“Персональное спасибо тем, кто хорошо написал экзамен — такие моменты и заставляют поверить в то, что преподавательский труд и силы были вложены не напрасно.”

Actually, “и” is used here for emphasis, to draw attention to the exact reason for a teacher’s pleasure. The person who wrote the sentence implies not only that the moments make him believe, and so on, but that these moment are the very reason why he felt his work was not in vain. “it is (exactly) these moments that make one believe his work and effort as a teacher have not been in vain".

You may express pretty much the same thing with “именно” ("именно такие моменты заставляют поверить") or using both words ("именно такие моменты и заставляют поверить").

Sometimes words are used just for emphasis. EXAMPLES:

** “.. Я и ушёл” ~ “And (so) I left” (it is implied that the decision is justified by what he said before; there was some story before that sentence; this person thought “I should go"; and then he says “So I did").

Without “и” the sentence would only mean “I left/went away/ (insert your translation for leaving the place)". With “и” placed at the beginning of the sentence it would be “И я ушёл", which is more like “And then I went away", which only connects the sentence err.. to the previous experience, without emphasizing the person’s desire to go away.

** “Так и поступают настоящие друзья” ~ “That’s how a true friend acts” (= “this is exactly what true friends do"; The sentence is similar to your example).

Without “и” it would be “True friends act this way”

Хм.. Пожалуй, “писать экзамен” - это малоупотребимое выражение. Обычно говорят “сдавать экзамен".

“…такие моменты и заставляют поверить в то,…”

Don, would you mind commenting on this section a bit. I don’t really understand this sort of construction, particularly how “и” works here.

Don responds: this use of и is confusing here because I didn’t include the sentences that lead up to it. The word и in certain contexts can be translated as “both, and, also.” In this context I take it as “also.” In the previous sentences the writer had said that she had enjoyed working with her students. They had also sent her kind personal messages, and receiving those messages produced those moments that “also make me believe that my work and effort as a teacher were not in vain.” I had left out the “also” in the the translation because it would have been confusing without the preceding context.

Your question, by the way, is excellent. It shows that you have the eye for detail that makes good language students.

Oddly enough, I find in translation that it is the little words that throw us off (at least in the middle stages of our Russian studies) than the big words. Really big words like достопримечательности tend to have only a couple of meanings. Short words tend to have many. Distinguishing which of those meanings the author had in mind, especially if the meaning is more emotional than denotational, is what makes translation an art as well as a science.