Tackling Hard Questions | Studying Effectively for GCSE's & A-level's

hey friends and welcome back to our series and studying facts league for gcses and a levels in this video we will be discussing how to tackle difficult questions these strategies will mainly apply to science and maths based questions and both can also be applied to a few other subjects as always time stamps will be in the description down below so do check those out during the video

so firstly i think that's something worth addressing is how you should decide which questions to do which is something i think that many students get wrong to begin with there's no point in picking some outrageously hard maps question from the end of year 13 a-level exams when you just started your a-levels in year 12 you won't get anywhere or learn anything by doing that so i think that the best thing to do is to do questions that are just outside your comfort zone doing too many questions inside your comfort zone won't lead you to improve as much and even while doing too many questions too far outside your comfort zone as you'll spend most of your time getting stuck and getting nowhere but with questions that are just outside what you're currently comfortable with you can do them with enough thoughts and efforts and they allow your abilities to improve much faster than they otherwise would and gradually as you do more of these questions just outside your comfort zone and get more of them right the size of your comfort zone increases and the questions that were outside your comfort zone are now well within your comfort zone and the questions that were way too hard to begin with you find that are now more manageable and this whole idea is related to zone of proximal development in case you're interested now the question becomes how do you tell if a question is just outside our comfort zone well i don't think there's a surefire way to tell but the approach that i like to use is by looking at the question and even it's painfully obvious and i can see exactly what i need to do from start to end in which case it's not worth doing because it's too far inside my comfort zone or i can sort of see where this question is going but i can't quite complete it or feel this question is nothing like i've seen before so that maybe there's a trick at play here i know which topics are relevant but don't know how to piece them together for this question in which case i should attempt the problem and figure out because it lies just outside my comfort zone and in the final case the problem may be too difficult and i have literally no idea where to start in which case i should come back to it later once i become better at solving of the problems so this approach isn't perfect it may cause you to initially miss some questions that look easy but have a twist on them or may cause you to skip over some questions that play hard but have a trick that make the question much easier and like i said before it's not a perfect strategy it's just the best one that i've been able to come up with but as uh as you use it more often you should get a better sense of what questions lie just on the edge of your comfort zone especially as it increases in size and has a greater circumference or surface area so now that we roughly

know which problems are worth doing i think it's helpful to learn about something called focused and diffused thinking essentially we have two modes of thinking a focused mode and a diffused mode and this is something that uh the american professor of engineering barbara oakley wrote about in her book called a mind for numbers essentially focused thinking is when you focus on one particular problem and try hard to understand it and attempt some many uh different things to try and solve the problem many of which may not work whereas diffused thinking is when you let your mind wander without thinking about anything in particular this can happen when uh say you're going on a walk doing household chores doing exercise or even lying in your bed and staring into this the important thing here is to remember that you cannot be in both modes at the same time now the reason why diffuse thinking is useful is because it allows your brain to make unfamiliar connections between different ideas as bob rowley explains you can think on both modes of thinking as having a pinball board on your brain when you're in focus mode then you can imagine all the rubber bumpers being really close together so the ball will move in a tight pattern it cannot travel far before heading into another bumper so it tends to stay focused around one region now this is useful for when you're focusing on one particular task and need to use everything you know about that topic to solve the problem but sometimes you need to think outside the box to solve some problems and this is where diffuse thinking comes in diffuse thinking can be thought of as when the rubber bumpers are further apart and more spread out this allows the ball to travel more easily between different areas meaning that your thoughts can vary more widely so with these two modes of thinking the idea is that you start off in focused mode by trying to make progress on a difficult problem and once you get stuck you either take a break or switch to a potentially easier problem which you can still do your brain will keep the more difficult problem running in the background and try to make sense of it without you making much of a conscious effort to do so and after your break or finishing the easy problem you may go back to the harder problem and realize that you have figured something out here you may have experienced this yourself before and not entirely understood why you may have been stuck on a difficult maths problem and decided to take a break and after you came back to a problem after the break you may have noticed that you are suddenly able to solve it maybe you were able to spot a mistake and you're working out or maybe you thought of a new way of tackling the problem or figured out some trick that the problem was trying to get at personally i have experienced this countless times i remember one particular case where i spent maybe 30 minutes trying to solve a difficult uh physics or maths problem i can't remember which one is now before bed and decided to give up on it and then go to bed because i had skills tomorrow but when i woke up at around two or three am to go to loot i saw the problem still lying on my desk and suddenly it struck me what i was doing wrong so i reattempted the problem and managed to do it under 5 minutes and then went back to bed feeling accomplished with myself now this happened because before sleeping i was focusing intently on the problem but got stuck and i couldn't quite solve it so i decided to go to bed during which my brain entered diffuse thinking and spent some time reviewing everything that happened that day to clear out any garbage then while sleeping uh when it reviewed the problem it made a connection uh from the problem to something else i already knew and once i made this connection the next time i saw the problem it appeared to be significantly easier than it was before and you don't have to go to bed to activate diffuse thinking even going on a walk doing household chores or just doing nothing in particular maybe enough to uh solve the problem but don't watch tv or scroll through social media as for most people this isn't enough to enter defused thinking most of the difficult problems that i've figured out were during my commutes to and from school when i didn't have much to think about i often made a connection between a problem i was struggling with and something else i knew when walking or waiting for the trauma and whatnot and the best part is that once you've made the connection before then you won't forget it no matter how hard you try this is great because often for difficult maths and science problems making connections is really useful because firstly you get better and faster and making connections between problems and the things that you've learned and secondly once you've made the connection before then you can make the same or a similar connection next time so much more quickly and you may have notices for some really quick thinkers that you have met before the main reason they can solve the problem much faster than you is because they did something similar before or made that important connection that was useful for the question before this means that they can now make this connection much faster or use a connection they've already made before to solve the problem much more quickly now do bear in mind that more often than not you won't be able to go from focus to diffused and back to focus mode and suddenly be able to solve the problem you may have to repeat this process several times alternating between periods of focused and diffuse thinking sometimes even across a whole day or two depending on how important you think the problem is so let's say you spend 25 minutes trying to solve a difficult maths problem you have two choices you could even be stubborn and spend another 25 minutes trying to solve it and you may or may not be successful or you could take a break and move on something else and maybe uh when you come back to the problem after a few hours you will be able to solve it in five minutes after coming back to it thus you will have saved yourself at least 20 minutes compared to the previous case but if you still don't solve it after focusing for another five minutes then taking another break and coming back to in a few more hours may allow you to solve the problem in five minutes again thus saving yourself 15 minutes instead of uh 20 minutes now whilst the numbers depend on you and the problems and whatnot the main message here is that rather than focusing on a difficult problem for too long and getting nowhere it's much better to instead take a break from the problem and do something else entirely and when you come back to the problem then you may then be able to solve it and save yourself time and sometimes even after all this you may still not be able to solve the problem and that's just life i wouldn't recommend setting yourself a time limit or a limit on how many times you can come back to the one problem to prevent you spending forever on that problem there are much better problems to work on out there which you can learn much more from so it's not worth spending too long on one problem for me after still not being able to do a problem after coming back to a couple of times i would either ask a friend or a teacher who can do the problem for a hint or i would just give up and look at the solution then to make sure that i understood the solution i would take a screenshot or take a picture of the problem and put it in a hard problems folder on my computer and come back to a problem in a few days to make sure that i actually understood the solution by trying to reproduce it for myself by tempting the problem again

so focus and defuse thinking isn't just something a few crazy people do everyone i have spoken to about this here in cambridge does this to some extent many of my friends and even my supervisors even many of history's greatest thinkers did this too for example thomas edison who was a famous inventor and a businessman after spending some time on a difficult problem he would lie back on his chair and hold some ball bearings in his hand when his mind and body was relaxed enough and he began to doze off the ball bearings would drop onto the hard floor and wake him up and he would get back to work often entering this diffused mode of thinking through dozing off allowed him to make some progress on the problem he was working on and then he would just repeat this process until he completed the problem even the spanish artist salvador dali is said to have done something similar with a key in his hand uh when it came to painting and getting inspiration and even many chess grandmasters do this as well if you have seen a chess tournament then you will have noticed that many of the players spend time looking away from the board that's because focusing on the board for too long and one particular set of moves closers and minded possibilities switching to diffused thinking by looking away and trying to think of other things allows them to open up their mind to new moves that could help them win ultimately they do to prevent themselves from trapping themselves into one line of thinking in this particular game a popular chess example is from a 2004 game where a 13 year old chess player named magnus carlsen was facing gary kasparov who was then the top rated player in the world magnus decided to get up walk around and briefly look at other games and you would expect that he would end up losing the match by doing this and distracting himself uh but he actually ended up tying against gary which was a surprise to many that's because magnus entered the defease mode of thinking and used it to think of new strategies for helping him potentially win the game now of course you don't have to lie back on your chair with ball bearings trying to doze off going on a short walk doing some chores or some exercise or even lying back on your chest staring at the wall for a few minutes may help you make progress on some difficult problems so

we briefly discussed when you should look at solution after struggling with a problem i think that another relevant point worth addressing is whether you should use your notes when tackling difficult problems now a place where many students go wrong is when they do problems from a textbook and they look at their answers at the back of the textbook and feel themselves into thinking that they knew how to get those answers when they didn't notes are an odd middle ground because answers can be hidden in your notes sometimes so should you use your notes when doing these difficult problems and my recommendation is that whilst it's better than just copying answers directly from the end of a book or a mock scheme i would suggest that you should avoid using the your notes and first and try to make as much progress with the problem as you can without them research has shown that when students struggle with a problem before being shown how to solve it then the solution is much better learnt and more durably remembered than if they looked at the solution um after starting the problem and giving up after a few seconds in the book make it stick the signs of successful learning the authors even say that trying to come up with an answer rather than having it presented to you or trying to solve a problem before being shown the solution leads to better learning and longer attention of the correct answer or solution even when your attempted response is wrong so long as corrective feedback is provided so whilst using notes is useful because they can help provide this corrective feedback for your wrong response looking at them too soon can destroy any opportunity for remembering and learning this material you may just end up copying down what's written in your notes onto the paper instead but if you can't start the problem and you're completely stuck and have no idea what to do and have tried diffused thinking a few times then i would recommend that you look at your notes but only do it line by line because in many cases often a single line is enough for you to figure out the rest of yourself and if instead you look at your entire notes or the answer then you should save the problem into a separate folder and make a reminder to come back to it and attempt it again in a few days to make sure you've actually understood your notes or the solution and how to solve that problem so

ultimately the big picture here is that often by losing concentration and zoning out we can think more clearly and can often solve difficult problems more easily and in less time but yeah that's basically for this video and i'll see you next one