Pre-service secondary mathematics teachers' anticipation and identification of students' thinking in the context of modelling problems*

This study investigated pre-service secondary mathematics teachers' (PSMTs') anticipation and identification of students' thinking as they engaged in examining and analyzing student work on four modelling problems. The study comprised four two-week-long cycles. The data were collected through individual reflection papers and written group reports on students' ways of thinking from 25 PSMTs enrolled in a semester-long (15-week) elective course. Data analysis focused on the PSMTs' anticipation and identification of students' ways of thinking in the context of modelling problems over the cycles. Results indicated that the PSMTs were able to anticipate and identify some of the students' possible solution approaches, errors, and difficulties for each modelling problem used in the study. However, some of their anticipations remained vague throughout the study. On the other hand, identifying students' different responses helped most of the PSMTs to increase their awareness of students' various ways of thinking throughout the study. The implications of the findings for PSMTs' anticipations, identification, and learning about students' thinking are discussed.