Some teachers teach beginners to practice fingering first and then play the music, and some teachers teach beginners to play the music directly and practice fingering in the music. Which of these two methods is better?

Both methods can be used, and there is no essential difference. But personally, I prefer to let beginners learn some basic fingering first and then learn piano music. Such as the right-hand eight methods and the left-hand chanting, yao, chuo, note and overtone exercises. Strict training of these basic fingerings can lay a good foundation for future piano learning. Just as Peng Zhiqing said in the preface of his "Tongxin Pavilion Fingering Analysis Micro": "Fingering is the beginning, the foundation of real qin learning". Learn qin music directly without a little fingering foundation, although it increases the interest of beginners at the beginning. But it may not be a good thing for future development.