Abstract
Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices. As most previous literature has studied feedback provided on homework or video prompts, how teachers provide such feedback in the classroom is poorly understood. Here, sixteen lessons taught by five teachers were purposefully sampled from a larger video study (172 lessons) as lessons with high-quality feedback according to a standardized observation instrument. The analysis focused on the instructional situations in which teachers provided feedback. When teachers provided procedural feedback, the situations were orderly and effective. Feedback on conceptual understanding and mathematical practices was provided in situations when students were especially challenged, and entailed a series of complex decisions, thereby placing demands on the teachers to manage both the students’ understanding and behavior. We argue that researchers should focus on how teachers and students negotiate the instructional situation to allow for feedback on conceptual understanding or mathematical practices.
Highlights
Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices
We aimed to answer the following research question: What distinguishes the instructional situations in which these teachers provide procedural feedback from the situations when they provide substantive feedback? We focus on oral feedback provided during lessons, because this constitutes the majority of feedback provided by teachers (Ruiz-Primo & Kroog, 2018) and may impact students more than written feedback on assessments and homework (Shavelson, 2003)
We identified two types of instructional situations where teachers provided procedural feedback and two types of instructional situations where they provided substantive feedback
Summary
Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices. Research on how teachers provide feedback in mathematics shows that teachers mainly tend to address procedural skills (Stovner & Klette, in review; Casey et al, 2018; Runnalls & Hong, 2019; Sánchez-Matamoros et al, 2019; Son, 2013). A main contribution in the present study is that we investigate feedback in authentic in situ mathematics lessons and not in experimental or other artificial situations This complements previous laboratory and intervention studies by elucidating the repertoire required to provide substantive feedback while managing the complexity of the instructional situations. Within AfL, feedback is communication to students about how they are doing and what they can do to improve, so that they may direct their learning (Wiliam, 2007)
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