A science teacher was a teacher who taught science in school, such as primary school.
For Wesley Crusher's science project in 2364, he created a model built on the same principle as the USS Enterprise-D's tractor beam. After the crew of the Enterprise later became infected with polywater intoxication and was later saved by Wesley's comparable modification based on his project to the Enterprise's own tractor beam, preventing its destruction by a stellar core fragment, Commander William T. Riker suggested to Captain Jean-Luc Picard that "it's only fair to mention Wesley in a log entry, sir." Picard agreed that , "fair's fair," adding "and let's credit his science teacher, too." (TNG: "The Naked Now")