First, tell your parents only the positives. For example, they have apps that you can use for school. A great deal of apps are free, too, along with it being a great investment. Other than that just try to be creative.
You can't just 'convince' your parents to pay $200+ for an iPod Touch just for you. It doesn't work that way. Convincing is nearly impossible, but just try waiting for Christmas.
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Do research on the benefits if listening to music and convince them it is good for your health.