At senior high school mathematics level, it is a critical task to realize the transfer from "passive learning" to "active learning". The aim of this paper is to propose the teaching and learning of "problem-solving centered mathematics" as one promising scheme. The word of "problem-solving centered mathematics" should be interpreted in a wide sense. In this scheme, students pose mathematical problems from a given situation, solve them using their acquired mathematical knowledge and skills, and then make new mathematical problems using a so-called "what if not?" strategy.
As an example of this scheme, we explore a typical development of mathematical problems which can be posed from a situation; consider squares inscribed in a certain square. The development of them is summarized in a lesson plan.