Relationships Between Teachers’ Interactions with Learner Errors and Learners’ Mathematical Identities

Teachers’ Error-handling Practices Within and Across Lesson Phases in the Mathematics Classroom

“…We, therefore, distinguish between slips and conceptual errors. As mentioned in the introduction and then further clarified in the methodology, this study focused on conceptual errors, which might be considered either misconceptions, or yet incoherent knowledge pieces that are productive in some situations but not in others (Gardee & Brodie, 2021;Scheiner, 2020). According to a knowledgein-structures' perspective, students' misconceptions can be characterized as systematic patterns of errors (Scheiner, 2020).…”

“…Discussing errors with the students will give teachers access to students' current thinking (Gardee & Brodie, 2015). Students might understand and learn better when errors are discussed in the classroom, rather than being corrected or avoided (Gardee & Brodie, 2021). If teachers avoid or ignore the error, the students will not have access to understand why their errors are incorrect.…”

“…In such situations, the teacher thus involves the students in the discussion more than in other phases. How teachers handle students' errors can have significant implications to students' learning (Ingram et al, 2015) and using students' errors as springboards for inquiry has been emphasized by several scholars (Bray, 2011;Brodie, 2014;Gardee & Brodie, 2015, 2021Ingram et al, 2015;Santagata, 2005;Schleppenbach et al, 2007). It can be argued that when the teacher uses students' errors to set up a discussion with the class, the errors can act as productive pathways for building new concepts (Boaler, 2015).…”

“…Errors can provide opportunities for learning if the reasoning and underlying errors can be identified and explored as part of learning activities (Brodie, 2014). Alternatively, certain error-handling practices could also influence students to develop unproductive mathematical identities (Gardee & Brodie, 2021). Due to several dimensions of the role of errors for students' learning, research has examined different strands of teachers' error-handling practices in mathematical teaching, such as how student errors can be treated as an opportunity for learning in the classroom (Ingram et al, 2015), how teachers from different cultures handle errors differently (Santagata, 2005;Schleppenbach et al, 2007), and how teachers' beliefs and knowledge influence their error-handling practices during whole-class discussions (Bray, 2011).…”

Supervisory Performance of Cooperative Teachers in Improving the Professional Preparation of Student Teachers

“…In hindsight, Jordanian universities have started to develop special programs for preparing teachers in line with the recommendations of the Jordanian educational reform movement. These programs have sought to provide student teachers with appropriate knowledge, skills and tendencies that would contribute to the preparation of the teacher (Makovec, 2018;Fraihat et al, 2022;Gardee & Brodie, 2022), because there are essential things considered to ensure a high level for the teacher to participate in developing the teaching and learning process (Makovec, 2018;Verde & Valero, 2021). Teacher-preparation programs accompanying the educational development process have been characterized by the inclusion of the so-called education field-training, which is a transitional stage between academic and behavioral education and the practicality of the teaching profession in order to bridge the gap between theory and practice (Verde & Valero, 2021;Zega & Lase, 2021).…”