From problem-solving to problem-posing: Are the ways in which 11–12-year-old students solve pattern problems related to the types of problems they pose?

We understand pattern problems as non-routine problems that require finding implicit regularities and mathematical structures to generalize beyond immediate evidence. Our study examines in what ways 11- and 12-year-old students’ approaches to solving pattern problems are related to the types of pattern problems they pose in an unstructured task. Data were collected during four sessions in which fifty students first solved a sequence of pattern problems requiring near and far generalization and later engaged in a problem-posing task. We analyzed students’ written productions to characterize the strategies they used and the extent to which they were able to generalize. We also categorized the problems they posed into null, incomplete, variation of a solved problem and new problem. Results reveal that those who did not pose any problems, or who posed null or incomplete problems, in the problem-solving task had mainly resorted to strategies that had little to do with generalization, such as extending the given drawing. In contrast, students who posed variations of previously solved problems or entirely new problems, had mainly used strategies oriented toward generalization, such as mixed strategies and the continuation of arithmetic progression. Although our findings are context‑specific, they contribute to ongoing efforts to better understand how problem‑solving experiences relate to students’ ability to pose new problems. We conclude that research seeking to explore problem-posing processes should provide students with opportunities not only to pose problems, but also to discuss and solve them, thereby facilitating a more comprehensive understanding of their reasoning processes.