Unit 3: Reasoning and Explaining (MP2 and MP3)

# 3.2 Beginning to Reason: Definitions and Conjectures

*Higher order questions generally challenge the student to provide additional information and engage in deeper understanding and reflection, and ultimately promote greater conceptual development."*

Nathan & Kim, 2007

Explaining and justifying are at the heart of mathematical reasoning. By becoming aware of the language patterns of students, teachers are able to scaffold mathematics instruction and support students in moving toward justifications and generalizations.

Two studies that focused on discourse (Mendez, 2004) and teacher elicitation (Nathan & Kim, 2007) found that explanations, justifications, and generalizations coincide with the reasoning practices of students. This work provides the basis for a hierarchy of questions and responses between teachers and students. The researchers found that teachers move up and down the hierarchy of questioning in response to student needs.