Metacognitive reflections on trajectory strategies in mixed reality: real-time and retrospective reports during mental jigsaw puzzles

Real-world object fitting often requires indirect, detour-like trajectories due to physical constraints, such as lifting and maneuvering physical puzzle pieces. Reflecting this, recent work using three-dimensional puzzle stimuli has reported asymmetric reaction time (RT) patterns around 180° in fitting tasks—and unexpectedly, even in classical mental rotation tasks that require object matching. This finding challenges the classical assumption that equal angular disparities yield equivalent RTs. One possible interpretation is that RTs reflect not only rotational but also translational components of mental manipulations; however, classical matching tasks contain no physical obstacles that would necessitate detour-like trajectories. Thus, behavioral RT data alone are insufficient for determining whether detour-like mental translations are actually involved. To address this limitation, the present study incorporated metacognitive reflection on translational trajectories during both fitting tasks and classical matching tasks. Participants first completed both tasks under speed–accuracy instructions, after which they retrospectively selected the animation (shortcut vs. detour trajectories) that best represented their strategies during these earlier cognitive tasks. These retrospective reflection reports were compared with real-time reflection reports to assess their malleability. Replicating previous work, RTs showed robust asymmetries around 180° in both tasks. Crucially, subjective strategy reports diverged from these behavioral patterns: retrospective reflections mirrored RT asymmetries in the fitting task but not in the classical matching task. Moreover, metacognitive reflections were malleable in the fitting task, whereas they remained stable in the matching task.