What is Conceptual Understanding

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.