Those of us who have had the experience of having children that have been in school can see the difference. It takes that passion out of them, and it takes awhile and lots of deschooling to rekindle that fire! It takes lots of prayer, lots of relaxing on the part of both parent and child and just following whatever interests the child has, and more prayer and more relaxing (ever relax through grit teeth?) but that love of learning can be re-ignited!

I look forward to seeing the differences in how my youngest (age 2) learns compared to her oldest sib (age 20). He was destroyed by the schools and further destroyed by me as I did school-at-home the first few years we homeschooled.

At age 20, while I've thought he was vegging in his room playing computer games for about two years when not at work, he's actually been de-schooling and unschooling.
He's learning C++ and composing music on his computer and planning out computer software games he wants to create.
He's written some small programs to facilitate stuff on the computer -- like a program that will automatically clean up files or do other little chores on the computer.
Ever watch someone write a config.sys or autoexec.bat from scratch on your computer when it crashed and your back-ups didn't work and you couldn't get your computer to run? My son did it for mine!

He also studies computer tech stuff and can fix/repair quite a bit concerning these contraptions.
His computer has been his 'guinea pig' and it's hard to believe that a six year old 486-33 has been souped up and modified and upgraded and tweaked till it runs equivalent to a Pentium 100 or so.

All this to say, if they've been in school and are burned out, let them do what they please for awhile -- it doesn't mean there's no structure in the house. There's chores, for example, that they must do in our house, and limits on TV and other 'mindless' things, so when they got 'bored' they find interesting things to keep them busy, and guess what? That's learning!