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No, meditation and sleeping are not the same thing, though it's certainly possible to fall asleep while meditating. You shouldn't listen to music, nor anything else while meditating. Find a quiet place, lie down, close your eyes, breath slowly, and keep your mind on one word, to the exclusion of every other thought. It doesn't really matter which word it is, as long you keep repeating it in your mind, over and over, and keep your mind on that word only. When your mind starts jumping to something else (and it almost certainly will), think something along the lines of "Pay attention," or "Stop thinking about that, think about your word," and return to repeating your word over and over, to the exclusion of everything else. Meditation has been shown to be relaxing, to prolong life, lessen the effects of stress upon your body, and improve conventration.
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Just think if you meditate for one hour a day and live for another sixty years you will have spent 2.5 years sitting thinking about nothing.
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your teacher is a wackjob but it's probably not going to do your grades much good if you bring that to her attention... just pretend like you agree with her and then ignore her.