Abstract
Mathematical writing has taken an increasingly prominent role in curriculum and assessment in the 20th century. Despite its presence on high stakes tests, and the benefits of students in gaining proficiency in this mode of mathematical communication, there has been no scholarly consensus on the definition of mathematical writing, and consequently, little instructional guidance for practitioners. This chapter employs genre theory and universal design for learning (UDL) to outline best practices for the teaching and formative assessment of explanatory mathematical writing across grade levels. After demonstrating how teachers can apprentice students into reproducing the dominant discourse of mathematical writing, the chapter also presents suggestions for centering student voice within mathematical communication through translanguaging, multimodalities, and remixed composition.
TopPart 1: Rationale For Mathematical Writing
Communicating in mathematics has been an essential feature for over 20 years. In 2000, the National Council of Teachers of Mathematics (NCTM) included communication as one of the five process standards, thereby highlighting communication’s importance to mathematics teaching and learning. Building on this, 10 years later the Common Core State Standards (CCSS; 2010) released the Standards for Mathematical Practice, which included two Standards that directly related to communication: Standard for Mathematical Practice 3: Construct viable arguments & critique the reasoning of others and Standard for Mathematical Practice 6: Attend to Precision. Although there are multiple ways to communicate using discourse in mathematics, this chapter focuses specifically on writing.
In mathematics, writing plays a critical role in advancing students’ learning by promoting reflection and clarification of ideas through explanations, descriptions, definitions, and critiques using specialized disciplinary language as well as supporting the development of productive mathematical identities (Marks & Mousley, 1990; Murphy & Hall, 2008; NCTM, 2000). Writing can empower students to communicate their understanding with others, and surveys suggest that students who write in mathematics class subsequently enjoy mathematics more (Powell et al., 2017). Writing in mathematics can take different forms, generally distinguished between writing about mathematics or writing in mathematics (Powell et al., 2017). Writing about mathematics includes activities such as journaling about feelings related to mathematics, reflecting on the problem-solving process, or reporting on a mathematician. Writing in mathematics includes activities where students explain a problem-solving strategy, compare two different approaches for solving a problem, or constructing a proof. This chapter focuses its attention on writing in mathematics.
When students write in mathematics, they may engage in different genres of mathematical writing, such as explanatory or argumentative (Casa et al., 2016). Yet, of all the genres present in mathematics, explanatory writing is the most commonly used by teachers (Gillespie et al., 2014), curricula (Casa et al., 2019), and state assessments. When students engage in explanatory writing, they typically explain what they did (e.g., how they used a particular strategy or procedure) or why they did it (e.g., why they used a strategy to solve a problem over another) (see Table 1).
Table 1. Released explanatory state assessment items
Smarter Balanced Assessment Consortium’s released fourth-grade item for Illinois
You need 120 pieces of chalk for Art Day. Your teacher has 6 boxes of chalk. Each box has 18 pieces of chalk. Is this enough chalk for Art Day? Explain the steps you used to figure this out. | Pennsylvania System of School Assessment released third-grade item
Mr. Tillman has a rectangular-shaped garden with an area of 24 square meters. What could be the side lengths, in meters, of Mr. Tillman’s garden? Explain why there can be more than one possible answer. |
Caption: This table provides two sample prompts for explanatory mathematical writing, both drawn from the Smarter Balanced Assessment.
Key Terms in this Chapter
Universal Design for Learning: A framework for promoting accessibility for all students by creating flexible instruction and assessment.
Mathematical Writing: Written text that describes mathematical concepts, procedures, reasoning, explanations, or proof.
Translanguaging: The ways people fluidly draw on and use all their language resources to communicate, such as using Arabic, English, and mathematical notations in a written sentence.
Explanatory Mathematical Writing: A written response to a mathematics prompt that describes what the author did (e.g., how they used a particular strategy or procedure) or why the author took the approach they did (e.g., why they used a strategy to solve a problem over another).
Discourse: The way people engage with themselves and others using a range of modalities (e.g., oral language, written language, gestures, body positioning/movement).
Genre Theory: A pedagogical approach to teaching writing that explicitly draws attention to recognizable and reproducible components of a form of social communication and utilizes gradual release of writing production from teacher to student.
Formative Assessment: Low-stakes and often frequent assessment intended to provide on-going feedback to the learner and teacher to inform instruction and learning.