Problem Posing as Providing Students with Content-Specific Motives

We interpret problem posing not as an end in itself, but as a means to add quality to students' process of learning content. Our basic tenet is that all along students know the purpose(s) of what they are doing. This condition is not easily and not often satisfied in education, as we illustrate with some attempts of other researchers to incorporate mathematical problem-posing activities in instruction. The emphasis of our approach lies on providing students with content-specific motives and on soliciting seeds in their existing ideas, in such a way that they are willing and able to extend their knowledge and skills in the direction intended by the course designer. This requires a detailed outlining of teaching–learning activities that support and build on each other. We illustrate and support our theoretical argument with results from two design-based studies concerning the topics of radioactivity and calculus.