Problem posing in the content of motion in one dimension

Abstract

Problem posing is a core mathematical activity, yet the “What If?” boxes that accompany worked examples in introductory physics textbooks — a built-in, structured invitation to vary a solved problem's conditions and pose a new one — have not been examined through a problem-posing lens. This study addresses that gap by applying three-dimensional framework, which characterises problem-posing activities along the dimensions of generating versus reformulating, routine versus non-routine problems, and low versus high metacognitive behaviour (planning, monitoring, evaluating), to the “What If?” features embedded in the chapter “Motion in One Dimension”. Using a qualitative content-analysis design, the study coded the three “What If?” boxes attached to Examples 2.7 (Carrier Landing), 2.8 (Watch Out for the Speed Limit!), and 2.12 (Not a Bad Throw for a Rookie!), together with the chapter's General Problem-Solving Strategy (Conceptualize, Categorize, Analyze, Finalize). The analysis shows that all three “What If?” boxes are reformulations that vary a single condition of an already-solved problem, that Example 2.7 extends into generation by introducing a new condition (a fixed deck length) to pose a solvable follow-up problem, that the three examples span the routine–non-routine spectrum from a direct re-application of a kinematic equation to the recognition that building height is an irrelevant condition, and that all three model high metacognitive behaviour by predicting the direction of a result before recalculating it. The findings also show that Serway and Jewett's Conceptualize–Categorize–Analyze–Finalize strategy maps closely onto Baumanns and Rott's planning–monitoring–evaluating triad. The findings imply that physics instruction can treat “What If?” boxes as deliberate problem-posing training, an application of What-If-Not strategy that physics textbooks appear to have converged on independently.