Throughout, R will represent an associative ring with center Z(R). A module X is said to be n-torsionfree, where n is an integer, if nx = 0, $x in X$ implies x = 0. An additive mapping $D : R o X$, where X is a left R-module, will be called a Jordan left derivation if $D(a^2) = 2aD(a), a in R$. M. Bresar and J. Vukman [1] showed that the existence of a nonzero Jordan left derivation of R into X implies R is commutative if X is a 2-torsionfree and 3-torsionfree left R-module.