What's a way to bring out the best in those around you? Expect them to already be the best, and let that attitude show. They will perform up, or down, to your expectations.
There are two named effects concerning how people react to their observers — the golem effect and the pygmalion effect. Naturally the golem effect is less testable, from an ethical standpoint. Both effects work best on the young, and it's hard to convince parents to allow their children to participate in a study that is designed to damage them. As in most sociological studies, college students get the worst of it. One study carefully gauged how people acted during a lesson they expected to be either excellent or substandard, and then had researchers act both attitudes out while a poor undergraduate gave them an improvised lesson. Independent judges found the performance of the "teacher" to vary greatly depending on the positive or negative responses — all nonverbal — that they were getting from their "students." On the unambiguously pygmalion side of things, one study had researchers telling elementary school teachers that randomly chosen students were likely going to go through tremendous intellectual development that year. The class was tested at the year's end, and the singled-out students had higher IQ scores, on average, than the rest of the class.
But do these effects really make a difference? Everyone gets nervous when they're in front of a crowd and can sense things aren't going well. This has to be particularly true for college-aged kids. After a few lessons, they might have learned to shrug off negative responses. And it's possible that the children who were singled out got more attention and care from the teachers, and weren't just benefiting from high expectations. Some studies indicate that expectation effects are minor, and that sooner or later people revert to their natural level of competence. Then again, when have great expectations ever turned out badly for anyone? Oh.