Problem posing in middle-grades mathematics classes

Abstract

Problem posing refers to the generation of new problems or the reformulation of previously given problems. Problem posing has received increased attention recently, but studies indicate problem posing is an emerging topic in mathematics education research. In this observational, interpretive study, I observed 88 mathematics lessons from six teachers in Grades 5 through 7. I analyzed transcripts from the 88 filmed lessons over 1 school year of instruction. I identified instances of problem posing across those 88 lessons in order to better understand when and how problem posing occurs. The teachers most commonly asked students to generate problems like an example problem, or they asked students to create contexts for routine mathematical exercises. I also focused on one teacher who engaged students in problem posing more than others in the sample. I interviewed that teacher in order to try to understand more about motivation to use problem posing and her past experience with problem posing. I asked stimulated recall questions and showed her video clips from her class in order to prompt her to reflect on various instances of problem posing from the school year. For Ms. Green, motivation to use problem posing included differentiation, connections to real-life contexts, and student engagement. Based on these findings, I recommend additional research to learn about the prevalence of problem posing as well as ways to encourage more teachers to use problem posing in mathematics classes.