This was obvious that the calamity came from an extra person. They had sensed a pattern based on history of the class. Various countermeasures came up but they were unsure of a permanent solution.
Let's look at the timeline:
1972: A student named Misaki Yomiyama died in a house fire. The students didn't believed he was dead and put his desk in the class. Over time, their memory garbled and completely forgot about him next year.
1973: The class founds that there is an extra person and one desk short (the soul of Misaki converted into a physical being that gave a illusion of extra person). The students ignore but calamity struck in order to give space for the extra. People got killed
1983: Katsumi Matsunaga and his friends went to shrine. He got an argument with the extra and accidently killed him. Next day, he didn't found the body. Calamity ended prematurely. He come to conclusion that if you kill the extra, then the calamity will stop. He taped the conclusion in a video recording. It is to be retrieved in 1998.
1988: Over the years, the students tried many ways to prevent the calamity, nothing proved to be successful. Eventually, they came up with a plan to ignore one student as if he/she doesn't exist, in order to make up for the presence of the dead person. For a whole year, the class would not acknowledge their presence or speak about them during school hours. This measure is followed in coming years.
1998: Kouichi Sakakibara got transferred to class 3-3. Believing that he might be the extra, students ignored him. Calamity struck before he transferred, thus proving he was not extra. Finds the tape. Kouchi finds out the extra amidst chaos. Kills her. Calamity stops.