Pre-service teachers' knowledge of proportional reasoning and how they recognize characteristics of students' understanding

This study examines pre-service teachers' knowledge of proportional reasoning and how they recognize characteristics of student's understanding. Ninety-two pre-service teachers solved 12 problems related to the 12 sub-constructs of proportional reasoning and analyzed three students' answers to each of the above problems. Results indicate that pre-service teachers solve problems correctly and recognize students' understanding in some sub-constructs linked to the fractional scheme but have difficulty in solving and recognizing students' understanding in the sub-constructs related to the discrimination between proportional and non-proportional situations and the ratio comparison. These results suggest that the knowledge of proportional reasoning and the recognition of students' understanding relay on the sub-constructs considered.