How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles

Interpreting and responding to student thinking are central tasks of reform-minded mathematics teaching. This study examined preservice teachers' (PSTs) interpretations of and responses to a student's error(s) involving finding a missing length in similar rectangles through a teaching scenario task. Fifty-seven PSTs' responses were analyzed quantitatively and qualitatively. Analysis results revealed that although the student's errors came from conceptual aspects of similarity, a majority of PSTs identified the errors as stemming from procedural aspects of similarity, subsequently guiding them by invoking procedural knowledge. This study also revealed two different forms of address and teaching actions in PST interventions along with three categories of acts of communication barriers. The broader implications of the study for international communities are discussed in accordance with the findings.