The math study tip they are NOT telling you - Ivy League math major

Summary

In this video, Han, a math and operations research graduate from Columbia University, shares his journey from struggling with math in high school to excelling in it. Despite initially hating math and performing poorly, Han discovered a new approach to studying: instead of struggling alone, he learned to understand and internalize answer keys before attempting problems himself. This method boosted his confidence and efficiency, leading to significant improvement. Han emphasizes the importance of practice and understanding fundamentals, encouraging viewers to tackle math challenges with a positive mindset and effective strategies.

Takeaways

• 😌 Han, the speaker, overcame a significant struggle with math and now excels and enjoys it.
• 🎓 Han graduated from Columbia University's engineering school, majoring in math and operations research.
• 🤔 People often assume intelligence is the key to math success, but Han's story challenges this notion.
• 🏫 Han was originally from China and initially chose the liberal arts track due to a poor understanding of math.
• 📚 Han's first high school math test was a failure, scoring significantly below the class average.
• 🔄 Han's initial approach to difficult math problems was ineffective, leading to frustration and a lack of progress.
• 📉 Han's negative attitude towards math created a cycle of avoidance and poor performance.
• 🛑 In college, Han adopted a new strategy: understanding the answer key before attempting problems independently.
• 💡 Han emphasizes the importance of grasping the answer key's approach and then applying it to solve problems on one's own.
• 📈 This method is more effective as it builds confidence, saves time, and leads to a comprehensive understanding of the material.
• 🔗 Han explains that math has its own barriers and requires understanding foundational concepts to make sense of advanced topics.
• 📝 Han suggests finding practice problems with thorough answer keys and working through them to identify and fill knowledge gaps.
• 🔢 Han recommends doing at least 20 practice questions daily to solidify understanding and improve math skills.
• 📈 Han's personal experience shows that with consistent effort, one can transform from struggling with math to excelling in it.

Q & A

What initially caused Han to struggle with math?

Han struggled with math initially because he found the content difficult to understand and couldn't follow the teacher's explanations.

How did Han's performance in math during high school affect his self-perception?

Han's poor performance in math led him to believe he was not smart and caused him to develop a negative attitude toward the subject.

What track did Han choose in high school and why?

Han chose the liberal arts track in high school because he was bad at math and science, finding them too difficult.

What change in strategy did Han adopt in college to improve his math skills?

In college, Han changed his strategy by thoroughly understanding the answer keys before attempting to solve problems on his own, which helped him grasp the concepts better.

Why does Han believe it's important to understand the answer key before attempting to solve a problem independently?

Han believes understanding the answer key first is crucial because it provides a correct approach to solving the problem, which helps in learning the right method and avoiding frustration.

How did Han’s new approach to solving math problems improve his performance and confidence?

Han’s new approach led to a sense of accomplishment and boosted his confidence as he was able to solve problems correctly on his own after understanding the answer keys.

What advice does Han give for dealing with difficult math topics?

Han advises thoroughly understanding the fundamental concepts and answer keys, practicing regularly, and seeking relevant practice problems with detailed answer keys.

How did Han manage to become one of the best students in his math class?

Han managed to become one of the best students by doing extra hours of math problem sets, in addition to his homework, and by consistently using his new approach to understand and solve problems.

What is Han’s opinion on the importance of paying attention to lectures and doing homework?

Han believes that paying attention to lectures and doing homework are still essential, even if one adopts his strategy of understanding answer keys first.

What analogy does Han use to explain the difficulty of learning new math concepts compared to other subjects?

Han compares learning new math concepts to learning about historical figures, noting that math requires understanding all its fundamental concepts, whereas historical figures can be quickly understood with basic information.

Outlines

00:00

🤔 Discovering a Hidden Math Talent

Imagine waking up one day with an unusual sensitivity to numbers, making math problems seem intuitive. This scenario is contrasted with Han's real-life struggle with math despite graduating from Columbia University's engineering school. Han shares his background, revealing that despite popular belief, he struggled with math growing up in China. He chose the liberal arts track in high school due to his difficulties with math and science. Despite initial failures and a low math test score, Han eventually became proficient in math through persistent effort and a strategic approach to problem-solving.

05:02

🔄 Transforming Math Frustration into Mastery

Han explains his approach to overcoming math difficulties. In high school, he would spend significant time trying to solve problems, often getting them wrong and feeling frustrated. In college, he developed a new strategy: understanding the answer key thoroughly before attempting the problem independently. This method allowed him to learn the correct approach, boosting his confidence and saving time. By repeatedly practicing this way, he gained a comprehensive understanding of math problems and their solutions, ultimately transforming his frustration into a sense of accomplishment and intellectual growth.

🔍 Understanding Math's Unique Challenges

Math often feels incomprehensible due to its technical barriers, unlike subjects like history or literature. Han illustrates this by comparing the ease of understanding historical facts to the complexity of grasping mathematical concepts like linear programming. The key to mastering math is recognizing the foundational knowledge that underpins new concepts. Gaps in understanding often stem from missed lessons or pre-requisites. Han advises addressing these gaps by working through practice problems and understanding answer keys to build a solid foundation, transforming confusion into clarity over time.

📚 Effective Strategies for Mastering Math

To overcome math challenges, Han recommends a focused practice strategy. Find relevant practice problem sets with thorough answer keys and commit to solving at least 20 questions daily. This targeted practice helps identify and address gaps in understanding, allowing for efficient learning. Han shares his personal experience of dedicating extra hours to math practice during his senior year of high school, which significantly improved his skills and earned him recognition from his teacher. He emphasizes that while the beginning is difficult, consistent practice and attention to lectures will eventually transform one's approach to math, making it more enjoyable and understandable.

Keywords

💡Sensitivity to numbers

Sensitivity to numbers refers to an acute awareness or perception of numerical data. In the video, the speaker describes waking up with an unusual sensitivity to numbers, symbolizing a newfound understanding and intuition for mathematical problems. This concept is central to the theme of the video, which is about transforming one's relationship with math from struggle to ease and mastery.

💡Math test

A math test is an evaluative tool used to assess a student's knowledge and skills in mathematics. In the script, the math test serves as a catalyst for the speaker's realization of their newfound abilities and understanding of math. It is a common experience for students and is used in the video to illustrate the contrast between the speaker's past struggles and their current proficiency.

💡Columbia University

Columbia University is an Ivy League institution known for its rigorous academic programs. The speaker mentions graduating from Columbia's engineering school, which adds credibility to their transformation story and expertise in math. It also provides a benchmark for the audience, showing that with the right approach, one can excel in math even at a high level.

💡Math and operations research

Mathematics and operations research are academic disciplines that involve the application of mathematical methods to analyze and solve complex problems. The speaker's major in these fields is relevant to the video's theme, as it underscores their deep engagement with mathematical concepts and their journey from struggling to excelling in math.

💡Struggle with math

Struggling with math is a common experience for many students, characterized by difficulty understanding mathematical concepts or performing calculations. The speaker's personal narrative includes their struggle with math during high school, which is a central theme of the video. It shows that even someone who eventually excels in math can have a challenging start, and it provides hope and a relatable story for viewers.

💡Liberal arts

Liberal arts is an academic discipline that includes the study of history, politics, geography, and other humanities. The speaker chose the liberal arts track in high school because they were initially bad at math and science, which contrasts with their later success in a math-related field and adds depth to their transformation story.

💡Natural science

Natural science is a branch of science that deals with the study of the physical world and its phenomena. In the script, the speaker mentions that despite later excelling in math and engineering, they initially chose not to follow the natural science track due to their struggles with math, highlighting the personal growth and change in their academic interests.

💡Answer key

An answer key is a document that provides the correct solutions to problems, often used for checking work or understanding the correct approach. The speaker discusses using the answer key as part of their learning process in college, emphasizing the importance of understanding the correct method before attempting to solve problems independently.

💡Linear programming

Linear programming is a mathematical method used to find the best outcome, such as maximum profit or lowest cost, in a model represented by linear relationships. The speaker uses it as an example to illustrate the abstract nature of mathematical concepts and the importance of foundational knowledge in understanding advanced topics.

💡Practice problem sets

Practice problem sets are collections of mathematical problems designed to reinforce learning and understanding. The speaker recommends doing at least 20 practice questions a day using the process they describe, which is a key strategy in their transformation from hating math to excelling at it and enjoying the subject.

💡Conceptual understanding

Conceptual understanding refers to the ability to grasp the fundamental ideas and principles behind a subject. The video emphasizes the importance of building a network of concepts in math, which allows for a deeper understanding and the ability to connect new information with existing knowledge, as opposed to just memorizing steps or formulas.

Highlights

The speaker, Han, experienced an unusual sensitivity to numbers and found math questions making sense to them.

Han graduated from Columbia University's engineering school with a major in math and operations research.

People often assume Han's intelligence in math is due to innate smartness, which is not the case.

Han struggled with math during high school in China, even choosing the liberal arts track due to poor performance in math and science.

Han's first high school math test resulted in a score of 49, with the average being 78 and the highest 96.

Han's initial approach to difficult math problems was ineffective, leading to frustration and a lack of progress.

In college, Han adopted a new system for tackling math problems, which involved initially giving up and then learning from the answer key.

Han emphasizes the importance of understanding the answer key and then attempting the problem independently.

This new method helps to trigger positive feelings and boosts confidence by completing questions correctly.

Han explains that learning math involves understanding not just the topic but also its foundational concepts.

Han suggests that missing knowledge can be the reason why math makes no sense at times.

Han recommends finding practice problems with answer keys to identify and fill knowledge gaps.

Han's strategy of doing 20 questions a day using the new method led to significant improvement in math understanding.

Han advises that the initial learning phase might be tough but assures that it will lead to a complete mind shift in understanding math.

Han's experience shows that with the right approach, even those who dislike math can excel and enjoy it.

Han's transformation from hating math to becoming a math major and enjoying the subject is a testament to the effectiveness of the method shared.

Transcripts

imagine waking up tomorrow and noticing

something is different you found

yourself unusually sensitive to numbers

upon arriving at school you're met with

a math test quickly scanning through the

exam you felt that all the questions in

your head simply make sense and the

answers just come to you this is

definitely not my experience Hi friend

my name is Han I graduated from Columbia

University engineering school that's my

I majored in math and operations

research as someone who is pretty

skilled at math and even enjoy studying

math people often have the impression

that I'm very intelligent and they think

the reason they're bad at math is

because they're not as smart as I am

little do they know that I really

struggled at Mass growing up I am

originally from China when I was in high

school all students has to study math

English and Chinese it could pick

between two paths liberal arts which had

history politics and geography or

natural science with physics chemistry

and biology with a slightly harder math

test consider hearing the fact that I

studied a math and Engineering in

college lots of people assumed that I

must have chosen the Natural Science

track surprisingly I did not I chose the

liberal arts track because that was

really bad at math and science they just

seemed so hard to me I couldn't

understand what the teacher was talking

about in the lecture I didn't know how

to do my homework I still remember my

first high school math test I had no

clue what's going on and I told myself

maybe it's just because the content is

really hard maybe if I don't get it no

one else will get it either but I was so

wrong I got a 49 and I still remember

the average was 78 and the highest was

96. by U.S standards I was definitely

getting C's and B's in my math classes

and I thought maybe just because other

people are smarter than me and I'm just

bad at math I got stuck in this segua I

hate math so I'm avoided studying it and

then I got really bad scores and I hate

math even more and then just felt so

defeated and just plain stupid if you're

struggling with math right now I fully

get you so in this video I'm going to

show you how I went from someone who

hated math to becoming someone is really

good at math and even enjoying and

loving math

so what I did when I was in high school

if I saw a very hard problem I would

look at a math problem and have no idea

how to approach it so I had to take out

my notes and textbooks and try to figure

it out after a while I would have some

idea and write down the first step

however as soon as I move on to the next

step it gets stuck once again finally

after 30 minutes I would manage to

complete the question only to check the

answer and find out it was still wrong

so at the drop down the correct answer

and just move on there's no way it's

going to be enjoyable for you if you

keep running into problems and getting

stuck every single step this experience

will only leaves you frustrated and

feeling defeated here is the system that

I use in college and it actually works

when I encountered a question I don't

start writing immediately instead I take

a moment to mentally walk through how

I'm going to solve it if I realize I

don't know how to solve it or foresee

myself getting stuck I just gave up yes

you heard me right just gave up instead

I look at the answer I take the time

time to thoroughly understand the answer

key and its Approach at each step once

I've grasped with the answer key I set

the answer key aside and try to solve

the question on my own now I know

precisely what the question is asking

about write down each step this time

don't give up too easily and make a

general effort to apply what I've just

learned from the answer once I've

completed the solution I compare it to

the answer key once again if I realize

I've done it incorrectly or I'm stuck at

a point I cannot quite recall I just

repeat the process understand the answer

key answer the question again

independently until I get right

a couple reasons why this is so much

more effective than the first one that I

did when I was in high school first of

all it triggers positive feelings

instead of feeling frustrated or don't

know where to start you get to complete

the question correctly on your own this

will give you a sense of accomplishment

which is my favorite part of being a

math major that I get all the hard

questions right I know how to do the

hard questions and make me feel good

good it would just boost your confidence

and intellect secondly this will save

your time and spend all the time

effectively before you were spending all

the time to try to figure out the

question on your own but actually you

may not be even on the right path you

might be completely wrong or just even

not even in the right chapter of the

book but the second approach allows you

to spend the majority of the time of

learning the answer keys which is the

correct way if you didn't understand how

the answer key did it but you would

immediately found the correct chapter or

the right part of your note to study

certainly it's so important that you get

to write the solutions completely on

your own from start to finish that will

give you a comprehensive understanding

of how to approach this question from

beginning to the end that next time if

you see similar questions you will know

it because you already know how to do it

completely on your own this time why

math makes no sense to you sometimes

technical things has barriers unlike

history and literature objects that you

may be able to have an understanding of

a term that you never heard of before

very fast but for math you just cannot

for example if you've never heard of

chinchu Huang Wikipedia tells you oh was

the founder of the Qin Dynasty and the

first emperor of unified China you

immediately have an understanding of who

hate is what did he do was he famous for

and he looked like this but if you want

to know what is linear programming and

then you Google it and the Wikipedia

tells you Lincoln programming also

called in your optimization is a method

to achieve the best outcome such as

maximum perfect or lowest cost in the

mathematical model whose requirements

are represented by being relationships

who someone first time hearing the term

linear programming they may go what the

hell is this this is how is this helping

me to understand what is linear

programming so when you try to learn a

math topic you're not just learning the

topic itself you are also learning all

its fundamental concepts and what's it

built upon so when you are in your

Calculus class and do you feel like oh

my God I have no idea what's the teacher

is talking about how come the teacher

jumps from one step to the other step

that everyone else seems to get it and I

just don't it's probably because there

are stuff that we missed from pre-calc

were the previous lessons that the

teacher didn't mention now we know you

don't get it it's only because you're

missing a note of knowledge so you

cannot connect a path together all those

no's and paths connect together become a

giant Network don't worry about it too

much if you feel like you missed a lot

of the knowledge before or you're just

way behind I'm going to talk exactly how

can you put your giant Network as fast

as possible together

and the plan found some practice problem

sets that have relevant questions you

can ask your teacher or professors or

just Google it online make sure it has

answer keys and the more thorough of the

answer key is the better the 20

Questions a day using the process I just

mentioned above I know it might be a lot

but I promise you it's really worth it

working through practice questions

you're zooming in on what truly matters

what what you're unsure about instead of

reviewing a whole old book or your note

from last semester when you found a step

you're not getting that's a clue about

what you're missing you're learning as

you go and you're putting it into

practice straight up you will see the

stuff that really matters more often and

the stuff that doesn't matter might not

even show up so when I was in my senior

year of high school I did two extra

hours of math problem sets in addition

to my math homeworks within one semester

not only that I caught up all the

materials I left it behind before but

also I become one of the best students

in my math class my math teacher really

liked me I was one of her favorite I'm

pretty sure you're not supposed to have

favorites but I was her favorite and I

love her the beginning is always the

hardest part it might take you forever

to understand the answer keys after you

build this jelly Network truly your mind

will work completely differently

obviously you still need to pay

attention to the lectures and do all the

math homework but you no longer will be

the person that hates math and have no

idea what's going on so thank you so

much for listening I really hope this

will be helpful to you