Investigating students’ arguments with real-life functional situations throughout a sequence of collaborative activities

Recent years have seen increasing interest in providing students with opportunities for developing important argumentation skills in the mathematics classroom. Social interactions with peers to critique alternative ideas, justify arguments, and build consensus, have been found to promote deep thinking and meaningful development of concepts. In this study we explored 9^th-grade students’ interactions during a sequence of specifically designed argumentation tasks on real-life functional situations to investigate the appropriateness of their arguments. Data were collected from the students’ written task responses, student reflections, small-group observations, individual interviews with the group members, and teacher interviews. Analysis of the level of appropriateness of the students’ individual and group written responses in each activity focused on three aspects: identifying variables, forming relations between them, and noticing contextual features of the real-life situation. We found evidence of students grappling with selecting two suitable variables and with conceptualizing the nature of their relation. It also appeared that aspects of the students’ social interactions played a role in students ignoring correct arguments and accepting incorrect arguments. We discuss implications for small-group argumentation and suggest avenues for future research.