A Comparison of Students' Problem Posing Under Different Task Conditions on Problem Validity and Mathematical Complexity

ABSTRACT This study examines how different task conditions influence the quality of seventh‐grade students' mathematical problem posing. The participants were 646 students from public middle schools who were assigned conditions: posing problems‐only or posing problems and solving the problems they generated. Students completed two semi‐structured problem‐posing tasks, one involving a growing pattern and the other a real‐life membership cost context. Student‐generated problems were analyzed using a two‐stage framework in which validity was evaluated based on whether problems were mathematical, aligned with the task context, and solvable, and mathematical complexity was examined according to the number of steps required for solution, with non‐solvable problems assigned a score of zero for group‐level comparisons. The results revealed consistent differences between the two conditions: students who only posed problems generated more valid and task‐appropriate problems and demonstrated higher levels of mathematical complexity across tasks and overall, whereas students who were required to both pose and solve problems obtained lower validity and complexity scores. These findings suggest that additional task requirements may alter the cognitive and procedural demands of problem‐posing activities, influencing the quality of students' generated problems. The findings further highlight the importance of considering task conditions when designing problem‐posing activities in middle‐school mathematics classrooms.