With an IQ of 200, Kanzaki is the most intelligent character in the series. Unlike many of her classmates in 3-4, her class terrorism started in elementary school.
Despite, or due to, her intelligence… she like playing around doing whatever she finds fun. This stems from her belief that life is ultimately meaningless, thus she spends her time having fun.
She initially starts her class terrorism after she develops a (very) close bond with her teacher, Fujimori-sensei. Fujimori-sensei started out by teaching her extra material, but Kanzaki inevitably outpaces her. Fujimori grew more and more frustrated over time, leading to a burst of anger… that leads Kanzaki to start her class terrorism. Her bond with Fujimori-sensei is essentially that of a daughter and mother, which made Fujimori’s outburst all the more painful.
Onizuka’s presence essentially changes her outlook on life, no longer suicidal or nihilistic (well…). This also leads her to (eventually) fall in love with Onizuka. She also reconnects with her old teacher, with both of them apologizing for each-others mistakes.
Her personality is playful overall. She views herself as better than others due to her intelligence, although she tones this down over time. When something happens she doesn’t like (Onizuka in trouble, her secret coming out) she tends to get incredibly serious, which occasionally leads her to do some… less than legal things.