Interpretation of Students’ Errors as Part of the Diagnostic Competence of Pre-Service Primary School Teachers

Abstract

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.

Identifying and dealing with student errors in the mathematics classroom: Cognitive and motivational requirements

“…Beliefs seem to determine how teachers interpret classroom situations, what knowledge they activate in this analytical process, and what instructional decisions they make. This is consistent with research evidence suggesting that constructivist beliefs play a strong role in teachers’ competences ( Larrain and Kaiser, 2022 ) and play a role of mediation between teachers’ knowledge and their instructional practices ( Leder et al, 2002 ; Wilkins, 2008 ; Yang et al, 2020 ). Moreover, the robust effect of constructivist beliefs on the specific facet of situation-specific skills in error situations is in line with the proposed role that errors play in open and student-oriented teaching approaches.…”

“… Türling et al (2012) and Gewiese et al (2011) provided examples of a situated approach, using video vignettes to assess teachers’ understanding and knowledge of strategies for dealing with students’ errors and difficulties as more situation-specific facets of teachers’ competence. Several other studies have assessed teachers’ competence facets in more situated approaches using video vignettes ( Lindmeier et al, 2013 ; Dunekacke et al, 2015 ; Bruckmaier et al, 2016 ; Lazarevic, 2017 ; Griful-Freixenet et al, 2020 ; Dreher et al, 2021 ; Keppens et al, 2021 ; Larrain and Kaiser, 2022 ), classroom comic scenes ( Herbst et al, 2011 ; Friesen and Kuntze, 2020 ), or teaching observations ( Schlesinger and Jentsch, 2016 ).…”

“…In their conceptualization of teachers’ professional error competence, Seifried and Wuttke (2010 , p. 147) specify several points that closely refer to these situation-specific skills: “understanding […] common learner errors and difficulties in learning” (interpretation) and “strategies for dealing with those errors and difficulties” (decision-making). In German-language discourse, in particular, the identification and analysis of student errors and their possible causes are often labeled “diagnostic competence” (e.g., Wuttke and Seifried, 2013 ; Hoth et al, 2016a ; Heinrichs and Kaiser, 2018 ; Larrain and Kaiser, 2022 ; Leuders et al, 2022 ). Research in this field has already indicated that teachers’ diagnostic competence depends on their professional knowledge ( Hoth et al, 2016a ) and their beliefs ( Larrain and Kaiser, 2022 ) and can be promoted through targeted coaching and learning opportunities ( Heinrichs, 2015 ; Larrain, 2021 ).…”

“…In German-language discourse, in particular, the identification and analysis of student errors and their possible causes are often labeled “diagnostic competence” (e.g., Wuttke and Seifried, 2013 ; Hoth et al, 2016a ; Heinrichs and Kaiser, 2018 ; Larrain and Kaiser, 2022 ; Leuders et al, 2022 ). Research in this field has already indicated that teachers’ diagnostic competence depends on their professional knowledge ( Hoth et al, 2016a ) and their beliefs ( Larrain and Kaiser, 2022 ) and can be promoted through targeted coaching and learning opportunities ( Heinrichs, 2015 ; Larrain, 2021 ).…”

The impact of mathematics learning environment supported by error-analysis activities on classroom interaction

“…Moreover, this study lies in the fact that it adopts the pedagogy of mistake and the theory of negative experience, which considers errors as positive opportunities to learn mathematics. Therefore, mathematics teachers shall capitalize mathematical errors and employ them in the teaching-learning process in order to assist students in overcoming them (Gartmeier et al, 2008;Larrain & Kaiser, 2022;Parviainen, 2006;Wildgans-Lang et al, 2020).…”