When I was in elementary school (a long time ago) I remember receiving report cards with two grades for each subject, one for achievement (A,B,C,D,F) and one for effort (E, S, NI). I remember being perplexed by an A/NI grade I got at one point. Anecdotally, it seems at least the assessment of effort has been in practice for some time.
My father was a NCAA champion wrestler, and I wrestled a bit myself. There are few physical endevours as challenging- wrestling requires you to be smarter, faster, stronger, and more agile while enduring pain and physical exhaustion longer than your opponent. Oh, and you have to be in this condition while you are cutting weight. In wrestling, there is no greater prize than winning that final match and achieving the title of champion. All of your peers and coaches will be singing your praises for that. There is no greater prize. But conversely, the greatest shame and condemnation for a wrestler is not losing, although it hurts. The greatest shame is not putting in 100% effort in to the match. In fact, this thought process goes beyond the mat and in to the life of the wrestler- he must make 100% effort in every aspect of his training, or he will either be made to feel like a failure or more likely he will punish himself for becoming one.
Most wrestlers never achieve any kind of championship, but they are proud of whatever they have achieved because they gave everything they had to give, and nothing less.
Teachers need to reward achievement because that is the way the world works. But, they simultaneously need to enstill a sense of pride in the efforts their students are making. This is no small task, I know. But it is one that can be achieved, with great effort.