An Investigation of pre-service secondary mathematics teachers’ knowledge of students’ thinking through analyzing student work

Didiş, Makbule Gözde
The purpose of this study was to investigate pre-service secondary mathematics teachers’ knowledge of students’ thinking within an undergraduate course context. The participants were twenty five pre-service mathematics teachers enrolled in this undergraduate mathematics education course which aims to develop pre-service mathematics teachers’ knowledge in and about mathematical modeling in teaching and learning mathematics. The design of the study contained 4 two-week cycles. In the first week of each cycle, pre-service teachers worked on a non-routine mathematical task to develop their own solutions. The following week, they analyzed and discussed actual high school students’ solutions produced on the same task through students’ solution papers and video episodes, where students presented their solutions to their classmates. The data were collected through pre-service teachers’ reflection papers, note-taking sheets, individual and focus group interviews, and observation notes. The findings showed many predictions of pre-service teachers were not consistent with students’ actual ways of thinking, especially, at the beginning of this research. However, great portion of pre-service teachers’ predictions have become consistent with them over time. In addition, analyzing students’ works helped pre-service teachers value students’ ways of thinking that was different from theirs, and develop process-oriented criteria to analyze students’ works. Furthermore, the findings showed that pre-service teachers were able to interpret students’ ways of thinking in three different ways “describing, questioning and explaining”. This study revealed that analyzing students’ works containing actual students’ solutions for non-routine tasks provided pre-service mathematics teachers with rich opportunities to learn about students’ thought processes in mathematics.