This paper extends work on "intentionality", from philosophy, psychology and education to an exploration of learners' meaning-making in L2 classroom task-engagement. The paper draws on both phenomenological and folk-psychological perspectives on intentionality, and employs John R. Searle's intrinsic (mental) and derived (observable) intentionality as a key analytical distinction. The empirical focus of the paper is an exploration of learners' meaning-making using a longitudinal data set of classroom and learner discourse from a Norwegian primary English-language classroom. The analysis details the teacher's derived intentionality for the classroom activity, and then looks at how the learners generate their own intentionality through their joint task-engagement. The focus on learners' developing intentionality is presented as a promising theoretical perspective on meaning-making in the L2 classroom, and as an addition to the analytical toolkit available to researchers investigating the dynamic nature of L2 task-engagement.