Using Metalanguage to Support Writing in Mathematics

• In Event: Reimagining K–12 Disciplinary Literacy: Access, Engagement, and Innovation Across Subjects

Abstract

Understanding the linguistic demands of mathematics is increasingly important, especially for word problems, which represent a unique interplay between arithmetic, linguistic, and textual factors (Daroczy et al, 2020; Lin, 2021). This study used Systemic Functional Linguistics (SFL) as an analytical and theoretical frame to explore how preservice teachers (PSTs) leveraged their linguistic knowledge to create complex word problems. The following research question guided this study: In what ways did PSTs attend to linguistic features when problem posing and use metalanguage to explain their problem posing choices?

SFL is a social semiotic language theory that offers a meaning-based metalanguage: a language for helping students and teachers talk about language shapes meaning in the context of word problems (Halliday & Matthiessen, 2013). Metalanguage develops students’ awareness of the linguistic challenges of word problems and supports them to work through these challenges (Gebhard et al., 2014; Schleppegrell, 2013). In this way, metalanguage can support students’ mathematical disciplinary literacy practice by supplying resources for them to make intentional meaning-based decisions in their writing and explain why they made those choices (Gebhard et al., 2014; Schleppegrell, 2013).

To investigate PSTs' use of metalanguage, 55 assignments were collected from a fall 2024 mathematics problem solving course for PSTs. This assignment was chosen because it explicitly required PSTs to identify the linguistic features of a word problem they had written and justify their writing choices using metalanguage. I conducted an ideation analysis (Martin and Rose, 2003) to analyze the taxonomic relations in PSTs’ posed word problems, focusing on processes (verbs), participants (referents and contextual nouns), and descriptors (e.g., adverbs, prepositional phrases). Also, by connecting PSTs' posed problems with their written metalanguage justifications, I identified how they applied specific linguistic features and explained these choices.

Analyses revealed that PSTs effectively used referents, processes, and descriptors to create situational contexts that demonstrated careful attention to how referents evolve across problem steps. For example, one PST posed the following problem, “There are 2 squirrels sitting on a tree branch. Then 6 more squirrels climbed on the branch and joined them. Each squirrel has 5 acorns with them to eat. How many total acorns did all of the squirrels bring?” In explaining how they posed this problem, they stated, “I had to add acorns to modify the number of referent in the second step to make it go from one referent to two.” The complexity of modifying this referent from one to two can be visualized, as in Figure 1.

The findings indicate that PSTs engaged in complex linguistic moves to construct mathematically sound and linguistically clear word problems. Their use of metalanguage to justify their choices underscores their awareness of these linguistic maneuvers, supporting their development of disciplinary linguistic knowledge (Turkan et al., 2014). This research highlights the value of metalanguage in enhancing PSTs' disciplinary linguistic knowledge for mathematical thinking and problem posing. These findings have implications for curricular development, assessment, and point to future research into the complexities of teaching and learning word problems.

Author

• Michelle Nguyen Kwok, Texas A&M University