As an Asian myself, let me tell you...there is no hope! Mwa hahaha! jk. It'll take a long time to re-establish trust, but it can be done!
As you've stated:"I can't actually prove to them I'm trustworthy, since the times I'm actually on are so little it has practically no effect."
You're right; you can't re-establish their trust in you by demonstrating your "proper" usage of a computer, at least not directly.
Gain back their trust by being reliable and honest with other tasks (chores, curfew, etc.)
Don't try to do everything all at once, but start by say being 20% more reliable with laundry duty, 30% more reliable with cleaning your room, and so on.
Here's some common situations you can use to your advantage:
Group Projects:
- A week in advance, tell them, "Mom/Dad, I'll have go to [Friend A]'s house for 1 hour after school for a group project," stick to that time, and be back home in exactly one hour.
- When they ask "What subject", "Which teacher", "Who's [Friend A]'s dad?",etc, answer them calmly and (if you can manage it) cheerfully. This will make it seem as though you have nothing to hide AND that you've become so good at managing your time, planning a study session is a breeze.
Passing by the grocery store on the way home:
- Use a bit of your allowance to buy bread, steel wool or some other cheap item that you know for sure your home is running low on. If you have no idea, then just buy a snack you know your Mom/Dad will like. Mention you thought they might like it when you give it to them. Don't buy rice, bc Asian parents have specific brand preferences, and they'll call you a careless child for not knowing it. Plus it's expensive so they'll just KNOW you're up to something!
- Alternatively, call up your Mom or Dad and very, very casually inquire if they need anything. I'd suggest if you're a boy, to call Mom instead of Dad, bc a lot of Asian moms have soft spots for their sons. (Same with Asian dads and their daughters in a lot of countries).
When the topic of your parents' home country comes up in conversation(Assuming you're the child of immigrant parents):
- whether you care about hearing what happened in the year 19xx or whatever for the 50th time, at last appear genuinely interested. Ask some questions and listen to the answers. Your parents grew up there, so they think of it very fondly. Your attempts to learn to their home country will be appreciated.
- If a topic related to their home country comes up in History/Social Science/any class, take you class notes and worksheets and ask your parents for more information. This helps your parents see your dedication to schoolwork, and makes them feel fulfillment as well because they helped you learn something. Bonus: if they don't feel like answering and accidentally yell "Go Google it!" then well ;)
- Don't overdo this or anything else on this list--they'll definitely get suspicious and catch on to your evil scheme if you do!
Also
Appear to have a fixed schedule:
-despite how flexible you made your schedule for the day, at least come out from your room and do a certain task(watch TV, do chores, whatever) at a fixed time everyday. This will show your parents that you are indeed managing your time well.
After about four to six months of sneakily scoring brownie points with Mom and Dad...
...start asking for more time on your laptop.
- Start with REALLLYYY small "extensions" somewhat regularly--no more
than 5 minutes! And only for when you're doing schoolwork, and
nothing else! Then slowly over the course of the year, increase it up to half an hour.
- Actually, start asking for extensions a little sporadically throughout those 4-6 months. When I say sporadically,I mean sporadically! No more than ten in total, unless something urgent comes up!
- If all is going well, at this point your parents should not be supervising you as strictly. If not, um...well, ramp up the charm!
Don't give a reason for the extension as "I've been more responsible lately, so give me more time." Nope nope. They'll only catch on to your "ulterior motives" for what you did and call you a lying, manipulative & ungrateful child.
- instead, mentally time yourself so that you know some kind of work is going to be just about unfinished, and ask for time to finish it up. And actually just use the time to finish it up.
Around the finals, I'm assuming there'll be more papers due, so a few weeks before the finals, tell them over dinner that you'll be needing more time on your laptop for studying, because of the papers due at the end of the term.
Hopefully after one year of being nice and showing your parents how responsible you are, they'll have a different view of you, and trust you more! Good luck.