Teaching science and engineering involves students being asked to solve problems. The two most common approaches are complementary. Firstly, traditional lecturing initially presents the fundamental material that the students need to solve the chosen problem; then students learn about applying this knowledge through problem interaction. Secondly, problem-based learning (PBL) initially engages the students in solving the chosen problem; then the students - often through the guidance of the lecturer - discover the fundamental material "themselves". In both approaches, lecturers must identify learning objectives, and ensure that the problem both facilitates students in meeting these objectives and helps to identify which objectives have not been met by particular students. We have observed that students also learn by watching others trying to solve problems. For example, with traditional lectures the lecturer often presents a solution to a classic problem in manner that simulates, quite artificially, the way in which the problem can be solved. The advantage of this is that the lecturer has complete control over the material being presented. The disadvantage is that the students do not observe a real problem-solving process. In contrast, students watching other students problem solving (during PBL) offers the advantage of them observing a real problem-solving process. However, the lecturer has less control over them meeting their learning objectives. We report on a third (middle) way: the students formulate the problem to be solved and then observe the lecturer trying to solve it. The lecturer guides the student in problem creation and selection, and so ensures that the problem is suitable for meeting the learning objectives. Our experience shows that students learn more from watching the lecturer struggling (and often failing) to solve the chosen problem than from observing the lecturer presenting an obvious solution. Lecturers must be encouraged to exploit rather than hide their fallibility