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How the Brain Learns Math and Science: Focused Mode vs Diffuse Mode Thinking

How your brain uses both focused and diffused thinking styles to learn challenging subjects!

Published on June 6, 2017

Wouldn't it be great if you never had to worry about getting a good grade in a Math or science class again?

A photo of a brain represented as a puzzle with a puzzle piece missing, part of the lesson on How the Brain Learns Math and Science with the focused and diffuse modes

Does having more confidence in your abilities to the point where you've eliminated all math/science anxieties sound too good to be true?

It doesn't take an Isaac Newton, Albert Einstein, or Stephen Hawking to recognize that these things probably wont ever be completely possible to achieve.

However, here are a few things that are very possible to achieve:
  • Speed up your mastery of math and science subjects!
  • Reduce stress about your ability to conquer these subjects!
  • Improve your grades in tough classes!
If you think that any of this might be helpful for you, then please keep reading because in this post I'm going to share an important discovery about how the brain learns math and science. You can begin using this to advance your results as soon as you're ready!

We've all been there. 

You're working diligently to crack a math problem. You're pretty sure your strategy is right, but the numbers are still coming out wrong.

You check your calculations again, but get the same answer. Your muscles tense up. You bite your lip.

Your blood begins to boil. You crumple the scratch paper mess on your desk up into a ball, throw it aside, and rip the textbook open yet again.

Maybe if you just re-read the chapter for the thousandth time, you'll get the right answer, you think to yourself...

...but in reality, you probably won't!

The truth is that mastering math and science subjects is hard! While persistence is a necessity, there comes a certain point when it stops being helpful.

The human brain has two different modes of information processing at its disposal, and trying to brute force your way through a problem like this prevents you from utilizing both methods!

Focused Mode vs Diffuse Mode Processing

In A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra), Dr. Barbara Oakley talks about two different systems the brain uses for learning. 

When you're focused intently on something such as reading a blog post, solving a math problem, or thinking logically, you're using the focused mode.

On the other hand, when you're relaxed and not actively trying to solve a problem, you're using the diffuse mode.

Once when I was taking physics in undergrad, I left the library after working on a tough problem for a while without making much headway. 20 minutes later when I was on the bus, I got a sudden flash of insight out of nowhere, and realized exactly how to solve the problem!

Those who have studied math/science subjects for a while have probably experienced something similar. 

The reason is because the brain processes these subjects by alternating between the focused mode and the diffuse mode.

Below is a short list of some characteristics of both modes.

Focused Mode:
  • Where learning starts
  • Conscious processing
  • Activated by concentrating on a task
Diffuse Mode:
  • Activated by relaxing and not focusing on anything in particular
  • Produces "flashes of insight"
  • Helps you grasp the "big picture"
  • Works on problems in the background
Utilizing Both Modes Makes All The Difference

We need to use both the focused mode and the diffuse mode in problem solving. However, you can think of them as both canceling each other out. For example, when you try really hard to solve a math problem, you're using the focused mode, which prevents the diffuse mode from assisting with solving the problem!

When you then switch gears, the diffuse works to solve the problem, but blocks the focused mode from assisting!

This switching from focused mode to diffuse mode and vice versa is how hard math and science problems are solved, and how challenging abstract concepts are understood.

I strongly encourage you to take Oakley's advice to heart! 

This means trying your best to gradually learn the material starting with the focused mode. When you hit a stumbling block, take a break and let the diffuse mode take over, then come back to it at a later time. 

You'll probably find that the material seems somehow "different" during your next session.

In reality, the material is exactly the same as it was the last time you studied it; your understanding has just gotten better. 

Keep doing this, and eventually I guarantee it will stick for you! The key is to get to this point BEFORE your tests, rather than after your tests (or never), and your grades will skyrocket!


In conclusion, I want to revisit the benefits I mentioned at the start of the post to show you exactly how you can use this new knowledge.
  • Speed up your mastery of math and science subjects 
Understand that these subjects are complex, and thus require lots of repetitions to master. Spacing your study sessions out allows both the brain's focused and diffuse modes to coordinate together to generate true comprehension. 

I strongly recommend starting your studying as early as possible (even before class if you can). Your brain needs lots of time to process the material using both modes before it's going to click!
    • Reduce stress about your ability to conquer these subjects 
    It's easy to come out of a lecture feeling somewhat demoralized after a lot of the material flies over your head. Remember though, just because you don't understand the material now doesn't mean you won't crack it eventually! 

    I can recall another time in undergrad while taking organic chemistry when it took me about a full week of repeated attempts to finally get a certain topic down to perfection (for those wondering, it was stereochemistry).

    Was this stressful? Sure.

    Did I have doubts about my ability to master it? Yes, I'll admit I did from time to time.

    But I stuck it out, and finally the day came when I sat down for some focused studying, and the material was crystal clear!

    The key is to stick with it and don't get discouraged because you're not getting it as fast as you'd like to, or as fast as other people are. Although it can sometimes feel like everyone else understands the material but you, I can assure you this is rarely ever the case (more on this topic in another post...)!
    • Improve your grades in tough classes
    Hopefully by now it's clear how understanding the brain's two modes of learning can help you achieve better grades. Of course this is a major oversimplification, as the science of learning is much more complicated than this. However, it's still very helpful to think about learning math and science subjects in this manner. It's now up to you to apply this knowledge, and watch your grades shoot up in the process!

    Want to learn more? Check out Dr. Barbara Oakley's book A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra).

    I can almost guarantee it will be one of the best decisions you've ever made if your goal is to improve your performance in math and science subjects quickly! Thanks for reading!

    Disclosure: Both of my links to this book are affiliate links. Basically, this means I'll get a commission on sales from people I recommend who buy it. I only ever recommend books if I've read them myself and am willing to stand behind the quality for 100%! 

    This post first appeared on Test Prep Champions, please read the originial post: here

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    How the Brain Learns Math and Science: Focused Mode vs Diffuse Mode Thinking


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