To "sell sb short" means to give less (to a person) than you should.

I interpret the meaning of "sell someone short" a little differently than Peachey. See this definition: https://www.google.com/search?q=sell+somebody+short&ie=utf-8&oe=utf-8 to sell someone short = to undervalue them, to not have enough faith or confidence it them, to not see their full value/potential Granted, if I don't see someone's full value, then I would probably not give my full effort (as Peachey said), but I think this is a side effect, not the real meaning of "to sell someone short". I think this sentence Although multimedia can be a valuable tool in the classroom, teachers who only teach their "old-fashioned" way will not be selling their students short. is saying that, even though the teacher is using an old chalkboard instead of modern multimedia, this does NOT mean that he undervalues his students' potential. He may still believe they are capable of great things. It just means that he thinks a chalkboard is adequate to teach his students what they need to know.