Why you understand the math but CAN'T solve problems
Summary
TLDRIn this video, Han, a Columbia University graduate, shares her journey from struggling with math to mastering it. She emphasizes the importance of active learning over passive learning, explaining that understanding concepts is not enough; practice is crucial. Han provides actionable tips to improve math skills, such as redoing questions until correct and using the Feynman technique to ensure deep understanding. She also addresses common issues like memorization, problem-solving tricks, and common mistakes, offering strategies to overcome them and enhance math performance.
Takeaways
- 📚 Han, the speaker, graduated from Columbia University and studied math and operations research, highlighting her credibility on the topic.
- 🔄 Han struggled with math in high school, receiving C's and D's, which shows that she overcame significant challenges in her math journey.
- 🤔 Han suggests that understanding math but not being able to solve questions correctly is a common issue among students.
- 📉 The motivation to practice math can fade with wrong answers, leading to frustration and the end of practice sessions.
- 🔍 Han emphasizes the difference between passive and active learning, stating that the latter is more effective for mastering math.
- 📈 Active learning involves doing something beyond just receiving information, such as discussions, practicing, and teaching others.
- 🚫 Passive learning, which includes listening to lectures and watching demonstrations, is less effective in math and science education.
- 🔄 Han recommends redoing questions independently when they are wrong, as understanding the solution is not enough.
- 💡 The 'Feynman Technique' is suggested as a method to improve understanding by explaining concepts as if to a child.
- 🧠 Active recall and spaced repetition are recommended for memorization, which is sometimes necessary in math.
- 🛠 Collecting and applying problem-solving tricks in a 'toolbox' can help with specific math tactics that are not commonly known.
- 🔍 Paying attention to common mistakes, such as calculation errors or misreading problems, is crucial for improvement.
Q & A
What is the main issue discussed in the video script?
-The main issue discussed is the struggle of understanding math concepts but not being able to solve math problems correctly, and the importance of active learning over passive learning.
Who is the speaker in the video script?
-The speaker is Han, a recent graduate from Columbia University who studied math and operations research.
What was Han's initial experience with math in high school?
-Han struggled with math in high school, often receiving C's and D's despite investing a lot of time and effort.
What is the difference between passive learning and active learning as described in the script?
-Passive learning involves receiving information from outside sources without internalizing it, such as listening to lectures or watching demonstrations. Active learning means being actively involved in the learning process, such as discussing, practicing, and teaching others.
Why is active learning more effective in math and science education according to the script?
-Active learning is more effective because it involves doing something beyond just receiving information, which helps in better understanding and applying math concepts.
What is the 'fan technique' mentioned by Han?
-The 'fan technique' is a learning method used by Richard Feynman, where one explains a concept as if to a child, which helps uncover areas of misunderstanding.
What should one do when they get a math question wrong according to the script?
-One should redo the question independently until they get it right, which is a form of active learning and helps in understanding where the mistake was made.
What are the four types of problems one might face when studying math as outlined in the script?
-The four types of problems are understanding problems, memorization issues, unfamiliarity with specific tricks or tactics, and making silly mistakes.
Why is memorization often unnecessary in math according to Han?
-Memorization is often unnecessary because everything in math can be proven, and understanding the concepts is more important than memorizing specific equations or steps.
What is the recommended technique for memorization when it is necessary?
-The recommended technique is active recall and spaced repetition, which involves actively trying to remember information and revisiting it over time to reinforce memory.
How can one prevent making silly mistakes when solving math problems?
-One can pay close attention to common mistakes, understand why they occur, and adjust their approach or writing style to avoid such errors in the future.
Outlines
📚 The Struggle with Math and the Importance of Active Learning
In this paragraph, the speaker introduces their journey with math, highlighting their initial struggles in high school with poor grades and a lack of understanding despite their efforts. They mention their eventual success after learning from top teachers and realizing the importance of active learning over passive learning. The speaker emphasizes that merely listening to lectures or watching demonstrations is not enough; one must engage in discussions, practice, and teaching others to truly internalize mathematical concepts. They also mention the common issue of understanding math in theory but failing to apply it correctly in problems, suggesting that active learning is crucial for mastering math.
🔍 Identifying and Overcoming Math Challenges Through Active Learning
This paragraph delves deeper into the concept of active learning, explaining how it can help overcome various types of math problems. The speaker advises that when a question is answered incorrectly, it's essential to revisit it independently until it's correctly solved. They introduce the 'Fan Technique' for understanding concepts by explaining them as if to a child, which helps uncover gaps in understanding. The speaker also discusses the issue of memorization, suggesting that while it can be useful, understanding the underlying principles is more important. They mention the need for active recall and spaced repetition for memorization. Additionally, they address common mistakes, such as calculation errors or misreading problems, and the importance of being aware of these to avoid them in the future.
Mindmap
Keywords
💡Passive Learning
💡Active Learning
💡Math Practice
💡Frustration
💡Understanding vs. Application
💡Diagnostic Process
💡Mistake Analysis
💡Active Recall
💡Spaced Repetition
💡Problem-Solving Toolbox
💡Silly Mistakes
Highlights
The speaker has a background in math and operations research from Columbia University.
Initially struggled with math in high school, receiving C's and D's despite effort.
Realized the importance of active learning over passive learning for effective math comprehension.
Passive learning involves receiving information without internalizing it, while active learning is engaging in the learning process.
Research shows active learning is more effective in math and science education.
Math is a skill that requires practice to be mastered, similar to driving a car.
The speaker suggests that understanding math without being able to apply it is a form of passive learning.
When a math question is answered incorrectly, it should be revisited independently until solved.
Reviewing wrong answers is a diagnostic process to identify gaps in understanding.
The speaker emphasizes the importance of 'treatment' after diagnosis, which involves understanding and correcting mistakes.
Four types of problems are identified: understanding, memorization, tactics, and simple mistakes.
The 'Feynman technique' is recommended for better understanding of concepts.
Active recall and spaced repetition are effective for memorization.
Cultivating a 'math problem-solving toolbox' helps in applying tactics to various problems.
Common mistakes should be noted and avoided in future problem-solving.
The video provides actionable tips that transformed the speaker's experience with studying math.
The speaker's journey from struggling with math to succeeding in hard classes at Columbia University.
Transcripts
you've just learned about the new math
concept everything makes sense to you
you feel energetic and motivated to
tackle the questions until you get a
wrong answer the motivation slowly Fades
away you feel the frustration building
bringing your math practice to an end
you can't help but wonder why you
understand the math but just can't get
the questions right hi welcome to my
channel my name is Han I just graduated
from Columbia this may I studied math
and operations research in college as
someone who has been battling with math
for over 17 years now I have not always
been a math person when I was in high
school I really struggled with math I
often received C's and D's in my math
classes and no matter how much time and
effort I put in it I just cannot get the
questions right and receive the scores
that I wanted on exams I thought I might
not be smart enough and couldn't pursue
a career in stem especially there were
students in my class put in way less
time than I did but Reed really good
grades so after thousands of hours
practicing math and learning from some
of the best teacher in the world I
finally realized that I was just doing
it wrong so in this video I'm going to
explain to you why you understand the
math but you just couldn't do the
questions right I will also show you
that how you can fix it with some
actionable tips that completely
transformed my experience with studying
math and helped me succeed in some of
the hardest classes Columbia University
let's just get into
it for a context let me explain to you
how I was studying before I realized
something was wrong I would really pay
attention in class and carefully take
notes I spent hours looking at how to
solve different math problems going over
each problem carefully to see how it's
done you may stop me and be like hold on
that doesn't sound bad it sounds like
you were a really hard worker but if you
pay close attention the problem here is
it's solely passive learning and no
Active Learning at all passive learning
is a method of learning where students
receive information from outside sources
and try to internalize it which include
listening to lectures reading and
watching
demonstrations and active learning means
you're actively involved in the learning
process basically means you're doing
something besides just receiving the
information and which includes
discussions practicing questions and
teaching others in our education system
there are lots of passive learning and
very little Active Learning many
research Studies have shown that passive
learning is not as effective as active
learning in math and science education
so if you feel like you're spending lots
of time in studying math but still not
get good results it's probably because
you are doing too much passive learning
and not enough active learning math is a
skill to help you solve problems you
have to know how to use it by doing it
you wouldn't say that you can drive a
car just by watching someone else drive
and memorizing all the traffic rules you
have to get into the car and practice
this way you can know how it feels which
part you have problems or any
complications you may run into so I hate
to break this to you but if you only
read and listen how the math is done
sometimes you may think oh I understand
the math but actually you
don't so how can we actually do more
active learning in our math studying if
there's one thing I wish you can take
away from this video is if you get a
question wrong always redo it
independently until you get it right
lots of time people get really upset
when they get a question wrong and start
thinking oh what is wrong with me I just
cannot understand why I cannot do math
you know what the question in front of
you is literally telling you what's
wrong what I often did was if I get a
question wrong I just read through the
answers and try to understand it and
just move on but again the problem here
is if I only read the solutions and try
to understand how it's done it's still a
form of passive learning you wouldn't go
to the doctor spend two days doing all
the lab work for a physical exam and
receiving a result that says you have a
heart issue and you just go oh crap they
say I have a heart issue and just move
on with life you would actually follow
up with the doctor take pills every day
or pursue whatever the necessary
treatment it is until the disease is
cured or under control every time you
practice a question it's a diagnostic
process to see whether you understand
the math concept and your ability to
solve the questions and you need to
realize that the diagnosis is not the
most important part and what truly
matters is the treatment you've already
invested all your time and efforts in
reading the question trying to
understand the question thinking about
the question write the question if you
don't follow up with what's wrong it's
really just a waste of time so follow up
with the question that's wrong figure
out precisely which Step you made a
mistake really trying to understand why
you made that mistake and how you can
prevent it from happening again and
doing the question again is the followup
doctor appointment that they will tell
you whether the disease is truly cured
or not cuz the doctor May tell you yeah
you know what you're good to go or they
may tell you it's still there you still
haven't fix it or they may even say that
ah your heart disease is cured but now
you have a liver disease so make sure
you test yourself by doing the questions
again until you get it right so how do
you actually follow up with your math
disease and then found the treatment for
it AKA how to fix the problem so ENT
entally you compare your wrong answer to
the correct answer and figure out which
exact step that you had the problem in
my experience there are four type of
problems let's just dive into each one
of those firstly an understanding
problem might arise when you feel to
grasp a math concept or the equation you
recently learned or perhaps you don't
understand the question itself to help
you understand math better consider use
the fan technique it is a learning
method that used by the no prize winning
physicist Richard fman basically the way
you understand a concept is by
explaining it as if you're explaining it
to a child while doing this notice which
part did you struggle to explain what
details did you miss what part is really
hard for you to put into simple words
answering those questions will show you
which part are you missing the act of
explaining to yourself or teaching
others is a form of active learning
sometimes when we thinking about things
in our own mind we think we understand
it well but we may miss some important
stuff so the best way to uncovering
those details is to explaining it out
loud verbalize it and teaching someone
else who doesn't know about the topic
and the more you can put it into simple
terms the better understanding you have
about the topic secondly you might face
issues with memorization when you can't
remember an equation function or the
specific step GS required to solve a
particular type of problem in my opinion
in math memorization is really often
unnecessary because everything can be
proven if you're really motivated not to
memorize anything you don't even need to
memorize 1 + 1 = to 2 because there are
162 pages of proofs in abstract algebra
to prove y 1 + 1 equal to 2 therefore I
highly recommend you try to understand
everything before you just straight jump
into memorization but in our daily math
studying memorization does have an
important role because it really can
save us time in situations where
memorization is necessary the best of
techniques is active recall and space
repetition s some questions may need a
specific trick or tactic that you're not
just familiar with and my recommendation
will be just practice more questions but
whenever you encounter a new trick pay
attention how it applied in what type of
question and then collect that trick in
your math problem solving toolbox next
time you see a similar question you can
just pull up your toolbox and use the
tricks that you've collected like a
Pokemon situation the fourth you do
actually know how to answer questions
and you could have done it correctly if
you hadn't just made a single silly
mistake believe me I understand the
frustration I experience it all the time
especially with more challenging
problems the answer just become really
lengthy and requires so many steps
making it really hard not to make
mistakes so pay close attention to the
common mistakes that you make and keep
these in mind the next time you work on
the question is a calculation error or
did you misread the problem for example
I used to make silly mistakes like in
the last line it was 45 but the next
line I just randomly magically write 6 5
so I noticed that and trying to figure
out why turns out the way I wrote four
was really close to Six so I just
changed the way I write for and then
just pay more close attention so that's
today's video thank you so much for
[Music]
watching
浏览更多相关视频
Becoming good at math is easy, actually
The math study tip they are NOT telling you - Ivy League math major
The HACK to ACE MATH no matter what - Caltech study tip
how to study MATH EFFECTIVELY | get STRAIGHT A's in exams
Learning how to learn | Barbara Oakley | TEDxOaklandUniversity
How to Excel at Math and Science
5.0 / 5 (0 votes)