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The easiest/best way to keep track of what they're doing on the computer is to just have it in the open. They're far less likely to get into stuff they shouldn't if a parent can just look over and see what they're doing. As opposed to hidden in their room or in the basement or a less traffic area.

Something like Disney Circle can be good too to limit time and track usage, it's not just about trusting them but doing a reasonable level of protecting.