A non-volatile memory cell includes a switchable resistor memory element in series with a switch device. An array of such cells may be programmed using only positive voltages. A method for programming such cells also supports a direct write of both 0 and 1 data states without requirement of a block erase operation, and is scalable for use with relatively low voltage power supplies. A method for reading such cells reduces read disturb of a selected memory cell by impressing a read bias voltage having a polarity opposite that of a set voltage employed to change the switchable resistor memory element to a low resistance state. Such programming and read methods are well suited for use in a three-dimensional memory array formed on multiple levels above a substrate, particularly those having extremely compact array line drivers on very tight layout pitch.