Becoming good at math is easy, actually
Summary
TLDRThis 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
🧠 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.
📚 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.
🌟 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.
🚀 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.
Mindmap
Keywords
💡Math Anxiety
💡Passive Learning
💡Active Learning
💡Practice
💡Fundamental Knowledge
💡Procrastination
💡Intuition
💡Conceptual Understanding
💡Efficiency
💡Fireman Technique
💡iPad
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
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