Epistemological and methodological foundations of creating a learning trajectory of children’s mathematics
Résumé
This paper argues for creating learning trajectories of children’s mathematics by integrating evidence of shifts in the mathematics of students, theory of goal-directed instructional design, and evidence of instructional supports. We networked two theories in support of this stance: a radical constructivist theory of learning, and Duality, Necessity, Repeated Reasoning (DNR)-based instruction. We exemplify how our networking of theories guided methodological choices by drawing on a program of research aimed at understanding and supporting students’ ways of understanding quadratic growth as a representation of a constantly changing rate of change. We close by discussing challenges for creating and sharing learning trajectories.
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