Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh | Big Think

Anyone Can Be a Math Person Once They Know the Best Learning Techniques
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Po-Shen Loh is a Hertz Foundation Fellow and Carnegie Mellon mathematics professor who thinks that history is a much harder subject than math. Do you agree? Well, your position on that might change before and after this video. Loh illuminates the invisible ladders within the world of math, and shows that it isn't about memorizing formulas-it's about processing reason and logic. With the support of the Fannie and John Hertz Foundation, Po-Shen Loh pursued a PhD in combinatorics at the Pure Math Department at Princeton University.
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PO-SHEN LOH:
Po-Shen Loh, PhD, is associate professor of mathematics at Carnegie Mellon University, which he joined, in 2010, as an assistant professor in the Department of Mathematical Sciences. As a Hertz Fellow, Professor Loh received his PhD in combinatorics of the Pure Math Department at Princeton University. His thesis discussed several original results that he discovered during his graduate study in joint projects with his advisor and other collaborators. Professor Loh studies questions that lie at the intersection of two branches of mathematics: combinatorics (the study of discrete systems) and probability theory.
Prior to his work at Princeton, Loh received the equivalent of a master's degree in mathematics from the University of Cambridge (United Kingdom) in 2005, where he was supported by a Winston Churchill Foundation Scholarship. He received his undergraduate degree in mathematics from Caltech in 2004, graduating first in his class, and his undergraduate thesis later received the Honorable Mention for the 2004 AMS-MAA-SIAM Morgan Prize.
In his spare time, Loh has maintained his involvement with the United States Mathematical Olympiad program. He is now the head coach of the national delegation, as well as a lead fundraiser for the organization. As a high school student, he won a silver medal at the 1999 International Mathematical Olympiad (IMO), and following his win continued to be active in the training of high school students at the U.S. national Math Olympiad Summer Program. In 2004, he served as the deputy leader for the U.S. team at the IMO in Athens, Greece, where our national team placed second. After completing his PhD, Loh again, served as deputy team leader for the United States at the International Mathematical Olympiad from 2010 to 2013. Afterwards Professor Loh was promoted to national head coach of the U.S.A. IMO team, and on his second attempt, Team U.S.A. won first place, in a competition with teams from over 100 countries represented.
Earlier this year, Loh received an NSF CAREER award, the most prestigious NSF award for junior faculty, which honors outstanding research combined with a commitment to teaching. Professor Loh is the founder of the educational technology startup expii.com, a crowd-sourced platform for the world to share interactive lessons in math and science.
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TRANSCRIPT:
Po-Shen Lo: I think that everyone in the world could be a math person if they wanted to. The keyword though, I want to say, is if they wanted to. That said, I do think that everyone in America could benefit from having that mathematical background in reasoning just to help everyone make very good decisions. And here I'm distinguishing already between math as people usually conceive of it, and decision making and analysis, which is actually what I think math is.
So, for example, I don't think that being a math person means that you can recite the formulas between the sines, cosines, tangents and to use logarithms and exponentials interchangeably. That's not necessarily what I think everyone should try to concentrate to understand. The main things to concentrate to understand are the mathematical principles of reasoning.
But let me go back to these sines, cosines and logarithms. Well actually they do have value. What they are is that they are ways to show you how these basic building blocks of reasoning can be used to deduce surprising things or difficult things. In some sense they're like the historical coverages of the triumphs of mathematics, so one cannot just talk abstractly about “yes let's talk about mathematical logic”, it's actually quite useful to have case studies or stories, which are these famous theorems.
Now, I actually think that these are accessible to everyone. I think that actually one reason mathematics is difficult to understand is actua...
For the full transcript, check out bigthink.com/videos/po-shen-l...

[@bigthink]

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[@curtiscarpenter9881]

I failed math GCSE I on the other appreciate game theory, I think it needs in education to be treated as a separate subject within its teaching, that is more methodical that appreciates different learning styles.🤯🤯🤯

[@sharemarket3821]

I really want to thank the team and all professors. I am from rural area and I am getting such a pure knowledge at my fingertip. I really from heart thank all of you. Please bring more knowledge on this. We will be very thankful

[@deepdude4719]

I agree history is more difficult than mathematics.

[@abhishekaabhi4992]

Absolutely sir I experience it

[@jensova5735]

Would you please suggest what are those prerequisites are?

[@smol_chilli_pepper]

This is so true. When I was younger, I was so bad at maths until I got a teacher who sat down with me and started from scratch and fully explained and taught me what I didn't know. She saved my life because if I moved forward without a basic understanding of mathematical concepts, I would have continued to fail for the rest of my life

[@math_the_why_behind]

That is one good teacher!

[@zeldazane4797]

You are so lucky....i wish if I also got such teacher

[@futurez12]

Absolute BS! There are PLENTY of people who haven't 'failed' in life who are bad at math. Who told you it was a life failure to struggle at math?

[@petergreen5337]

You have hit a great truth. A good teacher is key.

[@matteobarberis1149]

What are those basic concepts i need to know?

[@ElenaSemanova]

I absolutely love how he's hyped about maths. You can literally see it in his eyes.

[@tuffbear7603]

@Levulite ::: the VIRGIN with CONFIDENCE I’m Asian and failed math exam three times. I hate Math.

[@tuffbear7603]

@Levulite ::: the VIRGIN with CONFIDENCE Oh, that’s just my profile picture. I have other Asian friends who are also bad at math like me. Many other Asians too. You just taking the stereotype too seriously and believing it too much.

[@tuffbear7603]

@Levulite ::: the VIRGIN with CONFIDENCE Ok sorry, I’m not the kind of person to understand jokes as much. I think I’m on the autistic spectrum

[@math_the_why_behind]

Ikr!

[@sovereignboss1841]

@Unovan Cloud I think that guy is probably from India or arab country cuz asia is too big. And I think what you mean by asian good at math is probably chinese, japanese of Korean asian guy, well they really are good at maths, cuz man these countries are top one

[@gaurigoyal5744]

There is a professor in Oxford who once said that Maths is just another language we can understand the world through. It really changed my perspective about maths. It's not just about numbers and statistics and geometry and trigonometry, but rather it's a language. A language through which we can communicate with the universe itself.

[@iunderstandlittle]

that was really beautifully put.

[@Rejee-wq5om]

What a beautiful answer i agree. And for math is the language of the universe,it is complete itself, Math is perfect. Some say we Invented math, i Say no we Discover Math.

[@farzad1021]

​​@@Rejee-wq5om I will say the fundamental of math that is numbers are discovered. But the symbols and methods to do math are more likely invented.

[@shellybelly1071]

This is so true. My dad is basically a math genius and he explained to me that 'all smart mathematicians are not aware of the maths itself, but rather the *principles* of the maths'. Since then I have never failed a test.

[@user-in1yw9ty5t]

Wow that's awesome.

[@mevorathfjorathk.6219]

I completely agree, I was getting under 50% in every maths test. I then was introduced to physics (maths with an apparent purpose). I approached maths with an I love it attitude for the next two years because I loved physics. I also ignored people saying "don't worry you did poorly, maths is hard." I stopped messing around in my free time and decided to learn maths to a point where I was average. my view of average increased as I got better. Now there is the dreaded b+ . This was simply due to a change in mind set, hard work and replacing peoples opinions with difficult goals. " if you don't sacrifice for what you want, what you want will be the sacrifice."

[@samirhussain458]

Preach!

[@astolfo9377]

anonymous john I hate physics but I love maths

[@mauriciorv228]

who said the phrase in quotes?

[@mauriciorv228]

Saint Frank L. No just curious

[@user-xw4od8kb7y]

same for me but i got into programming so i wad forced to learn maths :d

[@chriswise5337]

I like this argument. I was never good at math until I started taking my math classes online. I'm a slow note taker and it takes me a while to understand concepts, so in a traditional classroom setting I fall behind the curve really easy. But with online classes, I can rewind the lectures, pause them to catch up, and use multiple sources of learning to figure out a concept rather than just depending on the professors way of learning which may or may not work for me. There are some downsides to learning purely online, but in regards to math online for me, the benefits outweigh the costs.

[@imanuelwahyu2313]

khanacademy , coursera etc....youre welcome

[@chriswise5337]

I'm taking them at a local community college, but I use Kahn Academy or other math channels on youtube to figure things out/refresh my memory

[@DvDick]

Chris Wise I too use internet a lot to understand math, I find it much easier to sift through many sources and find the one I'm most comfortable with, than relying completely on lectures and my professor's notes

[@avs6362]

Chris Wise same here!

[@emilyx903]

Chris Wise what program do u use??

[@physicsman3788]

This dude is insane. He was educated in Caltech, Cambridge Part III and later Princeton, those are best schools for theoretical physics and maths in the world.

[@haritinasakova4327]

i see why he didn't have time to brush his teeth

[@GlamourAlice]

Lmao!!!​@@haritinasakova4327

[@qutsbvrxur3634]

​@@haritinasakova4327dude.

[@Arpit.singh.]

I felt in love in Mathematics because i have practiced it excessively. Per day 4-5 hrs of question solving made me so confident that my approach to solve questions is completely changed and became efficient

[@r3dghok427]

I'm learning Mathematics, any advices? (Sorry for my bad English)

[@lly_09]

Has it shown positive effects? Jus asking. I'm really bad at maths, and also I never practice it. I thought the difference might be in practicing or others....

[@mastershooter64]

@@lly_09 it's definitely practice and having the right mindset

[@aaronrashid2075]

Absolutely agree. I have been studying the likes of calculus and other stuff to prepare for physics because physics was interesting. I then just started loving the maths itself (still love physics but preparing using the maths made me love it more was my point)

[@satioOeinas]

Khan acadamy

[@operatorlink]

math requires lots of practice and everyone gets better at various pace. At universities there isn't time for practice, topic are taught for a week and moved on to the next

[@Myrslokstok]

He who must not be named Yes but was rejected first by mankind and mathematical society for years before acceptance.

[@osculocentric]

He who must not be named I agree with you, I had very less marks in Mathematical Physics, so much that if I show it to someone in my current field of research they will judge me to be incompetent, but currently I work in the field of Theoretical Physics. I had a lot of time after my M.Sc to cope and improve on my previous failures, what helped me was that I started working on a research project and understood a lot of intricacies and understood it works on just simple concepts related to Linear Algebra. On the way I learnt that Maths works a lot by intuition, there are infact books written by the greats like Hilbert's "Geometry and Imagination" which underlines the ideas which led him to innovate things like Hilbert Space etc.

[@smithsmitherson9449]

I got my degree by starting at algebra in my college. There is time to practice. You may fail a few times but there is time if you study and forget about life.

[@goxr3plus_studio]

Smith Smitherson '' FORGET ABOUT LIFE '' I CRY 😂 😂 😂 😂 😂 😂

[@rahulpullal3872]

Maths doesn't require practice

[@blackpenredpen]

What a wonderful breakdown! Thanks professor Loh

[@gardenmenuuu]

Thank u too sir

[@AshishSingh-753]

God commentent

[@zaherramashaa3762]

To learn calculus follow this guy

[@mohammadhassanjan2064]

thats loh

[@theimmortalphysicsmaths3962]

Oh my god you are there bprp

[@ThemisTheotokatos]

I was the worst in math but I needed to learn computer science. So I went on and started learning online from youtube khan academy etc and now I feel like a pro. From simple addition to integrals, probability and logic and It really opened my mind. My thinking process changed. I really recommend learning math. Its not just for school

[@devenderkhanna8517]

Hey can you tell what you started with? Like for basic to get better?

[@ThemisTheotokatos]

@@devenderkhanna8517 I started from the basics. Addition multiplication negation and division. Just to warm up. Khan Academy provides a great roadmap just check the math section and start from the beginning because math is a chain. You will never understand second grade equations if you dont understand the simple ones. Or you will never understand derivatives if you first don't understand the slope of a line or even the very equation of a line. You need to keep consistent and determined. Good luck

[@noor-rrr]

How much time any did it took you to master till calculus and nay tips, like note taking, practice sessions, any tips, it would be really helpful

[@typicallydumbperson721]

I havent master calculus yet but my gameplan is to understand the concept very well and understand the relationships between them. Understanding relationships between mathematical concepts usually brings you "Ohhh, thats why" or "Damn bro this is incredible" moment and only there, actually solving problem till it became automatic

[@twentyeightO1]

same here, I am learning Machine Learning and it requires me to know calculus. I'm auditing a course on Coursera but i'll definitely check out Khan Academy.

[@michaelpisciarino5348]

0:23 Math and Decision Making 0:50 Reasoning/Logic 1:35 Chain of Deduction (miss a part, you can be lost) 3:18 Learn at your own pace

[@GoToMan]

Hey, I like your way of structuring the things. I am not aware if you remembered the structure with conscious effort or not but, I found your way of thinking, given the fact I surmise about your thinking based on this comment, to be very similar to that if Bill Gates. Would be great if we can talk more! Share any of your social channels(if you are ok)

[@lx4302]

Dhanush Mendu ok boomer

[@antiochussoter377]

In 1:35(the reson math makes me angry)

[@maheshverma5508]

Thanks

[@user-rj2hx5fs4y]

I skipped the video to 1:35. I'm completely lost!

[@15SecNut]

I am a full-time math tutor for an accelerated high school and this is 100% correct. More specifically, I noticed that there are about three locations in math knowledge that generally destroy a student's comprehension. The first is the memorization of times tables. Now, usually, I am against memorization in math, but I think basic times tables are an absolute must for higher level mathematics. Too often I see students pull out a calculator for things like "8 x 7". I think times tables should be memorized through comprehension, but this memorization plays a bigger part later. The second area, which I think is also the most beneficial to our rational thinking, is order of operations. In America, students usually learn this right before high school, so even if they don't grasp the concept, the teachers will still simply pass them. Now, the pattern I noticed while working with students is that these two areas compound once they get to factoring in Algebra 2. I've also noticed that this is where students start to give up on math. I think it's because factoring, in my opinion, is easiest to solve using mental math. But, because a lot of students don't remember their basic times tables and have a loose grasp on orders of operations, they're forced to use idiotic workarounds that only complicate matters.(diamond method, box method, etc.) It's at this point that the shaky foundation of mathematics finally falls apart as further curriculum is dependent on the ability to factor. But, that's just what I've noticed. :p

[@josephinhiding3595]

I would add that people seem unable to recognize patterns. For example in algebra, trignometry or calculus, inability to recognize an underlying pattern results in an inability to apply a formula or method.

[@SebastianLopez-nh1rr]

15SecNut I don't agree with you, the things you mention are not what they should memorize. They can deduce multiplication as well whenever they want or just a calculator (although it helps on speed memorizing it)(please look for the history of computers, the women, at NASA, calculating things is trivial work); and order of operations is simply something that doesn't exist, it's just a convention, real maths doesn't rely on such a thing. The problem is that algebra isn't taught the right way, the way where what you do is obvious, the way where you learn to deduce your way into algebra so you can never forget it's basic principles. The fundamental things he talks about are often quite more simple, like building blocks simple. Just as a reference, I'm an excellence student in engineering and I've successfully went through courses like partial differential equations and complex analysis. I don't know order of operations, I've never used it, parenthesis and deduction do the work; Maths shouldn't be subject of interpretation, maths should be transparent and straight forward. Btw the most basic thing you need to know about algebra is, do the same thing to both sides of the equation.

[@josephinhiding3595]

I'll give you another idea. And that's the amount of hours put in. Some studies show that to be an amateur at something requires 4,000 hours but to be professional or top level you need 10,000 hours. You will note that Professor Terry Tao, considered by some to be one of the worlds best current mathematicians, spent many hours on his own doing mathematics at an early age; even if it was just summing large columns of numbers. Further, you have to keep stretching, that is always greater challenges. Also, young people mature at different paces and a school system that caters to the lowest common denominator or even the average isn't going to maximize results. Talent doesn't rise without effort/hard work .. it would be wrong to assume that innate ability is the only criteria. I still remember our High School algebra teacher .. 4 days a week we had about an hours homework .. there was at least one really challenging problem that was very hard to solve .. you'd be lucky to get it with 1/2-1hr of extra effort on top of the 1 hour load. Needless to say it paid off. However, with 6 or 7 subjects the same amount of homework/effort would be a bit of a killer for most people, let alone youngsters, and probably unhealthy.

[@pakassassin9605]

omg man , you described exactly what i went through , i didn't memories the tables , i have huge problems with factorising even now , i am already a college student and still weak at maths due to this .

[@gabrielpauna62]

PAK AssAssIN why dont you just replace them with an unknown or simplify it, go to a physics lecture they hardly make a calculation - they just identify symmetry

[@xeztan]

Absolutely spot on. Math is pure reasoning and analysis, it always makes me laugh when people think that being good at math means being able to multiply insane numbers in your head in just seconds. People who can do things like that are certainly talented but there's a lot more to mathematics than ridiculous computations lol

[@Holobrine]

Interesting how projection works. They think being good at math means being exceptionally good at where the hole in their tracks was, when in reality they just didn’t have that hole and kept moving forward.

[@sharonjuniorchess]

Arithmetic is NOT maths but it is one of three areas especially in the early years. So competence & confidence are important in determining future performance. Fractions are a great area to reinforce previous learning and to refresh & relearn these skills but in a new way which can open up new insights about numbers. Finally a good grasp of arithmetic can provide a great foundation for algebra. Students are often taught the mechanics without understanding the why and this understanding should be encouraged. Today with computers students can draw down other explanations and then ways of testing their understanding. Key is encouraging curiosity & willingness to explore and play around with problems. We miss a great opportunity by not presenting mathematics alongside the footsteps of the mathematicians who first wrestled with these problems. A sense of history would go along way.

[@Pompicz]

@@sharonjuniorchess wow you're absolutely right actually, we do this with physics, why not with math?, In physics it always helped me to understand these things deeply, I remember wondering about this too in high school

[@domtg1597]

Kinda as long as you have accurate axioms but humans can get weird about that

[@periklisspanos7185]

Aaaaaaaaa

[@shanasakai2238]

I badly needed this since I'm bad at Mathematics that is why I'm starting to study the basics again. It's one of my dreams to be good at Math. Thank you for this inspiring video.

[@alex_5199]

Same, we can do this!

[@avery0444]

Are you there yet??

[@shavala2589]

YES, exactly I have been telling students that if they miss one concept they will miss part of the chain. If you miss the class on the quadratic equation there goes your whole understanding of what to do when the teacher ask simplify using the quadratic formula. Good to know professors are teaching that it is important not to miss math class. :)

[@allknowledge7146]

"if you miss one link in the chain, you will end up lost" Yep. I know it first hand.

[@totalfootball7924]

🤣 seconded

[@Albus_TheProfessor.]

Thirded

[@positivefraud3012]

Fourthed

[@nyx211]

One problem of the way that schools teach mathematics is that they focus too much on calculations and memorization of formulas and algorithms. Computers can do the calculations billions of times faster and they can store every single textbook you'll ever need. Schools should focus more on translating important, everyday problems into mathematics, the construction of mathematical proofs, and the ability to spot errors in arguments. They also should test students' abilities to intuitively explain their results. A simple 1 hr test doesn't allow enough time for thinking in order to show understanding.

[@Myrslokstok]

nyx211 You should learn some usefull skills, if it includes math so be it, and learn that then.

[@jptuser]

if schools started teaching analysis rather than calculus no one will ever be interested in mathematics.

[@123rishika8]

U are right according to me

[@mostazezo]

instead geometry can i learn the laws of my country

[@aliceOcean938]

You are absolutely right, agree 100%. I feel like this is my issue I have been encountering

[@daddy6757]

His enthusiasm and energy for math is contagious.

[@ILikeWeatherGuy]

too bad universities have their own schedule.

[@tehyonglip9203]

I think universities and tests are more based one answers based exam, what method you used are not important, in fact the numerical answer is more important than the technique used

[@michaelyoung4550]

yes, but if you do this before hand and get really into it, ,then you might consider doing a university course on it once you're more confident and interested in it all

[@HowToTop10]

Haha yea right?

[@boxxer221]

Universities teach you why the maths works the way it does. It's up to you to use those concepts to create solutions to questions.

[@eferrari96]

Teh Yong Lip not here in Germany depending on your class.

[@xGrinch101]

The thumbnail is all chemistry not math😂😂😂

[@balajichandrasekaran6312]

xGrinch101 just noticed

[@PLxFTW]

Mathematics is the basis and everything else is built on top.

[@horseworms]

Have you ever taken a chemistry course? Stochiometry, Molar ratios, Equilibrium, etc. It might as well just be called an applied math.

[@samuelskillern7365]

It may not be arithmatic, but it uses it.

[@MrBiggest1307]

might have well*

[@TimeManInJail]

This is depressing... So hes saying the public education failed me because I was simply a statistic that just get pass on to the next grade. Now im reaping the consequences alone.

[@kasondaleigh]

Wow! I wish I had known this. A good teacher makes all the difference! I finally understand some trig when I had a teacher who SPOKE NO ENGLISH, but illustrated the concepts with such clarity and enthusiasm that my brain caught on. I went on to take a theoretical calculus course and loved it, then I got lost in the mire again. This is such crucial information! Thank you!

[@tc2241]

Interesting, I came to a similar conclusion when I started delving into Advance maths and used Khan academy to catch up. It was amazing to see what I had a a weak grasp in and how, at my own pace, if could strengthen them. Lead me to believe that math is simply a poorly structured subject in our school systems, rather than something nefarious.

[@jiafeistan7657]

same!!

[@Ishfaqmajeed476]

Bro How can i join khan Academy to learn Math

[@aprendeinglesrapidoygratis9379]

It would be nice if schools could take this man's approach to learning math, and let students learn such a fundamental subject at their own pace.

[@aidenkim6629]

This is why I love math and computer science!! You can deduce a lot from knowledge you already have and figure it out yourself by using logic.

[@haphuongle2920]

I agree on individualized education. It would help for other subjects as well. It is especially helpful for students with special mental/ health/ situational needs, like those with dyslexia, teenagers rehabilitated from weeds and drugs, or just didn't have a chance to access school on time.

[@DJSkunkieButt]

As a self taught software engineer who picked up on crypto analysis for fun, I fully agree. I used to suck at advanced math when I was in high school. It wasn't until I started to pick up on engineering things outside of school that concepts started to click and advanced math became easy as hell. That being said, the main issue at hand is our garbage ass school system. It's set up to not care about your education as a student, but rather, just get mass results. Which I understand, teachers can only do so much and it's a solution that is monetarily feasible. But it doesn't produce meaningful results. It's set up for a learn and forget system, profit gains, and wasteful efforts. School does not work for people like me. I am already a salaried engineer without a degree because school failed to teach me. It's mostly a waste of time and if we really cared about kids education, we would reform the system. Does this mean I know what to do? No. I just know it doesn't work but we need a change.

[@gabrielpauna62]

DJSkunkiebutt there are emotional & psychological issues during adolescence which make school redundant . For many school also fails in getting us ready for adult life :(

[@malcolmbryant]

Too true, Gabriel.

[@joehudson440]

DJSkunkiebutt I find your argument very compelling. I saw myself as a math person long ago. I was also a victim of the poor education system. A teacher once told me that algebra might be too hard for me because the concepts would be very difficult to grasp. However, I succeeded at college level math. Anyone can learn math if he or she is willing to put forth the effort.

[@seanpaulson9098]

I agree. That being said alot of it falls on the parents and them failing to prepare their kids. Although alot of times this is because most kids grow up with one parent or distant relatives.

[@natashadas5280]

Wow! That is impressive! How did you find this field and go about teaching yourself engineering?

[@Tracy_AC]

I completely agree. I think he nailed down the problem exactly. The most upsetting thing for me, is that the link that most people seem to be missing in their mathematical thinking is somewhere around second grade. I TA for undergraduate math, and one of the difficulties I have noticed most often is that students have a poor understanding of fractions and ratios, which goes back to second grade. This is something I have noticed throughout my education at every level. Without an intuitive sense for fractions and ratios, higher level mathematics becomes just a manipulation game that is more akin to how a computer works than to real understanding.

[@isaacjohnson8752]

I flunked out of calc 2 at one point (two actually). I then went 3 years without doing math at all. Then I got a job tutoring at a community college while I got an electrical certificate. I learned from other tutors and also from helping other students. This filled in the missing links described here. I am in my last two semesters of a physics and applied math degree, and I do very well. It’s not easy by any stretch of the imagination, but I still give most of the credit to my tutoring experiences. We need to allow people to discover math at their own time and pace. Math should be explored, not force fed. I really enjoyed this professors insight.

[@johanhendriks]

One of the most valuable things I learned at university was "The order in which to learn each topic". Exactly as is described in this video, you need to know about certain concepts before you can grasp some others. Even having all the right books won't help you if you don't know in what order to read them.

[@guitarraccoon1541]

My current 7th grade math teacher literally said "All you need to do is know the formulas". It may sound a bit like "All you need to do is understand the formulas and why they work" but considering how he gives us the formulas without explaining anything, I don't think that's what he means.

[@cricticalthinking4098]

Yup that's pre-college math in a nutshell. Then that student who was amazing at remembering formulas goes on to become a math major and is unpleasantly surprised at the reality.

[@mahuk.]

I'm not going to say school was useless, because I did have some good teachers and still have some good memories. But being forced to learn at a pace that I don't feel comfortable with, and using a set of stupid rules that don't aply to my way of thinking just ruined my whole school life. My real school is my bookshelf and the Internet, and my teachers all those who took the time to write something useful to learn. Almost everything I was bad at I learned by myself and scored the higher grades when I finally had a window to be at peace and study by my own, instead of being shamed in public for not being able to comprehend.

[@TheFyreSA]

Hello Mahuk. I know this is 4 years late, but would you mind sharing with me how you taught yourself to be better at maths? I am currently trying to do that myself.

[@mahuk.]

@@TheFyreSA I kinda like how in the internet you'll get reminded of old comments, and also makes me wonder if one day someone will remind me of the dumb things I said in my teenager days. Anyways; The thing is I never became good at math. I am still the slow person of the group, but I taught myself discipline, so I can get the work done in the time I have, albeit sometimes slower than the guy who has both a gift for math and also discipline. With math, 99% of the time it is not about racing, it is about getting the answer right. I am good with logic though so I am always the first to identify and fix the problem with programming software :P The long story short is I learned discipline. With it I overcame math and many other issues in life. But I can't think of a short answer to what I did so I'll list some of the things I did if you're interested on a long read: - During university I would always be lost during class but I made sure to take notes of all the things I could, so when I got home I would study everything until I learned it correctly. - The next applies more to University, but make a network of people you can ask when you're struggling. Unlike high school in uni a lot of classmates are willing to help because if you become good at something you may save them later on. Also speak your problems with your teachers and ask for guidance, not all of them are monsters. Opening up and telling my problems to classmates helped me a lot. They told me how they struggled and what they did to fix their problems so I used some of that for myself. - Sleep properly. Your brain will perform better. I know it is hard when we're under loads of stress. I was working during my first and second year and getting 4 hours of sleep so it can be rough, but try to sleep properly. - If you are bad at organizing as I was. Make a schedule and follow it. And if it fails, instead of ditching it, try to understand why it is failing and see if 1) you can fix the problem so you can now stick to the schedule or 2) modify your schedule around the problem so they are not colliding with each other. Do NOT drop the schedule unless you're confident you can perform good without one. - Also every Saturday I would religiously dedicate it from early in the day to study until I learned everything I didn't get during the week, and if I couldn't do it during the day, I would also dedicate Sunday. Having Sunday free was my own reward for getting things done in Saturday. I am slow, so I have to dedicate extra time from my free time to compensate (schedule). - Identify how you're using your time, identify what is not important for you and cut the unnecessary things, but do not cut all the entertaining. Rest and having fun are part of having a healthy brain. Too much fun is bad and too much study is also bad. Find balance (schedule again). - Lastly but not least. KZbin. In some classes I owe more to those indian teachers in youtube than my actual teachers. Internet is a powerful weapon. *Use it*

[@TheFyreSA]

@@mahuk. I wasn't really expecting a reply to be honest, much less such a thoughtful one, so thank you. May I ask if you have any favourite youtube channels/internet resources you recommend I check out?

[@mahuk.]

@@TheFyreSA No not really. I mean I do, but the math heavy channels for calculus, algebra, etc. are not on English. I mainly used English videos when I needed something on a specific matter in programming, mechanics, or a specific software where the manual wasn't helping too much. What I also used a lot, even though it may be an unpopular opinion was uh... being good at finding PDF files of good _resources_ I used the book of Calculus from Varberg, Purcell and Rigdon. I also used book of calculus from Larson. Serway for Physics, and the Ogata 5th edition for automation in case you're into that field. My take is if you're a student and you're broke, it's is morally ok as long as you buy it after you get your degree. I have it sitting on my bookshelf now, but to each one their own.

[@TheFyreSA]

@@mahuk. thank you! I’ll definitely check out those authors!

[@diegodesigns3976]

I feel lucky on having a great teacher who introduced *common sense* in math and made it enjoyable in 7th grade. I always took my time on my homework and would work on a question till’ 12am if I did not understand it. Math was something I liked because I could be in my own little bubble and problem solve. The flexibility of math due to its connections gives me freedom in learning. To see results after working hard and pushing my brain is amazing. Now math comes easy to me and I have A’s in all my math courses in my time in high school.

[@spencerkeane1852]

I was not really good at math throughout middle school and high school, but still made it into Engineering school. So to prepare myself for college, I was able to develop a study method to review all my deficiencies before the start. I learned that being put in an accelerated class in middle school may have resulted in me picking up those deficiencies. I really do agree with Po-Shen Loh, and by using these principles my math reasoning in my Mechanical Engineering courses has become a powerful beneficial tool. I am also taking my final math course, Differential Equations and happy to say I've become more of a math person.

[@stevet6676]

Interesting video. I liked the contrast between learning history and math. After a career in industry, I taught high school chemistry and physics for several years in the city of Chicago. I was very dismayed by the level of math knowledge in general. What I would like to add to the discussion are two points: first, because a student is "bad" at math, doesn't = they are "stupid" or unable to learn it. They need to see and understand the importance of knowing the subject. Second, education does not need to be torture. For anyone interested, a great book on education is "The Smartest Kids in the World and how they got that way" by Amanda Ripley. Last thought: find a reason to learn. The future belongs to you.

[@YooBro219]

This is very true. From my experience, In high school I got D for basic maths but later one when I went to college and I started to understand the basic concept better. I struggled and failed twice before I scored an A for Concept of Calculus than on Cal I and Cal II were easier for me to master.

[@ian-eg4hy]

I was always bad at math but I saw this video a year ago (around December 2022 and January 2023) and decided to challenge this belief of his that everyone is a math person. So I started learning math from scratch, I did take some breaks here and then but one year later I'm now on algebra and I'm SO much better at math that I ever was in school. And what's crazy is that I also enjoy doing it. So I can say he is right

[@MCPhilosophy]

“Everything builds on what to already know” - David Eagleman

[@mikicerise6250]

This is a great insight. Here in Spain when I was studying for my written driving exam the classes were actually circular. You had one book with every chapter you need and a few teachers who would cycle through the book. You could join the class any time you wanted, start with any chapter, and stay for as long as you need. You can repeat the chapters as many times as you need before the test just by waiting for the class to cycle back to them. It seems like this would be a good model for teaching maths. I wish I could have a teacher like this for maths, but I am older now and it's hard to find tutors for people my age.

[@rhythmandacoustics]

KHAN ACADEMY

[@derekfrostbeard6419]

I'm just now taking Discrete Structures, my first proofs course, and what I am learning gives me a deeper understanding of even addition! I wish a simpler version of Discrete Structures was integrated into Elementary School curriculums.

[@jennykeeling3716]

I just went through two years of struggle with a level maths because I missed the most of the content for the first year (we had a teacher that was always absent) and then had to try and fill in those holes in the second year whilst learning new stuff and it turned out to be a complete disaster. Then Corona struck and i got bad grades. I still have the feeling that I can really understand maths if i break everything down and build up again with the basics and this video has made everything so much clearer as to why i struggled so much!

[@jjong-donramsay5937]

i completely agree with you. you just spit facts. this is also my thoughts about math. "if you miss one link in the chain, you will end up lost" this is what i say to everyone else.

[@Thaibodian1]

This would have helped me so much if they had taught us this at school! This is the foundation of how to really master the subject of maths!

[@zhonlino]

THIS IS GOLD!! Been wondering about this all years in school and college. Wonder why no one step in and make the changes

[@goditian2526]

Tell me one thing If it's about math then why is the thumbnail salts?

[@shemmoirichards]

@@goditian2526 yeah it's full of chemical equations. They just chose something "sciencey" for the thumbnail.

[@madeshmadesh9598]

I completely agree with you. The strange thing in math is its so deep and interlinked, hence it turns to be fragile. If the link in the chain is lost the whole chain is lost. Match math with your pace, then maths comes into your pace

[@813ENTERTAINED]

This is true im going through this (currently)!! And I’m in college. it is a must for you to go home and study this stuff on repeat until it makes sense , math builds on itself meaning once you have leaned basic concepts (i.e: multiplication) they can ALWAYS be applied to later concepts

[@psykhe849]

Thank you, sir. I can completely agree with this statement. I, for all of my early life, felt I was just doomed to be bad at math. As I learned, I learned every subject I love comes back to math. I finally decided to at least learn some math. I went in not expecting anything and came out thinking about everything. Once you have the connection with math click, and I do believe everyone can with the right approach, it almost becomes easy. I am saying this as someone who originally thought I could never, ever be good at math. Math is actually really cool, once it starts to click.

[@soumyaneelmanna3097]

This advice is good when you become a Mathematician, not as a student. When you have 3 hours to complete 25 huge sums, you don't deduce everything in your exam. You memorize it.

[@nirasharasangijayalath9273]

If you practice it enough, it just comes naturally when you see a problem. You can't learn mathematics by memorizing the procedure.

[@muhammadridho7680]

Exam sucks

[@howmathematicianscreatemat9226]

@@nirasharasangijayalath9273 well, the reason why my colleagues say that average intelligence (they say „basic“ intelligence) is enough to do university maths, is because to actually pass the exams, you don’t need to be a true bridge builder. You just need to be able to walk over the bridge and use some tools others created. But to be an A student, you need to be able to create some tools yourself. So, if people truly wanna be able to apply it afterwards to all sorts of things which are superficially extremely unfamiliar to maths like specific social work or criminal investigation master/airplane crash investigator, they need to be able to have advanced thinking skills but not to pass…

[@goPistons06]

This video is very useful. I would add one more thing. math is beautiful, and very challenging, so enjoy the challenge! See it as taking a difficult hike, playing Chopin, or learning a new language (which it is, in a way). There is much pleasure to be gained in tackling a challenge meticulously, gradually, and with dedication, and seeing the slow but gradual progress that takes place, until one day you see that you finally reached the top. I have learned much math on my own, and at my own pace, and it gives me great pride and confidence to be able to do it. No matter what your particular case is, try to be able to enjoy this wonderful challenge!

[@gdivya1895]

This is so true.. i missed just 2 weeks worth of classes and could not catch up for the rest of the year . I did not get what I was doing wrong , why I was unable to understand anything. But now I know , I missed the basics and without a solid foundation, any building is doomed to fall.

[@theaminswey9733]

There's a book called A Mathematician's Lament by Paul Lockhart, everybody should read it, especially our kids❤

[@ranjeetkumarom8863]

Where to find it

[@montazmeahii6029]

I just purchased it based on your recommendation.

[@mrborat2493]

@@montazmeahii6029 And what do you think?

[@mjcard]

Why ?What is it’s main premise?

[@rhythmandacoustics]

@@mjcard Argument: Math is hard because of the way it is taught. He uses the analogy of learning to play music. You learn by doing and having fun, and not memorizing notes by notes straight away and make it tedious.

[@iuricpeixoto]

Totally agree, when I was lost in math, i had to learn the basics first, and only after that learn the actual subject that I was studying

[@XIII-TheBlackCat]

Makes sense, I was in a different math class every week in high school/middle school/elementary because I would move to stay with a family member or some teacher thought I wasn't grasping something. I also wasn't allowed to go to the library by myself until I was 15, so needless to say I struggled a lot.

[@exposingthedarknesswiththe9190]

That was well explained and very logical and helpful. It was easy to follow while explaining a link left out can derail an entire train. Something teachers don't have the time to assistant a struggling students, they're simply left behind in frustration. Here is where a teacher's assistant would have a positive impact repaired the link. People don't always grasp these concepts at first, but can with a little help they will. School are not usually structured to give the necessary help when needed, if to have a successful class.

[@coolkid_]

Why is everyone pointing out the thumbnail is Chem not math?! Math can be applied to anything, Chem, bio, physics?! If u had a grocery store cash register as the thumbnail thatd too

[@neildutoit5177]

A chemistry student can enjoy math and be really good at it. But they'd still be a chemistry person. Not a math person. To be a math person, you need to do math for its own sake, not as a means to an ends.

[@alexisxander817]

"when was the war of 1812?" I died laughing! this guy is a genius!

[@ezen.j7438]

I watched this video a while back but now it makes more sense more than ever.

[@Pilgrim182]

Never someone put it like this to me. Great explanation on how important are foundations in math, and how you can lose it on the way; but identifying the problem can make you able to resolve it. Thanks!

[@hibaimene9684]

i love the energy that flows out of this guy he makes me smile ;D thanks for sharing ill try to reconnect with my math luggage and see where i'll lead

[@MrPetoria33]

In my experience, you need to be able to grasp enough of one small part of math to begin to appreciate it and start thinking deeply about it, desiring to know from pure intrinsic curiosity rather than extrinsic goals. Then you will naturally be drawn to other areas of math because its subjects are deeply and surprisingly interconnected. Math is simultaneously art and science: it is intrinsically beautiful; it just takes some time and help to be able to look at it in the right way. All of this is completely and monstrously ignored in conventional schooling thanks to ignorant and shortsighted bureaucrats. Self-learning techniques are really the best option. Even conventional learning with the best teachers must end eventually. Moreover, bad teaching must be overcome via self-learning if the student wants to progress despite failures of the educational system. So I applaud all those attempting to democratize education online and make lifelong learning easier. Thank you for all you do.

[@martinmohammed4087]

I think the key thing I will take out of this is: Stop being anxious about not knowing all the fundamentals very deep but rather be more confident to look up things **recursively** when the time asks for it (to fill in the gaps I do sense). Just in case learning vs just in time..

[@aryan19671]

Thank you ❤️for making this video 🙂Love from India 🇮🇳

[@curtiscarpenter9881]

Like speed reading with literature simplification is a pillar of improving one step at a time.📈📊📑🥇

[@Akkarsollum]

For basic mathematics, everyone could do it with hard work but to actually have a successful path to get a Phd on Mathematics. You need to be a special person to actually understand the patterns and generic rhythm to have a constant success in math problems. That is why you don't see many people with phd in mathematics. Science is different, it is all about discipline. You actually see if you are good in math, if you compete at national level and score 70% in every math test for the competition.

[@Myrslokstok]

Akkarsollum Think so to, it is absolutly the hardes subject. It is technical crazynes. They like to make it accesebly and interesting, but it is hard.

[@howmathematicianscreatemat9226]

Excellent Post

[@RunOfTheTrill]

You dont need to be a special person. Thats literally his entire point.

[@howmathematicianscreatemat9226]

@@RunOfTheTrill he was talking about understanding Highschool maths

[@lilac624]

I understand your point emphasizing the importance of pre-requisites and letting the students learn at their own pace and fill in those gaps.

[@nompond]

I loved how he explained with gestures. It felt like I can picture what he was explaining!

[@rafaelmarroquin4429]

I think like everything u have to practice a lot and really focus on it.

[@bearybearbear7514]

I think what he says applies to me. If I don’t know Algebra 1, I can’t suddenly do algebra 2 and pre calculus algebra. However, not knowing the Protestant revolution won’t prevent me from understanding the fall of the Holy Roman Empire.

[@queenzam]

Your comparison helped me a lot. As a history person, I understand that history is made of the bigger picture to understand the now (not the whole since there is still the future and we know nothing about it) , but with math is about small parts matter. I liked your comparison cause it made me (kinda of) understand maths. Thanks!

[@adamrubinson6875]

Very good video! I completely agree with the underlying message!

[@harisatulaulia300]

Lovely to watch. It has been 1 week since I decided to learn math from scratch. Cause i'm bad at math when I was in school.

[@teev7]

I wish you the best of success throughout your journey 📈

[@ernestoporrascollantes7921]

Most of maths teachers are stupid pedagogues. As far as we keep victimizing the victim (in this case the student) we are doomed. The reality is: bad pedagogy is a recipe for failure, for if a blind man guides another (blind man) both go into the abysm.

[@ChumX100]

Many mathematitians have this anxious tone in their voices, it's like they are exposed to a different abstract world for too long each day and that somehow alters their usual cognitive abilities in a recognizable way.

[@zerge69]

Faster minds.

[@alisonoz7219]

amazing video bro! thank you!!

[@johnadriandodge]

Very nice! Thank you for sharing.

[@spacetimemalleable7718]

I totally agree with Po-shen Loh. The difficulty in math is the chain of dependencies. If one link is poor your understanding is severely hampered. What Loh however neglects is: One must have the DISCIPLINE to go back, FIND AND FIX ALL THE MISSING Links. This takes extreme perseverance. To find all these gaps, one needs also to do as many problems as possible. I.e. HOMEWORK. It aggravates me when schools/teachers are reducing homework and in fact are considering it's abolition. It's analogous trying to be a great athlete but NOT Training at all - egregiously ignorant. So did Stephen Curry or LeBron James just become great basketball players with ZERO practice??

[@BiophysicalChemist]

Most people are turned off by mathematics because it is generally presented in a very dry, abstract manner. One of the pitfalls of modern academia is that everyone is so afraid of being wrong, so much so that we have become overly reliant on pure symbolic manipulation in our obsession for rigour. Instead of using art and creativity to inspire awe for the mystical beauty of the mental realm of pattern and forms, we present the next generation with a piles of uninteresting texts filled with rules and definitions, then expect them to figure out what it _really_ means by themselves. Children build amazingly complicated conceptual frameworks such as language so quickly because they are constantly _playing_ with them, using words and new ideas to explore and interact with a world they find immeasurably fascinating. But once they start approaching adulthood in today's society, upper academia trades awe and wonder for this deathly serious tone, and then we all wonder why so few people have an interest in, much less a true understanding of, mathematics and the physical sciences.

[@gernm18]

Languages are much more interesting than math. Languages require creativity, and allow it. Languages allow you to be wrong, and you have fun with it. Math = not fun. Languages can be taught in a boring way too, with too much emphasis on writing.

[@cx777o]

@@gernm18 but let yourself play with the idea that math can be indeed a language, just on a scale where it expresses everything around us. This would mean math can indeed be fun because you can try to express a phenomenon in a mathematical way and understand the logic behind some actions. It should also not depend on the subject to allow you to be wrong sometimes: its you who is in charge of perspective to allow yourself to get something wrong in mathematics. That doesn't mean you can't work on correcting your mistakes in math as you would do while learning a language.

[@gernm18]

cx777o that is interesting for sure, see nobody ever made me think of math that way. When you say it is like a language it becomes interesting.

[@cx777o]

@@gernm18 glad to hear that i wish you best of luck in exploring maths

[@lx4302]

I agree with your second sentence, damn.

[@curtpiazza1688]

Great pep talk...thanx!

[@id0lv3]

This is absolutely right, I've been suffering from math since primary school until i graduated from intermediate school I've found a teacher that really simplified mathematics and i loved and, i was able to fill up all my holes and now I'm in the last grade of highschool and math is one of my favourites subject along with physics, i got double A+ and tomorrow is my mid term exam and i will hopefully got the A+ along with the other grades.

[@antor.morsalin]

My mind blew when I started doing math my self with the help of online vides . It’s like my iq went from 90 to 140 in a few months . I suddenly started to get top marks in my class and even started understanding other very hard topics easily .

[@mmarvin8332]

How was you're math level before and now how is it going? is there any advice you can give me? because i really don't believe myself... (╯︵╰,)

[@EpistemicPolymath]

Now I feel like what was lacking here is how to properly get started. I definitely feel I have some missing links, but how to find what they are? What are some good resources out there to help myself get back on track and keep moving in the right direction. That would have made this message more powerful.

[@EpistemicPolymath]

+‫كلنت غرام‬‎ ‏It isn't that I am looking for a type. Rather I am trying to go back through from the beginning and make sure I have been learning correctly. But I am trying to become a better logical thinker, programmer, etc so I am interested in whatever will help me accomplish that.

[@218Flows]

go on youtube, search for profrobbob, go to his playlists, select pre-calc, trig, algebra, etc.. start from the beginning, make sure to play the videos on 1.5 speed or so if you want to brush up on stuff you already know !

[@benesgro4531]

Thank you!

[@justinsantos5751]

I'm 16 and I just enrolled at "Kumon," an afterschool math program. The program doesn't teach you directly, but rather you would be given worksheets with plenty of questions to answer, this is where self learning comes in. The worksheets range from level A to O, starting from basic arithmitic up to differential and integral calculus. So basically it starts at the root making it easy to understand further lessons. I started last month and now I'm on level H- Linear/Simultaneous Equations, Inequalities, Functions and Graphs. I tried learning math on the Internet by watching those youtube videos but watching is uninteresting for me than answering on your own. Just search Kumon on google for more info, maybe there is one near you. (Pardon me for grammatical errors, it's not my native tongue.)

[@thavs]

Khan academy is a great place to start

[@merhawitesfaye7780]

Your just explained it very well. Thank you.

[@BibleNerd22]

This was encouragement.

[@freddygill3425]

I totally agree. You can't miss anything in math. If you do, you risk becoming completely lost. But if you systematically build one principle upon the next and stay practiced, math can be a joy! Good day sir!

[@zanetruesdale8336]

this guy has a nice jaw

[@911Salvage]

You forgot to add "No homo."

[@beastbeast4727]

@@911Salvage no homo just gay

[@kravm16]

My man definitely mews

[@vikneshmaniam5618]

Bruh

[@jesuslovesyou7130]

Lol

[@mathewmathewgamba.5823]

Thank you for the information

[@rambleswolf]

I totally agree with him! During school, I lost my way by missing certain key links in my chain. So recently, at the age of 28, I started to teach myself basic Pre-Algebraic Mathematics. A month ago, I didn't know how to do really basic Arithmetic like long division or my 7 times table, but now I'm working through arithmetic operations with ease! Fractions have started making a lot more sense for me too! Hopefully I'll keep this up and eventually get good at Algebra, Trigonometry and maybe even Calculus! 😁

[@wtfquebec]

The thumb nail is chemistry lol

[@thepubliusproject]

This is a wonderful explanation of what math is, especially compared to other subjects. Well done, Dr. Loh!

[@mehulsrivastava6934]

*Thank You Mr. Helpful*

[@MOHNAKHAN]

Very Great Lecture...

[@MrXandervm]

I FULLY AGREE! everybody can be a meth person! you just have to be open minded and try it! btw, anybody here knows how i can get rid of these bugs crawling under my skin?

[@OllihuAkbar]

Xander vM With more meth, of course.

[@FocusMrbjarke]

Xander vM i always liked school because of all the meth

[@dashingmay]

Xander vM can one excel at math if they do meth?

[@tompurcell1499]

I thought Paul Erdős' smoking meth while doing math was a myth.

[@juliusballaran5150]

made mah day bruh hhuahah :D

[@amey777]

I am meth person

[@ylent1200]

Amen

[@sure8247]

You are high....

[@38Fanda]

you should do a tedxtalk

[@sangwaninbox]

hahahaa this made my day ,,,thank you

[@amey777]

@@sangwaninbox 🤣🤣🤣

[@hadjaadam3674]

Wow this is eye opening ,Thank you very much

[@partspieces8165]

Applaud to this guy, breaking it down to the nature of the subject & giving us the confidence back again

[@torquevonthorne948]

Varys, replying to Littlefinger: "No. Chaos is no stair. Math is."

[@IsaacDarcheMusic]

"If they wanted to" is more than one word.

[@warrenarnold]

XD you young man, you young man are good at math

[@cbskwkdnslwhanznamdm2849]

Thank you sir! Greetings from California!

[@MsGnor]

Po-Shen Loh, I love your enthusiasm ❤️ Benoit B. Mandelbroht's beautiful fractals got me hooked on maths.