Teacher support for argumentation and the incorporation of contingencies in mathematics classrooms

Argumentative orchestration in the mathematical modelling cycle in the classroom

“…From the two cases studied (Soledad and Ángeles), we selected 10 episodes that met two criteria: the students perform a relevant action belonging to the mathematical modelling cycle and the teacher participates in the students' interaction. The episodes were analyzed considering teacher support actions associated with an argumentative orchestration (Solar et al, 2021).…”

“…Specifically, collective argumentation requires teacher support because specific actions can strengthen different steps in students' argumentative processes (Yackel, 2002). This support can be provided through teacher actions or questions (Conner et al, 2014) or specialized methods to promote argumentation such as argumentative orchestration (Solar et al, 2021). This support for collective argumentation comprises a variety of resources and strategies: first, mathematical tasks open to discussion that require a variety of resolution strategies or allow for various positions in order to promote debate among students; second, communicative strategies such as the encouragement of participation, dealing with errors, and deliberate questions (Solar & Deulofeu, 2016); third, strategies for recognizing students' thinking, which include the teacher's elicitation and acknowledgment of thinking patterns in their students (Ball et al, 2009).…”

“…Lastly, we identified the teacher support actions present in each of these 10 resulting episodes. For the purposes of this study, when we use the term "teacher strategies", we specifically refer to two of the three dimensions of argumentative orchestration (Solar et al, 2021): communicative strategies (Lee, 2006;Solar & Deulofeu, 2016): participation opportunities, dealing with errors, and deliberate questions; and recognizing students' thinking (Ball et al, 2009): eliciting students' thinking and recognizing their thinking patterns. We excluded mathematical tasks open to discussion because they lie outside the scope of the present study.…”

“…We excluded mathematical tasks open to discussion because they lie outside the scope of the present study. Table 1 shows the teacher strategies and support actions (Solar et al, 2021). Q1: Asking questions that encourage students to explain and describe answers and procedures rather than yes-no questions.…”

“…Therefore, the teachers were found to employ a variety of argumentative orchestration support actions, with the most recurrent ones being communicative strategies (Solar et al, 2021): participation opportunities, dealing with errors, and deliberate questions. In contrast, teacher support actions associated with the recognition of thinking patterns-eliciting students' thinking and recognizing students' thinking patterns-were less recurrent, with the latter action only being found in Ángeles' case.…”