Learning to Prove: A Taxonomy of Objectives

We consider the educational objective of learning how to prove a statement in a mathematically rigorous way and we break down this educational objective into several partial objectives following the standard taxonomy of Bloom, 1956]. Three advantages stem from this approach: rst, the partial objectives are more manageable in the process of curriculum development; second, it is easier to individuate the teaching strategies that are most eeective for each educational objective; and, nally, we discover some objectives that are often neglected, but are in fact surprisingly legitimate | these include the rote learning of proofs, the ability of interpreting mathematical statements, the analysis of proofs and proof techniques, and the ability of reading the current literature.