A five-phase model for mathematical problem solving: Identifying synergies in pre-service-teachers’ metacognitive and cognitive actions - Yimer, Asmamaw; Ellerton, Nerida F. (ZDM, 2010)
Based on empirical data from a study of pre-service teachers engaged in non-routine mathematics problem solving, a five-phase model is proposed to describe the range of cognitive and metacognitive approaches used. The five phases are engagement, transformation-formulation, implementation, evaluation and internalization, with each phase being described in terms of sub-categories. The model caters for a variety of pathways that can be adopted during any problem-solving process by recognizing that the path between these five phases is neither linear nor unidirectional.