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This paper describes a narrative-oriented approach to the design and analysis of a computational system and a set of activities for mathematical learning. Our central contention is that programming can offer a key to resolving the tension between the different representational structures of narrative and mathematical formalism. In the course of describing our approach, we make a distinction between the epistemiccognitive elements of narrative and the social, cultural and affective elements. We then elaborate the theoretical grounds of the individual epistemic facets of narrative. We propose a link between narrative theories of learning and constructionist traditions, specifically the notion of situated abstraction. This link suggests the possibility of further dialogue between the two academic communities.