A disordered material that cannot relax to equilibrium, such as an amorphous or glassy solid, responds to deformation in a way that depends on its past. In experiments we train a 2D athermal amorphous solid with oscillatory shear, and show that a suitable readout protocol reveals the shearing amplitude. When shearing alternates between two amplitudes, signatures of both values are retained only if the smaller one is applied last. We show that these behaviors arise because individual clusters of rearrangements are hysteretic and dissipative, and because different clusters respond differently to shear. These roles for hysteresis and disorder are reminiscent of the return-point memory seen in ferromagnets and many other systems. Accordingly, we show how a simple model of a ferromagnet can reproduce key results of our experiments and of previous simulations. Unlike ferromagnets, amorphous solids disorder is unquenched; they require training to develop this behavior.
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