This qualitative study sought to understand middle school students’ developing mathematical arguments in a linguistically and culturally supportive classroom that featured mathematical writing and oral conferencing. Writing tasks and conferencing focused on developing the core algebraic practice of justifying by emphasizing audience and revision. Inequitable learning opportunities in mathematics education continue to precipitate academic failure and under-achievement among underrepresented and minoritized (URM) students. Classrooms that make use of mathematical writing and discussions and focus on student reasoning can enhance learning opportunities for URM students (Moschkovich, 2013). This study examined how the arguments of middle school students changed in a classroom where mathematical writing and conferences, conducted during remote instruction caused by the global COVID-19 pandemic, provided opportunities for reflection and potential revision. The study was guided by the following questions:
1. When asked to do mathematical writing and supported with conferencing in a remote context, what kinds of arguments did students make?
2. How did the mathematical arguments of individuals change over the course of a unit of instruction on generating, selecting, and justifying claims?
3. In what ways did students revise their mathematical arguments during conferencing?
Examination of student work revealed the ways that their efforts to justify changed. Upon examination of the Convince Forms, I found that students expanded arguments from describing procedures to making arguments and using examples in mathematically sound ways, and from making no claims to selecting claims and even generating claims of their own. After examination of the mathematical conferences, I found that students expanded their efforts to justify, employing additional proof schemes (Healy & Hoyles, 1998), and revised conjecture-testing procedures (i.e., exemplifying) and meanings for formal words.
The findings highlight how students who are multilingual, low-achieving, or designated as special education engage in mathematical argument with support. Moreover, this study illustrates how mathematical argument can be conceptualized as a constellation of approaches that include refining how different parts of an argument can be used in dialectic with the others, i.e., how the use of examples, the further generalization of claims, and further exploration of how to justify can support each other.