On understanding mathematical problem-posing processes

Abstract

Problem posing engages students in generating new problems based on given situations (including mathematical expressions or diagrams) or changing (i.e., reformulating) existing problems. Problem posing has been at the forefront of discussion over the past few decades. One of the important topics studied is the process of problem posing as experienced by students and teachers. This paper focuses on problem-posing processes and models thereof. We first provide an overview of previous research and then present the results of a scoping review regarding recent research on problem-posing processes. This review covers 75 papers published between 2017 and 2022 in top mathematics education research journals. We found that some of the prior research directly attempted to examine problem-posing processes, whereas others examined task variables related to problem-posing processes. We conclude this paper by proposing a model for problem-posing processes that encompasses four phases: orientation, connection, generation, and reflection. We also provide descriptions of the four phases of the model. The paper ends with suggestions for future research related to problem-posing processes in general and the problem-posing model proposed in particular.