Adidactical problem-posing as captured by scripting journeys: Investigating sums of consecutive integers

Research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and full extent of this relationship requires detailed elaboration. This is especially true when problem-posing arises in order to facilitate problem-solving, such as during the investigation of an unfamiliar mathematical property or phenomenon. In this study, groups of participants used scripting to record their mathematical activity as they made conjectures and justified conclusions about sums of consecutive integers. We analyze the unprompted problem-posing found within these scripting journeys using three facets of a problem-posing framework: mathematical knowledge base, problem-posing heuristics, and individual considerations of aptness. Our analysis reveals how these aspects of problem-posing emerge within a mathematical investigation, how they are related to surrounding problem-solving, and the kinds of mathematical insights and realizations that act as catalysts to promote further problem-posing activity.