Mathematical writing is an important yet underutilized mode of discourse. Teachers play an important role in implementing and engaging their students' mathematical writing. However, research on mathematical writing does not offer suggestions for how teachers can engage students in mathematical writing. The purpose of this chapter is to contribute to this area of research by describing how teachers implemented a systematic mathematical writing intervention during a summer school program. The student writing resulting from the intervention demonstrated that students can successfully engage in mathematical writing. Further, students' written work showed key elements of mathematical writing and indicated an understanding of the subconstructs of fraction conceptualization that appeared to be absent prior to the intervention.
TopBackground
The National Council of Teachers of Mathematics ([NCTM] 2000; 2014) has long called for teachers to engage students in meaningful mathematical discourse that is designed to (a) advance students’ understanding of mathematics and (b) engage students in mathematical reasoning. Writing is one way to engage students in such discourse. However; studies of mathematical writing have included a wide variety of definitions, types, and purposes with varied attention to advancing students’ understanding of mathematics and engagement in reasoning (Colonnese et al., 2020). For this chapter, we drew from the Elementary Mathematical Writing Task Force to define the purpose of mathematical writing as writing to reason and communicate mathematically (Casa et al., 2016).
In studies of students writing to advance their understanding of mathematics (a), findings have demonstrated that mathematical writing can help to advance students’ understanding of mathematics and improves students’ mathematical communication skills (Graham et al., 2020; Bangert-Drowns et al., 2004). Further analysis of pre- and post- assessment of students’ writing have demonstrated increases in students’ mathematics achievement (Cohen et al., 2015; Tan & Graces-Bascal, 2013; Kostos & Shin, 2010; Cross, 2009).
In response to the need for discourse to engage students in mathematical reasoning (b), writing provides students with a way to justify and explain their reasoning (Kramarski & Mevarech, 2003). Students can use writing to both reason mathematically and share their reasoning with others (NCTM, 2000). Because of the permanent nature of writing, students are able to monitor their progress, reflect on, and evaluate their thinking (Graham et al., 2013) – all components of the metacognitive process (Cross, 2009; Pugalee, 2001; 2004).