A rewriteable nonvolatile memory includes a thin film transistor and a switchable resistor memory element in series. The switchable resistor element decreases resistance when subjected to a set voltage magnitude applied in a first direction, and increases resistance when subjected to a reset voltage magnitude applied in a second direction opposite the first. The memory cell is formed in an array, such as a monolithic three dimensional memory array in which multiple memory levels are formed above a single substrate. The thin film transistor and a switchable resistor memory element are electrically disposed between a data line and a reference line which are parallel. A select line extending perpendicular to the data line and the reference line controls the transistor.