The idea that the brain controls movement using a neural representation of limb dynamics has been a dominant hypothesis in motor control research for well over a decade. Speech movements offer an unusual opportunity to test this proposal by means of an examination of transfer of learning between utterances that are to varying degrees matched on kinematics. If speech learning results in a generalizable dynamics representation, then, at the least, learning should transfer when similar movements are embedded in phonetically distinct utterances. We tested this idea using three different pairs of training and transfer utterances that substantially overlap kinematically. We find that, with these stimuli, speech learning is highly contextually sensitive and fails to transfer even to utterances that involve very similar movements. Speech learning appears to be extremely local, and the specificity of learning is incompatible with the idea that speech control involves a generalized dynamics representation.