A windshield wiper includes a support structure, a scrubbing wiper assembly, and a motor. The scrubbing wiper assembly is slidably attached to the support structure and has a central longitudinal axis extending in the elongate direction between a first end and a spaced apart second end. The scrubbing wiper assembly includes a slider element and a wiper blade rigidly secured to the slider element. The motor is mounted to the support structure and is engaged with the slider element to reciprocally move the scrubbing wiper blade along the central longitudinal axis. The reciprocation can impart a linear torque to the slider element. Methods of cleaning and polishing a windshield using a windshield wiper are also included.