Aspects of teachers' knowledge for helping students learn about ratio

Ratio (and associated topics such as fractions and proportion) is known to be an area of mathematics that students find difficult. Multiplicative thinking is necessary, and students benefit from a wide range of strategies and representations for interpreting ratio. This study examined aspects of teachers’ pedagogical content knowledge for teaching ratio, and investigated their knowledge of a typical misconception together with the strategies that they would use for dealing with such a misconception. The nature of the numerical examples that they suggested might be useful in teaching was also examined. Most teachers were able to recognise the misconception, but not all were able to generate examples that might help students to deal with it. Teachers also appeared to have only a limited repertoire of strategies to assist students.