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This is a phenomenographical study that aims to investigate if students and teachers have the same opinions about what is good mathematical problem solving. The study investigates the importance of communication, mathematical reasoning, and strategy when solving mathematical problems. The study also wants to investigate how different ways of teaching can affect how students learn and what kind of teaching they prefer. The result of the study shows that students and teachers agree about what is good problem solving, i.e., they agree that strategy and the communication of solutions are essential in regard to mathematical problem solving. The study also shows that where it differs in opinions is regarding how mathematical problem solving should be taught. Teachers think that the best way to learn problem solving is to work in pairs or in groups. The students, on the other hand, prefer to work alone.