The degree of understanding is determined by the number and the strength of the connections. A mathematical idea, procedure, or fact is understood thoroughly if it is linked to existing networks with stronger and more numerous connections. Active learning techniques are designed to increase the number of connections students develop among mathematical ideas. Relational understanding is demonstrated by knowing what to do and why while instrumental understanding involves a multiplicity of rules rather than fewer principles of more general application. The advantages of relational understanding include improved adaptability to new tasks and less dependence on memory.
Relational understanding promotes the building of effective connections internally.
Active learning techniques are designed to promote just such understanding. They go on to assert that procedural knowledge is meaningful only if it is linked to a conceptual base. One focus of active learning strategies is to develop a firm understanding of concepts. Prior to a seminar, students are given an assignment that includes reading and problems. They receive a series of conceptual questions on the assignment to write responses to prior to the next class session.