The purpose of this paper is to use a general class of indefinite theta functions to explain and generalize an example of a Maass waveform that was constructed by Cohen from two functions σ and σ*, studied by Andrews, Dyson and Hickerson. For this, we construct certain functions attached to an indefinite binary quadratic form and show that they are ‘nearly’ Maass waveforms. We call these functions mock Maass theta functions. In certain special cases we obtain actual Maass waveforms. These are the same as in the work of Maass.