Most educators would think of heuristics when it comes to solving closed mathematical problems, while many researchers believe that mathematical investigation must be open and is different from problem solving. In this chapter, we discuss the relationship between problem solving and investigation by differentiating investigation as a task, as a process and as an activity, and we show how the process of investigation can occur in problem solving if we view mathematical investigation as a process consisting of specialising, conjecturing, justifying and generalising. By looking at two examples of closed mathematical tasks, we examine how investigation can help teachers and students to solve these problems when they are stuck and how it can aid them to develop a more rigorous proof for their conjectures. We also deliberate whether induction is proof and how heuristics are related to investigation. Finally, we consider the implications of the idea of solving mathematical problems by investigation on teaching.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.