Your supervisor is looking at the entire phrase "directions for future work" as a singular topic. This is technically possible if, in fact, there is a topic on the agenda labeled "directions for future work". As your Google search suggests, however, this is not normally how native speakers or anyone else who uses the language thinks about that phrase.
Idiomatic and natural American English is "Finally, directions for future work are discussed and concluding remarks are given". "For future work" is a complement to "directions", which is the grammatical subject of the sentence. Subject-verb number agreement requires a plural verb.
Can you keep your supervisor's version? If your supervisor doesn't buy this answer or someone else's answer that the verb should be "are" and not "is", you will have to keep your supervisor's version, I suspect. Unless your name is listed as the author, I doubt that you want to argue about such a minor thing as a grammatical error. Your supervisor can deal with the embarrassment of being wrong. You can always think "I told you so" and smile secretly at your supervisor's chagrin.