Abstract
Disciplinary writing in mathematics supports the use of words, symbols, and visual representations, allowing one to communicate more fully in writing than through speech alone. This chapter explores the disciplinary writing of 394 fourth-grade students who shared their numerical reasoning in written explanations to seven whole-number and fraction comparison tasks. Data were collected via whole group administration procedures and students' explanations were scored using a validated framework for evaluating numerical reasoning. Results include descriptive statistics and qualitative analyses of student responses using the framework's five categories. A difference was found between the types of reasoning students shared for whole-number tasks versus those shared for fraction comparison tasks, favoring the incorporation of more conceptual reasoning for whole-number tasks. The framework is a practical and effective tool that teachers can use to examine the depth of student reasoning and disciplinary writing to document such reasoning.
TopDisciplinary Literacy
Addressing disciplinary literacy in K-12 education has become a focus of discussions about learning and teaching in the various content areas (Fang, 2012a; Håland, 2016; Shanahan & Shanahan, 2008, 2012). Disciplinary literacy “is grounded in the beliefs that reading and writing are integral to disciplinary practices and that disciplines differ not only in content but also in the ways this content is produced, communicated, and critiqued” (Fang, 2012a, p. 20). In other words, discipline-specific literacy reflects the norms and values of experts in each field (Moschkovich, 2003). Research in disciplinary literacy has identified distinctions in how these experts read and write in the various disciplines (e.g., Johnson et al., 2011; Shanahan & Shanahan, 2008). Proponents of disciplinary literacy argue that literacy instruction should transcend general strategies that apply across content areas to include strategies that reflect disciplinary practices (Fang, 2012a; Shanahan & Shanahan, 2008, 2012) so that students develop “disciplinary habits of mind (e.g., reading-writing, viewing-representing, listening-speaking, thinking-reasoning, and problem-solving practices consistent with those of content experts)” (Fang, 2012a, p. 20).
Key Terms in this Chapter
Numerical Reasoning: Making sense of number and operations.
Disciplinary Literacy: Reading, writing, listening, and speaking that reflect the norms and values of experts in the field.
Framework: Rubric consisting of multiple, non-continuous categories.
Conceptual Understanding: Reasoning founded on the intrinsic mathematical properties of the components of the task with or without describing a specific procedure. Evidence of reasoning does not require written words and may be demonstrated through use of visual representations or abstract symbols.
Algorithmic Reasoning Strategy: Application of a set of rules that guarantees a correct solution will be reached; remaining reasoning parts are trivial for the reasoner.
Fraction Sense: A conceptual understanding of fractions as numbers.
Disciplinary Writing in Mathematics: Precise means (words, symbols, or abstract symbols) of conveying a logical flow of reasoning.