Students use ** conceptual understanding **of mathematics when they:

• recognize, label, and generate examples with a concept and without a concept;

• use and interrelate models, diagrams, manipulatives, and varied representations of concepts;

• identify and apply principles (i.e., valid statements generalizing relationships among concepts in conditional form);

• know and apply facts and definitions;

• compare, contrast, and integrate related concepts;

• recognize, interpret, and apply the signs, symbols, and terms used to represent concepts;

• interpret the assumptions and relations involving concepts in mathematical settings; and

• reason in settings involving the careful application of concept definitions, relations, or representations of definitions

or relations.