From Mistakes, We Learn: Variations in Teacher Dis/Position Toward Errors in Mathematics Classrooms
Mistakes are commonly perceived by students and teachers as an evidence of a lack of knowledge and ability (Brown, & Quinn, 2006). Recently, U.S. and Mexico mathematics education reforms has been calling to promote a positive status of errors in mathematics teaching and learning. The purpose of this mixed-methods study is to examine secondary mathematics teachers’ dis/positions toward mistakes in two contexts: their own mistakes and their students’ mistakes. The study employs the frame of teacher dispositional functions (Beyers, 2011) which includes cognitive, affective, and conative characteristics. The frame provides a better understanding of teachers’ dis/positions toward errors based on the type of frames they enact during classroom episodes. This study also seeks to contribute to the literature with the aim of emphasizing a critical role that teachers’ disposition and framing toward mistakes play in student learning and understanding. The study was conducted using an explanatory sequential mixed methods design. During the quantitative phase, the Error Orientation Questionnaire (EOQ) (Rybowiak, Garst, Frese, & Batinic, 1999) was used to measure mathematics teachers’ disposition toward mistakes. The participants for this phase of the study (N=106) were selected using convenient sampling from the US-Mexico border region. The qualitative phase was conducted using classroom observation protocol and semi-structured interview with a purpose of explaining the quantitative results. In this follow-up, the purposefully selected subset of teachers’ (n=3) framing were closely examined at the level of a moment-to-moment classroom interaction in the context of errors (Greeno, 2009). As integration of quantitative and qualitative phases, narratives of the selected teachers’ disposition were unfolded and analyzed using meaning coding technique (Kvale and Brinkmann, 2009). The study’s main finding confirms an alignment between teachers’ disposition and their invoked positional frames in mathematics classroom. Teachers’ practices reflected their disposition toward mistakes from multiple perspectives including cognitive, conative, and affective characteristics. However, tensions were identified between teachers’ understanding of mathematical reform that proposes a productive role of errors in mathematics learning and teachers’ attempts to apply teaching strategies that incorporate error analysis. Furthermore, in some cases teaching practices had the unintentional and inadvertent effect of perpetuating correctness as paramount (Louie, 2017). Those cases provided an example of challenges that teachers face when productively using errors in the classroom as suggested by the reform movement. In this study, two opposite error frames were identified: 1) productive framing that provides student autonomy and support for using errors as tools for their learning; 2) non-productive framing that reinforces an idea of student incapacity to cope with their own mistakes and, subsequently, positioning errors as learning deficiencies. Furthermore, the study findings suggest that having a productive disposition toward mistakes does not guarantee teachers’ positioning to frame errors productively in mathematics classroom.
Mathematics education|Educational evaluation|Educational psychology|Personality psychology|Behavioral psychology
Alvidrez, Mariana, "From Mistakes, We Learn: Variations in Teacher Dis/Position Toward Errors in Mathematics Classrooms" (2019). ETD Collection for University of Texas, El Paso. AAI27665012.