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

Anyone Can Be a Math Person Once They Know the Best Learning Techniques | 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, filling in any gap they have,
mathematics would change from being the hardest subject to the easiest subject. I think everyone is a math person, and all
that one has to do is to go through the chain and fill in all the gaps, and you will understand
it better than all the other subjects actually.

100 thoughts on “Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh

  1. Not many think that memory parts a essential parts of programming and Maths ?
    What Memory and maths ?
    Maths and programming both Involved Intelligence but Memory plays a key role ,because in maths and programming you have to chain the smaller concept to solve the bigger . This chaining of smaller parts is where memory is involved.

  2. 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.

  3. I kind of disagree. I was good at math all the way up in university until I got to courses like intro to real analysis. For the life of me I couldn't come up with the proofs myself for the exercises. I could understand given time and study a proof but coming up with it myself, even after hours of staring at the exercise I couldn't do it.

  4. This is so true…I was very poor in mathematics till 7th grade(So poor that I wanted to take arts in senior high school )…In 8th grade I started talking extra mathematics classes..Our tutor used to beat the shit out of us when we used to make mistakes….Eventually I ended up qualifying at maths olympiad at national level without even knowing the syllabus for the exam…

  5. I really, really love maths but I'm weak at it. I did 'miss a link' in the chain during my senior school years. I was not afraid to ask questions but I came to realise that my maths teacher had selected a small group of the very brightest, who would set the pace. I fell behind and there was no way back. Exams fail.
    I took my exam as a mature student and passed but I'm still not good at it.
    I would love to get better, even now, because when on those occasions I see numbers working, I am motivated to do more.

  6. Maybe that's why I like immunology, it's a chain of logical sequences…


    And the reason I'm bad at mathematics is because I'm lacking the fundamentals?

  7. except when you are studying calculus in Russia and the professor is always pissed off because you can't integrate in your head then math isn't easy or fun….

  8. I think most people say to themselves, "Why bother, when the set-theoretic foundation of mathematics is riddled with antimonies, and the entire structure could collapse at any moment. Sure, it would be different if there were an organized push to replace set theory with quotient-set theory as the foundation, but due to complacency and normalcy bias, that's not going to happen. So I'll just check Instagram instead."

  9. The problem with math is that many people don't end up using it. Especially algebra. I've talked to many successful people and they all agreed that most of the math being taught in high school and in college are a waste of time. Math has also been proven to be the one subject that drives people of school.

  10. Ugh.. missed a day where we learned long division in the fourth grade and that devil of a woman refused to help me learn. That ONE day set me back for a very long time. I didn't catch back up until junior year in HS! smh

  11. I've struggled with math until college where I majored in Anthropology and had to take linguistics. Anyone who's ever struggles with math should know that math is just language of value, in order to learn a new language you must memorize certain values (numbers) and tools (deduction, line graphs, equations are all just devices or tools for value) within math. Language itself is how we communicate specific value (thoughts and ideas) into others, without miscommunication.

  12. “I am not a math person” follows from poor numeric fluency at a young age. Many students in America are given a calculator before they develop their numeric fluency. This is similar to using a crutch before they learn to walk and then give up trying to run. It’s also like trying to grasp a compound sentence when they have only a rudimentary grasp of the meaning of some words in a language. In sports, if you are bad a technique you work on it outside of practice on your own. The same goes for math skills and that is where the caveat comes in. Students are taught they should be able to do all their work at school in class. That is a disservice because it gives them the impression that they must be stupid in this area if they can’t. It’s unfortunate, but that is how kids think, and some adults.

  13. 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

  14. Take Sufficient time to Learn Algebra, and you're going to have the great power of Reasoning. Learning Maths is like Playing the Most Challenging but Interesting Game. When you lose don't be frustrated, Take more time (But Carefully Reviewing those procedures you moved through.) Compare Worked Examples "But least". Don't take to Much Worked Examples as they might be tedious and may let your mind depend much more on them. Maths if Funny, if you find the right way to go through, No Concept is Difficult as they interact and depend on each other.

  15. Dear math
    Please stop asking me to find your x
    You need to move on.

    Dear math
    Please stop asking me to solve your problems , grow up and solve them your self.

  16. Actually history works on cause and effect. Miss a week, impair your deductions for the next week's. Example: Rusia fought Austria. Austria won. Why? Cuz they fought and lost badly to Germany before and French was backing up Austria and they were at their peak. Very simple to make the links. History is a story you can create even if you don't have answers yet simply by going back in time. Understand that and you can go for a failing student at that subject to talking more than the teacher each class, by weaving the historical tapestry that leads to future events. Take it from experience and good luck ^.^

  17. Seeing math as a squence of presuppositions and consequences is definitely an integral part of mathematics, but that doesn't mean that no requisite would be required to learn it. On that front, I think have a good understanding on how to tackle higher math can be helpful, and this visual guide kind of illustrate how: mathvault.ca/10-commandments

  18. Whatever he just said is so true….
    I face this trouble everyday
    For example I want to solve definite integral problem I need progression(a lot of algebra) concept I need trigonometric function understanding, exponential function, logarithmic function… In the end limit and definite integral understanding.,….
    Actually Mathematics is a subject which is extremely related with its own components….. In the above said situation if you don't know one component it could be difficult to solve a problem, you would think math is difficult.., but if you know all the components…. Math is easy and beautiful…

  19. Isn’t it the language of science ? The language of the invisible driving force of this wonderful mega living organism we call “ life” ? Math is magic

  20. 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??

  21. Absolutely right, about the "chain". Miss a few history lessons, you can still understand the rest. Not so with maths. In my first year of secondary school I started to not understand what was being taught. Weeks went by and it got worse. I got nothing but bad marks. By the time they realised I had a real problem I was at the "bottom" of he class, with marks averaging 2 to 4 out of 20. I never recovered. I understood nothing in Maths lessons, I dreaded them, maths was a threat (of not getting into University), and it was a constant source of bad marks. I realised that results were the same whether I made an effort or not, so I gave up, became bored and loathed maths.
    To this day, more than half a century later, I still do, and my level is still what it was when I started secondary school, aged 10.
    On the other hand I doubt whether everybody can really be a "maths person". Some of us are better than others. But most people seem to be able to achieve levels higher than mine.

  22. Totally correct. I could never do even the most basic of Maths. But because I want to learning fashion design I need to understand measurments and some Algebra. I started purchasing Math workbooks where the sums and problems are written out. I have now become addicted to Maths. I am learning and working hard at home to get to grips with it. how I wish I would have did this at school/

  23. …and yet,.today society wads up youth and tosses it into the giant wastebasket called, " Guidelined Education. "

  24. I agree, there needs to be a math diagnostics tool that helps you identify your problem areas to fill in. Maybe a math learning program that tests your skills of independent concepts.

  25. You don't have to "memorize" anything in math if you're exposed to amounts of things prior to language(naming those amounts). And what is easier, to describe a shape of a leaf(geometry), or it's structure, elements, properties, colors, photosynthesis in it, and so forth(cytology, botany, chemistry, whatever else)…??? And digits are not numbers =P….even if you put several in a row, it's a compound numeral(representation, that's why you can do it in, say, roman numerals). There's only a little "tough" part in arithmetic and then algebra – numbers are not perseptible, you can't see them or touch, or smell =D…your thinking has to gradually climb up to purely conceptual level, without physical references, and again, if done step by step you go with ease. It's tough if too much and too fast is thrown at you…. Hope this encourage s someone.

  26. I want to preface this with the statement that I am 100% certain that Po-Shen Loh knows much more about everything he is talking about that I do. But screw it, this is the internet and I have an opinion!

    Rather than asking students to learn at their own pace in order to make these long chains of deductions that form the foundation of all mathematics, I personally like the idea of integration of those chains as a reinforcement. What do I mean by that? I'm glad you asked.

    I think we should be teaching the concepts of every high school math course as early as 4th grade but no later than 6th. That means connecting geometric postulates to the concepts of arithmetic. An example would be connecting the area of rectangles to your multiplication tables. Another might be connecting circles to both multiplication and division while also bringing up some basic concepts of algebra. This would be a good time to start talking about circles and angles in terms of radians. Once you've introduced and begun speaking in the language of these concepts, kids have the context necessary for trig/pre-calc. But rather than go that route, we should just start sprinkling in trig and calc wherever we can.

    Talking about functions in algebra? Show their power using calculus. Show that areas are connected to slopes. Blow some minds. When you're graphing functions and talking about slopes… introduce the dy/dx notation, at least. Doing some trig? Emphasize the connections between triangles and circles. Throw some imaginary number plane situations at kids and use that to demonstrate that dimensionality is arbitrary. That's pretty useful to have in your back pocket later.

    Doing some analysis? Maybe solving multiple equations at once in algebra? Introduce linear algebra. Introduce matrices. Introduce the spacial component of linear algebra to some 13 year olds. They won't hate you. I promise. Statistics? Plenty of connecting tissue between stat and calc to be exploited in certain settings.

    Just saying, rather than assume the way we've been teaching it so far is the only way, it's worth thinking about how to reinforce those fragile chains by turning them into loops.

  27. I agree, people learn best when they get to learn at their own pace, unfortunately, that concept is foreign to colleges. Frankly, I hated mathematics in college, but I'm excited to do some self-teaching during the summer.


  29. A chain of superimposed learning concepts (curriculum of interwoven sequences) is the technically appropriate approach to an understanding of the temporal loop-coordination superposition conception.

  30. too summarize, i think, math requires a more linear thought processing in the more you distance yourself from formal science the more the thought processing will get non linear..

  31. I guess i’m in the minority but i’m actually pretty good at Math ( specifically Multiplication and Fraction ) but it’s also my favorite subject, my tip for people having trouble, all you need to do is improve your critical thinking and understanding. You need to higher your attention span and listen to your teachers or professors, if you know the instructions, you can easily solve problems ( Math is unique because you don’t need to memorize stuff unlike other subjects, all you have to do is understand the instruction then bam, you can solve various problems ).

  32. Being good at math is exclusively based upon genetics. Some people get it naturally and it is entirely impossible for others. It's just nature.

  33. Math is subject in which you mug the method and practice to become master

    But other subject like physics is theory in which you apply logic and imagination to become master

  34. I was once bad at math, because i simply didnt care. I understood math perfectly fine, i just never practised or did old exam papers. But this year i started to do alot of past papers and practise problems. I started to make a math note book, and i went from being near below avrage. To get the highest grade possible in math🤭 so i realized that i always loved math, but because i didnt give a damn. I obv got bad grades.

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