Your best bets for finding psychology on NCIS are the episodes where the team gets to venture into the realm of profiler-style tactics. Here are a few examples:
"The Good Wives Club" -- The team finds the mummified remains of a woman in some abandoned Marine housing. The investigation leads them to look at a similar recent case in Florida, and ultimately to an unlikely suspect.
"SWAK" -- An envelope with bacteria is sent to NCIS headquarters. Kate and Tony are put into quarantine, leaving the rest of the team to find not only the sender but also the motive behind the envelope.
"Mind Games" -- Gibbs interviews a serial killer about to be executed to get him to reveal the locations of his victims' bodies. The team gets more than they bargained for when they discover the killings have continued while the killer was incarcerated, and thus they have to find another killer.
"Bait" -- A teenager with a bomb holds a classroom hostage. Gibbs offers himself as a hostage, leaving Tony in charge of the situation. (Lots of negotiation = lots of psych)
"Bloodbath" -- The team investigates what looks like a murder scene but turns out to have been staged by a man against whom Abby has a restraining order for stalking. The stalker is taken into custody, but it turns out that he's not the only threat against Abby.
"Smoked" -- The team investigates a dead man found in a chimney. When he's identified, it turns out that he's been missing for years and is a suspected serial killer sought by the FBI, who then join in on the case. The joint FBI/NCIS investigation takes a shocking turn when they find recently killed bodies and evidence indicating that the chimney man may be a victim, not the perpetrator.
"Murder 2.0" -- The team investigates a series of killings where videos of the crimes (along with cryptic pictures) have been posted on the Internet.
"Broken Bird" -- Ducky is attacked at a crime scene and the team investigates, delving heavily into Ducky's past. (Any episode focusing on Ducky is a good bet for psych themes.)
"Reunion" -- Three bachelor party guests are found murdered, and the investigation leads them to a man who had been bullied by the dead guests when they were all in high school. (The murders are consistent with how the bullying victim was tormented.) It looks like a straightforward case of revenge, but there's more going on.
"Code of Conduct" -- A Marine with a reputation as a prankster is found dead, and the case becomes a whodunnit with several twists along the way.
In general, if your teacher is interested in crime shows with plenty of psychological concepts, Criminal Minds is a far surer bet. NCIS still rocks, though. Hope that helps!
EDIT - Fixed a couple of typos.