"Exaggerated independence and broadness" may emphasize independent learning and extensive knowledge. Boasting independence may mean encouraging students to think independently and make decisions independently in the learning process, rather than just accepting teachers' guidance and explanation.
"Encyclopedia follows nature" may emphasize a learning method that follows the laws of nature step by step. Class encyclopedia may refer to all kinds of knowledge of a class or a study group, while following nature may refer to teaching and learning according to the laws of nature and students' development.