Investigating undergraduate students’ mathematical reasoning via problem posing

Abstract

Despite the increasing amount of research into mathematical problem posing, research shows that much is still unknown about students’ cognitive processes when engaged in problem posing. In this study, 16 undergraduate students’ problem-posing products and processes are examined in order to shed light on the forms of mathematical reasoning that the students engage in while posing their own problems. To better understand these products and processes, we compare them with the previously encountered problems during class (class problems). Using Lithner’s framework (2008) alongside these comparisons, we were able to characterize the forms of reasoning that the students engaged in while posing their problems. Findings of the study indicate that while posing their own problems, most students relied on class problems and only made minor changes to these problems. As expected, their solutions to these problems were mostly similar to the class problem solutions. However, there were a few problems (28%), that were structurally different from class problems and whose solutions showed creative ways of thinking. The findings of this study provide useful insights into the cognitive processes that students engage in while posing problems. The insights can be used to better support students in posing better problems.