The Calculating Fireflies: Symbolic Computation. A Pedagogical Proposal.

A pedagogical proposal that integrates symbolic computation in SageMath to teach sums of powers using the Faulhaber-Narayana Machine, a combinatorial framework based on Narayana numbers. Through a narrative and collaborative approach, students explore patterns, formulate conjectures, and validate results, transitioning from arithmetic to symbolic thinking. The project emphasizes accessibility by using free software to promote experimental mathematics in educational contexts with fewer resources.