Contrary to popular belief, doing squats with full range of motion actually strengthens your knees. this might help you: how to squat properly
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Hell yeah performing a full squat is harder than a half squat. And I'm not surprised your knee is feeling better. Here's a little Rip wisdom for your reading pleasure.
Originally Posted by Mark Rippetoe
I cannot keep good form for ever squat, my pc is weak. Any ideas? Should I still increase the weight each workout it wait?
You know in any skilled movement it takes tons of reps to learn it. From a sports background consider that making any "move" second nature takes like 500 reps. Practice those 500 reps with shitty form though and you get a learned shitty response. I'd say only do the weight that you can accomplish with correct form for at least 500 reps before you really start introducing very high levels of stress (high weight/intensity).
Yeah, a form video for some folks to help you out with is a good idea too.