Understanding the Potential of Anticipation, Teaching, and Response to Struggle in the Learning of Mathematics

Abstract

This qualitative semi-structured interview study investigated how the opportunity to learn with productive struggle emerges in a teacher’s beliefs, anticipation, planning, teaching, and response to struggle in learning mathematics. In this study, the experiences of student struggle in the teaching and learning of fractions was investigated through the experiences of three fifth grade and one sixth grade teacher. The purpose was to understand how the phenomenon of productive struggle in learning mathematics was impacted by teachers anticipation, planning, teaching, and response to struggle. The central research question asked: What role does productive struggle play in the design and implementation of mathematics lessons? Three interviews provided a progressive focus on the phenomenon as each participant’s experience with productive struggle was illuminated. Attendant questions guided the interviews: How do teachers perceive their role and the role of students as it relates to learning with productive struggle? How do teachers prepare for anticipated struggle when planning for mathematics instruction? How do teachers respond to evidence of struggle in student learning? and Do the responses have the potential to invoke a productive struggle for students? The findings provide compelling evidence that the phenomenon of productive struggle in learning mathematics is directly impacted by a teacher’s beliefs about the role of struggle in learning mathematics. Seven findings emerged: (1) Teachers describing a student-centered and constructivist learning environment were more likely to indicate an opportunity for learning that fostered productive struggle, (2) Teachers describing a teacher-centered and transmissionist learning environment were more likely to indicate a diminished opportunity for learning with productive struggle, (3) Teacher descriptions of students’ mathematical understanding indicated a relationship to their teaching philosophy, (4) Teachers’ beliefs provide a strong indication of an opportunity or lack of opportunity for their students to learn with productive struggle, (5) Teachers who believe that struggle is a benefit to student learning create this opportunity, while teachers who believe that struggle is a barrier remove or diminish this opportunity, (6) Teacher inability to recognize productive struggle among students in their classrooms impacted their responses to evidence of student struggle, and (7) Teachers removed the opportunity for learning with productive struggle when students demonstrated a prolonged struggle following probing. Expanding upon important research on productive struggle, the findings of this study suggest that understanding the relationship between our beliefs, practices, and ability to identify productive struggle has a direct impact on students’ opportunity to learn with productive struggle.