Many successful recent approaches to developing innovative mathematics curricula and to conducting research on learning and teaching mathematics have used the construct of "learning trajectories" as a foundation. However, the developers and authors have interpreted and applied this idea in different ways, leading to a need for discussions of these variations and a search for clarifications and shared meanings. Further, the construct of learning trajectories is less than a decade old, but palpably has many roots in previous theories of learning, teaching, and curriculum. The purpose of this special issue is to present several research perspectives on learning trajectories with the intention of encouraging the broader community to reflect on, better define, adopt, adapt, or challenge the concept. This brief article introduces learning trajectories from our perspective. The other articles provide elaboration, examples, and discussion of the construct. They purposefully are intended to be illustrative, exploratory, and provocative with regard to the learning trajectories construct; they are not a set of verification studies.
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