Both of the underlined verbs describe actions of the professor, and therefore they are singular; also, "repartido" is a past participle, which never changes form, regardless of the number and gender of the subject of the verb (in this case "ha").
To me, "ha repartido" (instead of "reparte") sounds odd, but you might want to wait for a native speaker's opinion on that. Are you trying to translate something into Spanish or just trying to understand the sentence?
It has to be 'reparte'. (but I won't fight with a past perfect I almost never use...)
And also, is the professor Argentinian? (the "los deja boquiabiertos a los estudiantes" has a double object, quite typical of Buenos Aires, at least).
oh, sí i guess i don't need the second los, gracias. to Chris K, I am just trying to formulate a sentence about education out of the blue. And i think i will go with reparte! thanks to both of you for your input