In the dictionary I have, the def. of motivo is (1)reason, cause and motive and (2) motif. No where does it mention motivate. Because the french translation for motivate is very similar to motivo I was able to come up with the correct term. Is this something wit duo translation or an omission in my dictionary?
When the direct object is a person or domestic animal/pet, you must use the personal 'a'. This personal 'a' is only to be used in this sense. Since he/she was talking about HIS students, you need the personal 'a'. If instead he was generally talking about motivating students, it would be "Motivo los/las estudiantes."
This link explains it better than me talking in circles: http://www.studyspanish.com/lessons/persa.htm