Abstract
Complexity and emergence are core notions for understanding and improving learning. On one hand, with complex concepts students struggle and learning becomes very difficult. On the other hand, emergence phenomena looks like magic or cognitive illusions, they seem to rely on extra qualities not included in the subjacent phenomena. Can the teacher simplify complex notions without changing them? In order to do that, we argue complexity and emergency are not exclusively inherent to objects or phenomena. They also depend on the perceptual, motor and cognitive system of the student. Thus, if the teacher helps to connect notions and phenomena to students' innate and embodied knowledge, then these notions become less complex and the emergent phenomenon loses its magic: it becomes logically connected to the subjacent phenomena. In this paper we present empirical evidence of the effect on students understanding due to the connection stablished in two core curriculum mathematical concepts that are considered very challenging.
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