The Collaborative International Dictionary of English v.0.48:

Strum \Strum\, v. t. & i. [imp. & p. p. Strummed; p. pr. & vb.
   n. Strumming.] [Probably of imitative origin. Cf. Thrum.]
   To play on an instrument of music, or as on an instrument, in
   an unskillful or noisy way; to thrum; as, to strum a piano.
   [1913 Webster]