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A Mind for Numbers: How to Excel at Math and Science (Even If You Flunked Algebra)

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Here is a small example: how are you reading books? Are you highlighting key ideas? Maybe you’re like me and trying to highlight every useful piece of information. But study had shown that this technique not only useless, but could be harmful. You should try to understand the basic idea, try to recall it without looking into the book and only after that, you may highlight key pieced with some insightful notes on the martins.

Taking responsibility for your own learning is one of the most important things you can do. Avoiding Overconfidence and the Power of Teamwork Testing in itself is a powerful learning experience, it changes and adds to what you know, also making dramatic improvements in your ability to retain the material. This is known as the testing effect.Multitasking during the learning process means you don’t learn as deeply, this can inhibit your ability to transfer what you are learning. The Value of Learning On Your Own Mental Contrasting: think about where you are now and contrast it with what you want to achieve. The contrast of where you want to be with where you are now that makes the difference. Use the focused mode to first start grappling with concepts and problems in math and science. After you’ve done your first hard-focused work, allow the diffuse mode to takeover. Relax and do something different. This was an epic moment in my life because I found out that my greatest fear was indeed my true passion in life. I just loved the harmony and beauty of algebraic expressions and calculus formulas especially the meaning behind all of these abstract symbols. With intuitive method of teaching of the khan academy and some mental exertion I managed to learn so many precious things in maths even difficult parts of calculus and I got an A in my AP exam. Since three years ago I have never stopped learning mathematics (except few months for TOEFL) and currently I am studying for the GRE test. Which I am really thrilled by this process and it is not stressful anymore at all. The most important thing is that I’ve decided to keep learning maths for the rest of my life, especially probability and statistics.

One disadvantage of looking at worked-out examples to form chunks is that it can be easy to focus too much on why an individual step works and not on the connection between steps.The diffuse mode helps us gain new insights on problems we’ve been struggling with and to see the “big picture”. When we’re trying to understand a new concept or solve a new problem, we don’t have existing neural patterns to help guide our thoughts. If we relax and let our minds wander, we allow different areas of the brain to form new connections. For example, the best language programs, such as those at the Defense Language Institute (where Oakley learnt Russian), combine focused mode (structured practice with plenty of repetition and rote) and diffuse mode (free speech with native speakers). Equations are not just things you plug numbers into to get numbers. Equations tell a story about how the physical world works. The key to understanding an equation is in understanding that story – that is far more important than getting the right numbers. Mathematicians tend to like teaching math in an abstract way, because they believe that it helps with transfer. They worry that learning math in a discipline-specific approach makes it harder to apply math in flexible and creative ways later. However, it’s often easier to learn an idea if it’s applied directly to a concrete problem, even if that makes transfer harder later on. So there ends up being a constant tussle between concrete and abstract approaches to learning maths. Oakley thinks both concrete and abstract approaches have pros and cons. Don’t rely on teachers, but do reach out to good ones Happy to see the late Seth Roberts show up. He went too far and dogmatic, but his impulse towards self-experiments is great.

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