Magnetoresistive effects (R(0)- R(H))/R(H) exceeding 500% are found at room temperature in a field of 7mT in nanocontacts between Fe{sub 3}O {sub 4} crystallites. The shape of the I(V) curve depends on field and the magnitude of the magnetoresistance is correlated with the resistance, the largest effects occurring when R>100 k{Omega} . The explanation proposed involves hopping transport of spin-polarized electrons through a narrow domain wall pinned at the nanocontact; spin pressure on the domain wall pushes it out into the electrode, leading to the nonlinearity of the I(V) characteristic. Application of current-induced wall motion in a simple fast-switching magnetic memory element is proposed.