Digital Fabrication and Hidden Inequalities: Connecting Procedural, Factual, and Conceptual Knowledge

The paper uses digital fabrication as a learning environment to demonstrate the importance of conceptual understanding of one-variable inequalities. These inequalities are hidden within two-variable inequalities used to construct geometric shapes the borders of which are the graphs of basic functions from the secondary mathematics curriculum. As graphing skills in the digital era are mostly procedural, an emphasis on hidden inequalities as tools for digital fabrication of specific regions in the plane and their borders connects procedural and conceptual knowledge in mathematics. Under the umbrella of collateral learning framework, the paper discusses the notions of transitive inference and necessary and sufficient conditions. The software program used for digital fabrication is the Graphing Calculator 4.0 produced by Pacific Tech.