Katagiri's theory of mathematical thinking began in the 1960s and was mostly completed by the 1980s, and his lesson study groups have been using his ideas since 1960s, until today. If you are involved in research you may feel that it is an old theory for your reference as it is necessary to refer to the newest articles for research, but in the context of lesson study it serves as the theory that has been approved and used by a great number of teachers in the last half century.
Teachers consequently prefer this theory because of the many evidences that they experience in the process of developing children's mathematical thinking in their classrooms. Many of these experiences are well explained by this theory. He has published 81 books in Japanese for teachers to explain how to develop mathematical thinking. He is still writing. His theory was translated into Korean
and he has been working with Korean teachers, too.