After Gohan published the "Groundbreaking Science", and in the midst of increasing enthusiasm in ki-based martial arts, the hope-filled words of many wishing for the establishment of a school began to reach even Master Roshi's ears. However, citing his old age, the Turtle Hermit refused to accommodate these requests—instead, he passes down that role to Krillin and Tien Shinhan.
For Krillin, his experiences in past battles had left him overwhelmingly awed at the gap in power between Earthlings and those of tremendous physical capabilities, such as the Namekians. Thinking hard about what role human warriors could play, he decided on a supportive mindset. Even if he could not deliver a decisive blow to an opponent by himself, there were ways to use aspects of the battle to one's advantage—such as waiting for an opportunity to reduce the enemy's speed or strengthen one's ally. He persuades the new generation of warriors that it was absolutely crucial to have a person who could play such a supportive role, that such people are needed in these battle roles in order to fight against truly overwhelming opponents. He had acted in precisely this capacity during many of his battles with Goku and the others, and he is convinced that assistance was not a "lesser" role.
Perhaps Krillin's decision to establish his school in the town in where Goku had first demonstrated his strength was an expression of his competitive spirit. Such beliefs continue to be carried by the "Turtle Hermits", even after Krillin's death.
Tien Shinhan, who had previously trained alone, makes the "New Crane School" official. His pupils are the "Crane Hermits".
Tien Shinhan had been lost in apprehension. Through his experiences in past battles alongside the Saiyans, Piccolo and others, he's come to acknowledge the gap in power between humans and aliens, but refuses to accept it. While continuing his training as he travels all over the world, Tien Shinhan comes to the conclusion that instead of playing a supporting role, it was important to focus on perfecting ki based attacks. Tien Shinhan remembered how Goku used a Super Spirit Bomb against Majin Buu during their battle; that was the first time he had sent him his energy. Even in the battle against the Androids, whose power greatly outclassed his own, an well timed Neo Tri-Beam—although it did not deliver serious damage—seemed to have potential. No matter how strong an opponent is, if one can push their ability to gather ki for attacks to the extreme, it would be a great advantage. This key point was never forgotten. Tien Shinhan's belief of attacking with concentrated ki blasts at precise moments is carried on by subsequent "Crane Hermits".
Could it be that the reason Tien Shinhan decided to open his dojo at the Pleasant Mountain (formerly Fire Mountain) was in order to not forget about the Turtle Hermit's teachings?