Non cursive hand seems like an incredibly slow way to write, impractical for classes etc. is this because everyone is bringing a laptop to class and just doesn't write much at all? I'm from the UK and as far as I know they still move kids into cursive as soon as possible. From personal experience at school I recall the quality of my writing was dramatically improved once I moved to a computer so I can understood a move in that direction. I'm just surprised cursive isn't still used because for note taking situations it is still incredibly useful.

Handwriting generally refers to both joined and non-joined writing. If there is a need to distinguish, usually people say cursive or print. As in "Print your name and sign below..."

Cursive in my experience is very difficult for someone other than the writer to read- even when it is written neatly, it is more difficult to read than print or type with a decent font selected :)