Miss Ayumi teaches the class A-ko, B-ko, and C-ko are in, usually riding up to school in a moped. It's not unusual for A-ko and C-ko to pass her on the way to school. Miss Ayumi's usually seen teaching poetry, and she gets scared whenever anything happens that could get her in trouble, such as C-ko's incessant crying or B-ko's comments on how boring the class is.
She's still single and looking for a husband, and she starts going to unusual lengths to get one, such as praying over a hexagram-marked pendant (a fact which will confuse things later on), but Mr. Daitokuji ultimately makes an arrangement to fix her up with K. The wedding ALMOST takes place, but it gets cancelled at the last minute by a number of unusual but interconnected factors.
As for that pendant Miss Ayumi has that resembled a number of alien clues...total coincedence.