- Solve more problems to enhance learning at [0:31]. - Seek well-curated problem lists from textbooks or resources at [0:43]. - Preview end-of-chapter questions before reading the chapter at [0:51]. - Don't move on until you've worked through chapter exercises at [1:07]. - Use resources like Khan Academy for a structured problem set at [1:32]. - Learn programming to discover mathematical applications at [1:47]. - Teach or explain concepts to others to solidify understanding at [2:55].
As a 3rd year math professor, I totally agree that teaching is a great way to learn math and that working problems is the most reliable way to discern your own level of understanding. Thanks Grant and Lex!
studying the history of math can also lead a student to get a sense of where all the math problems came from, how human beings got their mind wrapped around a particular type of math problem rather than something else.
All of this rings true for me. I'm a 40 something programmer but I really want to be an astronomer. I'm teaching myself undergraduate level math and physics (and astronomy too). I buy text books and I read the chapters and to every problem at the end of each chapter. I buy those "3000 worked problems in physics" books and to the problems. I have a daily ritual of working problems. I can't overstate how effective that has been at helping me get better at mechanics or calc or whatever. I also occasionally give presentations to a science group I'm a part of and that whole teaching bit... I very much agree. I do the presentations because I learn SO much in the preparation. I've thought about creating videos on subjects, even if I don't every publish them, because of the focus it brings. It's the whole Feynman technique. If you can't explain something simply, you probably don't understand it well enough. Prepping to teach something also exposes all of the gaps in your understanding. Great clip. It's all really good advice.
@@jamjohnson2023 Both. I took a decent amount of math in college, but that was 25+ years ago so I had forgotten loads of it. I decided to start all over and learn it properly, trying to be more rigorous about it this time round. I buy text books that seem to be well rated (it's always a crap shoot, but the internet definitely makes this easier) and then I go through them a section at a time and I do the problem sets at the end of the sections/chapters. Supplementing the texts with online lectures and vids is really help too. I watch some short clips about a subject then read the text on it. Watching a lecture after having read the text really helps with comprehension I find. I've hired tutors now and again as well. This has been the hardest part... finding someone to help. The success of the above approach varies with how "popular" the topic is. Astronomy has been the biggest challenge (oddly enough) b/c most content is popsci... or at the graduate level. Finding good undergrad lectures that are "in the goldilocks zone" is harder there.
@@pipertripp learning on your own time and effort is very impressive, not many have the drive to do that. Do you feel that you do it from a point of discipline or from a point of it being an interesting and engaging pursuit for you? I am asking mostly because I was not a good student in high school, i was completely uninterested and unmotivated and didnt apply myself at all. Now, at 20, I look back and hit myself because I realize how interesting and useful these topics can be if I had applied myself to them, and how much I need them to advance my life. I am now going through an algebra 2 textbook to relearn alot of what I neglected, and am considering remedial classes before going to college, where I would likely pursue a bachelors in aeronautics. It is a great challenge to me, because I have taken the easy path for so long that keeping my focus and attention on something that does not an immediate reward is somewhat difficult. Thank you.
@@jamjohnson2023 for me it's definitely a passion. I'm a programmer by trade, so I'm not doing this to land a job. I'm getting ready for school... I want to go back and get another degree... probably in physics or astronomy. I want to "semi-retire" into helping others do research and teaching interested highschool or college kids. I love the idea of creating some really compelling after school programmes for kids that are up for it, but time will tell. I was a good student, but I was rubbish at maths in HS. I had an "awakening" in college and I ended up taking a fair amount of it. I really surprised myself in that regard, but I was never a good student of mathematics... I was always focused on "surviving" the problem sets and I didn't take the time to really wrestle with the derivations. It's why I've forgotten all of the material. I'm not making that mistake this time round. I'm a much better student at 45 than I was at 20, that's for sure. But there's way less pressure and I can learn at my own pace. That makes a huge difference. You're in a good place now b/c you understand the value and you're doing this b/c you want to. That's really fundamental. You're coming from a place of intrinsic motivation it sounds like. That's a very good thing. Get yourself a good foundation in mathematics and strive to understand WHY things work the way they do rather than just learning how to bang out formulas. Learn the derivations yourself. This will do two important things for you. 1.) you'll never have to intentionally memorize formulas and the material will stick with you much longer. 2.) You'll learn how to think like a mathematician and your reasoning skills will increase. You can do all of this now starting in Algebra. Here's a fun one, learn how to derive the quadratic formula and the Pythagorean theorem. Those are great proofs that apply directly to stuff you already know. Their both elegant, geometric proofs that you will likely understand without too much effort. Finally, take a look at the "Feynmann Technique". There are numerous vids on you tube about it. I'm sure he didn't invent it, but made the idea popular perhaps. Either way, it's a good way to think about learning and ways to maximize your comprehension.
@@pipertripp That is a very noble pursuit. I can see logic in understanding the reasoning and the purpose of the concepts rather than rote memory of the formulas. I will definitely keep that in mind going forward, and will make a point to study those three things. You have been very helpful and inspirational, thank you.
@@DyneTyrreal and here we are in India going to have a new education reform being implemented from the 2021-22 session which is heavily influenced from USA and Canadian Education system. 😭
@@hmm7458 mujhe ghnta farak nhi pdta. The guy above in the comments said that US edu system needs to be changed and since our new education reform is heavily influenced from the USA and Canadian Education system then surely we are going to face similar problems with this one in the future. So I just made a comment on that. Chill bruhh I appreciate the new education reform btw.
I'm yet another example of someone that learned to love math later in life as a programmer motivated by solving programming problems. I was always pretty good at math, but never really enjoyed it. But the thrill of solving a complex math problem that actually helps you achieve some real world end goal is what has given me a newfound appreciation for math.
I can confirm... got more interested in math after learning to program. Trig suddenly had applications if you want to move your little 2D tank in an arbitrary angle that's not just along one of the 2 axes.
Stewart's Calculus was a fantastic text because you can buy an answer key with FULLY worked solutions and find out exactly what you did right and where you went wrong.
I agree that teaching is the best way of learning. In a way, when you are writing or teaching something in your own words, I see it as if you are dismantling and breaking down the subject into small units and then rewording, transforming and building them up again into your own work such that it is embodied by your thought process which is uniquely natural to you. This then becomes largely unforgettable, like you don't forget how you tell your stories but may find it difficult to tell a story as somebody else says it.
I fully believe the remember %90 of what you teach. That's part of the reason I started making mathematics videos myself, to improve my own understanding of certain subjects.
Programming absolutely helped me get into math and see it from a different perspective. Also using Desmos to graph different functions and shifting and moving modifying the values helped as well.
Honestly Grant's videos were irreplaceable in my understanding of fundamental parts of many topics, solving examples will really solidify your learning but an intuitive understanding of the topic will allow you to be more flexible and creative while solving those problems.
Teaching is 100% the best form of learning, also one of the final steps. It forces you to find the gaps in your knowledge and consolidate what you know in digestible way
when I was around 4 or 5 I thought maths was the most boring, useless thing in the world and I couldn't understand how anyone could like it. But I absolutely loved puzzles at home and finding curious little problems. I remember specifically one time I was stacking together 4 bricks of lego where there were two green bricks and two blue bricks and I was fascinated by all of the different arrangements. It took me a little bit longer to understand that the very maths I thought I hated was exactly the same as the puzzles I loved. It isn't about the numbers, its about the patterns and the underlying beauty. I think if schools showed this more, people would be more likely to love maths because they would view it as less of an unfortunate tool that you need to know, but more of a beautiful thing in its own right.
I did math exercises in text books through kindergarten to masters in engineering. Did not understood much. Did not remember much. Understanding and visualizing what really you are doing is very important.
1:54 - true, me myself, i am 26 years old. i was a dumba$$ at math in high school and university. it was a shame, but now that i have deepend my knowledge in programming and wanting to get into the job market, i know I have to learn and i want to learn math. wish me luck
Totally good advice. I began to get A's in math ... I could hardly help myself, when I began to do the homework of EVERY PROBLEM IN THE BOOK ... *TWICE* It really helps if you have the answers or a tutor, but every problem in the book, twice. Three times if you have the time, a test, or an especially hard subject, like Differential Equations. Tutoring or teaching is a good way to retain the information and integrate it into your brain. Of course that was decades ago and I have forgotten a lot of it, but the ideas and concepts still live on. I should have been a math teacher!
" You remember 10% of what you read. You remember 20% of what you listen to. You remember 70% of what you actively interact with in some way. You remember 90% of what you teach. "
Math is often presentes as something useless that's completely disconnected from practicalities, which is quite the opposite from the truth. We learn Languages to communicate better to others, we learn History because it lets us know what happened, we learn Geography to have a peek on how the world is like, but when it comes to Math it is "You have to do it because that's the way it is". I just got interested in Math after I had a very good teacher at the last year of high school. He was a bit of a deadpan, not very charismatic, but showed us the practical side of Math, but then life went on and I didn't think too much about it. Latee on I got into Technical Art and it often involved Trigonometry, Programming and finally Engineering, and those last two involved many aspects of math in a very practical way.
Start with programming and use that to get motivated in math. We would have a better ecosystem but those 2 things are usually in the order that does not motivate more understanding.
Yep, programming is one of the best way to engage with mathematics. But, i think its more in obtaining what i call "algorithmic thinking", that is when you see a problem, instead of rushing for solutions, you start by devising ways and steps to obtain solution. And checking results too.
This guy is just being pretentions Feynman personality gets perfectly conveyed in his autobiography Feynman dedicates like four chapters to his awkward and some sad memories in his life He didn't read his autobiography for knowing the person but just read it because he wanted to say he read it
In regard to teaching being a good way to learn, would simply attempting to explain how to do something out loud while by myself work? So essentially teaching an imaginary person. I've just enrolled in a data science degree and there's a lot of math in it.
While explaining to yourself does help *you* understand, it *might not* be the case that *someone else* will understand *your explanation*. Furthermore, an imaginary person cannot give feedback (if they understood your explanation). In that case, I think explaining concepts in 'laymen terms' to other people around you (family, friends, ..., I for one usually do this in small talk or when speaking to friends) will help you think about the concept you're teaching and also help you boil it down to simple ideas. Say you explain to someone about derivatives for instance - if they don't know calculus, then you need to think about what basic ideas/concepts you need to establish for them to understand derivatives. So you introduce them to rates of change, maybe limits if you're inclined enough and so on; Then you use those concepts in your explanation of derivatives, or whatever the subject may be. Two things: This kind of approach also helps you solve problems, because explaining the problems also helps you understand the problem to a greater degree. Also, The more you do this, the better you'll get at it.
Haha I first got into programming too and now I am more interested in pure math than say applied math XD Programming is actually applied math. It borrows a lot of ideas from higher level maths. I was amazed when I first discovered the concepts I initially learned from programming in the heart of higher level math.
More and more applications of pure math are finding their way into machine learning and artificial intelligence systems, There is Algebraic Topology trying to understand equivalences between different Neural Network architectures, Algebraic Geometry for analyzing data and much more. Give some time to a subject in pure math and some years later it will find its way into applied math.
So he has said at the beginning of the video that it's better to interact with textbooks than it is to watch lectures or videos but at the end of the video he said that you only remember 10% of the stuff you read and 20% of the stuff you listen to I am confused
The real problem is finding problems (sorry) that you can solve with some struggle versus spending time on problems you probably won't be able to solve because you don't think of a particular argument that allows you to solve it, or because you didn't actually understand the theory behind it. That's my problem at least. In university we spend more time on theory than on exercises, which leaves very little time to solve problems.
because CS made math exciting for me. The thought of being able to use math and solve problems using programming is exciting, due to which jumping over hurdles becomes exciting...
Can I please have a suggestion for a math textbook? I can find a million of them, and therein lies my problem. I am sure there are some that are better than others
I disagree with Grant’s notion that his videos don’t actually promote ‘real’ learning. As a non-maths person I’ll sometimes watch his videos and gain intuition about some concept that I can apply to programming, design, etc. Sometimes just encountering a new concept is enough, because it can inspire further inquiry.
yea. he really gives that "little kicker" that makes it work. you´d think "ohhh... calculus is all about numbers i really eventually gonna make a brutal mistake" but when you see his animations of formulas. those formulas will be set in stone like a fortress!!!
You remember 10% what you read... You remember 20% what you listen to... Nah, definitely not true in my case. Easier for me to learn from reading than listening.
Teaching may be the best way for one to learn and master complex concepts; however, clearly such statement implies that the one teaching is not 100% taught on the subject, in which most can agree we don’t need their audience remembering inconsistent / incorrect information..whom may end up spreading the misinformation. So, if a person wants to learn a subject by teaching it aloud, then make sure the audience is either a.) your dog or b.) individuals whom are with great understanding that they should take each class with a grain of salt… 🤷🏻♀️👀😮💨
I've been kind of realizing this approach after the last year or so of fumbling, BAD. Coming from this guy is MORE than 'validating'. . .if there's anything I've learned in the last year isn't how hard this is as a discipline, but add on top of it the knowledge and creative approach he has taken on top of it as well. Because of this, I know not only how finite I am in this field--and probably intellectually--but also have been given a glimpse of how immense this dude's intellect is.
it's referring to like, low stakes teaching where if you get it wrong it's okay, informally explaining to friend or colleague or something, not like "become a tutor in a subject you dont understand"
Algebra is mandatory in college. Why? Where in life will I need to calculate a parabola? I think this mindset is due not because it is useful but because of a sense of competition between states and administrations. It just isn't a useful or relevant thing to learn. Instead we should teach things that are useful and relevant like Critical Thinking, Social Skills, or even Civic Patriotism. Hell, even Manners.
Mainly so you can learn statistics easier and read graphs. Again its only College algebra it is 1 semester for a 4v year degree that isn't stem and if you get a high enough SAT, ACTor ged score you can skip it.
This content is a revelation. I read a similar book that was a watershed moment for me. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell
Only thing your proving is that nothing has changed and probably nothing will ever change. fear of opinions that are not constrained to your personal standards proves my point 10 fold. We have become complacent and our values are degrading fast because of it. Whips and strong arming is now in control of our political process not our bloody votes at all.. A whopping 50% of the effort it takes to run a country is now focused on that. The best prime minister we could ever have will be a hermit who only speaks in sign language. if parliament has a diversity of thought the fact that whips and strong arming is being used to control such things is the saddest realisation in the last decade.
How do you learn by teaching since you can’t teach what you didn’t yet learnt by teaching? It’s paradoxical, never made sense for me this advice… seems like words thrown without thinking…
"I hear and I forget. I see and I remember. I do and I understand."
--Confucius
- Solve more problems to enhance learning at [0:31].
- Seek well-curated problem lists from textbooks or resources at [0:43].
- Preview end-of-chapter questions before reading the chapter at [0:51].
- Don't move on until you've worked through chapter exercises at [1:07].
- Use resources like Khan Academy for a structured problem set at [1:32].
- Learn programming to discover mathematical applications at [1:47].
- Teach or explain concepts to others to solidify understanding at [2:55].
As a 3rd year math professor, I totally agree that teaching is a great way to learn math and that working problems is the most reliable way to discern your own level of understanding. Thanks Grant and Lex!
Same goes in reasoning for teaching approaches in a H-Ed ESL course. Everything's comin up Hitsuzen
"You remember about 90% of what you teach" that's why i talk to myself so much, my wife wouldn't understand
studying the history of math can also lead a student to get a sense of where all the math problems came from, how human beings got their mind wrapped around a particular type of math problem rather than something else.
True bro... That's what I'm doing nowadays. Like where did this formula originated from and why the idea of making it even came....
Exactly not knowing the fundamental concept of things makes it difficult to understand and apply better
Now that's a new one. Very Interesting. Any particullar historians or starting points to get me in the right direction?
@@andso7068 Mathematics for the Nonmathematician by Morris Kline
yes that's such a simple way to get started with math as a beginner, good job!
All of this rings true for me. I'm a 40 something programmer but I really want to be an astronomer. I'm teaching myself undergraduate level math and physics (and astronomy too). I buy text books and I read the chapters and to every problem at the end of each chapter. I buy those "3000 worked problems in physics" books and to the problems. I have a daily ritual of working problems. I can't overstate how effective that has been at helping me get better at mechanics or calc or whatever. I also occasionally give presentations to a science group I'm a part of and that whole teaching bit... I very much agree. I do the presentations because I learn SO much in the preparation. I've thought about creating videos on subjects, even if I don't every publish them, because of the focus it brings. It's the whole Feynman technique. If you can't explain something simply, you probably don't understand it well enough. Prepping to teach something also exposes all of the gaps in your understanding. Great clip. It's all really good advice.
Hey very impressive. Did you take mathematics in college or are you teaching yourself? If so, what is your method for doing so. Thank you.
@@jamjohnson2023 Both. I took a decent amount of math in college, but that was 25+ years ago so I had forgotten loads of it. I decided to start all over and learn it properly, trying to be more rigorous about it this time round. I buy text books that seem to be well rated (it's always a crap shoot, but the internet definitely makes this easier) and then I go through them a section at a time and I do the problem sets at the end of the sections/chapters. Supplementing the texts with online lectures and vids is really help too. I watch some short clips about a subject then read the text on it. Watching a lecture after having read the text really helps with comprehension I find. I've hired tutors now and again as well. This has been the hardest part... finding someone to help.
The success of the above approach varies with how "popular" the topic is. Astronomy has been the biggest challenge (oddly enough) b/c most content is popsci... or at the graduate level. Finding good undergrad lectures that are "in the goldilocks zone" is harder there.
@@pipertripp learning on your own time and effort is very impressive, not many have the drive to do that. Do you feel that you do it from a point of discipline or from a point of it being an interesting and engaging pursuit for you? I am asking mostly because I was not a good student in high school, i was completely uninterested and unmotivated and didnt apply myself at all. Now, at 20, I look back and hit myself because I realize how interesting and useful these topics can be if I had applied myself to them, and how much I need them to advance my life. I am now going through an algebra 2 textbook to relearn alot of what I neglected, and am considering remedial classes before going to college, where I would likely pursue a bachelors in aeronautics. It is a great challenge to me, because I have taken the easy path for so long that keeping my focus and attention on something that does not an immediate reward is somewhat difficult. Thank you.
@@jamjohnson2023 for me it's definitely a passion. I'm a programmer by trade, so I'm not doing this to land a job. I'm getting ready for school... I want to go back and get another degree... probably in physics or astronomy. I want to "semi-retire" into helping others do research and teaching interested highschool or college kids. I love the idea of creating some really compelling after school programmes for kids that are up for it, but time will tell.
I was a good student, but I was rubbish at maths in HS. I had an "awakening" in college and I ended up taking a fair amount of it. I really surprised myself in that regard, but I was never a good student of mathematics... I was always focused on "surviving" the problem sets and I didn't take the time to really wrestle with the derivations. It's why I've forgotten all of the material. I'm not making that mistake this time round. I'm a much better student at 45 than I was at 20, that's for sure. But there's way less pressure and I can learn at my own pace. That makes a huge difference.
You're in a good place now b/c you understand the value and you're doing this b/c you want to. That's really fundamental. You're coming from a place of intrinsic motivation it sounds like. That's a very good thing. Get yourself a good foundation in mathematics and strive to understand WHY things work the way they do rather than just learning how to bang out formulas. Learn the derivations yourself. This will do two important things for you. 1.) you'll never have to intentionally memorize formulas and the material will stick with you much longer. 2.) You'll learn how to think like a mathematician and your reasoning skills will increase.
You can do all of this now starting in Algebra. Here's a fun one, learn how to derive the quadratic formula and the Pythagorean theorem. Those are great proofs that apply directly to stuff you already know. Their both elegant, geometric proofs that you will likely understand without too much effort.
Finally, take a look at the "Feynmann Technique". There are numerous vids on you tube about it. I'm sure he didn't invent it, but made the idea popular perhaps. Either way, it's a good way to think about learning and ways to maximize your comprehension.
@@pipertripp That is a very noble pursuit. I can see logic in understanding the reasoning and the purpose of the concepts rather than rote memory of the formulas. I will definitely keep that in mind going forward, and will make a point to study those three things. You have been very helpful and inspirational, thank you.
why is Grant being interrogated by an FBI agent about this?
Underrated comment
Lol
😆😆
MIB
🤣🤣
I'm one of the guy who turned to Maths because of programming.
@@snghnishant Education needs restructuring in the USA, too many classes that are unnecessary are taught and paid for
@@DyneTyrreal and here we are in India going to have a new education reform being implemented from the 2021-22 session which is heavily influenced from USA and Canadian Education system. 😭
I turned to programming from maths.
@@snghnishant why are you crying bro.. they are going to teach kids programming from 6th standard now.. damn lucky brats
@@hmm7458 mujhe ghnta farak nhi pdta. The guy above in the comments said that US edu system needs to be changed and since our new education reform is heavily influenced from the USA and Canadian Education system then surely we are going to face similar problems with this one in the future. So I just made a comment on that. Chill bruhh I appreciate the new education reform btw.
Dude every sentence Grant says has value. I love it.
Grant’s voice literally cures my depression
I'm yet another example of someone that learned to love math later in life as a programmer motivated by solving programming problems. I was always pretty good at math, but never really enjoyed it. But the thrill of solving a complex math problem that actually helps you achieve some real world end goal is what has given me a newfound appreciation for math.
I can confirm... got more interested in math after learning to program. Trig suddenly had applications if you want to move your little 2D tank in an arbitrary angle that's not just along one of the 2 axes.
Stewart's Calculus was a fantastic text because you can buy an answer key with FULLY worked solutions and find out exactly what you did right and where you went wrong.
I agree that teaching is the best way of learning. In a way, when you are writing or teaching something in your own words, I see it as if you are dismantling and breaking down the subject into small units and then rewording, transforming and building them up again into your own work such that it is embodied by your thought process which is uniquely natural to you. This then becomes largely unforgettable, like you don't forget how you tell your stories but may find it difficult to tell a story as somebody else says it.
I fully believe the remember %90 of what you teach. That's part of the reason I started making mathematics videos myself, to improve my own understanding of certain subjects.
Agree teaching is the best way n fastest way to learn something n retain in memory for longest period
The feynman way...
active recall
Programming absolutely helped me get into math and see it from a different perspective. Also using Desmos to graph different functions and shifting and moving modifying the values helped as well.
Honestly Grant's videos were irreplaceable in my understanding of fundamental parts of many topics, solving examples will really solidify your learning but an intuitive understanding of the topic will allow you to be more flexible and creative while solving those problems.
aynen
I thought 3Blue1Brown was a 40 something year old, but here he looks 20.
not to mention handsome
I believe he mentioned he is 27 in a 9-month-old Q&A video, just in case you are interested.
Teaching is 100% the best form of learning, also one of the final steps. It forces you to find the gaps in your knowledge and consolidate what you know in digestible way
I have masters in engineering. I am just begining this journey. Just realized how addition work and what really is multiplication.
ain't no way
when I was around 4 or 5 I thought maths was the most boring, useless thing in the world and I couldn't understand how anyone could like it. But I absolutely loved puzzles at home and finding curious little problems. I remember specifically one time I was stacking together 4 bricks of lego where there were two green bricks and two blue bricks and I was fascinated by all of the different arrangements. It took me a little bit longer to understand that the very maths I thought I hated was exactly the same as the puzzles I loved. It isn't about the numbers, its about the patterns and the underlying beauty. I think if schools showed this more, people would be more likely to love maths because they would view it as less of an unfortunate tool that you need to know, but more of a beautiful thing in its own right.
I love love love your comment!
I did math exercises in text books through kindergarten to masters in engineering. Did not understood much. Did not remember much. Understanding and visualizing what really you are doing is very important.
Hearing is voice is soo soothing considering the massive help I associate with it
His videos are top shelf!
Grant is such a savior of our species. Seriously, his influence on mathematics can't be overstated.
1:54 - true, me myself, i am 26 years old. i was a dumba$$ at math in high school and university. it was a shame, but now that i have deepend my knowledge in programming and wanting to get into the job market, i know I have to learn and i want to learn math. wish me luck
I agree with him about percents. I learn so much by teaching it than both of them combined. Studies have shown teach someone makes you better learner.
Indeed! Programming is what boosted my interest in Maths.
Glad to have found you, particularly now. Hey, thanks.
Totally good advice. I began to get A's in math ... I could hardly help myself, when I began to do the homework of EVERY PROBLEM IN THE BOOK ... *TWICE*
It really helps if you have the answers or a tutor, but every problem in the book, twice. Three times if you have the time, a test, or an especially hard subject, like Differential Equations. Tutoring or teaching is a good way to retain the information and integrate it into your brain.
Of course that was decades ago and I have forgotten a lot of it, but the ideas and concepts still live on. I should have been a math teacher!
Sigh… very time consuming tip but it’s true :)
"
You remember 10% of what you read.
You remember 20% of what you listen to.
You remember 70% of what you actively interact with in some way.
You remember 90% of what you teach.
"
Math is often presentes as something useless that's completely disconnected from practicalities, which is quite the opposite from the truth. We learn Languages to communicate better to others, we learn History because it lets us know what happened, we learn Geography to have a peek on how the world is like, but when it comes to Math it is "You have to do it because that's the way it is".
I just got interested in Math after I had a very good teacher at the last year of high school. He was a bit of a deadpan, not very charismatic, but showed us the practical side of Math, but then life went on and I didn't think too much about it. Latee on I got into Technical Art and it often involved Trigonometry, Programming and finally Engineering, and those last two involved many aspects of math in a very practical way.
True! I also never liked math, before I started programming. Now I see how important it is and very amusing actually!
I learned at LOT teaching Karate. I think that knowledge might have been a lot deeper that what I had been taught.
So odd seeing Grant’s face because I live for his series
Learn it, know it, teach it, preach it
Start with programming and use that to get motivated in math. We would have a better ecosystem but those 2 things are usually in the order that does not motivate more understanding.
Yep, programming is one of the best way to engage with mathematics. But, i think its more in obtaining what i call "algorithmic thinking", that is when you see a problem, instead of rushing for solutions, you start by devising ways and steps to obtain solution. And checking results too.
So big answer is doing more exercises?
the last sentence is what most people don't get to understand
grant sanderson is one of my favourite humans.
Just did a bunch of algebra in bed at 4 am thanks
Which os the best maths textbook for learning all the maths topics required on the filed of computer science.
This guy is just being pretentions
Feynman personality gets perfectly conveyed in his autobiography
Feynman dedicates like four chapters to his awkward and some sad memories in his life
He didn't read his autobiography for knowing the person but just read it because he wanted to say he read it
My name is Casper Sanderson, im Honored
In regard to teaching being a good way to learn, would simply attempting to explain how to do something out loud while by myself work? So essentially teaching an imaginary person.
I've just enrolled in a data science degree and there's a lot of math in it.
While explaining to yourself does help *you* understand, it *might not* be the case that *someone else* will understand *your explanation*.
Furthermore, an imaginary person cannot give feedback (if they understood your explanation).
In that case, I think explaining concepts in 'laymen terms' to other people around you (family, friends, ..., I for one usually do this in small talk or when speaking to friends) will help you think about the concept you're teaching and also help you boil it down to simple ideas.
Say you explain to someone about derivatives for instance - if they don't know calculus, then you need to think about what basic ideas/concepts you need to establish for them to understand derivatives. So you introduce them to rates of change, maybe limits if you're inclined enough and so on; Then you use those concepts in your explanation of derivatives, or whatever the subject may be.
Two things: This kind of approach also helps you solve problems, because explaining the problems also helps you understand the problem to a greater degree.
Also, The more you do this, the better you'll get at it.
Wow….I thought grants voice was only pleasant in his videos…that just his voice
Haha I first got into programming too and now I am more interested in pure math than say applied math XD
Programming is actually applied math. It borrows a lot of ideas from higher level maths. I was amazed when I first discovered the concepts I initially learned from programming in the heart of higher level math.
More and more applications of pure math are finding their way into machine learning and artificial intelligence systems, There is Algebraic Topology trying to understand equivalences between different Neural Network architectures, Algebraic Geometry for analyzing data and much more. Give some time to a subject in pure math and some years later it will find its way into applied math.
So he has said at the beginning of the video that it's better to interact with textbooks than it is to watch lectures or videos but at the end of the video he said that you only remember 10% of the stuff you read and 20% of the stuff you listen to I am confused
The pic from Goodwill hunting was a click bait ?? Not cool !
i'm 25 and know like high school math, i went up to grade 12 advanced functions and got a decent grade a 77%. Is it too late to learn math?
it is never too late to learn anything...
Actively trying to explain thing is crucial.
I think these advices will work with everything including math
Spot on! Wanna learn something well? Start teaching it!
Why is there no sound?
The real problem is finding problems (sorry) that you can solve with some struggle versus spending time on problems you probably won't be able to solve because you don't think of a particular argument that allows you to solve it, or because you didn't actually understand the theory behind it.
That's my problem at least.
In university we spend more time on theory than on exercises, which leaves very little time to solve problems.
True to get good at competitive coding too.
I learned linear algebra because of MATLAB
@James Gyoke The official branding of the software is in all caps, no joke.
Wow, Khabib shaved his beard.
1. Do problems more than you would have done naturally .
Look problems before theory.
2. Learn to programme.
3. Teach Math.
I like khan for math watch some lecture do some problems. With the physics section it flys over my head
because CS made math exciting for me. The thought of being able to use math and solve problems using programming is exciting, due to which jumping over hurdles becomes exciting...
I made a good solid D in calculus and UNIV of NT
I hated math. Was horrible at it. Started programming as a hobby. Now i think math is kinda fascinating.
Thank you
Grant is the best
teach for learning
If we mastered math everything else involving science, technology, and engineering would be less complex
Can I please have a suggestion for a math textbook? I can find a million of them, and therein lies my problem. I am sure there are some that are better than others
I disagree with Grant’s notion that his videos don’t actually promote ‘real’ learning. As a non-maths person I’ll sometimes watch his videos and gain intuition about some concept that I can apply to programming, design, etc. Sometimes just encountering a new concept is enough, because it can inspire further inquiry.
yea. he really gives that "little kicker" that makes it work. you´d think "ohhh... calculus is all about numbers i really eventually gonna make a brutal mistake" but when you see his animations of formulas. those formulas will be set in stone like a fortress!!!
You remember 10% what you read... You remember 20% what you listen to...
Nah, definitely not true in my case. Easier for me to learn from reading than listening.
Teaching may be the best way for one to learn and master complex concepts; however, clearly such statement implies that the one teaching is not 100% taught on the subject, in which most can agree we don’t need their audience remembering inconsistent / incorrect information..whom may end up spreading the misinformation. So, if a person wants to learn a subject by teaching it aloud, then make sure the audience is either a.) your dog or b.) individuals whom are with great understanding that they should take each class with a grain of salt… 🤷🏻♀️👀😮💨
THAT VOICE
TY
Mathbits is great too!
You skipped the question of why to learn math. As Nietzsche said, those who have a why can bear almost any how.
thanks :)
That voice!
I'm also a programmer who discovered the pragmatism of Maths. I only recently taught myself geometry, algebra, stat, and physics:)
So true lol, programming really can drive to math.
Oh my god I wish I watched this earlier
I think that he's referring to the Richard Feynman technique.
Well implicitly kinda yeah.
I've been kind of realizing this approach after the last year or so of fumbling, BAD.
Coming from this guy is MORE than 'validating'. . .if there's anything I've learned in the last year isn't how hard this is as a discipline, but add on top of it the knowledge and creative approach he has taken on top of it as well. Because of this, I know not only how finite I am in this field--and probably intellectually--but also have been given a glimpse of how immense this dude's intellect is.
If you’re teaching something, you should already know what you’re teaching
it's referring to like, low stakes teaching where if you get it wrong it's okay, informally explaining to friend or colleague or something, not like "become a tutor in a subject you dont understand"
The idea of"you just remember 10 percent etc." Is false
turn it into money and it will all make sense
i love it
I would give a larger percentage to what you read
The education system fucking sucks
true
Algebra is mandatory in college. Why? Where in life will I need to calculate a parabola? I think this mindset is due not because it is useful but because of a sense of competition between states and administrations. It just isn't a useful or relevant thing to learn. Instead we should teach things that are useful and relevant like Critical Thinking, Social Skills, or even Civic Patriotism. Hell, even Manners.
Mainly so you can learn statistics easier and read graphs. Again its only College algebra it is 1 semester for a 4v year degree that isn't stem and if you get a high enough SAT, ACTor ged score you can skip it.
Khan academy rocks!
❤️❤️❤️❤️
This content is a revelation. I read a similar book that was a watershed moment for me. "Game Theory and the Pursuit of Algorithmic Fairness" by Jack Frostwell
lex is kool tho
Maths
Best way to learn math: have high enough IQ.
And that's all fox.
Only thing your proving is that nothing has changed and probably nothing will ever change. fear of opinions that are not constrained to your personal standards proves my point 10 fold. We have become complacent and our values are degrading fast because of it. Whips and strong arming is now in control of our political process not our bloody votes at all.. A whopping 50% of the effort it takes to run a country is now focused on that. The best prime minister we could ever have will be a hermit who only speaks in sign language. if parliament has a diversity of thought the fact that whips and strong arming is being used to control such things is the saddest realisation in the last decade.
Фор алгоритм
How do you learn by teaching since you can’t teach what you didn’t yet learnt by teaching? It’s paradoxical, never made sense for me this advice… seems like words thrown without thinking…