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

Abstract

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.

KEYWORDS:

• Anticipating students’ thinking
• mathematical modelling
• modelling problems
• pre-service secondary mathematics teachers
• teacher knowledge

Acknowledgement

The authors would like to thank Dr. Erdinç Çakıroğlu and Dr. Bülent Çetinkaya for their comments on the earlier version. The authors are also grateful to the editor and anonymous reviewers for their constructive comments and criticism.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was partly supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under grant number 110K250. Ayhan Kursat ERBAS was supported by the Turkish Academy of Sciences through the Young Scientist Award Program (A.K.E./TÜBA-GEBİP/2012-11).