<p>It’s important to memorize and understand the rules. One must know what, when, where, how, and, why a rule may apply. Many of us do not realize that spoken languages are full of rules that become second nature because we have been practicing said languages for our entire lives. The written form of those languages packs new rules that can’t be properly expressed in a verbal manner. Think of Oxford commas, capitalizing certain letters, etc. How does one properly express that in a verbal manner?</p>
<p>Mathematics, similar to English, is a language and the faster one begins practicing it in a “linguistic”, logical manner, the better one becomes at Mathematics.</p>
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<p>Many people are terrible in communicating their knowledge to other people, especially if there are language and cultural barriers. Translating from French to English is not that difficult because both languages are very similar; however, translating from Japanese to English is more difficult due to the cultural, linguistic, etc. barriers present (you’ve probably seen hilarious Japanese to English translation attempts).</p>
<p>Mathematicians face similar translational difficulties. Mathematicians see the world in a mathematical way and it is difficult to communicate mathematical ideas when others do not see think mathematically. It takes 2 to communicate; if the general public is not willing to think mathematically there’s little the mathematicians can do.</p>
<p>This ties back to the language thing. If you start seeing the world mathematically, it becomes much easier to learn Mathematics. If I throw a baseball, does it trace a parabola or a line? My front door is rectangular, does Pythagora’s theorem apply to it? Start thinking that way and you’ll be on your way. It has certainly helped me a lot and has made me realize that the more I learn Mathematics the less I know of it.</p>