Teaching interrelated concepts of fraction for understanding and teacher's pedagogical content knowledge

Fractions are perceived as one of the most difficult areas in school mathematics to learn and teach. The most frequently mentioned factors contributing to the complexity are fractions having five interrelated constructs (part-whole, ratio, operator, quotient and measure) and teachers' pedagogical approaches to address these constructs. The present study used the five interrelated constructs of fraction and the Knowledge Quartet Framework to investigate a teacher's teaching of fraction in a New Zealand Year 7 classroom. Video recordings and transcribed audio-recordings were analysed through the lenses of the five integrated constructs of fraction and the Knowledge Quartet Framework. The findings showed that students often initiated uses of fractions as quotient and as operator, drawing on part-whole understanding when solving fraction problems. The study showed that the teacher's focus in connecting the constructs and procedures of the lesson as well as shaping the classroom discussion when the lesson unfolded supported students' learning of the fraction constructs. [Author abstract]