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Of Divergence and Curl

This semester, I am working part-time as a tutor in Calculus II. This is our second last week before study week and exam weeks, but it is only now that I realized my own goal and strength.

Usually, we just need to discuss the tutorial questions that are given by the lecturer. So I need to take a look at the questions first, solve them and explain to class on how to solve them. This is where the first source of my boredom and decreased self-worth came from. The way the tutorial is handled is boring and tiring.

Well first, I need to take some time to look at the question and write down the whole damn solutions for all questions. Usually I get help from the other tutor, Syukor, to provide me with the solutions since he is far more hardworking than I am. But as weeks go on, it gets truly exhausting and uninteresting. Look at the questions, prepare the answer, and explain to the students. My job became a chore, and I don't feel the satisfaction of doing it. I don't feel like I'm helping my students in a meaningful way, and I don't think that I am worthy to receive the payment from this job. Of course, I don't want to stuck in this loop until the last day of the semester.

So during my last class, instead of just answering the exercise questions, I decided to ask my students on the meaning of some terms discussed that week. Particularly, I asked them what is divergence of a vector? What is the definition of divergence? What is the meaning of the value that we get after calculating the divergence? What does a zero divergence mean? And I did the same for curl, conservative and the definition of Greens' Theorem. Not surprisingly, they didn't know the answers.

I believe that most of them don't even bother to read any of the definitions in the notes or the reference book. They will always search for the formulas and just memorize them, or only use them to answer their exercises.

The thing is, all of my students are good at calculation, given that they know and remember the related formulas. But it just that they never pushed themselves to know more than what is will be asked in exam. Besides, I believe that they won't learn or remember much by the time they finish their final exams because they don't even know what they are learning in the first place. I even asked them the definition of gradient, and only a few could at least try to answer.

Their responses were mixed, but it is way better than just discussing the answers, where their responses were indifferent. By going beyond memorizing and formulas, at the very least I can make them think on what it is that they are learning. I should have done this early in the semester.

As of last week, I truly feel like I am contributing something to my students, even if not all are giving positive responses. I would be happy if even there's only one or two of my students who took the lesson positively, and I hope that their views on Mathematics changed into a better direction. That is my goal, to make students understand their Maths better, by learning the way a pure mathematician would learn (or at least close).

I appreciate it when the students are thinking.


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