From Output to Understanding: How Programming Outputs Mediate Mathematics Learning via Perturbation

Abstract Programming has been advanced as a productive epistemic tool and catalyst for K-12 mathematics learning. Specific to the context of block-based programming, researchers have examined the supporting and constraining roles of immediate visual feedback in students’ mathematics learning. Yet few studies offer a fine-grained cognitive account of how mathematics learning unfolds as students engage with different kinds of programming feedback. This study examines two primary students’ programming-based mathematical activities around the concepts of angles and polygons, providing a qualitative, thick description of how programming outputs mediate their learning. Adopting the Piagetian notion of perturbation, we show that both unsatisfactory and satisfactory outputs can elicit perturbations and intellectual needs for students, which in turn motivate different coping mechanisms that resolve the perturbations and thereby conceptual development. These findings contribute to a theory of programming-based mathematics learning by specifying how perturbation functions as a mechanism that moves students beyond low-level reading of programming outputs towards reflective and analytical reasoning with the outputs. We also discuss implications for teaching mathematics in programming contexts, including how to support reflective discourse around programming artifacts.