibly easy.
@@retiredbore378 It's all pretty hazy, but I think it was a bit more general/rough and ready than integration by parts, more a case of writing down an educated guess about the answer, differentiating it, comparing with the starting point, and tweaking the guess to make everything fit. Having done so many exam papers, making the guess was pretty easy for quite a few of the questions.
@@GreenWhitePurple If you train people but you hate people asking questions and wanting to understand why things are done the way they are, I think you're in the wrong job.
@@GreenWhitePurpleIt seems to me you've tried to follow your instructions on how to train other people by following instructions given to them, yet violated them yourself.
You teach people why they should follow the instructions (i.e. the correct data format, so it can be sorted, filtered, etc. down the line) so they can recognize failures of some subsystem, self-correct, and possibly improve it. Pure instruction followers are called machines.
You failed to follow instructions (didn't explain to trainees the reasons), now there are unwanted results.
Because you didn't question the processes during your training, you are failing to understand the consequences of your own actions, similarly to the people you've mentioned.
I've learned some things about teaching from the specific directions in textbooks or worksheets. A well-written question will get students to answer in the form you want/expect/need naturally, versus always losing some points for not answering in the right form, telling why, etc.
In the Netherlands in math, physics, university, et cetera, I have never needed to circle/box/underline my answer. It's in the end of the problem, everyone can see that you go on to the next question after it. If you get a mistake, you get points deduced for mistakes you make. If your whole method works, but you plug in the wrong numbers, you get a point taken off for that, not the method. If you do, you can fight it and get that mistake corrected.
Re: Method marks, it is not so much marks based on how good or not your method is - mores so, it is how well you have demonstrated your method so that the examiner can see you have understood the mathematical process needed to get to the answer and not just got lucky.
Under the "method doesn't matter if its right" philosophy, Person A guessing and landing perchance on the correct answer, Person B getting half way though and then taking a stab at an answer that happens to be correct, and Person C who diligently followed a mathematical method to not just get the right answer but be confident in that answer, would all get the same marks.
Brain dump comments:
- Digital exams are only a problem because the government doesn't fund schools appropriately enough for us to have the equipment for 200-300 students to sit a computerised exam at the same time.
- We don't use scantron and we also have like 6+ different exam boards in the UK and each one has it's own style of writing exam questions, so every subject has to teach the technique for their specific exam.
- Showing method is an anti-cheat method, and it will depend on the question and paper. There are literally questions that ask you to show your working so its required. Also lowest common denominator for teaching
- ensuring some kids will get error carried forward marks if they make a dumb mistake when under pressure
- You're right about y=mx+b - downside of rote learning
- The dot is confusing in countries where they use the period for decimals, it makes more sense in countries where they use the comma for decimals. In the UK, we use the central height dot for decimals and a period interchangeably too.
Just to note, you don’t have to use PEEL (or PEAL) paragraphs for creative/persuasive essays. Also, even with the English Lit exams, PEEL is just a base line, at least my teacher pushed us not to stick strictly to it because it can limit you, as long as you critically analyse a text, remembering to include a quote here or there, that’s fine.
Insight from marking mocks, for DT GCSE specifically. Using Peel for long answer questions, shows that you're analysing pros and cons for choices and justifying why you've made a certain decision in the design of the product. "X wood is good because it is more sustainable, which means it is better for the environment overall," or something like. But on our maths questions, you can get full marks for giving the correct answer, no working out, but we can give marks for method, despite wrong final answers.
I believe that PEEL (or PEAL) encourages clear and logical expression. It is actually very useful when writing scientific papers - especially if you want your paper to catch the eye and attention of the non-specialist.
@@retiredbore378 Exactly - I've used frameworks for proposals that aren't dissimilar on numerous occasions both within sales and education of internal stakeholders.
Most of those frameworks and structures are American in origin, too. It's like we're teaching MBA fundamentals at junior levels with things like PEEL.
Ultimately I think the emphasis on exam technique, espeically stuff like PEEL/PEAL, is bc of how standardised the marking has to be to be kept the same across the country. If ur paper is being marked by some random person who might not even be a teacher across the country, there needs to be a mutual understanding of specifically what will or won’t get marks otherwise everyone would be doing something different, and it would be much more up to individual examiners discretion to award marks for whatever style of writing they like, which ruins the standardisation.
When I was at school pretty much every kid who got an A & above in Mathematics GCSE had a private tutor or was being tutored by a parent or family member.
I can say that I learned nothing about Math from school teachers, everything I learned was through supplementary education with private tutors face to face & 1-on-1
The point of requiring essay answers to be structured in this way is to enable whoever is marking the paper to easily find and identify the statements that are deemed acceptable to be worth one point each.
So, when it comes to algebra, we didn't use a dot in my school; we just placed the variables next to each other (so rather than 3x*y, we'd just write 3xy). Likewise for parens, we'd use 3(x+y) rather than 3*(x+y). I can't remember when I first came across the dot as a multiplication symbol, but I never actually used it until I encountered vector maths.
thats how i remember doing it
Same here, at a certain point in our schooling we were told that x is now invisible. If 2 things are next to each other with no symbol is a multiplication. But also when I did maths in secondary school we only ever called something x if it was the letter, for x the symbol you'd say times by or for a calculator it was the multiply button.
From the US, I also would rarely use the dot or x to indicate multiplication in higher math courses. Parentheses to break up numbers is much clearer. So like you already have 3xy, but you need to multiply that by 5 for some reason, you’d write 5(3xy) or (5)3xy
Thats how I was taught too, in the 1970s in the UK.. The only place I ever found the use of the dot as a multiplier was when we got to multiplying matrices, and for some reason (probably something to do with Victorians, these thing often are!) we were taught to use a dot between each matrix to signify multiplication. Yeah I though it was weird too....
However, Evan's other point about the decimal point position, well, he comes from a generation which has grown up with computers, calculators, and other types of readout, where it is true the convention has always been to use the "full stop" symbol from the old typewriter keyboard as the decimal. But thats not how we were taught as kids to do it in handwriting. When I was a boy, everyone who wrote out a decimal number would put the decimal point where it belongs, where it was always put before mechanics came into it.... in the middle like this >> 3·1415 ... I mean, there is even a character for it in the character set!
That was the world before calculators came along, and for some reason, probably ergonomic I don't actually know, they put the dot on the floor and from the 1970s onwards, the general public was educated to recognise the full stop as a decimal point if it was between two numbers. Their calculators and their dad's Apple][ and their bedroom VIC20 all made them used to it and our generation who grew up then sort of became "bilingual" by default. But still, when writing decimal numbers in handwriting, the decimal goes IN THE MIDDLE, where it always was before technology moved it.
Thats why its not useful to use it as a multiplier symbol in handwriting. Until recently I never met any brit over 40 who writes the decimal point on the line.
Where do most people use decimal points? probably in money, as we all use it every day. But bear in mind that until 1970 in the UK we didn't have decimal coinage, so our ancestors didn't need to write it, print it, or type it in relation to finance at all. It was all £sd So the average joe would hardly ever see a decimal number in print unless they were a mathmo or an scientist or an engineer.
So, you young whippersnappers who know only the computer age... NO, decimal points always went in the middle!
But seriously, I'm easy with the modern solution. Im used to it now. Just don't go thinking it was always like that because it wasn't, and more recently than you might imagine.
Love your videos !
I'm older than Evan and you explained this better than I could to him.
I just interviewed two candidates for a paid intern position. 3rd year Engineering students (4 year course). They got the maximum possible mark for VCE (end of school) They initailly sounded OK. Then I got to my "quiz" section where I ask questions about technical matters that I could have answered in high school. They were hopeless. They said thaey could not remember the answers. I do not remember the answers - I understand the subject matter. I think that is the difference. So much of it is rote learning and regugitation. These people are going on to be our doctors, engineers and lawyers... They don't understand the topics, how is that going to go?
I so agree with you on mathematics. So did Richard Feynman. If you got the right answer then you get the marks. If you got the wrong answer then watch out...!
I didn't notice it before, but since you mentioned it in one of your videos, YOUR VIDEOS ARE CRISP, I love the 50 FPS
The method being so shit section had me in stitches, was the most British comment and most American response I have ever seen 🤣🤣🤣
i’m from ireland! and this past year i done my leaving cert.. its an exam you do at 18 that’s inbetween gcse and a levels from what i gathered and determines what university or college you go to. If you go to any irish person you know and ask them about the leaving cert they would probably tell you about the “leaving cert nightmare” phenomenon, which is experienced by millions of leaving cert takers! i know you live in the uk but i think you would find the similarities and differences very interesting and probably surprising!
I take A-Level Further maths and my maths teacher tells us to always write our method to show a ‘rigorous mathematical argument’, so that we could explain our method to another person. Showing your method is especially important in ‘proof’ questions in an exam, as I assume it has been a tradition to show all your method among mathematicians to enable peer review and credibility. However, I do agree that method marks can be ridiculous. Btw, I would love to see you try the A-Level Further Maths exam and maybe some Maths Oxford/Cambridge admission questions, as they are more to do with problem solving and are very different from questions you would see in an exam.
He has a degree in maths so, except where he's rusty, he should be able to manage Further Maths pretty easily (the thing about A-levels - in my experience at least - is when you're in it they feel like a _huge_ step up from GCSE but once you've done a degree, not so much).
Method marks are more about showing your workings. Certain questions have follow through marks which does mean you could get a marks for something silly.
The dot is not introduced until alevel, in my case, as we show that algebra just doesn't need the times sign. A curly x for algebra is different than a times sign. Most schools have homework online for maths know so * is known.
Also you don't lose marks for not putting the answer on the line as long as it's clear where it is. The line is also dotted so are fine with fractions
we dont use the x symbol for multiplication in algebra at all, we just use brackets, because it is confusing to have two xs but i think the dot is also confusing, so we just took the easy way out and wrote stuff out like 8(5x+9)
Even though I left school years ago, I found this fascinating! Never considered as a Brit how much of the emphasis of our learning was to benefit to the examiner and not learner. I still would choose a curly x and x for multiplication as opposed to a dot!!
22:32 what you might miss on the confusion on this, is in (some) UK schools, we are taught to put the decimal point at mid-height rather then the bottom line. (Just got check out the BBC bite-size topic on decimals, shows examples of it!)
Well, just put the decimal point in the correct position, and the problem is solved. No confusion.
Decimal points go at mid height. Dots indicating multiplication go at the base of the numbers. It's not some schools, either, it's all of them, because that's the convention in the UK.
I had to think about this because it confused me when i saw it.. and realised it's because i do - and have always - put my decimal points in the middle! Maybe it's just the difference between normal everyday mathS and the advanced stuff. Once you start adding letters into maths my brain switches off anyway so not surprised i've never heard of this lol
almost the entierity of the world and all of the academic setting teaches to use a decimal at the base of the numbers and the multiplication as a dot in the center. the uk needs to adapt, just like how in the start of the 19th century they finally switched from Newton's fluxion calculus to Leibniz's better notation. the uk is just lacking behind.
@@mytube001 - but what is the _correct_ position?
I went to school in the 60's and 70's - decimal points went at mid-character height.
I went to university in the 80's (then again in the 90's and 00's) - the decimal point went at mid-character height.
I worked in the aerospace industry until 2 years ago - in all hand-written applications the decimal point went at mid-character height.
If using vector multiplication, the terms to either side of the dot were placed in parentheses.
No confusion . . .
The way she explained PEAL actually made sense to me. It also immediately reminded me of the Five Paragraph Essay before it was mentioned in the video.
PEEL is about essay writing and structuring your answer so that the point is easily understood and links to the question that is being asked. It's so that students don't waffle and waste exam time.
I tutor GCSEs (mainly maths and physics now but used to tutor english too), and what you're saying about exam technique is kind of true in how it's taught but not at all in how it's marked. An english mark scheme does not care at all about PEEL paragraphs as long as your point is clear and well articulated. The reason kids are taught PEEL is because it's a quick and easy way to teach a whole class of 15 year olds how to form a critical argument on paper. That's absolutely a useful skill that they will take forward! But if you can make convincing arguments that are well-supported by the source material using other methods, those will be marked in the same way. Likewise in sciences, the only thing that does annoy me about exam technique and GCSE mark schemes is the focus on using specific scientific language. You can write an answer that is correct and makes it clear that you understand the subject material but because you used one word over another, no marks. Thankfully this mostly goes away at A Level.
You might not use this form in the future, but you learn to follow a template which is something you will often need in the future. E.g. resumes, scientific work, manuals, applications...
And it is easier to evaluate and grade by the teacher, if everything follows the same scheme and is not jumping around wildly.
We didn't have such strict rules in engineering classes but you still needed to present the question, the way to calculate it and the result. Just getting the correct numbers out of nowhere would be suspicious. You also need to have the correct units.
And our thesis also needed to follow rules.
Decimal is no "point" in e.g. Germany because we use "," as decimal point. And in scientific formulas you often don't write anything for multiplication. E=mc2 ! An x would be much more prone to error as x often is used as a variable.
Not really. I have made several resumes in my time and to be lazy I used the "template" from Microsoft Word. I can assure you there are over a dozen different default templates on Microsoft and where things are placed in completely different area or take up different sizes. This fact alone means there is know actual template. Put it wherever you want as long as you the last three jobs or best skills are on your resume somewhere written and highlighted on the page you can get hired. The template is just for decoration not function. If it were for function there would be a standard template instead of twelve-ish. English should not be treated like math formulas, it doesn't teach English it teaches technique. Formulas/templates should be learned in math and sciences only. Templates CAN be used in English but should not be treated like it's the only answer. People not good at structuring there thoughts CAN be encouraged to try it but those who don't have that problem shouldn't be punished for it.
There is no one size fits all for any of thsoe documents and all of those docuemnts need to be written and organized very differently. A scientifc report isn't going to be formatted anything like a resume, which won't be anything like a manual etc..
It's the teachers job to grade these, it's not the students responsibility to make it easier for the teacher, thats just lazy and instills these bad formating habits that are irrelevant in practical scenarios for no good reason.
What is the logic for the apostrophe? im nto familiar with german language at all. Does it have a totally different use? It makes sense to give it similar functionality to it's language counter part, which in english to essentially seprate ideas and/or break up phrases and sentences. Which is why in alot ofprogramming languags the , generally denotes that the data ether side are two seperate variables or data types.For example a vector2(x,y) is just two numbers numbers ussually denoting a direction or position on a 2d plane. Where as in both and programming a period has no equivelance, you don't need anything to denote the end of an equation in most cases. when you do it's just = or empty space.
From the US: Agree in most formulas you wouldn’t write any kind of operator for multiplication, but when working problems by hand you often need to indicate multiplication without just smashing all the multipliers immediately next to each other. I usually find parenthesis to be the most clear in these scenarios rather than an x or a dot. So if you have a term 3xy that you need to multiply by 5, you’d write (5)3xy or 5(3xy)
@@kodaxmax It's not the apostrophe but the comma. And it's used in a wide area of the world including most of Europe as decimal separator. I never heard connecting it with language structure.
But in most scientific calculations you have (nearly) no numbers or values but variables. You only insert the numbers (and units) in the end. So no problems with that.
I'm doing A-level maths and i can tell you that the number of times the algebraic variable x and the multiplication sign x coexist whilst writing any given question is exaztly zero. Therefore no confusion. Conversely, when writing lazily, it is possible to weite a decimal point slightly too high, such that if i were to use a dot for multiplication, there could be confusion.
Decimal comma FTW