An analysis of unexpected responses in middle school students’ mathematical problem posing from the perspective of problem-posing processes

Abstract Using data from a problem-posing project, this study analyzed the characteristics of middle school students’ responses to problem-posing prompts that did not match our assumptions and expectations to better understand student thinking. The study found that the characteristics of middle school students’ unexpected responses were distributed across three different problem-posing processes: 1) orientation responses related to different interpretations of the problem-posing prompt or situation accounted for the majority; 2) connection responses related to making connections among pieces of information accounted for the second most common type; and 3) generation responses related to generation of problems only accounted for a very small proportion. Additionally, it was found that the problem-posing prompts influenced the distribution of types of unexpected responses. These findings contribute to our understanding of problem-posing processes and have implications for the design of problem-posing tasks. Most importantly, this analysis reveals that even though these responses are unexpected, students’ responses make sense to them and our objective should be to make sense of their responses.