Structural Correspondence in Mental Models
Mental models have structural correspondence (isomorphism) to the situations they represent, with relationships between model elements mapping onto relationships between real-world elements.
This is an axiom because it identifies the fundamental property that makes mental models useful: structural isomorphism. This isn't merely correlation but a theoretical claim about how representations relate to what they represent—through preserved relational structure.
The concept comes from structural mapping theory and mental model theory (Johnson-Laird). A mental model works not by resembling reality superficially but by preserving the relevant relational structure. A subway map doesn't look like the physical layout of tunnels, but the topological relationships (which stations connect to which) are preserved. This structural correspondence enables reasoning: conclusions drawn from manipulating the model correspond to valid inferences about the real system. When models fail, it's often because the structural correspondence breaks down—the model preserves the wrong relationships or fails to capture critical structural features.
This axiom matters for the curriculum because it explains what makes a model good or bad. It's not about detail or complexity but about structural fidelity to the relevant aspects of the situation. This axiom guides model construction (identify critical relationships to preserve), model evaluation (test structural correspondence), and model application (recognize when structural assumptions break down). It connects to analogical reasoning, domain transfer, and the distinction between superficial similarity and deep structural correspondence.