Pre-service Middle Grade Mathematics Teachers’ Ability to Notice: The Case of Fractions

Abstract

There is an increased attention to integrating student understanding in classroom instructions. However, interpreting how students understand concepts and responding to them on the basis of their understanding in the moment is not an easy feat. The purpose of this study was to investigate pre-service mathematics teachers, grade 5-8, ability to notice student understanding of the concept of fractions. In addition to investigating pre-service teachers’ ability to notice, this study also aimed to analyze pre-service teachers’ own understanding of fractions. A mathematics education course was designed to engage pre-service teachers with teacher noticing activities, which consisted of solving high cognitive level tasks, explaining student solutions for the same tasks and responding to the students on the basis of their understandings. The data included pre-service teachers’ responses to a quiz and mid-term exams that consisted of various open-ended fraction questions. Additionaly, classroom instruction videos during three weeks also served as main data sources. The results of the study demonstrated that the pre-service mathematics teachers struggled with the concept of fractions, specifically writing story problems to illustrate fraction expressions or solving fraction expressions without using standard algorithms. Additionally, they also struggled with explaining students’ solutions and deciding how to respond to the students on the basis of their understandings of fractions.