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In this study, the variety in quality of instruction in fraction lessons at Grade 5 in Dutch primary schools was investigated. Twenty-four teachers participated in the study. To examine the quality of instruction of fraction lessons, Hill’s mathematical quality of instruction framework and general pedagogical instruction strategies (seen to contribute to effective teaching) were combined into an observational scheme. In particular, it was investigated if profiles based on lesson observations could be identified using cluster analysis, and how these profiles could be characterized. The cluster analysis was validated by comparing different types of cluster analyses, discriminant analysis as well as via expert consultation sessions. Results showed six profiles of fraction lessons, which differed in terms of the extent to whether teaching was connectivist or transmissionist in nature, and the extent to which teaching was student-focused or content-focused. The study contributes to existing studies by developing the  Quality of Instruction for Fraction Lessons (QIFL)  framework, and by showing a more nuanced and richer picture of the teaching of fractions than previous studies. In terms of practical implications, the study showed that it is the combination of organizing a lesson well, a good pedagogical climate, and a focus on understanding the subject matter that contributes to good teaching.

Portraying Primary Fraction Teaching: A Variety of Mathematical Richness, Pedagogic Strategies, and Use of Curriculum Materials