Becoming good at math is easy, actually

Summary

This video script by Han, a Columbia University graduate, dispels the myth that math proficiency requires high IQ or innate talent. Han shares her personal journey from struggling with math to mastering it through active learning and practice. She emphasizes the importance of not just understanding but applying math concepts through problem-solving. Her strategy involves understanding the solution process, attempting problems independently, and using the Feynman technique to ensure comprehension. Han believes that everyone can excel in math with the right approach and mindset.

Takeaways

• 🧠 The common myth that math is only for those with high IQ or natural talent is debunked; becoming good at math is achievable for anyone with the right approach.
• 🎓 Han, the speaker, graduated from Columbia University with a focus on math and operations research, showing that success in math is possible through effort, not just innate ability.
• 📚 Han struggled with math in high school, indicating that early challenges in math do not determine one's potential for improvement.
• 🤯 Math anxiety is widespread, affecting approximately 93% of adult Americans, which underscores the importance of finding effective learning strategies.
• 🔑 The key to becoming good at math is active learning, which involves engaging in discussions, practicing problems, and teaching others, rather than passive learning like listening or reading.
• 📉 Han's initial approach to math was passive, which was ineffective, highlighting the need for a shift to active learning methods.
• 🚀 Active learning has been shown by research to be more effective in math and science education, emphasizing the importance of practice and application.
• 🛑 When faced with a difficult math problem, Han suggests taking a moment to mentally plan the approach before attempting to solve it, which can prevent aimless attempts.
• 🔄 If a problem seems unsolvable, Han recommends looking at the answer, understanding it, and then attempting the problem independently, repeating the process until mastery is achieved.
• 📱 Han uses an iPad for studying math, which offers convenience but also misses the tactile satisfaction of writing on paper, suggesting a balance between digital and traditional study methods.
• 📝 The 'Feynman technique' is mentioned as a way to test understanding by explaining concepts in simple terms, which can help solidify one's own comprehension.
• 🌟 Believing in one's ability to become good at math is the first step, and recognizing that everyone experiences math anxiety is important for maintaining a positive mindset.

Q & A

What is the common misconception about math ability according to the speaker?

The common misconception is that math is for people with high IQ and natural talent, but the speaker argues that becoming good at math is achievable even without these perceived traits.

What university did the speaker, Han, graduate from and what did they study?

Han graduated from Columbia University, where they studied math and operations research.

Why did Han struggle with math in high school?

Han struggled with math in high school because the materials did not make sense to them, and they could not understand what the teacher was explaining in class.

What is the difference between passive learning and active learning as mentioned by Han?

Passive learning involves receiving information from outside sources and trying to internalize it, such as listening to lectures or reading textbooks. Active learning, on the other hand, requires active involvement in the learning process, like engaging in discussions, practicing questions, and teaching others.

Why is active learning more effective in math and science education according to research?

Active learning is more effective because it involves the learner in the process, which leads to better understanding and retention of information compared to passive learning.

What is Han's approach to practicing math problems?

Han's approach involves first mentally walking through the problem, looking at the answer if they don't know how to start, understanding the solution, and then attempting the problem independently until they get it right.

Why does Han suggest giving up on a problem if you don't know where to start?

Han suggests giving up on a problem initially to avoid frustration and time waste. Instead, they recommend understanding the correct answer and then attempting the problem again to learn from the process.

What is the 'Feynman technique' mentioned by Han?

The Feynman technique is a method to test understanding by explaining a concept to someone else, ideally someone without much background on the topic, using simple language. It helps to ensure that the explainer fully understands the material.

How does Han feel about the belief that everyone can become good at math?

Han strongly believes that everyone can become good at math, emphasizing that math anxiety is normal and that understanding and practice are key to overcoming it.

What is the importance of understanding the fundamental knowledge in math according to Han?

Understanding fundamental knowledge is crucial because new concepts in math are built upon previous knowledge. Without a strong foundation, it's difficult to grasp more advanced topics.

How does Han describe the transition from a 'slow brain' to a 'fast brain' in terms of math problem-solving?

Han describes the transition as a process where through repeated practice, the conscious and slower reasoning brain becomes internalized, allowing for faster, intuitive problem-solving that feels like second nature.

Outlines

00:00

🧠 Overcoming Math Anxiety Through Active Learning

The speaker, Han, challenges the stereotype that math proficiency is solely a product of high IQ and natural talent. Drawing from personal experience as a Columbia University graduate in math and operations research, Han recounts struggling with math in high school due to a lack of understanding and self-confidence. Despite being labeled as 'naturally smart,' Han emphasizes the importance of active learning over passive learning, which involves engaging in discussions, practicing problems, and teaching others. Han explains that active learning has been proven more effective in math and science education, and encourages viewers to practice math problems as a means to truly understand the subject, rather than passively trying to comprehend it.

05:01

📚 Effective Math Practice Techniques and Tools

Han introduces a method for practicing math problems that involves initially giving up on a problem if it's too challenging, then studying the solution, and attempting the problem independently until it is mastered. This approach is highlighted as efficient and effective for learning. Han also discusses the benefits of using an iPad for studying math, including the convenience of not carrying heavy books and the ability to organize notes digitally. The speaker then transitions into a sponsored segment, endorsing 'Paper-like' screen protectors for the iPad, which provide a paper-like writing experience, and mentions the ergonomic benefits of the 'Note-er' collection and cleaning kit for maintaining a clean screen.

10:02

🌟 Cultivating Intuition and Mastery in Math

Han emphasizes that understanding math is not about memorizing steps but grasping the underlying logic. The speaker suggests using the Feynman technique, named after Nobel laureate Richard Feynman, as a way to test comprehension by explaining concepts in simple terms, ideally to someone unfamiliar with the subject. Han encourages viewers to believe in their ability to excel in math, acknowledging that math anxiety is common and that everyone can improve with the right approach. The speaker explains that math is built on layers of knowledge and that gaps in understanding can cause confusion, advocating for a strong foundation in fundamental concepts to facilitate learning and problem-solving.

15:04

🚀 Transforming Slow Brain to Fast Brain in Math

The final paragraph discusses the transition from conscious, slow brain processing to fast brain intuition through practice and familiarity with mathematical concepts. Han illustrates this with the example of recognizing a cat instantly due to pattern recognition, suggesting that the same process applies to math when fundamental concepts become second nature. The speaker concludes by encouraging viewers to practice and internalize math concepts to the point where problem-solving becomes intuitive, and to believe in their potential to excel in math, leaving viewers with a positive message to like, subscribe, and look forward to the next video.

Keywords

💡Math Anxiety

Math anxiety refers to the feeling of tension, apprehension, or fear that individuals may experience in relation to math. In the video, it is mentioned that approximately 93% of adult Americans have experienced some level of math anxiety. The script emphasizes that overcoming this anxiety is a crucial step towards becoming proficient in math, as it often stems from negative experiences and a lack of confidence in one's math abilities.

💡Passive Learning

Passive learning is a method of learning where information is received from external sources, and the learner attempts to internalize it through activities like listening to lectures, reading, or watching demonstrations. The video contrasts passive learning with active learning, suggesting that the former is less effective for mastering math. The speaker shares their own experience of passively trying to understand math without success, highlighting the need for a more engaged approach.

💡Active Learning

Active learning is a learning approach where the learner is actively involved in the learning process. This can include engaging in discussions, practicing problems, and teaching others. The video emphasizes the effectiveness of active learning in math and science education, stating that it is more effective than passive learning. The speaker shares their realization that practicing math problems actively, rather than passively trying to understand them, was key to their improvement.

💡Practice

Practice, in the context of the video, refers to the act of repeatedly working on math problems to improve understanding and proficiency. The speaker argues that becoming good at math is about practicing a lot of questions rather than trying to understand concepts solely through reading or listening. The script provides a personal anecdote about how the speaker transitioned from passive to active learning by practicing questions, which led to a breakthrough in their math abilities.

💡Fundamental Knowledge

Fundamental knowledge refers to the basic concepts and principles that form the foundation of a subject, such as math. The video explains that a lack of understanding of fundamental knowledge can lead to confusion and a sense of being lost in more advanced topics. The speaker suggests that building a strong foundation in basic math concepts is essential for overcoming math anxiety and improving proficiency.

💡Procrastination

Procrastination is the act of delaying or postponing tasks or actions. In the video, the speaker admits to procrastinating when it came to studying math or doing math homework due to the negative experience of not being able to solve problems. Procrastination is presented as a barrier to learning and improving in math, which can be overcome by adopting a more proactive approach to practice.

💡Intuition

Intuition, in the context of the video, is the ability to understand or know something immediately, without the need for conscious reasoning. The speaker discusses how people who are good at math often rely on their intuition, which comes from having practiced and internalized fundamental concepts to the point where they become second nature. This intuitive understanding allows for faster and more efficient problem-solving.

💡Conceptual Understanding

Conceptual understanding refers to the ability to grasp the underlying principles and ideas of a subject, rather than just memorizing facts or procedures. The video emphasizes the importance of understanding the logic behind each step in a math problem. The speaker shares their method of learning by first understanding the solution to a problem and then practicing it independently until they can solve it on their own.

💡Efficiency

Efficiency, in the context of the video, refers to the effectiveness and economy of effort in learning. The speaker advocates for an efficient use of time by not spending too much time trying to figure out a problem independently but instead looking at the answer to understand the correct approach and then practicing it. This method is presented as a way to maximize learning and minimize frustration.

💡Fireman Technique

The Fireman Technique, named after Nobel Prize winner Richard Feynman, is a method for testing one's understanding of a concept by attempting to explain it in simple terms, as if to a child or someone with no background knowledge. The video suggests using this technique to ensure that one truly understands a math concept, as the ability to explain it clearly indicates a deep level of comprehension.

💡iPad

In the video, the speaker mentions using an iPad for studying math, taking notes, and doing homework and practice questions. The iPad is presented as a convenient tool for digital learning, allowing for easy organization and access to materials. However, the speaker also acknowledges the satisfaction of writing on paper and discusses using a screen protector that mimics the feel of paper to bridge the gap between digital and traditional learning methods.

Highlights

Math proficiency is not solely dependent on high IQ or natural talent.

The speaker, Han, graduated from Columbia University with a focus on math and operations research.

Han experienced difficulties and frustrations with math in high school, despite being a good student.

Approximately 93% of adult Americans have experienced some level of math anxiety.

Han discovered a method to become good at math that involves active learning and practice.

Passive learning, such as listening to lectures, is less effective than active learning for math.

Active learning involves engaging in discussions, practicing problems, and teaching others.

The importance of practicing math problems to learn how to use math effectively.

Han's personal method of practicing math involves understanding the solution before attempting the problem independently.

The use of an iPad for studying math, taking notes, and doing homeworks.

Paper-like screen protectors and notaker collections enhance the digital study experience.

Efficient time management is crucial when practicing math problems.

The misconception that looking at the answer first equates to memorization rather than understanding.

The Feynman technique as a method to test and ensure understanding of a concept.

Believing in one's ability to become good at math is the first step to overcoming math anxiety.

The importance of foundational knowledge in math and how gaps in understanding can affect learning.

The role of the 'slow brain' and 'fast brain' in learning and understanding math concepts.

The transformation from conscious reasoning to intuitive understanding through practice.

Encouragement to like and subscribe for more helpful content on math and learning.

Transcripts

so you want to become good at math based

on all the movies and shows we were told

that math is for people that have high

IQ and natural talent but actually

become good at math is pretty easy even

if you don't think you have the math

Gene so take me as an example my name's

Han I graduated from Columbia University

I studied math and operations research

because I majored in math and I got

pretty good grades some people assume

that I was naturally smart little did

they know I was filling my math classes

in high school but the materials just

didn't make sense to me I couldn't

understand what the teacher was talking

about in the class I remembered that

every time when I ask for help I can see

the frustrations in their eyes because

I'm just so confused being defeated by a

math problem and just constantly looking

dumb really didn't help my

self-confidence I always procrastinated

in terms of studying math or doing math

homework back then because I know that

every time I try the problems I just

couldn't figure it out no matter how

long I tried and that's just such a

Negative experience so I end up like

always tried to avoid doing math

homeworks and just this thought of going

to math classes make me nervous because

being in a classroom and couldn't do

anything else but just listening to the

teacher explaining things that I have no

idea what's going on was such an

emotional draining thing and turns out I

was not alone approximately 93% and

adult Americans indicate that they had

experienced some level of math anxiety

you know what even though I was so

terrible at math when I was in high

school one day something just clicked

and I finally felt like I cracked the

secret Cod of becoming good at math so

for context let me explain what I was

doing back in high school I would try to

pay attention in math classes and take

all the notes that I can take and I

spent lots of time looking through

textbooks and I would really try to

understand those math problems well I

sounded like a hard worker right but

something must be wrong when you spend

all that time trying really hard but

just have no result so little young H

just thought oh I must be stupid but

that's so far away from the truth the

say is stop always trying to understand

math but actually all you need to do is

to practice so back in high school all I

was doing was passive learning and

basically no Active Learning so passive

learning B basically means you receive

information from outside sources and you

try to internalize it such as listening

to lectures or reading or watching

demonstrations so Active Learning on the

other hand means you have to actively

involved in the learning process like

engaging in discussions practicing

questions and teaching others and

there's so many research shows that

passive learning are not as effective as

active learning in math and Science

Education so in real life we use math to

help us solve problems like calculating

how much tip you should live and in

school they test your MTH skill by

asking you to solve math problems so

either way you need to know how to use

math by practicing it you wouldn't say

you can drive a car just by watching

someone else drive and remembering all

the traffic rules you have to get into

the car and practice so you really don't

have to spend a lot of time trying to

understand math by reading it's like

understand all the mechanism of how a

car move what really matters is you know

how to drive so if you want to be good

at math all you have to do is practice a

lot of questions but there is a reason

why lots of people don't like math

because when you go practice questions

you either don't know where to start and

you're just completely confused or maybe

you can start by doing the question and

you go check out the textbook and you go

back and forth and you spend a lot of

time in just one thingle question

question and eventually you still get

the question wrong that's just such a

Negative experience I have personally

experienced this so many times let me

tell you nobody likes that this

experience will only make you feel

frustrated and defeated so let me share

with you my favorite ways of practicing

a question that doesn't make you feel

like you want to stab yourself with a

fork so when I encounter a question I

don't start writing immediately instead

I will take a couple moments to mentally

walk through how I'm going to solve it

if I have no idea how to solve the

problem I will just give up yes you

heard me right I will just give up

instead I will just go look at the

answer of the question I take time to

thoroughly understand the answer and its

Approach at each step once I've grasped

the solution I set the answer aside and

try to solve the question on my own and

I will write each step down this time I

won't give up too easily I will make a

genuine effort to applied what I just

learned from the answer and once I

complete the solution I compare it to

the answer key once again if I realize

I've dant incorrectly or I'm stuck at a

point that I can't quite recall I would

just repeat the process understand the

answer then attempt the question again

independently until I get it right so a

couple reasons of why I think this way

of practicing a question is really

really effective okay I just want to

take a quick break and share that I

basically only use my iPad to study math

take notes and do all the homeworks and

all the practice questions on my iPad

the great part of using my iPad to study

is that I don't have to carry all the

papers and the books and pencil with me

all the time and I can like copy and

paste all the notes that I want and also

I have just so many materials in there

but the only downside is that I kind of

miss writing on paper you know there's

just something satisfying about writing

on real paper with a real pencil that's

why I was so excited to discover the

sponsor of this video paper like paper

like is this really cool screen

protector it makes my iPad screen feels

like a piece of paper so when I write on

it I get the feeling back it's basically

the best of both World digital paper

that feels like real paper during exam

season sometimes I would write on my

iPad for like 12 hours a day and my

hands like get sore at the end but with

paper like it just makes using iPad much

more comfortable they have this notaker

collection that also has this little

pencil grip in them which I really like

because they just like make holding the

iple pencil much more ergonomic and

comfortable this collection also include

a little cleaning kit that makes keeping

your screen clean Super convenient you

can just spray this to your iPad and you

can just wipe it and clean your iPad

which is just so so cool I genuinely

think that paper leges just make my

workflow much more enjoyable and just

helps me be more productive so check out

paper like use the link in my

description and thank you so much paper

like for spons answering this

video so a couple reasons of why I think

this way of practicing a question is

really really effective at really safe

time and I think it's a really efficient

way of using your time so instead of

spending a lot of time trying to figure

out a question on your own and you might

not even on the right track you might be

completely in the wrong chapter you

could have used that time to practice

like multiple questions and I'm not

saying that there's absolutely no value

of trying really hard to figure out the

question on your own all I'm saying is

that if you look at a question and you

don't know how to do it and you probably

will spend a lot of time going back to

the textbook and trying to figure it out

on your own you could have used that

time to actually look at the correct

answer and try to understand the correct

way because the purpose of practicing a

question is to learn from this

practicing session so it really doesn't

matter if you get the question wrong or

right the first time when you try this

answer it really matters is are you

moving on before you actually know how

to answer the question compared to those

scenarios first is that I did a question

I got it wrong and I got so upset so I

move on or the second one is that I know

I probably can't do it independently

then I look at the answer and I learn

every single step and then now I do the

question again and this time I try

really hard so I know how to actually do

the question so instead of spending the

majority of the time in trying to figure

out the question on your own spend the

time on you know you can actually do

this question the key is that don't move

on to the next question until you can do

the question independently on your own

you are 100% checked that you know how

to do the question don't try to just

understand math by reading it you should

make sure you understand the questions

by practicing it and distribute your

time more efficiently another common

concern is that oh if you just look at

the answer and you do the question

you're just memorizing it you don't

actually understand the question so the

way I think about it is that if I

actually understand the math then I

understand the logic behind it example

for a question it's given a and the

answer is d i know the logic behind each

step I know given a it should lead to B

and I know given B it lead to C and

given C it lead to D well if I'm just

memorizing it I probably will just

memorize oh given a then D so the

fireman technique which is famous

technique that help people to understand

things better it's invented by Nobel

Prize winner Richard fan it basically

means that if you want to test yourself

whether you fully understand something

you explain it to someone else ideally

that someone doesn't have lots of

background on what you're talking about

imagine you're explaining it to a child

and if you can really explaining

everything using the simplest language

then you fully understand this thing I

use this technique sometimes I just

pretend I'm teaching someone else or

it's actually even better when someone

asking me a question I would just try to

explain it to them that's a really good

way to test whether you fully understand

the question or not and a thing that I

always say is that you might think that

you're bad at math but you actually

you're not I truly truly believe that

everybody can become good at math and

everybody experiened some level of math

anxiety and that's completely normal

even though I study some pretty high

level math in college and I still had

the same feeling as before sometimes if

I skipped the one class I couldn't

understand the next class completely the

first step of becoming good at math is

to believe that you can become good at

math and whatever you're experiencing

that's completely completely normal just

the nature of math it has layers that

you cannot skip so when you feel like

sometimes you don't understand math why

it doesn't make any sense because each

New Concept each new topic is built on

its previous knowledge for example if

you want to learn calculus you have to

learn pre-calculus first which means you

probably need to learn algebra geometry

and gometry and all those subjects has

its own fundamental knowledge as well

and all those knowledge basically can

form a giant Network and this is also

why school have prerequisites for stem

subjects so if you feel very lost in

your Calculus class and you're very

confused why the teacher jump from one

step to another step and everyone else

seems like oh they just understand it

and you have no idea what's going on

it's probably because that's like a

concept note that you're missing and

they assume you have the background so

they don't always explain it and when

you're like facing a new problem or like

you're learning A New Concept and you

felt like you're slower than everyone

else it's not because you're stupid or

anything it's probably because you're

not familiar with all the fundamental

knowledge enough it's because you're

probably passing at each step and trying

to understand at each step trying to

make sense to yourself while someone

else that's really familiar with all

those concept they can just like jump

through those and then without even need

to think too hard about it your brain is

always working and it's slower in terms

of like reasoning processing and

conscious thinking like when you heard

most of things the first time you your

brain is trying to understand them have

you experienced something like you read

a book and every single word is going

into your head but after like a couple

sentence and then you realize oh shoot I

actually didn't read anything and you

have to read the sentence again because

you were not processing them you're not

using your conscious brain to think them

and this part of your brain this slow

brain you're using is when problem

solving and reasoning happened and on

the other hand we also have this fast

brain that we relies on recognizing

patterns and intuition thoughts or like

gut feelings you really don't need to

even think about about it and your brain

just automatically processed it for you

really really fast before you even

realized it for example like this is a

cat do you really need to think about oh

what is this I have seen this before

what is this oh oh I remember I saw it

last time somewhere and then you're like

oh that's a cat no you really don't need

to do that because you have seen a cat

so many times before so now you see a

cat before you even realize it your

brain already knows it similarly in

terms of math if I ask you what is 1+

one you will know it's two you don't

need to think hard about it so when

someone is really good at math

especially the people that are really

fast with math they had more experience

in terms of all those Concepts they just

practiced it so many times and lots of

the basic concepts like geometry or

algebra they don't even need to think

hard about it so when they're learning a

new topic they brain is automatically

relies on all those fundamental topics

that they know so well so they takes way

less time to process to excel math all

we need to do is combine those aspects

so basically by practicing and using our

conscious brain so many times that it

becomes second nature to our brain that

it already internalized that we don't

have to do the reasoning and processing

anymore that's when we transform form

our slow brain and all the efforts to

fast brain and intuition so next time

when you see a problem your brain will

immediately recognize the familiar

elements and put together a solution for

you so if you think this video is

helpful please hit the like And

subscribe button thank you so much for

watching I will see you next time

bye-bye love you