Interpretation of students’ errors as part of the diagnostic competence of pre-service primary school teachers
Peer reviewed, Journal article
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Original versionLarrain, M. & Kaiser, G. (2022). Interpretation of students’ errors as part of the diagnostic competence of pre-service primary school teachers. Journal für Mathematik-Didaktik, 43(1), 39-66. doi: 10.1007/s13138-022-00198-7
Understanding students’ thinking and learning processes is one of the greatest challenges teachers face in the classroom. Misconceptions and errors have the potential to be a rich source of information for identifying students’ thinking and reasoning processes. However, empirical studies show that pre-service teachers (PSTs) and teachers find it challenging to focus their interpretations and pedagogical decisions on students’ thinking processes when they identify students’ mathematical errors. Based on the theoretical approach of noticing, the study described in this paper examines primary PSTs’ diagnostic competence in error situations before and after they participated in a seminar sequence implemented at several Chilean universities. Our analyses focus on PSTs’ competence with regard to formulating hypotheses about the causes of students’ errors. The proposed hypotheses were categorized into those that attributed errors to students’ lack of conceptual understanding, those that explained errors in terms of lack of procedural understanding, and those that assumed a failure of instructional strategies. In addition, the relationships between PSTs’ diagnostic competence, their beliefs and university learning opportunities were examined. The results indicate that PSTs’ diagnostic competence in error situations and the changes of this competence were related to PSTs’ beliefs, practical experiences, and learning opportunities. Overall, the findings suggest that it is possible to promote changes on PSTs’ diagnostic competence during initial teacher education. The paper concludes with implications for teacher education and future research.