Abstract: This study examined the connection between subject matter knowledge (SMK) and pedagogical content knowledge (PCK) among a group of Chinese pre-service mathematics teachers teaching three-term ratio. Both video-based interview and task-based interview approaches were employed to investigate six pre-service teachers’ (PSTs) conceptual understanding of ratio and their PCK on teaching the topic. The results suggest that the PSTs had an unstable and inconsistent understanding of the concept of ratio, which influenced their presentation of the concept of three-term ratio. Those who possessed multiple understandings of this concept tended to be more flexible when choosing different representations. Some implications for future studies on investigating the relationship between SMK and PCK and for teacher education were discussed.

Key words: subject matter knowledge, pedagogical content knowledge, the concept of ratio, pre-service secondary mathematics teachers