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.