Characteristics

Descriptions

Precision

-Be explicit about precise definitions (e.g., use definitions as a basis for logical reasoning);

-Pay attention to precise statements (e.g., present mathematical ideas clearly).

Coherence

-Demonstrate interconnectedness of mathematical ideas (e.g., show the algebraic and geometric representations of a mathematical concept and idea, where appropriate);

-Show logical/sequential progression of mathematical ideas (e.g., show a deliberate effort at scaffolding mathematical ideas from simple to complex, specific to general).

Purposefulness

-Emphasize key or big mathematical ideas;

-Provide rationale for why key mathematical ideas are relevant to the teaching of a particular mathematical topic at hand.