I think you are looking for the word 'Envy', but you should also look up The Jante Law http://en.wikipedia.org/wiki/Jante_Law

"A peaceful and civilized nation"? Is there any nation fitting that description anywhere?"

Iceland, maybe. 0% spendage on military, and on top of the rankings (at least before the banks there took a trip under the permafrost)

The problem I often encountered in school was that when you had finished problems given by the teacher you were awarded with nothing to do.

Another thing is that teachers rarely encourage kids to really test their knowledge, rather it is just completing the subject that is the main goal, for both parts (students and teachers) not gain a wide understanding of the subject.

School should be a place where you evolve to discover what you can do very well, and a place to get help with things you have problems with grasping.
Nowadays it is much more "help with problems" than "discovery of skills".