The HACK to ACE MATH no matter what - Caltech study tip
Summary
TLDRThe video script narrates the journey of overcoming math anxiety through a transformative approach to learning. It emphasizes the importance of understanding math concepts rather than rote memorization, using creative problem-solving skills to grasp the essence of mathematics. The speaker, who once struggled with math, shares personal experiences and strategies that led to success in math competitions and advanced classes. The video offers a three-step solution to improve math skills: breaking down problems, reviewing foundational concepts, and attempting to solve problems independently before consulting solutions. It encourages viewers to adopt a mindset that values comprehension over memorization, setting them up for success in math and beyond.
Takeaways
- 🤓 The feeling of being 'dumb' in math is common, but it can be overcome with the right approach.
- 🏆 Success in math is not just about memorizing formulas; it's about developing math sense and problem-solving skills.
- 🎓 Understanding the foundational concepts behind math problems is crucial for solving more complex ones.
- 🔍 When faced with a math problem, break it down into smaller, manageable parts to tackle each concept individually.
- 📚 Review and truly understand each foundational part of a math problem, rather than just memorizing it.
- 💡 Use resources like Khan Academy and YouTube to deepen your understanding of math concepts.
- 📝 Attempt to solve math problems from scratch without immediately looking at the answer key.
- 🤔 Write down everything you know about a problem and try to make connections between those pieces of knowledge.
- 📈 Compare your initial attempts at solving a problem with the provided solutions to build problem-solving skills.
- 🌟 The key to becoming good at math is not memorization, but comprehension and applying a creative mindset.
- 🚀 Embrace the process of understanding math and building your skills, as it will pay off in the long run and help you succeed in real-world applications.
Q & A
What was the speaker's initial experience with math in sixth grade?
-The speaker struggled with math in sixth grade, feeling embarrassed and confused while peers seemed to understand easily.
What did the speaker's dad teach that transformed their math skills?
-The speaker's dad taught them the magic secret of understanding math concepts deeply, which led to improved problem-solving skills and success in math competitions.
How did the speaker's perspective on math change over time?
-The speaker went from struggling with math to enjoying it so much that they preferred solving math problems over writing essays.
What is the 'magic secret' for being good at math according to the speaker?
-The magic secret is not memorizing formulas but understanding the true nature of math and developing problem-solving skills.
What is the first step in the speaker's three-part solution for improving math skills?
-The first step is to break down a math problem into its foundational parts and understand each part thoroughly.
How does the speaker suggest reviewing math concepts?
-The speaker suggests using resources like Khan Academy and YouTube to watch videos and understand the origin and reason behind each concept.
What should one do when faced with a difficult math problem?
-One should try to solve the problem independently, write down everything they know about it, and only refer to the answer key after attempting a solution.
Why is it important to not immediately look at the answer key when solving math problems?
-Looking at the answer key too soon prevents the development of problem-solving skills, which are essential for real-world applications and success in math.
What is the speaker's advice for students who struggle with remembering formulas?
-The speaker advises students to focus on understanding the concepts behind the formulas rather than just memorizing them.
How can understanding the fundamentals of math lead to better problem-solving?
-Understanding the fundamentals allows students to solve more complex problems with less effort, as they can apply their knowledge effectively without relying on memorization.
Outlines
🤔 Struggling with Math and the Secret to Success
The speaker shares a personal story of feeling lost in math class during sixth grade, unable to understand the subject like peers. However, after learning a 'magic secret' from their father, they transformed from struggling to excelling in math, even winning competitions. The paragraph emphasizes the importance of math sense and problem-solving skills over rote memorization of formulas. It introduces the idea that understanding the essence of math makes solving problems easier and more enjoyable.
📚 Beyond Memorization: Mastering Math Skills
The speaker discusses the common issue of students struggling with math due to poor teaching methods and the misconception that math is about memorizing formulas. They argue that understanding the true meaning of mathematical concepts, like square roots, is more effective. The paragraph provides a three-part solution for improving math skills: breaking down problems into foundational parts, reviewing and understanding each part, and attempting to solve problems without immediately checking the answer. This approach is shown to build problem-solving skills and confidence in math.
🌟 The Power of Understanding: A Lifelong Skill
The speaker concludes by highlighting the long-term benefits of truly understanding math rather than just memorizing it. They stress the importance of building a strong foundation in math to succeed in real-world situations. The speaker shares their own success in math competitions and encourages viewers to adopt this mindset. They also invite feedback and questions from the audience, showing a commitment to helping others improve their math skills and overall academic performance.
Mindmap
Keywords
💡Math Sense
💡Problem-Solving Skills
💡Foundational Math Concepts
💡Understand vs. Memorize
💡Private Tutoring
💡Math Toolkit
💡Real-World Application
💡Flipped Switch
💡Math Anxiety
💡ACT and SAT
Highlights
The speaker struggled with math in sixth grade, feeling embarrassed and confused.
The speaker's father taught them the 'magic secret' of being good at math, leading to success in math competitions and advanced classes.
The difference in math ability among students is extreme, and there might be a 'magic secret' known by good students.
The 'magic trick' in math is not about formulas but about problem-solving skills and understanding the relationships between shapes.
The speaker demonstrates a problem where a simple rotation of a shape makes the solution obvious, highlighting the importance of creativity in math.
The speaker is a private tutor who helps students improve their math skills and test scores by teaching them these problem-solving tricks.
Students often struggle with math because they focus on memorizing formulas rather than understanding the underlying concepts.
The speaker emphasizes that math is not about memorization but about understanding and applying concepts.
The speaker provides a three-part solution to improve math skills: breaking down problems, reviewing foundational concepts, and attempting to solve problems without looking at the answer key.
Understanding the unit circle and its relationship to trigonometry is used as an example of foundational math knowledge.
The speaker suggests using resources like Khan Academy and YouTube to deepen understanding of math concepts.
The importance of attempting to solve problems independently before looking at solutions is emphasized for building problem-solving skills.
Comparing one's initial attempts with the provided solutions is crucial for learning and developing problem-solving abilities.
The speaker's personal experience shows that understanding math concepts can lead to long-term success and a 'magical' difference in performance.
The speaker encourages students to adopt a new approach to learning math, focusing on understanding rather than memorization.
The speaker invites students to share their progress and ask further questions, showing a commitment to helping them succeed.
Transcripts
has this ever happened to you in math
class the teacher gives you a paper of
problems to solve you look around and
all of your peers are breezing through
the assignment you're still stuck on
problem one all the numbers and letters
blur together in your mind and you feel
dumb this is exactly my experience in
sixth grade I was working on problems
with three classmates and they just
seemed to get it while to me the math
was like a foreign language I was
embarrassed that I was so confused so I
just nodded along pretending like I was
keeping up with them while slowly dying
inside like man this is hopeless I'm
just dumb I suppose later that year my
dad taught me the magic secret of being
good at math and starting from eighth
grade I went on to win math competitions
eventually winning a gold medal state
level I was in advanced math classes
taking both AP calc BC and AP stats my
sophomore year now I would rather solve
100 math problems than write one essay
so what click for me math tends to be
the hardest subject for many students
but then the best or easiest for other
students why is the difference so
extreme there must be a magic secret
that the good students know well there
is so today you'll finally learn the
truth behind why you struggle in math
and of course the solution warning you
might begin to like math let's go we'll
start with quick magic in an example the
question is what is a ratio of the area
of the Red Square over the area of the
Blue Square basically the area of this
divided by the area
of everything in these blue borders now
I'll give you a moment to think about it
see if you can solve it real quick
that's the fun try it
all right maybe you tried it maybe you
didn't you might have been thinking uh
I'm gonna assume you know this side
length is one and then do some circle
diameter Square relationships to then
get the side length of this big square
and then once I get the areas of both
squares I'm just going to do one area
divided by
the other area now either you thought
that or you're like man I'm not seeing a
problem like this anywhere before I
don't know how to solve it here comes
the trick I'm gonna redraw this shape
now what if I simply turned the inside
Square
45 degrees like
[Music]
whoa do you see anything special do you
see anything that makes the problem
really easy yes indeed if we cut it up
like this you can see that in each of
these four quadrants the red area is
actually half of the blue circle area so
the answer is really easy you don't need
to do any calculations at all it is
simply one half whoa it's just like
magic
magic drop a like right now if you
thought that was cool come on guys
that's that's really awesome right
that's an instance showing that if you
have problem solving skills and you're
creative in math and understand the
relationships between shapes you can do
one little adjustment or one little flip
of the shape and get the answer so much
more easily now I know your schoolwork
probably doesn't look like this question
but here is the headline it doesn't
matter how many formulas you know to
solve that area problem and other math
problems it's about math sense and
problem solving skills the better your
understanding of what math truly is the
easier the solutions will be for you I'm
a private tutor right now for the ACT
SAT and for the math section I can
always get my students up to make that
one of their easiest sections
significantly increasing their scores
because of these tricks that I show them
that flip of the mindset I hear all the
time I can't remember the formulas I
can't solve it because I've never seen a
problem like that before that that was
my students struggle and probably yours
as well you think that adding math is
just adding more formulas to your brain
more tools to your toolbox but let me
ask you this if you were a construction
worker who wanted to improve what would
be more helpful relying on adding more
tools to your toolbox or increasing your
actual skills as a construction worker
if you add more tools Without Really
knowing how to use them you're just
going to get more and more overwhelmed
as the construction worker like you
won't be able to get anything done
you'll just be piled under this
accumulating weight of all these new
things you have to remember and use just
like in math if you're not improving
your real math skills you'll fall more
and more behind because there's so much
more and more to memorize but when you
really learn and understand you solve
more problems with less effort like no
wonder those math students find it their
best subject using your math toolkit
becomes easy when you don't have to
think hard about what to use when and
how to use it and at the end it is like
magic like check out these comments from
students who watched my ACT SAT Math
tricks video I didn't have to try and
remember those tricks from all those
years since I took the act and sat so
long ago I just had that math sense
that's always there that's going to help
me solve any problem that comes my way
the truth is it's not your fault I'm
sorry but there are many
subpar teachers out there I've seen it
with my own eyes one of my students
right now tells me that his teacher just
writes some things on the board sits
back and goes learn it and then gives
him the test that is not math guys so
really don't feel bad if you have been
living your life so far not knowing that
this is the real way to get good at math
another quick example before we go into
the solution think about square roots if
you were just trying to memorize square
roots like you learned that square root
of 25 is five then if someone asks you
what is the square root of 36 you
wouldn't know because you never learned
it it's not in your memory on the flip
side if you knew what the square root
actually means as the inverse of
squaring a number then you know what the
square root of 36 is imagine the next
time you take your math test and all the
solutions just come to you here's how to
make that happen this is the three-part
solution you should do this while
practicing math number one take your
math problem and break it into Parts
often we don't even realize that we
don't actually understand the little
foundations behind the bigger more
complex math problem so for example if
you have a big geometry problem and
using the unit circle is part of it then
the concept unit circle would be a piece
of that math problem so you would break
that math problem into unit circle then
maybe algebra operations whatever other
tools that you would need to solve that
math problem number two once you have
your math problem broken into those
foundational parts and you know the tool
you need for each part then review the
tool you use for each part so in that
unit circle example the tool or concepts
you might need are what the X Y
coordinates are all around that Circle
and what the radians are around that
Circle ask yourself do I know this
because I'm memorizing it or do I know
it because I understand it if it is the
former and you don't actually understand
it then watch videos on that concept and
the origin the reason behind why all of
those numbers are around the unit circle
Khan Academy and YouTube both have
excellent resources so just watch as
many as you need to understand it maybe
even do some practice problems repeat
this process for each foundational part
of your original problem so that you
actually understand and have the
fundamentals good again if you don't
feel confident and strong in the little
Concepts that make up a big problem then
every big problem and the bigger and
bigger problems that come after that
will be even harder this works for
basically any math problem and I know I
used the unit circle but the reason I
bring that up is because me after like
eight
many years of not using the unit circle
or even seeing it in front of me if you
gave me a blank unit circle I would be
able to fill in all of those numbers
right now
That's The Power of understanding and
not memorizing and that's also why I can
take the ACT Math Live and get a 36 on
it even without any preparation right
now number three solving that initial
big math problem try to solve it on your
own from scratch without looking at the
answer key even when you do get to a
problem and feel stuck don't look at the
answer key yet I know it's really
tempting because the solution's right
there in the back of the book but don't
do it stop stop it first write down
everything you know about the problem in
front of you if like an act problem it
asks you how do you make this number
even the term there is even so think
back to everything you know about even
numbers when I did this with my student
and my student said an even number is
divisible by two he immediately knew how
to solve the problem at first my student
was stuck then I simply asked him what
do you know about even numbers he told
me and then he knew how to solve it on
his own after you think about everything
you know about that one problem try and
draw connections between those things I
encourage you to write that down this is
like your attempt at a solution think
about it for a few more minutes and then
if you're still stuck yes now go into
the answer key now when you're looking
at the solution compare it to your
initial thinking and see how similar or
how different it might be this is where
the learning and problem solving ability
gets built over time this last step is
so so important because if you only look
at the solutions instead of trying the
problem yourself as much as you can
first you won't build problem solving
skills the real world doesn't just hand
you Solutions on a silver platter you'll
have to figure them out on the job
otherwise your boss is going to hate you
man that's why this approach of
understanding an attitude of wanting to
build your math skills will set you up
for success in the real world too
foreign
to flip the switch at the beginning when
I was getting taught by my dad I was
like this is taking so long why are you
explaining all these things I just need
to get the problem done all that upfront
effort will pay off so much in the long
run trust me from my experience you can
see from my math Awards now that just
having this flipped switch and going
back to the foundations and
understanding things will make a huge
difference a magical difference and just
think about it it might be hard to flip
the switch right now but it's going to
be even harder to catch up if you fall
farther and farther behind I stress this
again because so many students think
that this is what math is math is not
memorizing repeat after me math is not
memorizing it's really not good to read
the solution and just try to memorize it
you will automatically yourself go down
the right path if you understand we
should go back and take a shot every
time I say understand in this video
knowing how math Works will make you the
master of any map class no matter what
get excited about trying this new
approach and I'm really excited too to
see your progress so keep me updated in
the comments let me know how your math
grades are going yeah ask me any other
questions you have how else can I help
you Ace school and life let me know and
give me a thumbs up thank you so much
I'm using an accent randomly thank you
bye
foreign
[Music]
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