  The Murnaghan--Nakayama rule is a combinatorial rule for the character values
of symmetric groups. We give a new combinatorial proof by explicitly finding
the trace of the representing matrices in the standard basis of Specht modules.
This gives an essentially bijective proof of the rule. A key lemma is an
extension of a straightening result proved by the second author to
skew-tableaux. Our module theoretic methods also give short proofs of Pieri's
rule and Young's rule.
