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Thread: Learning to Think Mathematically

  1. #1
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    Learning to Think Mathematically

    I'm in High School, and in studying for the ACT Math exam, I discovered that the secret to doing well on it is not simply to know the Math, but to understand the Math. For example, if you know how to solve an equation, but you don't readily think of what the next step could be to simply an already nearly simplified equation or in a question that doesn't make it obvious that an equation could be simplified, you use time trying to think; after 30 seconds wasted, you may see the next step - or you may not.
    Another example: A pentagon has 5 vertices and 5 diagonals. An octagon has 8 vertices. How many diagonals does an octagon have? I immediately thought (8)(5), since 1 vertices has 5 diagonals. However, (8)(5) counts every vertex twice, as it counts the number of diagonals coming out of each vertex, not just the vertices they start in.
    I want to also be able to see a situation and relate it very quickly to a relation, function, etc. I've started to look at some resources

    How to build a solid foundation in mathematics????
    http://web.stanford.edu/~roypea/RoyP...24_Pea_85c.pdf

    and I was curious of what tips might be offered at this forum. I want a deep understanding of how the principles of mathematics work. Thank you in advance for the help.

    Edit:
    Resources like these are amazing:
    http://www.mathsisfun.com/geometry/unit-circle.html
    What is a trig function?
    I had never seen a visual representation of what trigonometry is before this. It makes it much more clear.
    Last edited by Sanjo; Oct 23rd 2015 at 07:10 AM.
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  2. #2
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    Re: Learning to Think Mathematically

    Maths is mostly about spotting patterns. In algebra this means seeing how you can build terms that will easily simplify.

    Generally, the way to get there is to practice.
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  3. #3
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    Re: Learning to Think Mathematically

    How can you actively practice this? I have been looking at conditions (such as when a number is raised to the x power) and investigating certain things to find patterns. Is there a better way than this or is continuation of this the key? Perhaps it's time to roll out the Sudoku charts?
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  4. #4
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    Re: Learning to Think Mathematically

    The best way is practice doing problems, I think.
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  5. #5
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    Re: Learning to Think Mathematically

    Yes; follow the 3 golden rules:
    1: practice
    2: practice
    3: practice
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