If you wish to learn swimming, you have to go into the water, and if you wish to become a problem solver, you have to solve problems. If you want to be a problem solver, you must solve problems.) - Polya The only way to learn mathematics is to do mathematics. (The only way to learn mathematics is to do mathematics.) - Halmos Some teachers demand that students. solve mathematics problems only by the method taught in class, This process can thwart initiative, compound frustration, and promote avoidance. (Some teachers require students to solve mathematics problems only by the method taught in class. This approach will hinder the development of original ability. , leading to failure and creating a mentality of avoiding difficulties) - Boyani When students are forced to develop their own approaches to unsolved problems, they benefit much more than from exposure to the mathematics alone. The problem is the heart of mathematics. The problem is the heart of mathematics. (Problems are the heart of mathematics.) - Halmos He who seeks for methods without having a difinite problem in mind seeks for the most part in vain. (People who don’t have a certain problem in mind and are looking for a solution are mostly in vain.) —— Hilbert The problem solver may do creative work even if he does not succeed in solving his own problem; his effort may lead him to means applicable to other problems, then the problem solver may be creative indirectly be leaving a good unsolved problem which eventually leads others to discovering fertile means． (Even if the problem solver is unsuccessful in solving a particular problem, he may have done original work; his efforts may have given him tools suitable for solving other problems. In addition, he may have left behind a very A good unsolved problem ultimately leads others to discover more effective solutions. In this way, he indirectly makes an original contribution.

) ——Polya One of the virtues of a good problem is that it generates other good problems. (Part of the value of a good problem is that it generates other good problems.) - Polya Each problem that I solved became a rule which served afterwards to solve other problems. (Every problem I solved became a rule that I later used to solve other problems.) ——Descartes