To know Katagiri's theory, it is better to be familiar with the several perspectives for developing mathematical thinking which are well known in mathematics education researches. Many of the researches have been done based on their own research questions through case studies by observing limited children in the context of social science. Those researches are out of the scope of this book, because this book is aimed at explaining how to design classroom practice to develop mathematical thinking. To give a clear position to Katagiri's theory, which has been used in the context of classroom practice and lesson study for developing mathematical thinking, here we would like to present some bird's-eye views of the theory.