Supportive roles of teachers' belief and knowledge regarding rationality of fractions

Mathematics teachers' belief and knowledge are two influential factors in mathematics education. Focusing on the supportive roles of the factors, this study examines the way they interact in practice when teachers encounter students' incorrect arguments. To do so, 84 male pre-service teachers were interviewed as to two specific situations where a student commits errors regarding rationality of fractions which challenges learners and teachers. Analysing syntactic and semantic interferences involved in the student's arguments and errors, this study identified three types of reaction in teachers' behaviour. The practical supportive roles of belief and knowledge in teachers' reactions and also implications for teaching and learning are discussed.