Engaging students in mathematical justification is extremely important from a learning-focused and a disciplinary perspective. Prior research has commonly found that middle grades students struggle to produce viable justifications, arguments, and proofs, yet these studies often consider students' justification in only one modality (oral or written). This presents an incomplete picture of students' abilities to justify and emphasizes mathematical justifications as a finished product rather than students' processes to produce them. This study concerns middle grades students' mathematical justification in both oral and written forms and attends to the relationship between students' collaborative work in small groups and the ways that they engage in the process of constructing written justifications. To this end, I qualitatively investigated students' work to construct written justifications in the context of small group work in a digital collaborative environment designed to support students' productive disciplinary engagement on open mathematics problems.I examined students' work in two teachers' classrooms and considered students' collaborative work and written justifications at multiple levels. First, I considered students' overall engagement in collaborative work and written justification over the course of mathematical tasks, and second, I considered localized instances where they made changes to their written justifications. To do this, I utilized a novel framework for considering productive disciplinary engagement in terms of student actions and frameworks to describe the mathematical completeness and validity of students' written justifications (Toulmin, 1958; Kosko & Zimmerman, 2019).At a general level, I found that as the level of problematizing, authority, accountability, and resources demonstrated during each group's collaborative work increased, students began to construct written justification that went beyond providing claims to attend to how and why the mathematics worked. Additionally, in this study as students encountered uncertainties about how to justify in written form and attended to the mathematical validity of their written justifications, they demonstrated increased levels of productive disciplinary engagement in collaborative work with peers. This engagement with oral and written justification was facilitated by features of the collaborative digital environment that supported students to develop authority for expressing and explaining their own mathematical ideas, gain accountability to question peers' verbally- or digitally-expressed ideas, and develop their own resources and mathematical inscriptions (or representations) for making sense of problems. These findings suggest that mathematical writing is a complex task that goes beyond simply transcribing the results of oral work, but also that engaging in written justification can help students to more deeply engage in collaborative work to make sense of mathematical ideas.
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