Karl's the popular guy in school, his circle included Touji, Kensuke, and Hikari. He acted as the leader and the moodmaker when he's hanging with his circle, but basically a rebel to the teachers.
Apparently, the school was a preparatory academy for military purpose, perhaps kinda like FFVIII school. Karl and friends regularly had to pass tests of unique subjects designed to shape a soldier with top military skills as well as good character.
This time around, for some reason the ethics test (sorta Confussian Classics test in Imperial Examination in the time of Imperial China) had to be taken in pairs. Everyone else could freely form pairs, only Karl wasn't allowed to, as a punishment of his recent problematic behavior. The teacher paired him with a mysterious girl not from his class, who looked like Haruhi from Ouran, had similar personality to Akashi of Tatami Galaxy, and voiced by Maaya Sakamoto......turned out it's SHIN(JI)KO. Karl found Shinko difficult, they never got along...
...until in the last minutes, Shinko saved Karl from getting a fail grade by giving him answer hints. It affected him deeply, he got crush on her at that point. After the test ended, Shinko was nowhere to be found at school. Later, Karl found that Shinko came to his school due to her circumstances, likely because of failing some subjects. And now that everything had gone to where it should be in Shinko's life, Karl got the impression that outside forces are not allowing him to advance their relationship, making the ethics test the first and the last time he could be with her. The dream ended there, kinda bittersweetly. ^^;