The purpose of this paper is to throw light upon the continuation (succession・development) of secondary school in new system (after the war) and old system (before the war) from an arithmetical and mathematical point of view. The results of this paper is the following. Mathematics for secondary school in new system (1947) gives students more examples and experiments than secondary school in old system (1944), and the students in new system (1947) are aware of mathematics in "life", and study "mathematics". Arithmetic for the higher elememtary course and mathematics for secondary school in new system (1947) is mathematics in connection with "life", and mathematics for secondary school in old system (1944) manages life probrem in connection with "mathematics". With respect to educational pupose and contents, arithmetic for the higher elememtary course opens into mathematics for seondary school in new system (1947).