The HACK to ACE MATH no matter what - Caltech study tip

Summary

The 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

00:00

🤔 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.

05:01

📚 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.

10:01

🌟 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.

Keywords

💡Math Sense

Math sense refers to the intuitive understanding of mathematical concepts and the ability to apply them effectively to problem-solving. In the video, it is emphasized as the key to becoming good at math, rather than just memorizing formulas. The speaker's transformation from struggling with math to winning competitions demonstrates the power of developing a strong math sense.

💡Problem-Solving Skills

These are the abilities required to approach and resolve mathematical problems in a creative and efficient manner. The video highlights the importance of these skills over rote memorization, using the example of a geometric problem that becomes simple with a creative adjustment.

💡Foundational Math Concepts

These are the basic principles and ideas that form the building blocks of more complex mathematical problems. The video suggests breaking down complex problems into these foundational parts to truly understand and solve them.

💡Understand vs. Memorize

This concept contrasts the superficial recall of information (memorization) with the deep comprehension of how and why something works (understanding). The video argues that understanding is crucial for mastering math and applying it flexibly.

💡Private Tutoring

Private tutoring refers to one-on-one or small group instruction outside of a traditional classroom setting. The video's speaker is a private tutor who helps students improve their math skills and test scores by teaching them these foundational concepts and problem-solving strategies.

💡Math Toolkit

A metaphor for the collection of mathematical concepts, formulas, and techniques that a student has at their disposal. The video suggests that it's more effective to understand and use these tools properly than to simply accumulate more of them without understanding.

💡Real-World Application

Refers to the practical use of academic knowledge in everyday life or professional settings. The video connects the development of math skills to success in real-world situations, where problems don't come with pre-packaged solutions.

💡Flipped Switch

A metaphor for a significant change in perspective or approach. In the context of the video, it refers to the speaker's shift from struggling with math to excelling in it after adopting a new understanding-based approach.

💡Math Anxiety

A feeling of stress or anxiety related to math tasks or learning math. The video addresses this common issue by offering strategies to overcome it through improved understanding and problem-solving skills.

💡ACT and SAT

Standardized tests in the United States used for college admissions. The video discusses the speaker's experience as a tutor helping students improve their math scores on these tests by focusing on understanding and problem-solving rather than memorization.

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

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