Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh bigthink
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- Опубліковано 31 лип 2024
- 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.
The Hertz Foundation mission is to provide unique financial and fellowship support to the nation's most remarkable PhD students in the hard sciences. Hertz Fellowships are among the most prestigious in the world, and the foundation has invested over $200 million in Hertz Fellows since 1963 (present value) and supported over 1,100 brilliant and creative young scientists, who have gone on to become Nobel laureates, high-ranking military personnel, astronauts, inventors, Silicon Valley leaders, and tenured university professors. For more information, visit hertzfoundation.org.
TRANSCRIPT
Po-Shen Loh: 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 actually because of that network of prerequisites. You see, math is one of these strange subjects for which the concepts are chained in sequences of dependencies.
When you have long chains there are very few starting points-very few things I need to memorize. I don't need to memorize, for example, all these things in history such as “when was the war of 1812?” Well actually I know that one, because that's a math fact-it was 1812-but I can't tell you a lot of other facts, which are just purely memorized. In mathematics you have very few that you memorize and the rest you deduce as you go through, and this chain of deductions is actually what's critical.
Now, let me contrast that with other subjects like say history. History doesn't have this long chain, in fact if you fully understand the war of 1812 that's great, and it is true that that will influence perhaps your understanding later of the women's movement, but it won't to be as absolutely prerequisite. In the sense that if you think about the concepts I actually think that history has more concepts than mathematics; it's just that they're spread out broader and they don't depend on each other as strongly. So, for example, if you miss a week you will miss the understanding of one unit, but that won't stop you from understanding all of the rest of the components.
So that's actually the difference between math and other subjects in my head. Math has fewer concepts but they're chained deeper. And because of the way that we usually learn when you had deep chains it's very fragile because you lose any one link-meaning if you miss a few concepts along the chain you can actually be completely lost. If, for example, you're sick for a week, or if your mind is somewhere else for a week, you might make a hole in your prerequisites. And the way that education often works where it's almost like riding a train from a beginning to an end, well it's such that if you have a hole somewhere in your track the train is not going to pass that hole.
Now, I think that the way to help to address this is to provide a way for everyone to learn at their own pace and in fact to fill in the holes whenever they are sensed. And I actually feel like if everyone was able to pick up every one of those prerequisites as necessary,
I think this is largely true. In high school, I got behind in my Algebra II class because I was goofing off too much at one point. I never recovered in high school. Everything after in math became nearly impossible for me because I failed to grasp a few key things that were pre-requisites for later things. I began to feel that math was hard and that I wasn't good at it. I would have failed that Algebra II course if not for a soft teacher that gave me a barely passing grade that didn't reflect my actual understanding. But a couple years after high school, I decided to go to college and study chemistry and physics. My math was in terrible shape though. I was completely lost in the first class I took, so I dropped it and switched to a remedial algebra course and then started systematically building up. I acquired the concepts steadily and didn't move forward until I understood everything at each point. I aced each math course after that. I loved calculus! I ended up deciding that I liked math and felt like I was pretty good at it. My whole problem in high school was that I got lost because I was inattentive at one point. My feeling that I was bad at math was erroneous. Math absolutely must be learned systematically. You can't skip steps.
My precalc teacher is hs was really bad but instead of blaming her I watched UA-cam channel organic chemistry tutor and god damn bro saved me
I relate to this so deeply.
Thanks for the point, will remember it
The other problem that may not be widely accepted is that majority of the people are just not that smart to think like that.
You missing a lot of learning time and trying to cramp up at last with the best bank in the buck topics/concepts is not really how learning works.
Fortunately, people have lives to live, so it's not depressing state at all. Unfortunately, it's not the best state of us either.
I noticed that once I started learning at my own pace I actually started to enjoy it and also could understand the subject on much deeper level.
I bet this is the key part of learning everything when it comes to "Learning for Everyone".
Perhaps the realisation that we all see the world different than others is a fact that makes sense.
Unfortunately, we cannot standardize that. What I mean is that if we actually make it standard that we do not have to cross to next class with everybody would make things more complicated. I don't know for the better or worse. In short, a LOT of work has to be done on time if the world needs to move forward.
I wish education evolves into "Personalized education", and a new world may born.
I'm just beginning my mathematics journey as someone in their 30s after really hating it at school, because of my surroundings. I always felt like I 'just wasn't good at it,' but I think it was just the methodology of teaching wasn't working for me. My friend would let me copy in class because I couldn't keep up, but when I was in the exam room, I ended up getting a B+. I think it was also a lack of confidence on my part.
In my 20s, I matured and realised I loved logic puzzles and simple math challenges and decided to start again and study a STEM degree through open learning. I'm starting from the ground up, using resources meant for kids where I need a really simplified explanation, and it's so satisfying when something 'clicks' after struggling. It's early days but it feels like I'm really overcoming a barrier I've had.
I love that you posted this. It gives me so much motivation and reassurance that I'm am not alone. I say this because I am also in my thirties and looking to go back to college for a stem degree. Good luck on all of your endeavors!!!!
Correct, some subjects depend more on historical facts and require more memorization (history, biology), and others are largely understood from a few basic facts (chemistry is my favorite example, as you can make surprising predictions about chemical reactions and the properties of substances from a handful of concepts).
Hello, I am a Bolivian who is learning English and therefore I discovered the UA-cam channel of this math Olympiad teacher, and I admire him a lot, I would like him to read this comment and tell me how to read a math book to learn the most and take notes indeed, or maybe tell me what I need to know to watch your videos
after university I discovered that if I sit down to learn a subject by myself, deciding what is the most basic concept I can think of that is related to that subject and following my own questions and reasonings from there, answering them by looking for info about each one on multiple sources (youtube, wikipedia, books, etc.) and taking notes of every topic I find while building this reasoning, I can learn most things and understand much better. With that being said, I think math is hard specifically because of the reasoning part. Mathematical reasoning is this misterious thing to me, where you are not very sure HOW your brain came up with the answer or the understanding. I don´t think most people is good at math reasoning/understanding.
i thing it's something that requires training, if all your life you have never worked to solve such mathematical problems then you brain is not trained to think like that, but as you practice more and solve more problems, you brain gets better at coming up with approaches and solutions for new problems.
But it does takes time and consistency.
this is the best
You're right! I've started in Reinforcement learning. Which pointed me to probability theory -> measure theory -> real analysis -> set theory.. Not sure when would I be able to get to the other end of the chain.. Though, I try to be resilient ;)
Thank you very much. Very inspirational!!
Kahn academy fills my boys gaps. Sal Khan is one of my heros.
Genius
I found this useful
i took math in the dark ages, more than half century ago....i sat with my granddaughter in her high school math tutor class the other day and was amazed. The way math is taught now does not seem like computation and getting answers clean and simple. There seems to be a way of thinking being forced into the explanation of learning about numbers. It is also obvious logical, ethical, and philosophical thinking are downplayed now as well as history. This seems on purpose because as the gentleman says math makes long chains that depend on the ones each link directly connects to....philosophical and ethical and logical thinking about the many varied areas of life are much more necessary.......math is a pencil drawing no matter how elaborate all lines running along in a path.....but thinking in philosophical and higher ways is like painting with oils and listening to music that influences the picture painted along with how the emotional experience you are having creates the feeling that will be captured in the painting and communicated to the observer. Math has its lane and it is best kept in its own lane
Hey, I'm in the Burgh too!
Like all good things in life it easy to talk about it but difficult to do.
This is what it means to "go back to the basics". If you lack in any area of math, go to that section on the internet, solve as many problems as you can, and continue up the chain
This is such good advice. When I'm struggling with textbooks and their convoluted explanations, I look at videos aimed at beginners or children, go back to the textbook and its much easier to understand.
Practice is key. And don't stop learning math until you're absolutely sure you won't need to come back. Starting over in the middle of a calculus sequence can feel impossible.
Not really an option when taking a course at school
There are new topics every week, especially for course like calculus
You are either on track every single week from the start to the end, or you are doomed
@@rakuuun4582I second this problem.
You need focus to go from being a non-math person to a math person, and the capacity to focus is itself a talent.
pretty damn smart
The problem with people not understanding say Logarithms is because it is a fked up term that doesn't mean anything AND it is put in an expression like a cart that is put BEFORE the horse. It should be another notation with a meaning that is obvious.
3:09 Encontrar un método (Kumon) donde cada quién no se pierda parte de la cadena de contenido que necesita si falta a una clase...la clave está en seguir paso a paso la secuencia, de lo contrario tendrá problemas para seguir aprendiendo.
I second this
Shishen
Terry the math wiz.
this is not terence tao 🤦♂
Went from G to A- in a month because I wanted to
Yes, actually happened
how
@@GoatzAreEpic had few close friends good at maths and at the same time I spam every exercises I can get my hand on within that month. Also watch some maths livestream. I was lucky enough to have local youtuber streaming past year papers.
Tldr, if you want good grades get used to the exam format,
but if you want to get good at maths you need to know why you need to get good at it. In my case, Im taking engineering.
I’ve been looking for a map of prerequisites. Does anyone have a good resource that isn’t a precalc textbook?
What do you mean by prerequisities? Prerequisites for what?
@@laithpi A visual depiction of the chains and of the dependencies of mathematics, for example, the dependencies of machine learning. Machine learning understanding depends on a, a depends on b, b on c, etc. In this way, I think you could see the fundamental building blocks of mathematics.
@@quentin2578 I can't give you a map of dependencies, but I can provide you with brief maps for the topics in each Computer Science and Mathematics, and you can figure it out yourself after some research.
@@quentin2578 Map of Mathematics
ua-cam.com/video/OmJ-4B-mS-Y/v-deo.htmlsi=yzro13d3qQdxTfS_
@@quentin2578 Map of Computer Science
ua-cam.com/video/SzJ46YA_RaA/v-deo.htmlsi=1tfa3V9JgCN-L7Nb
I have Dyscalculia
doesnt exist. You probably also think the multiplication table is to memorize, wrong. It's pattern and its a langauge. Go back to step one and understand it, then build it up
@@satoshinakamoto7253 have you ever talked to a therapist? Because Dyscalculua does exist. And it is hard to memorize, when the numbers flip inside your head.
@@SaraRankins. it doesn't. dyslexia doesn't exist either. The only real psychology is related to biology (to science). The rest is pattern recognition and making up illnesses to justify creating an industry. Most psy. is BS
@@satoshinakamoto7253 you seem like the guy who thinks depression isn't real either
@@SaraRankins. depression is a biological mechanism that tells you something is not right with your life. You're depressed because you're fat and dont have a gf, it's not that depression creates a miserable life, ITS NOT A DISEASE. Same as stress. Stress comes from not addressing something you should be addressing which you have some control over. If you dont address it , stress will occur. It;s not some sort of human mind thing. More on: ua-cam.com/video/MhqFyf3MrPg/v-deo.html&ab_channel=BulldogMindsetHighlights and ua-cam.com/video/qVsa-j7Ig_w/v-deo.html&ab_channel=FreshandFit
The question is, how to fill the tons of holes given the limited time ...
Find a few tutors. In my experience, they will help you understand concepts fast. Hope this helps.
This is why homeschooling is key.
And it's why good attentive parents who are devoted to their children's wellbeing and upbringing create adults who are able to thrive and function well in society.
@@tmc1373 “devoted to their children’s well being”…what planet are you on. Most parents don’t care about their kids anymore than a goat does about theirs. If you did care, then gun laws would be in place and zero tolerance shown to anyone who shoots another unless in proven self defence.
Schools in America are just places to send your kids to get killed and kids who are home schooled have no social interaction so learn nothing and just breed more ignorant Americans.
I agree cuz normal school would just skip stuff even if the kids don't understand it while homeschool you can control your education and learn at your own pace
It’s not easy for the parents who have to work long shifts though.
@@vidfreak727 should of thought of that before having kids. Smart people plan ahead.
The greatest blocks preventing my math is a stupid process and only having a 4.7 puches monitor. The latter sucks
😏
One of the questions I did not want to hear as a math teacher was "What is this good for?" Asking that question shows they do not know the true reason for studying math.
I am glad you were not my teacher. A real Math Teacher would be able to answer that question very easy.
@@hectorr6299 You study math to become a good thinker. Most of history it was thought of that way. For most people Algebra 1 is enough. Most math you will not use. I had to teach about complex numbers without knowing their use. Later, I found they had limited use for electrical engineers. Do you make the same request to your literature and history teachers?
@@hectorr6299 Know you are wrong about real math teachers.
If you ask me (not a math person, not teacher), I would say math is basically we trying to "engineer" our brains.
It's like developing muscles, but you're not exactly developing muscles. Our muscles develop automatically. You are trying to learn techniques and trying to find the best way in a sense to me effective while being efficient with your resources in order to develop muscles.
Why exactly? It depends who you may ask. For an absurdist, it just doesn't make sense to do anything at all.
Anyone? That is simply not true. Aptitudes and lack thereof for different things are a fact of reality.
Everyone has their own strengths. This idea that "anyone" can be good at math is silly.
It depends what we consider "good".
It's like saying the idea that not everybody can "cook" is not flawed. Everybody (with working hands of course) can cook.
Can everybody cook at the level of world class chefs? No.
Can everybody become better at cooking? Yes.
It depends upon objective.
@@IDMYM8 Fair enough.
Math is a tool kit - unfortunately you can't just jump from a hammer to a powertool overnight
Let's be real people, to be a proper mathematician an Iq of 130 or higher is kinda necessary. Meaning, less 2% of the population can be one. Otherwise, have fun to struggle you're all life
There are definitely great mathematicians that don’t have high iqs, they had to work harder that’s for sure
No, not everyone can. If you have 70 IQ you cannot (with almost 100% certainty) be a be a "math person" . It's the hard truth aprox 50% of variance in intelligence is genetic, and can't be changed. The other 50% can hardly be changed.
Intelligence is not only about speed or efficient, above and below certain thresholds there are almost qualitative differences. Below a certain IQ, you simply cannot manage absteact thoughts well enough to do anything more than basic arithmetic.
Good thing majority of the people do not fall in that category, so it's more of a great story of laziness (Maybe that also has something to do with genetic variations?). But yes, retardation is an unfortunate condition.
BRUSH YOUR TEETH.
i have no clue about math!
It cannot be understood and learned at all!