Beyond computation: Assessing in-service mathematics teachers’ conceptual understanding of fraction division through problem posing

Problem posing has long been recognized as a critically important teaching method and goal in the area of mathematics education. However, few studies have used problem posing to assess in-service teachers’ mathematical understanding. The present study investigated in-service teachers’ mathematical understanding of fraction division, which is often considered challenging content in elementary school, from three angles: computation, drawing, and problem posing. Two studies involving 66 and 193 primary and middle school teachers were conducted to reveal the in-service teachers’ mathematical understanding and whether drawing and problem posing affected each other. Although the in-service teachers rarely had the opportunity to pose mathematical problems in their daily teaching, they were able to pose mathematical problems in this study. In addition, problem-posing tasks were more useful in diagnosing the in-service teachers’ conceptual understanding than were computation or drawing. Thus, problem posing seems to have contributed to their conceptual understanding of fraction division on the drawing task.