Shirai Sae is a side character in Kodomo no Jikan. She is the instructor of Futatsubashi Elementary School, the equivalent of a Principal in the U.S. schooling system. She is very strict, by-the-book, and is feared by everyone. Her personality gains her the title "gloomy, serious, and plain" by her peers, which causes her to become bitter and anti-social in general.
Shirai scolds Kagami Kuro during one of the episodes for calling Aoki Daisuke a good-for-nothing virgin, in which causes Shirai to accidentally unveil her own virginity while in her rage. Kuro notices Shirai and likes her attitude towards Aoki, so she decides to make Shirai her friend, giving her fashion tips and suggestions on how to improve her appearance to others, which completely hits Shirai off-guard, causing Shirai to shrug Kuro off, leading to further situations in the future.
Aoki, being a new teacher, and according to Shirai, not knowing anything about teaching, combined with his enthusiastic, positive-thinking approach, make for a complete clash of personalities between the two. This causes just about every conversation they have together to end in an argument.