In this article, I will give you information about how to excel at math and science and overcome their fear. For the specific article, I'm going to cover the book 'A Mind For Numbers: How To Excel At Math And Science'.
Although the title is very specific the learning techniques in this book can apply to many different subjects 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:
1. Focused mode and
2. 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 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 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.
Einstellung Effect
This is where you have an already formed idea in your head of how to solve a problem that 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.
X= -b±√b2-4ac/2a
I'll give them multiple problems that require it. Like as following:
x2-2x+1=0, x2+4x-2=0
Then I'll give them something like this
x2-12=0, x(x-12)=0
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 grandmaster 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 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.
1. Attention
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.
2. Ways To Get Into Diffuse Mode
It may not just happen as you did as such a 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 understand the basics then focus on the problem and then alternate between that focused and diffuse mode of thinking.
Study Techniques And Tips
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.
1. Recall The Material
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.
2. Solving Problem
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 reading.
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 different problem on that topic and solve it completely on your own.
3. Struggling To Learn New Concept
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 through try to have the solution available but don't look at it unless you 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.
4. Go Into The Diffused Mode
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.
5. Not Do the Same Kind Of Problem
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 most efficiently.
If you want to learn the most in the shortest amount of time then once you successfully learn a concept and do maybe a couple of 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.
6. MixUp The Section Problem
Another tip that 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.
Procrastination
Now, I talked about procrastination but this book had a few takes on it as well. But I wanted to offer some more advice for those who have issues with procrastination.
1. Pomodoro Technique
One thing to try is the Pomodoro Technique which there are many articles and videos on it.
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 focus for that long, then afterward 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 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 want to make sure you understand the material on a deeper level and learn how to apply it.
2. Do Dislike Jobs
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 that momentum to keep going.
3. Mental Contrasting
Another thing to try is mental contrasting, where lecture you want to be compared to how 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.
Patient Persistence
Now when it comes to getting better at math or science, it all comes down to patient persistence. After so much time 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 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 overtime 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 of 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.
4-Minute Mile Story
I'll end this article with 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 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 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.
I hope this summary helped you, if you liked the article, don't forget to comment below the article, and follow me on paidforarticles.com.
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