One thing that I noticed to be surprisingly helpful is "false start": when you are a tiny bit ahead of your peers, just because you started learning the topic a little bit earlier. It gives you satisfaction and makes you enjoy the subject. When I was returning from library during my 5th grade, I stuck in a traffic jam, and read half of the physics textbook. It took me like 2 hours, maybe. In classroom I was the best student in physics, and it made me enjoy this subject. After few years I won first place in my city on a physics Olympiad. That 2 hours in a traffic jam is nothing in comparison to thousands of hours that I dedicated to learning physics later, but they gave me a privilege that made me enjoy the process of studying physics.
@@aj4138 I've switched to computer science. After graduating from school I had to decide if I want to make career in physics or computer science, and I've chosen CS, because making AI is not any less interesting for me, than doing physics, but gives more money. Now I am doing a master's thesis on program synthesis (that's AI that writes programs).
I remember writing some c++ code but I couldn't get it to work properly. I took a nap and woke up knowing exactly what line to change and it worked perfectly.
Legend has it, that Edison wouldnt sleep much at night, but every time he was stuck on a problem, he would go to an armchair and hold metal balls over a pan. When he would fall asleep, the balls would hit the pan and wake him up. Apparently this helped him solve problems
Dude, "taught to learn" and "taught how to learn" is the same thing. What you wanted to say is: "School gave me information, but never taught me how to learn that information effectively."
MaoItsMe it’s not the same thing. “taught me to learn” is referring that school introduced him into pursuing an education or understanding new concepts. “taught me how to learn” is talking about a specific method of learning technique.
@@diegoluna2471 Nope. By your logic "He taught me to ride the bike" is different from "He taught me how to ride the bike"... Yet, they are the exact same thing.
MaoItsMe yeah it can be interpreted that way but that’s not what he meant. technically they are two different things since “taught me to learn” is a little broad, leading to you thinking he repeated what he said. he’s not trying to say the same thing twice.
My tip: Imagine that the part of a subject you are learning hasnt been discovered, and you are the first to know about it and understand it. This will give you motivation to learn deeper. (from my experience)
It's true especially with mathematics, I personally don't think there's an innate ability that's impossible to overcome, with smart learning and a lot of hours, it's beyond easy to surprise yourself. The phrase "I'm not a maths person" is so harmful. I struggled a lot with mathematics (sitting in the lowest set) in high school, it frustrated me but after seeing I could drastically improve grades with a bit of self-motivation, it inspired me and I've recently graduated with first-class honors in university from a STEM field, and have a new found love for mathematics. It's so easy to be self-destructive, particularly when you're told you can't do something/you've done something wrong. Persistence and enthusiasm is key!
The reason I never understood math for the LONGEST time was because I never cared about the basics,I just looked at the way the teacher did the equation and tried to apply the process to my work that's why I never understood when to use the quadratic equation or Pythagorean theoram. If you you find it hard to understand maybe this might be the first step you take. I used to think I was stupid because everyone else got it and I didn't ,I mean I still am but not as bad.
Very true, I also saw math as something so hard, I hated it. But once I got to college I began enjoying mathematics which surprisingly made me pretty ok
Once in math class our teacher was teaching us how to solve certain equations and a kid gave a difficult question from the textbook to the teacher and the teacher and all of the students in class weren't sure on how to do it. After five minutes the class ended and later that day on my way home from school I was sitting in the bus and then I was thinking of the equation and suddenly the answer came to me and it was so simple. I find it cool how that french mathematician and I found the answer to the math problem on the bus.
@@HerbaMachina yeah, that is also what I always do and by the time I finish the other question, I always remember how to do the question as if I did the question, 1 hour ago.
The fact that people didn't succeed at first, took a break from trying to learn math, then picked it back up and ran with it later on in their life just further proves that this theory of learning works (in their context at least).
I had to make my physics homework one time and I got stuck on a difficult question where I couldn't come up with an answer. I decided to give up and go to bed. But when I was sleeping, the solution suddenly came up in my head! I quickly woke up to write it down (cause I would surely forget) and turns out that it was actually right. It's really weird.
I'm a writer on scientific topics. When I'm stuck, I walk my dog. As I'm walking my dog, when I'm not focused on the problem at all, the answer "just comes to me." Then I race home and make sure I write down what I came up with when I least expected it. I thought it was just me, until I saw this video! :)
Solutions come when we are in a relaxed mode (like u were calm walking the dog; in shower, before falling asleep etc). That's theta state of mind, which is when our mind is most creative.
This is why exams sort of annoy me. I need to have time to let my mind wander. I’m in Computer Science, I can’t help but feel like my career colleges in the future aren’t gonna set a stopwatch every time I need to set up an algorithm/work with a data structure. It’s a frustrating reality to face when you’re in school
Build in a short walk both before and after class. 5 minutes will do it. The brain needs to freewheel to process new material, and walking is great for this. And you need exercise anyway!
Colleagues* And yes. Yes, they will. Your manager will not be a programmer. Their job is make sure you get shit done when the company wants it, not when you think you need to finish it. And if you do finish on time, next time the deadline will be a day sooner, until you finally fail to meet it, and then you'll be called into a meeting to ask why you didn't get the job done on time. The day you finally stop making excuses will be the day you've officially grown up.
Since ya'll are here I want to share something that I got from Richard Feynman. Surely you're not going to sustain that understanding very long by purely just being good at it. There's a difference in knowing and understanding. So what Richard Feynman did is just,, letting his curiosity wander. From simple equations on a paper to looking for a real life situation that agrees with the equation, whether they're the angle of the casted shadow or anything else.... After figuring out something on your own with math and a little bit of imagination, you'll find learning to be more exciting and the next thing you know is, you can't stop thinking, you're avoiding your phone more than you realize because now, you're carried away by thinking. I personally do this before going to sleep or while I'm eating or when I'm bored. Maybe think of it as a little mind game :)
@@kaycecapisinio3541 This sounds fun but I didn't understand what u meant. Could u please explain it once again at my level of understanding. I believe that too is Fyneman's words explaining everything simply haha 😅. But really explain. I wanna try that too.
@@aneeshupadhya3170 I learned this method from Richard Feynman's book: Surely you're joking Mr. Feyman! Mechanical engineering students in mit are already taught advanced calculus but,, none of them knew how calculus was related to the French curve. Sure, they learned calculus but at the same time, not really. When you apply what you learn to the smallest things, subjects as advanced as calculus won't be that stressful instead, you'll find it fascinating. And when you're bored, you'll always go to things that once fascinated you instead of going through your phone so yeah,,, hope that helped
@Aneesh Basrur ohh sorry my bad. I start by observing and then thinking how it works. For example, when I walk home from school in the afternoon, I noticed that the building beside my house casts a shadow. I measure the building's height through estimation since the building is just literally beside my house. I know the height of my house, so I can easily estimate the height of the building. I also determine the length of the casted shadow through estimation using the length of the road lol. So when I get home, I sometimes look for the angle of elevation using cos. But sometimes for me, knowing how it is solved is enough 😂 so that when I encounter a similar word problem I can easily imagine it
Great video. Here are some other tips I've come across while 'learning how to learn': -- The presence of a smartphone on your table or backpack decreases your working memory and fluid intelligence. When studying or taking a test, put your phone away in another room, leave it in your car, etc. If you use your phone as a timer, you can just buy a cheap timer online for just a few dollars. -- Walking while learning flashcards (the study in particular was foreign language words, but I'm sure it works for anything) greatly increases retention a week later. I like to pace back and forth at a comfortable pace while doing Anki. -- After a Pomodoro, take a few minutes to close your eyes and think about nothing in particular. Don't force yourself to think about nothing -- just let your mind do what it wants for a minute or so. This allows your mind to process what it just learned and embed it deeper. Going from learning to immediately browsing your phone is too discursive for effective learning. Right now, I like to have a 45 minute pomodoro, take a 3-5 minute "mind breather," then take a 10 minute walk to go over what I just learned, and repeat. I can cite links to studies backing up all three bullet points if anyone is interested.
@Edi, suggest you change your study to Chemistry. There are plenty of diffusion problems there. Or should I say focus on diffusion. But if you can't focus ...... hhhmmm ...... now I'm getting a headache.
This video should be shown to every math student on the first day of class. Thank you!!! I've said since I've been in college as an older student, math is like martial arts; a couple of weeks worth of classes does not make you a black belt.
I've always felt very negative against mathematics, Sciences on the other hand I enjoy working on...and I've wanted to become a electrical engineer but I doubted myself because of math until I last year I decided to push myself even though I'm struggling with math and not seeing the results and it gets me demotivating but this video brought me out of it and now I feel better about it.
@@t3m077check out ilectureonline. and youtube videos for math intuition. without an intuitive view of the subject the math in EE will eat you up and spit you out. push through it!
My computer science teacher told me school isn't to learn specific material in classes but rather to learn how to learn. It's been very helpful to approach challenging concepts with that mindset and it's helped me realize the true potential of how I can become smarter and improve my skills.
I'm about to get my MS in mechanical engineering. Something that really worked for me was opening my homework assignment as soon as it was posted and reading through the problem set. I would spend maybe 10-15 minutes superficially thinking about the problems, and then I would close them. As I went about my day to day activity, the problems would be in the back of my head and I could spend a lot of time thinking about them, so when I finally had time to sit down and do that specific assignment, I already knew, mostly, what I needed to do.
@@dragonvarine7553 It is an excuse. You are literally making an excuse for why you can't succeed. A "valid" excuse is still an excuse. (in quotes because even that is dubious, whether the excuse is valid)
I was taught all this in a course named "Learning how to learn" in coursera for 6 days(of course,the course duration is 4 weeks and I managed to finish it in 6 days out of curiosity) and you demonstrated the entire syllabus in 11 minutes!!!!!!!!! Kudos to you
Future you: Hmm, I wonder why I was supposed to watch this Future you: **sees "ignore this time stamp"** Future you: Oh, I guess it's nothing. **watches a different video**
I really needed to tell you and everyone that how much true holds to this video. All my life I hated Math, because of some bias that my older brother hated it, and also because I literally never tried learning it, just always thinking "I am bad with numbers." One Statistics class in my Grade 12 year literally changed my life. Because in the pandemic, I put in hours for that class and literally fell in love with numbers. While I thought that one class would "pull my average down", it changed my whole life's trajectory. From aspiring to be a filmmaker, I took a gap year rejecting my offers to film schools and took Senior level Math courses. Some days ago, I got into my country's top double degree program for BBA and CS. It's all about the mindset really, once you decide to really pull your socks up, things can change dramatically. Thank you for this amazing video Zach.
another good example of diffuse mode thinking that came into my head was when you're in an exam and you'll skip a question come back to it and when you come back to it the second time being really easy to answer
How I study maths: Learn everything from the internet without taking notes(but write the topics name) Then after finishing that try to make all the notes without taking help of anything even if it takes days,(when it’s really like you are not getting it, rewatch the video and repeat the process) Practice lots and lots of questions(only check the solution after you solved the question and if you can’t solve rewatch the video and try to solve again) How I study science: Physics: Understanding derivation(not like basic maths but why the derivation was done in that way)and every terms of a formula is a must, because all the concepts are literally based on the derivation and if you mug up the formula but don’t know what the terms are you will be lost. While solving a question draw a rough diagram of the question and try to relate it with the derivation of the formula and apply the concepts. Plus make your own notes, professors notes are great, but making your notes will be better than the professor notes for you. And revise those notes at least for 15 min only the formula and the terms and derive it once every week. When understanding a physics concept try to relate it to your experience as physics is mostly based on real world applications. Chemistry: organic chemistry(every reaction and mechanism mug up),ingorganic chemistry(no hope :( only pray and numericals understand the concepts)
I'm a total newbie in solving integration. Actually I was gonna start right now so I decided to rest a bit and watch some videos on youtube. And then this showed up on my feed. Thank you this is going to be very helpful.
Have fun with it, like mental rubik cubes solving some integrals. I have used days on occasion to find a solution to some integrals, the satisfaction when you crack it is worth all the effort. Cant beat it.
Integration was hard at first, but you have to learn to recognize a few basic functions, then it becomes easier to know whether to go straight through with the power rule, convert trig functions using u-sub, integration by parts, knowing polynomial division and partial fraction decomposition, etc
I'm 36 years old, and your material is greatly appreciated. I'm hoping that more people in school or college can appreciate more topics like this. We fundamentally can easily get pressured what to think instead of how to think.
I'm glad that as I got older and wiser, my math got better. I can now do elementary algebra for fun rather than feeling stressed out about tests, how much time I have till the end of my second semester, my grades, etc.
2:34 This applies to me in programming as well. I’ll be trying to figure out how to implement a method or trying to fix bugs late at night. After a while of intense focus, I just go to sleep, wake up, and boom solution forms inside my head just like that.
I kinda reminisce my past experiences with my Calculus 1,2, and 3. I have that very proud feeling of self-esteem and because of that I vigorously studied all of my Maths until I get nearly flying colors for my grades from all of those subjects. The process I take to study those Maths was embarrassing though, in my opinion, because almost everyday I repeatedly read and read all of my Calculus section topics until I can answer (without any flaws) any example problem I can find in there without digging into a much deeper level of understanding. My mindset in that situation was that -- by just getting the pattern and procedural techniques in solving a maths problem I can proceed to the next example one. And if I'm done with all of the section topics for the day, if I had extra time for the day, as much as possible, I'll try to repeat any similar problem within that topic scope. So as you can see I'm actually just memorizing the patterns and techniques in solving a Calc problem and not digging into deeper understanding. I have grasp at this realization when my friend asked me something about an intriguing question from Calculus 1 regarding slopes, secants, and tangents. THE BIG THING that have happened was, even though I get a very good grade for that subject, I'm not able to explain it to my friend in an almost flawless manner like I used to solve Calculus example equations BECAUSE ALL I KNOW WAS THE PATTERN OR TECHNIQUE IN SOLVING ANY MATH EQUATION RELATED TO THAT TOPIC AND NOT THE QUESTIONS REGARDING WHY EQUATIONS OR RELATED MATHEMATICAL GRAPHS CAME INTO BEING. So grades doesn't define your level of understanding of a certain subject. Repetition is a key I know, but repetition is also a tool for getting tricked by the illusion about Maths. Simply answering all math equation problems doesn't guarantee that you know deeply the concepts about Math. DON'T STUDY THE PATTERN, STUDY THE CONCEPT because it will lead you to better answering a math equation/problem. This whole story of mine is attributed to a part of this RU-vid video which is "When your stuck with a math problem, don't just always look at the solution for that problem and say OH! That's how they solved it, and then proceed afterwards". That quote is the worst way to learn a math concept and I've been a victim of this ever since. You need to work out the problem without any aid of the solution section, don't always rely on viewing the answer to the problem because if that's your usual attempt then there's a huge chance your going after "learning the technique/pattern and not the MERE CONCEPT". With this video, my mindset kinda changed a little and surprisingly I thought of things about going back to study basic Maths such as trigo and basic algebra, getting B.S. Math. or making a RU-vid video about solving a math problem in a new way. SO YEAH! A SIMPLE MINDSET CAN CHANGE MANY THINGS. :))
Actually the big problem for me in physics is visualization and it plays a very role of you understanding physics concepts. Could you please comment on measures to increase visualization power , it would be a great help
Writing things down really helps too. Just having a few sheets of papers with basics written on them, from which you can mentally derive all the conclusions you need on a topic. Also I gave the JEE Adv. and in it I used a simple 4 step method while both learning solutions to problems and then actively solving them. Situation Analysis, Concept Extraction, Data Collation, and Attack on Requirements.
I found that reading out loud and then calling my friend to test me. My aim was simple to get a high distinction in that subject. And I spent 2 days to finish my entire semester of lectures. During my test I found that I could recall almost everything I read. I feel proud of that.
I envy the generation that grew up with youtube and the free knowledge found on internet. Its so much fun and easy to do things you like and learn more things you don't necessarily are well versed in. I just love the access that has been opened up. And I am nearly 40. So I saw the emergence of it all during my college days but not the ubiquitous nature of it all. Good luck to you all.
The idea sounds legit and actually worked for me plenty of times. I took a break from studying and then the problem's answer suddenly came to my head, but that happened in a matter of a few hours, half an hour the least. How can someone decrease the amount of time spent on diffuse mode? Because in the case of a test or an exam the time is limited and because of this time limit our stress level increases which makes us tend to the focused mode more, since we don't see the other method as successful.
I would assume that increasing your fundamental understanding of the basic skills required to solve a particular problem would assist in decreasing your diffuse period. If the basics are already known, consistent repetition would be the only other viable solution. The content in which a test or exam is comprised should already be known to yourself for a vast period prior to participating in said test or exam, therefore utilising a study routine that provides consistent repetition of the problems or concepts of which you find difficult, should provide you with the greatest improvement (routine should include strategies from the video, especially working to timed conditions). This routine should begin in conjunction with your classes and should also mimic the order in which you are taught concepts. That is if you are taught concept 1 in week 1 of class, you should be studying concept 1 throughout week 1 as homework, until you are confident in your understanding of the concept. Ideally, you should not be studying concept 1 in week 2 whilst learning about concept 2 in class, you should already have a fundamental understanding of how to apply the concept from your study the week prior. If done correctly you should be doing revision leading up to the exam or test, not learning. This style of studying should prepare you for any questions that you struggle to comprehend, and therefore decrease you reliance on diffuse time within and exam or test. I am unsure if this will help, but I will post it anyway.
True, when I am writing a paper or doing homework and I start becoming stuck or loosing interest I go into "diffuse mode" (or Sherlock Holmes mode) and start to walk around the room for a couple of seconds. This will help if you are not too busy thinking about it. IF you need extra advice try to just space out, relax, breath deeply, talk about the problem, and/or drink a good amount of water. Great video...thx
For decades I've concentrated in lessons...especially French classes...and then gone for a walk afterwards. The brain gets to be sidetracked for a while, and concentrates on aspects of the lesson that need practice. I learnt most of my irregular verbs, walking to the market on Saturday after class! Now, with uni looming, I look at maths vids that are well presented...Eddie Woo for example...but are a bit above my limit, so when I get out the text book or the question list, I have had exposure to the concept and instead of saying, Huh? What are they on about? I go 'Aha! I recognise that! The Aha moment is how the brain clicks into a subject. Treasure it.
Dude! You just confirmed something I believed my whole life and never knew anyone else thought or knew about it. The Einstellung effect. I've never heard of it til now. But I've always understood it and always believed it to be the biggest reason why people hit roadblocks when learning math.
I wanna share something personally When I follow the Pomodoro technique ( setting a timer for 25 minutes), getting into deep focus, after the period of 25 mins ends, I end up in such an intense state of focus that I don't want to take a break and move on This proves that action leads to motivation and the latter is completely false
Yea... I definitely didn’t get distracted several times throughout the video, but at the same time really wanted to learn so I skipped back every time I missed something.
1.Have diffuse and focused thinking 2.Read what you have read then recall it for a few times 3.after you solve a math question by seeing the solution do another same question 4.dont procastienajate
Awesome video! I also would like to confirm that it's true, your mind can shift as you get older. I didn't like Math in High School and now that I'm studying Computer Science I'm in love with it!
This book literally changed my life. Not kidding, even though diffuse vs focused thinking was enlightening, the part of the book that really shaped my learning was "over-learning vs interweaving". This was the part I was doing wrong. I think you should make a video focusing on that part.
One of my lecturers used to call "Recall the Material" as "Teddy-talk time". He said spend time covering the material, and the try and recall it as if you were teaching it. When you are comfortable with walking up to a whiteboard or flip chart and fully explaining the proof, or section or topic, THEN you have a good level of learning. There's still more after this, but it's a great start.
This is so true for diffused mode, I was so set on solving a physics problem, struggled on it but eventually went to sleep cos it got late. The next day, I tried it and thought with a more open mind, almost automatically making me see the method of solving it.
Thanks for the video! I'm a bit overwhelmed, thinking about the long road of math. Elementary algebra, intermediate algebra, algebra, pre calculus, calculus 1, calculus 2, calculus 3.
To the recalling the material part: read the thing twice before the first recall, because some bad books are written in such a way, that you need to read the last part to understand the first one, and then you should read it twice (or at least the first part twice)
Hello there :D dropping my notes from this video here - There are 2 modes of thinking. (Focused and diffused modes, both of them are important) - Focused: highly focused - diffused : relaxed and let your mind wander off(Break) and allows parts of your brain to connect and solve problems (background) Einstellung effect- Having a set idea formed about how to solve a problem which bars you from exploring new and more innovative ways to solve a problem (or better) (Alternate between focused and diffused mode, focus intensely on a problem and when you are stuck take a break like a walk, shower, sleep and then get back to it in focused mode, will help you solve it better since you have a fresh look at the problem, remember to understand the basics at least, think well about it) STUDY TECHNIQUES - study daily! don't do it all in one go! Because it's a slow process. - Recall material - read and then close the book and recite whatever you've learnt and then again repeat it ( the author said to do it at least twice but imma do it thrice) - SOLVING PROBLEMS( DONTS) 1) Attempt the prob and look at the sol and move on (Try on a diff problem and that same problem some time later) DOS- -make sure you understand the basics before you start the problem - work a problem all the way through(see solution unless you really need to) - repeat and understand the whys not just the hows -take a small break for a fresh mind -Practice lots -Dont solve too many similar questions but do try a few - Mix up the problems and the sections ( Practice the exercises in a random manner just like on a test after understanding the whole concept) - PROCRASTINATION - Pomodoro (imma do it lay it down break ) -Focus on the process not the product - Do the disliked jobs first - Mental contrasting ( Picture Where you wanna be later on in life when you are doing it and why you are doing it) - Patience persistent ( PERSISTENCE > INTELLIGENCE!!, (note to self: What the narrator said is so true you've been praised all your life for your "intelligence" but everything is working out for now but you know it well how badly you are about to fall behind your peers) -Learning to learn -things get fun when people are good at something, but when they are bad at something they get bored and not try so try to be ahead of your peers and show off! (works well) - Switch your mindset (allows to beat the impossible) Yeah so that's it My score in math on my last exam was 58/60 and in science I scored the same too unfortunately :/ . Will try to
Literally hated science at high school and failed it too. Now I’m reading up on it and I now see how many interesting things that have been discovered (or will probably never be discovered).
This once happened to me, I was stuck at a math problem that our teacher didn't discussed, due to sleep deprivation I fell asleep for hours and when I woke up I went straight back to that math problem.Surprisingly even though I just woke up a few minutes ago, an idea came to my mind and when I tried it I solve the math problem with ease. This happens very rarely but I hope I could master it so that I could further more excel in math.
Think of Math as if it's a language with numbers as it's alphabet, used for communicating with universe (can also be described as if it's a tool). Our lovely school mostly teached us on *how to correctly use* the tool/language(math), less with working on *how to make us utilizing* it's great potential so that we can operated/applied it into the universe. making us rarely use this language to our daily life.
You should get more subscribers. Thanks for the video btw. For someone like me who didn't learn math in all my high school years and now learning Math by myself to get into college to study Computer Science, this is gold.
This is a really great video and it has really put my mind at ease. The idea in my head that persistence is more important than intelligence when learning is really going to help me in my last year of high school and finals. Thank you!
6:45 and I think interleaving the problems. Studies show is helpful too. Like if you did one problem of one type, then, the next type than the next time, then, if you have time do one of each type again. This helps you get ready to figure out what type of problem you’re looking at.
One way(I noticed) to start training your mind on solving problems unconsciously is to start simple. For example you start the morning with an easy equation. you memorize it. go for a walk and literally try to distract your mind. Then whenever you want, just recall the same equation and try solving it mentally (that's why you pick something easy so that it's easy to remember). Once you do that just set the equation s level higher. And one day you don't even notice you're actually solving problems in the back of your head.
i study math right now for my master degree and i say chatgpt is such a big help. Its much better to hask him questions were you are stuck at then look at the solution
Im not sure if this is off topic but the diffuse mode thinking actually can be involved with art. For example, if you are struggling drawing a hand, just get distracted for a bit and once you come back to your drawing your mind is fresh and you know how to fix it.
When I was in Junior High School, I'm one of the most student that is bad in mathematics and science. I am having a hard time understanding trigonometry, geometry, and algebra (I know how to do binomial though) which caused me to say negative things to myself. To be honest, I don't really have interest in learning because they are boring for me back then. The only subject I was good at was English and to this day, I think of myself as below average in english. Until I became Grade 11 and I began to take things seriously because I don't have much time and also I don't want to stay like that so I decided to improve myself in every way. After some time, I noticed changes especially my improved grades (which was always low) and managed to be the top of the class and get into one of the achiever in the school. What I want to say is that hardwork and persistence does pay it off and reward you with greatness.
Can you please answer one of my question ? Why do we have to physically practice maths to get the concept and why don't we get the concept by just seeing the solved problems ?? Kindly answer
My Name because there are things within the problem that you don't know yet, and that won't be apparent by looking at the answer, so they have to be explained to you. Also, that is just how humans learn. Repetition drills it into our head until we don't have any gray areas because we have done it so many times.
Try to look at a photo of a really messy room and memorize everything you can. Then turn away and see what you can recall. The second you turn away you will realize you don't actually remember a lot of what you were looking at, even though you'd probably assume that you do. Same kind of thing with math. I have tutored students and shown them a solution and they say they get it, then I gave them the problem again 5 minutes later and it's amazing how often they can't do it.
I usually take a nap during exams and it freshens my mind up to continue with next questions. It actually helps when I'm stuck on a problem or my mental focus is dwindling.
Thanks a lot for this video! I still however have a question, when I'm studying maths I often find that what I don't understaand isn't the actual content I'm studying, lets say for example functions, but rather the "tweaking" they require in the process from the understanding of what you need to do to solve the problem to the solution, and the basic operations that I somehow fail to see but when I then look at the solutions seem obvious. I did understand the part of your video where you mentioned the 2 brain modes but I can't quite go to the gym in the middle of a test! Having said so, what would you recommend to get me over this problem?
to get the "tweaking", you need to try things. if something doesn't work try an other thing. do this for some time, if you re not successful. do something else for a while. then go back to it, you ought to be able to find this. if it is in a test. read the test first. if some questions seems obvious, try to do the other questions for a reasonable amount of time, if you fail at them. just do the obvious questions. and go back at trying the hard questions. if you want to build up intuition, do a lot of diverse problem, when you re alone and have some time to burn. things that have nothing to do with each other, like some abstract algebra then analysis then riddle then engineering then computer science. If you re in the habit of solving different kind of problem, finally you ought to find it easier
When I was a grade 1 student I got 15/100. After some years I saw my brother reading and practicing it. I enjoyed repeating what my brother done. After that I scored the best grade in Math's at school. I enjoyed it, I didn't have any stresses for getting good grades but I scored the best in Math's since grade 5!
I have one story to share. So, I study in a school that offers a mechanical course (which is not only focused on cars) and I had a hard time trying to figure out an equation that had something to do with a manometer in U, but the thing is. There can be many types of manometers, one can have a vacuum on one side of the U, the other one can be open both sides, etc. But at the time I only thought that there could be a manometer open on both sides of the U which increased the difficulty of the problem. Then we went to quarantine and, 6 MOTHS later when I came back to the same problem the idea that the question must be missing out some information struck to me, and I thought that the system actually needed to have a vacuum in one side and be open on the other. Therefore, If you are having any problems with your math test or your physics homework, simply leave it there and come back to it later ; D I'm sure the right idea will come to your head.
because you don’t learn math just by doing a couple of problems, i believe it would take the average person about 4-5 months to say they grasped and master must of the concepts in algebra but even then their still not masters, math is a language just like any other, in fact it is universal its something you learn over time, just like languages (spanish, english etc) your brain expands and gets accustom to keep flow of all the information you’re learning,so struggle keep practicing, atleast practice for an hour or 30 minutes a day and you’ll see results eventually
5:00 I really disagree with that. If you become good at reverse engineering a solution you can learn A LOT from seeing other people's work, the important thing is to have a good grasp of the fundamentals of whatever subject you're involved in before you start looking at a bunch of "answers". I found a decent amount of success applying this to math and programming. Edit: I guess 5:10 kinda addresses my point :P, but I've seen a few people who try getting into programming at an older age have trouble with looking at other people's code because they feel like they're "cheating", which I think isn't a good mindset to have while you're learning. Especially when you're trying to self-teach.
