Overview

This part is focused on naming and describing the features of a “good” mathematical explanation. There is also an opportunity to consider why it is crucial to teach students to explain.

Key Points

Explanations are more than descriptions of how one approaches a problem or what the solutions of a problem are. They also must address why those approaches work and why the solutions are sensible.

A “good” mathematical explanation:

• Has a clear purpose
• Has a logical structure
• Uses representations and language clearly and carefully
• Focuses on meaning and is oriented to the listener(s)

Students need to be taught about mathematical practices, including giving explanations, because:

• Practices ARE basic skills of mathematics
• Students may not be noticing the practices even when they are in use
• Using a practice skillfully and effectively requires understanding why it matters; knowing how it works; and becoming skilled with its use in different situations

Facets of mathematical practices, including explanations, can be made explicit by:

• Integrating work on mathematical practices with work on mathematics topics
• Modeling the use of mathematical practices
• Scaffolding students’ use of mathematical practices
• Establishing and maintaining an environment that supports engagement in mathematical practices