Maths - Things students should emphasize

Things should emphasize of the Maths

Students must always remember that the mathematical language (terminology and symbols) are just representations of mathematical thought. students of math get mired in or turned off by the language, when the focus should be more on mastering the concepts. Math is universal only in its use of common logic and common concepts.

The actual symbols (letters, words, sentences) of the language are not as important as the thought process.

The language itself, especially in writing, has become highly standardized over the years, just to assist in communication. But mathematics is valid no matter how it is represented, as long as all terms and symbols are well-defined to the reader. Sometimes there is no single way to express math, just as, sometimes, there is no single way to make an argument

Students should not stress too much over memorizing pages of facts and concepts.

Students should focus heavily on developing the skills and practicing the intellectual gymnastics that will enable them to think mathematically and solve mathematically posed problems.

Nevertheless, memorization is also useful, since of course nobody can possibly have the brainpower, memory, ability, time, or patience to prove all facts from first principles.

Isaac Newton "I can see so far, because I stand on the shoulders of giants."

One beauty of maths that separates it from other disciplines like science, is that the preconditions don't always need to be established.