How to develop problem solving skills | IIT prof's advice

hello everyone in the previous video I had discussed the importance of developing problem solving skills and developing language skills for school students studying between standards 6th and 10th in response to that video many students had requested me to discuss more elaborately on developing problem solving skills so in this video I'm going to do just that to discuss certain topics certain tips uh which can help you develop problem solving skills before I get into the points i' would just like to point out two things first of all I am not a master Problem Solver in fact quite the opposite of that all throughout my life I have had to struggle quite a bit on developing my problem solving skills because when I was at school I had made some terrible terrible mistakes and I had to overcome that so probably the things which I'm going to discuss based on my own firsthand experiences many of the students currently studying in maybe Class 7 8th 9th 10th especially if they are in the higher standards uh they are thinking that it's too late for them probably they'll be able to relate to me and this was the kinds of mistakes which ultimately led me to not being able to get through IJ in my first attempt although I was uh successful in my second attempt the second point which I want to mention is that I am very very enthusiastic about discussing this tips so probably on certain points I may go on an over enthusiastic rant so please bear with me however I think that if you are someone who is struggling with developing your problem solving skills if you uh listen to this uh extended discussion to the very end you will get benefited through some of the things which I have authentically tried to extract from my uh own experiences all right the first and foremost thing is that for problem solving for developing problem solving you have to approach it like you approach a game yes that's right so whether it is a field game like Cricket football or some kind of an indoor game like badminton maybe even chess or even a video game you know know for a fact that you cannot cannot play at the higher levels of the game without first gaining a Proficiency in the lower levels of the game take Cricket for example in the Gully Cricket just in front of your house if you cannot perform well how can you go to a field and perform well at that stage if you cannot perform well at that stage how can you even Harbor dreams of playing for your school if you cannot play well for your school how can you Harbor dreams for going to the state level for going to the National level so it always like that you have to keep on leveling yourself up and ensuring that each level that you reach and attain is something which you become proficient at and only then you can uh go to the next stage so how does that work for problem solving if it is similar to a game well in problem solving first of all you have to get yourself acquainted with the routine things the routine things means the kind of things which are taught at school it may sound a little bit of a boring advice but it is true it is true so just see if if you are if you're not familiar with all the theorems with all the things which are taught at school in a very routine way how can you even hope for going uh to more imaginative more creative kind of problems so that's that's the Stark truth it just doesn't work any other way that said it is also true that if you just keep on doing the routine kind of things you are never going to level up so you must pursue the challenges in a very very active way this is a key step towards developing problem solving skills what do I actually mean by that let me try to give you an analogy so see I have been riding bicycles all my life okay now I drive a car but uh even after becoming a faculty I was riding my bicycle so starting from my college I was doing this it was very easy for me and despite that the highest skill that I managed to achieve was that I could ride my bike by leaving my two hands from The Handlebar this was the top not skill that I developed during all those years like 15 years 20 years of riding bikes compared to that you take the example of another guy who is less than half my age and maybe he is competing in some kind of a those X sports kinds of things where they do all sorts of stunts with bicycles just imagine his level of skill and my level of skill how did he get to achieve that level of skill by actively pursuing challenging things on his bicycle day in and day out after you have done the routine things it is incumbent upon you it is absolutely mandatory for you if you're really interested in developing problem solving skills to go to the next challenge you have to seek out that challenge in a very active fashion there is no other way about it okay there is absolutely no two ways about it this is the way you have to go about doing it now now when we say like you have to go for more challenges what is ex exactly that well you have to go for more challenging problems certainly but it also means that for the higher level you have to start doing some of the routine things in a more challenging fashion in a more non-routine way what I mean by that is perhaps nowadays at at at at your current level of um of skills you are being taught the theory part by your teacher in some very traditional way but the next the immediately Next Level would be to start reading the theory on your own trying to delve deeper into that theory trying to learn the theorems by yourself trying to extract the meaning of that and then attacking the problems yourself if you can do that then yes you are really have gained a lot of proficiency in the traditional routine things and you're ready for the next next step and after that s uh considering that you are successful in this next step you are ready for the next challenge that would be to tackle higher and more challenging problems the the the thing which you have to remember okay so when you go for such kinds of more difficult problems is that you have to be patient about it this is well this is like the Bedrock Foundation of of your entire Journey okay this is the like the absolute truth of your entire journey of developing problem solving skills that you have to be patient and you have to let yourself not become frustrated at the continual failures that you are inevitably going to face what I mean by that is that when you face a more challenging problem you are of course not going to be able to solve it so what do you do well it is natural to become frustrated but you cannot let that bog you down so you have to take a look at the solution but just looking at the solution and getting to know oh yes that is the solution and then going on to the next challenging problem that is not the way the way is and here I'm telling you from my own very first firstand experience is that uh you have to really do a postmortem analysis of that problem you have to completely unearth your weakness extract the fundamental reasons why you are not able to do it was it because of some la of concept was it because that you perhaps completely forgot that you that you even knew a certain theorem which had to be applied here was it perhaps a lack of identifying a connection between two disparate Concepts so sometimes a particular problem will involve maybe two or three different concepts maybe from different chapters so you have to you have to kind of identify the link between these uh disparate apparently disparate Concepts so was it perhaps this failure on your part to identify that link that connection what was it what was that weakness that led to your failure in solving the problem this kind of a postmortem analysis if you do not do then well success will not be yours I'm sorry to say this but this is the truth many people they do this okay they do this kind of postmortem analysis after have failed to solve the problem but what they don't do and this this is the next important highlight of my suggestions is that sometimes they do manage to solve a problem successfully but even then a kind of um after the fact analysis is required meaning that it is possible that in your journey towards developing your problem solving skills you develop certain ideas certain intuitions certain U tricks maybe to solve certain problems you start getting some kind of bright ideas to solve problems now when you get such a bright idea and you are able to quickly solve a problem please do not get satisfied by that just like when you fail to solve a problem you have to do an analysis for this similarly after you have successfully solved a problem maybe in a very fast way uh absolutely celebrate the fact that you are able to do it but take a step back backtrack a little bit and try to une again extract for yourself what was it that led you to successfully solving that problem first of all try to think of the various ways that you could have taken which would not have led to the solution of the problem because it might very well be the fact that you were able to solve the problem successfully in a very very accidental manner which is a happy accident but it is an accident n nonetheless it is not something from your deliberate intention so while it is good that you successfully solved the problem you have to identify what are the steps that you could have with equal probability taken but somehow just accidentally you did not take so if you are aware of those kinds of pitfalls then and only then in another kind of situation something really Rel ated you will avoid making those kinds of pitfalls I know I'm speaking in a very abstract way but I have I have seen myself my own younger self do these exact same mistakes and that is why I'm trying to tell these things and those who have had some amount of struggle some amount of fight with themselves while solving problems they will know for effect what I'm talking about okay so a postmortem analysis for for failures and successes both are necessary absolutely necessary you must also try to find out that so it's kind of like slowing down your thinking deliberately so when you have a blazing thought it sounds very exciting but then you have to identify what was it that led to that kind of a brilliant blazing thought try to try if possible to slow down your thoughts try to think what was it that inspired that blazing thought that brilliant uh idea maybe you read something maybe you had done some kind of a very similar but apparently unrelated problem which inspired you so when you do a problem very quickly you don't realize what what is it that is probing you forward but when you slow yourself down you try to try to unearth these kinds of apparently unknown Connections in your brain only then you will be able to get familiar with your brain I don't know any other way to put it better but this problem solving skills developing problem solving skills is also very much a way of getting to know yourself better I I don't want to sound unnecessarily philosophical but it is what it is you have to you get to know your brain better by following these processes okay so that was about analyzing your failures and successes next up is beyond getting to know what was going inside your brain what you have to unearth and try to uh process what could have happened with the problem itself what I mean by that is and I completely owe this tip to Professor Jen Kapoor who had a crucial role to play in the development of the Indian Olympiad uh environment Professor Jane kapor was at I kpur uh so he had always uh stressed the importance of problem posing so just like problem solving is important to develop problem solving you have to develop a knack of problem posing means developing questions from your own when you solve a challenging problem uh try to pose similar sorts of questions initially the kinds of questions that you are going to pose are going to be very very simplistic in nature very very simple maybe you change the values a little bit here and there and then you see what happens then as you grow in maturity you will try to uh maybe make it a little bit more sophisticated and then a little bit more sophisticated and that's how you grow in your skills of actually understanding the heart and soul of the problem so when you make questions okay please do not think that it is only teachers who have the right to make questions anybody can make questions you as a standard six student can also make questions there is nothing stopping you okay who says that only like 30 40 year old people can only make questions you have full right to make questions take a question make something similar okay so when you do that the kind of insight that you will have into the motivations of setting up the problem that will help you in complete in a completely different scenario and who knows maybe the kinds of thought processes that you will develop in this process of posing questions will actually help you in uh solving something which somebody else may be posing to you but going through the same kind of thought process that you are going through now I hope you get my drift okay another thing is that uh when you do this kind of an exercise you have to uh sort of appreciate some of the more subtle Nuance things associated with with a with a problem and its solution what I mean by that is uh so certain problems have certain kinds of symmetries involved now identifying the symmetries appreciating the symmetries uh and symmetry need not always be like a like an absolutely concrete symmetry that you have in geometrical kind of problems rather you can have symmetries in algebraic problems also for example those problems which were which are like a square + b square + C Square so whatever what happens if you flip around the order of those things so uh that's that's a symmetry what happens if you break the symmetry so you may think that okay this is just like ridiculous I mean okay I mean we play around with this variables we play around with this parameters so what but believe it or not at the higher levels of Science and Engineering a lot of research work actually takes place by actually investigating these kinds of of symmetries and these kinds of things phenomena which happens uh on Breaking the symmetry so please uh I mean have a little bit of faith on what I'm trying to say here uh and and try to do this thing in a very active fashion another exercise that you can do for yourself is uh sometimes it's it's a bit fun to do it uh suppose you are in class 7 or 8 maybe even class 9 and you are pretty comfortable with some of lower class things things like I mean very simple things maybe addition multiplication of uh simple like algebraic problems okay something as as simple as that so those are the kinds of things which your absolute Juniors would be doing like little kids in school so imagine that you have a little brother like that or maybe some little nephew or something like that and then you wish to uh try to impress this kid or make this uh I mean have a little fun with this kid so how do you go about posing uh a question from those lower levels only for him so for this I will take an example a famous example from the life of the famous mathematician gaus I don't know whether this story is actually true or not but it is often associated with um Carl Fri uh gos so the story is like that um he they were given a problem of adding up all the numbers from 1 to 100 and he did it in a matter of a few seconds the trick that he did was to actually arrange the numbers I mean down below so it was like he arranged it from 1 to 49 and then from 51 to uh 99 so 1 + 99 is 100 2 + 98 is 100 all the way up to 49 + 51 is 100 so I mean the addition becomes much easier so you can perhaps take a little bit of inspiration from that and give to your nephew a similar problem of adding up the numbers from 1 to 10 okay so accordingly you do 1 + 9 2 + 8 all the way up to uh 4 + 6 and then you have remaining 10 and 5 and that's how you get 40 + 10 + 5 55 so there is that so why I'm telling you this is that just like you are having a little bit of a fun I mean by kind of changing the order of how Solutions are presented uh to kids in a similar way try to think of the kind of routine things that you are studying now maybe in quadratic equations maybe in linear simultaneous equations the routine things that you learn maybe in some geometrical problems uh those uh problems involving triangles and circles and quadrilaterals can you perhaps flip them on their head and have a little fun with them because when you go for some kind of challenging mathematical competitions or some kind of later on entrance examinations this is basically what the more experienced people the people who are were setting the questions they are doing okay so just like you are having fun with that little kid so also those senior people are having fun for the problems that you are doing at your high school level so there is that uh and believe me I mean the entire Olympia thing is philosophically just this having fun with the high school level algebra geometry basically the high school level maths of course there are certain higher order things also uh like number Theory but let's not get into that okay um there is another aspect which I would like to highlight is that as you are uh doing more and more problems getting to uh get becoming familiar with different uh ranges of problems you will find that um if you delve a little bit deeper you'll be able to unearth uh maybe even appreciate a certain hidden Beauty in certain problems sometimes this beauty may be directly apparent to you uh visible to you uh from the Symmetry uh this is something which I really liked in algebra problems the kind of very symmetrical things that used to come around in the expressions of some factorization problems even but I mean it is good to appreciate all this beauty but please do not get hung up on this because this is another mistake which I myself did okay trying to find some kind of a beauty some kind of an Elegance in each and every problem that you attack that is probably not a very healthy thing to do because there will be definitely problems which will not have any symmetry which will not have any beauty you just have to painstakingly do the steps uh so you have to be uh like acclimatize acclimatizing your brain with all sorts of things so adaptability is extremely important also so I have said a lot of things uh I would like to end this video by sharing one last very very important tip and that is uh when you were studying maths or something related to maths like physics uh try to think of your study material the kind of problem solving that you have to go through not just as some kind of a task or some kind of uh the the the content matter there as an agglomeration of some facts rather think of them as some kind of like a like an edifice of knowledge some kind of a body of knowledge or even better even better some kind of a device which you have access to to improve yourself to improve your brain this is extremely important because otherwise it just starts to look like a task like a menial task it is not that especially when you go into your study of geometry which is laid out as a series of theorems but just try to take a step back and appreciate that these theorems they kind of build on one another the proofs the construction ideas the connections they always build on one another so is it not such a beautiful Construction in itself the whole this whole body of knowledge this is such a beautiful construction that is built on one on top of another like an engineering structure so this kind of a if you if you appreciate the habit of studying maths uh geometry things like this in this kind of a sense where you try to develop an appreciation for this innate construction which is there to train you then you will try to really really appreciate the beauty of everything sometimes you may hear your teacher saying things like this the beauty of maths and all these things so you yourself will be able to appreciate these things so I could go on forever talking about these things I will just uh end on this note so uh the fundamental philosophy of problem solving is is that it is a journey of self-discovery okay you through this problem solving you get to know your brain and you get to build your brain so I wish you all the very best and uh people who are starting a bit late maybe in their class 9 or maybe class 10 uh please do not lose hope it can be done uh it will take effort it will consist of a lot of struggles it can be done for those who are much younger maybe in class six or seven you are in for a great ride ahead of you enjoy every moment of it try to enjoy it really and I wish wish you all the very best in this absolutely wonderful Journey thank you very much all the very best

Channel: jc

Views: 135,584

Keywords: jc, prof jc, IIT, IIT Kharagpur, IIT KGP, IITKGP, IIT prof, education, school, school education, high school, mathematics, problem solving, science

Id: sDf2C-ehLQg

Length: 24min 4sec (1444 seconds)

Published: Sun Nov 12 2023