Some email providers allow parental controls, that is, a way to monitor a child's use of email. Gmail, however, does not. Here's one way to monitor the amount of time your child spends on Gmail. First, if you have not already done so, create a Gmail account of your own. In iChat preferences under accounts, create a Gmail jabber account -- Google provides more detailed instructions about this on their site.
Then, make sure that chat is turned on on your child's Gmail account. This is easy to do, as the button is located at the bottom of the Gmail inbox page. Make sure that your child does not disable chat, obviously. Then, make your child a buddy who appears in your buddy list. iChat will now show when they log in and out of Gmail, so long as you keep iChat open.
You can even make a customized sound to alert you when they log in. You can make note of the time when they log in, or start a chat with them, and iChat will automatically note the exact time. This can be used to know exactly how long your child spends on their Gmail account.
[robg adds: While this isn't an ideal solution -- you have to be at your own machine with iChat running, for one -- it does provide at least some level of knowledge about someone else's Gmail usage. There is, of course, a much larger question about how to best monitor and control your children's computer usage in general ... and that's one question I'm not looking forward to facing in a couple of years!]
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