Student Engagement with Others’ Mathematical Ideas

Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom

“…We took inquiry as a process of collaboratively addressing complex, ambiguous tasks that require negotiation and mathematical evidence. The norms of mathematical inquiry follow those proposed by other researchers (e.g., Cobb, 1999;2002;Franke et al, 2015;McClain & Cobb, 2001;Yackel & Cobb, 1996) that go beyond simply explaining one's own work to engage with others' ideas (e.g., active listening, explaining and justifying ideas, building on others ideas, and sharing incomplete ideas). Our focus on argumentation practices in inquiry emphasised the negotiation and classroom discourse aspects.…”

Formatively assessing prospective teachers’ skills in leading mathematics discussions

“…Probing student thinking refers to the work that teachers do to follow on individual students’ thinking to get students to further elaborate their ideas (Herbel-Eisenmann et al, 2013 ), including actions that teachers can use to ask for clarification and elaboration (Erath, 2018 ; Prediger & Pöhler, 2015 ; Prediger et al, 2015 ), extend student thinking (Cengiz et al, 2011 ), and make communicative demands explicit (Erath, 2018 ). Orienting students to thinking of others refers to the work that teachers do to support students in engaging with others’ ideas, including “asking students to revoice (or restate) another’s idea” (Chapin et al, 2013 ; Herbel-Eisenmann et al, 2013 ), “posing questions to students about others’ ideas and contributions” (Herbel-Eisenmann et al, 2013 ), and “encouraging students to attend, listen and respond to peers’ contributions.” Such engagement supports student learning, and the teacher has a critical role in supporting this engagement (Franke et al, 2015 ). Making contributions refers to the direct contributions that teachers make to a discussion, such as “ensuring that substantive and relevant analysis is part of the discussion” or “introducing particular vocabulary” (a mathematical contribution).…”

“…Orienting students to thinking of others refers to the work that teachers do to support students in engaging with others' ideas, including "asking students to revoice (or restate) another's idea" (Chapin et al, 2013;Herbel-Eisenmann et al, 2013), "posing questions to students about others' ideas and contributions" (Herbel-Eisenmann et al, 2013), and "encouraging students to attend, listen and respond to peers' contributions." Such engagement supports student learning, and the teacher has a critical role in supporting this engagement (Franke et al, 2015). Making contributions refers to the direct contributions that teachers make to a discussion, such as "ensuring that substantive and relevant analysis is part of the discussion" or "introducing particular vocabulary" (a mathematical contribution).…”

Teacher Interventions for Advancing Students’ Mathematical Understanding

“…There is evidence that in classrooms that tend to support inquiry, teachers frequently exhibit eliciting actions, as they ask students to share ideas and then use them to encourage group discourse. The most prevalent supporting actions reported in the literature include reminding students of task goals and what they already know, revoicing learners' ideas, and introducing alternative strategies and conceptual explanations [6,8,9]. Although common practices associated with extending have been conceptualized to include encouraging reasoning, encouraging reflection, pressing for justification and generalization, and creating a space for the development of new mathematical insights [6,7,9], the potential outcome of these actions relative to learners' mathematical cognition remains unclear.…”