For more than 14 years, the National Council of Teachers of Mathematics (1989, 2000) has advocated that teachers of mathematics facilitate that students make connections of various kinds, in their learning of mathematics. Semiotic theories, including those of Peirce and those of Saussure and Lacan (each for different purposes), provide useful lenses for examining ways that teachers may facilitate the making of connections, for instance between home and school mathematics, or between mathematics and other school subjects, or between different branches of mathematics. This paper describes a nested chaining model that takes into account the need for interpretation and meaning making at each step in the sequences involved in connections. A nested model has the capacity to allow for webs of signification and meaning that take into account the complexity of the processes in ways that linear semiotic chains cannot. Examples are taken from research projects with graduate students, with pre-service teachers, and with practicing teachers.