There are always multiple ways to approach any one topic in education. Things will always change with different people, place, or time. When it comes to the importance of teaching mathematical theories, teachers must find the right balance of freedom. It is the responsibility of teachers to help students realize their potential. And most of the fun about mathematics is in the proofs themselves! However, at the same time, teachers must respect that fact that everyone has limited time and energy to absorb new information. For example, with an art student who wish to spend every possible spare minute on drawing, is it OK for teachers to give "extra" work that ultimately takes away the time that student has in subject(s) he or she enjoys? Another analogy is the idea of a remote, as someone mentioned in class. Math is like a remote control, a tool, used to make people's lives easier, if not possible. Although there must be those who are skilled and dedicated to manufacture and perfect this tool, the majority of us who use it don't necessarily need to understand how it works. In the end, there is no real solution or answer, as there will always be. Every situation is different, which is exactly why as teachers we need to be observant and vigilant to inquire new information in order to perfect our teaching methods.
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