The math study tip they are NOT telling you - Ivy League math major
Summary
TLDRIn 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
🤔 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.
🔄 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.
Mindmap
Keywords
💡Sensitivity to numbers
💡Math test
💡Columbia University
💡Math and operations research
💡Struggle with math
💡Liberal arts
💡Natural science
💡Answer key
💡Linear programming
💡Practice problem sets
💡Conceptual understanding
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
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