Learning to argue while arguing to learn: Students’ emotional experiences during argumentation for graphing real-life functions

Argumentation in school mathematics is an important but demanding practice that supports important learning goals. Much of the research to date has focused on students’ cognition but researchers are paying attention to students’ affective experiences that influence their learning, and particularly in socio-cultural settings. In this qualitative case study, we drew on an emotion coding scheme to investigate students’ emotions during a cyclic sequence of small-group argumentation tasks on graphing and critiquing graphs of real-life situations. Insights into the emotional experiences of argument construction, critique, and reaching agreement were gained by analyzing observations, written reflections, video data, and interviews of six 9th-grade students (aged 14-15 years). A wide range of emotions were observed and expressed throughout the sequence. We found examples of emotions, including tension and frustration, playing a productive role in the students’ mathematics learning because of their experience of argumentation. The emotion of tension experienced by some students when receiving and giving critique of their mathematical ideas seemed to trigger productive attention to misconceptions. The emotion of frustration experienced by some students seemed to trigger productive coconstruction of arguments and ‘aha’ moments of mathematical understanding. We also found examples of non-deliberative argumentation (disrespectful interactions, lack of final consensus) influencing emotions in the moment (distress) and in the longer term after the lesson sequence (disappointment). Implications and considerations for future research on argumentation for learning are discussed.