this video is going to cover the book a mind for numbers how to excel at math
and science and although the title is very specific the learning techniques in
this book can apply to many different subjects all the way to games like chess
now whether you're in high school struggling with math and science or
you're in college studying math science or engineering and doing well the
techniques taught here can apply to anyone because learning itself is a
science and there are practices to improve efficiency and performance no
matter what level you're at so let's get started. Now there are two modes of
thinking you need to be aware, of focused mode and diffuse mode. Focus mode is
obvious it's when you are highly focused on something like attempting a difficult
math problem with no distractions. Diffuse mode is what happens when you're
more relaxed and let your mind wander basically just like taking a break but
what this does is allows different parts of your brain to connect and solve
problems kind of in the background and I will elaborate on this soon but both
these are actually essential for deep learning and understanding when it comes
to especially math and science. Now to explain the significance of diffuse
learning I want to introduce something called the Einstellung effect. This is where
where you have an already formed idea in your head of how to solve a problem
which prevents you from finding a better solution, you're kind of zoomed into one
idea. I've tutored personally a lot in math and I've seen this all the time for
high schoolers here's a common one we'll be learning the quadratic formula and
I'll give them multiple problems that require it then I'll give them something
like this which they have done before and they go straight for the quadratic
formula forgetting that they can just take out an X and it's already factored
they were zoomed into one idea and it prevented them from finding a better way
to do the problem. This has also been shown in chess players sometimes players
have an idea in their head of what move they should do they try to continue to
scan the board for better moves however through studies of their eyes they've
shown that their focus stays on the original move they thought of, making it
more difficult to come up with a better one and this is where diffuse mode
thinking comes in. It allows your brain to relax and the neurons to connect and
kind of work in the background which allows you to see more of the big picture.
In the book the author shows a picture of a chess grand master during a game who
gets up from his seat and looks away from his game. He takes a short amount of
time to distract himself and let his mind wander so he doesn't become stuck
in a narrow way of thinking and this is what diffuse mode thinking really does
you just take a break from that intense focus then when you come back to the
problem you have a fresh mindset and often the solution or a better solution
comes to you much faster. A very famous french mathematician henri poincaré
struggled to crack a difficult problem so he decided to take a vacation and when
he was getting on a bus the answer suddenly came to him from a part of his
brain that continued to work on the problem in the background and you'll
hear of many stories where this kind of thing happens. So this is the foundation
for improving your skills, you need to alternate between focused mode learning
and diffuse mode. No you cannot just let your mind wander and wait for the
answers to come. You need to focus intently on a problem then when you are
stuck take a break for maybe two minutes maybe an hour and then come back and
focus again and the solution may come to you much quicker as you have a fresh
look at the problem. It may not just happen like you did for this
mathematician but resume the problem and it may surface faster than you think
ways to get into diffuse mode include going to the gym, going for a walk, going
for a drive, taking a shower, sleeping, and much more. And remember you can't just
look at a problem you have no clue what to do on and then take a break and think
you'll get to the solution you have to be logical you need to actually
understand the basics then focus on the problem and then alternate between that
focused and diffuse mode thinking. Now let's get into some more specific study
techniques and tips. When it comes to learning math and science learning fast
is like trying to gain muscle fast it'll just burn you out. Although you can maybe
memorize things very quickly you can't learn on a deep level in one or
two nights so that's why you need to learn a little every day or at least as
much as possible. Now the best study method they found for any topic is
attempting to recall the material that you have just learned. What you don't
want to do is reread material until you get it, this is one of the worst ways to
memorize or learn new material. What you want to do is read something new and
turn away or close the book and try to recall what you just read as much as
possible then read it over again and repeat that
one more time. They found just with two repetitions this worked better than
nearly any other method done in the same amount of time. But okay what about when
it comes to doing problems like in math, physics, engineering, etc which aren't
just memorizing things. Again here's what you don't want to do and this I thought
was very insightful because I know it will apply to a lot of people watching.
What you don't want to do is attempt a problem then when you don't understand
it you look at the solution and say "oh I see how they got that" and then move on.
This is one of the biggest illusions of learning math and science out there so
you should not fall for it you haven't learned the concept even though you
think you may have. If you need to look at the solution that's no problem but
then you need to do a totally different problem on that topic and solve it
completely on your own. So if you're struggling to learn a new concept what
you want to do is first read about the topic and make sure you understand the
fundamentals, ask your professor, your friends, or whatever it takes so you can
just get the basics, you don't just want to dive into problems without learning
the fundamentals. Then what you want to do is work a problem all the way through
try to have the solution available but don't look at it unless you really need
to, then if you didn't fully understand the problem you need to repeat it all on
your own and make sure as you're going through each step you understand why
it's being done not just how it's done, this allows your brain to make
connections rather than just reading the solution and thinking you have it. Then
you want to take a small break after a few problems, go into that diffused mode
thinking so you can come back with a fresh mind and if you don't get
something you need to practice it a lot, that's basically what this all comes
down to. It will take time but your brain is going to keep making
connections especially as you accomplish problems on your own. Now many students
on the other hand will do a certain math problem correctly but then right after
that they'll do more of those same problems, now this can be a good thing
and improve test scores for sure, but this doesn't maximize your time in the
most efficient way. If you want to learn the most in the shortest amount of time
then once you successfully learn a concept and do maybe couple problems
correctly, move on. If you had all the time in the world
then of course practice as much as you can but often that's not the case so
this is something to keep in mind. And another tip which I really thought was
interesting was to mix up the sections of the book you're doing problems in. Like
let's say your homework is in section 5.4 of the book, well do
some of those problems then do some from 5.3, then go back to
5.4, then maybe go back to 5.2. Especially if you're
struggling you'll need this practice. Now why do you do this? Because you want to
make sure that you could do all these problems on a test if you didn't know
what section things were on. If section 5.4 is all about synthetic
division, even if you get an abstract problem you still can assume it requires
synthetic division, but just given that problem randomly on a test would you
know to do that? This is something to ask yourself and a reason to kind of mix up
the sections you work on so that you can fit the pieces together. Now in another
video I talked about procrastination but this book had a few takes on it as well
and I wanted to offer some more advice for those who have issues with
procrastination. One thing to try it is the Pomodoro Technique which there are
many videos on but essentially to sum it up, set a timer for something like 25
minutes, maybe a little less or more but then solely focus on work for that time.
This is short enough where anyone can really focus for that long, then
afterwards reward yourself with some internet surfing or texting or whatever
but not for too long, maybe just a few minutes, and then repeat the process. Some
people argue that they feel rushed with the timer in the background when doing
something like math, but studies have shown that this actually helps because
it will make you become accustomed to being on the clock and feeling a little
stressed so that when you're taking a test and that stress occurs you're able
to perform better. Also you want to make sure you focus on the process not the
product. As in you should care more about the time you're putting in not how
much you're getting done. It doesn't matter if it takes two or five hours to
complete your homework (assuming you have the time) you really
want to make sure you understand the material on a deeper level and learn how
to apply it. Another very effective tool is to do the most important and disliked
jobs in the morning when you get up or maybe immediately when you get back from
school. This then do that momentum to keep going. Another
thing to try is mental contrasting, where you basically picture where you want to
be compared to now and why you are doing this. One student from the book was
quoted as saying that he put what his starting salary would most likely be on
his wall and framed it to remind himself why he's doing all this work and it
helped him with procrastination. Now I'm going to stop there with procrastination.
Now when it comes to getting better at math or science it basically all comes
down to patient persistence. After so much time of doing all these techniques
it will reshape your brain and optimize the way you learn and solve problems.
Persistence is often more important than intelligence. This author said that she
absolutely hated math all throughout high school and failed her way through.
She started studying just basic trigonometry when she was 26 years old
after being in the military, but she had a shift in her mindset and decided that
she was going to get good at math. She ended up getting a bachelor's in
electrical engineering, a master's in Electrical and Computer Engineering, then
a doctorate in systems engineering with a background in various subjects and she
said that it got easier for her over time because of how she was learning to
learn. And remember things typically get more fun when you're better at them.
People often are bad at something then because of that they get bored which
makes them not try and it's just a downward spiral from there. And
throughout the book she talks about many success stories or people who weren't
naturally gifted at math who then excelled later in life.
Just a simple shift in your mindset can do more than you may think. I'll end this
video one of my favorite stories of the four-minute mile. The four-minute mile
was assumed by experts to be impossible for the human body. In over a hundred
years of the timed mile no one had done it until one day in 1954 one person
finally beat it by less than a second. But then less than two months later
another person beat it, and since then thousands of people have beat it
including a few high school kids. And people say it was that switch in the
mindset of others that the impossible was actually possible that then allowed
the other people to beat the time more and more. So yes your mindset is more
powerful than you may think. Math is something I personally like a
lot but I still learned plenty and found lots of helpful techniques and tips from
this book which I've linked below if you want to buy it for yourself and support
the channel. I hope this summary helped you, if you liked the video don't forget
to comment, like, and subscribe and I'll see you all next time