In this paper, we develop a new conceptual framework for an important problem in language acquisition, the correspondence problem: the fact that a given utterance has different manifestations in the speech and articulation of different speakers and that the correspondence of these manifestations is difficult to learn. We put forward the Correspondence-by-Segmentation Hypothesis, which states that correspondence is primarily learned by first segmenting speech in an unsupervised manner and then mapping the acoustics of different speakers onto each other. We show that a rudimentary segmentation of speech can be learned in an unsupervised fashion. We then demonstrate that, using the previously learned segmentation, different instances of a word can be mapped onto each other with high accuracy when trained on utterance-label pairs for a small set of words.