Gokusen

The story of a young, idealistic teacher who enters Shirokin Gakuen in hopes of making a difference in the lives of students. However, Yamaguchi Kumiko is in for a rude awakening when she finds she will be the homeroom teacher of 3-D, the hardest class to maintain in the school. The students have multi-coloured hair, and sloppy uniforms, and show absolutely no respect for her. The leader of the class, Sawada Shin, is lazy but bright. He shows interest in Yamaguchi when he notices that she is different from other teachers. The students try to bully her into making her quit, but their attempts don't get them far.
What the class and the rest of the school do not know is that Yamaguchi Kumiko is actually the 4th generation heir to the Ooedo Group, a notorious yakuza clan. Even though her family would like her to take the title of Ojou when her grandfather dies, they have accepted that Yamaguchi would rather be a teacher.
Eventually, the students learn to respect their quirky teacher because of her devotion to them, and they even give her a nickname: Yankumi.
(Source: DramaWiki)
~~ Adapted from the manga “Gokusen” (ごくせん) by Morimoto Kozueko (森本梢子).