Across different conceptual domains that vary in inherent visualizability (e.g., physics kinematics vs abstract algebraic structures), to what extent do the same interaction-trace patterns—such as one-variable-at-a-time tests, revisiting informative contrasting cases, and longer prediction–test–explanation cycles—reliably predict durable learning and far transfer from interactive visuals, and in which domains do these patterns fail to distinguish genuine understanding from illusion-of-understanding?

Answer

Across domains with clear, stable visual mappings of structure to behavior (e.g., kinematics, basic probability distributions, many function/graph topics), the same interaction-trace patterns—systematic one-variable-at-a-time (OVAT) tests with dwell, revisiting informative contrasting cases, and longer prediction–test–explanation cycles—generalize well as predictors of durable learning and far transfer, outperforming confidence and in-the-moment accuracy. In domains where the core structure is only loosely or arbitrarily tied to the visual (e.g., many abstract algebraic structures, proof schemata, or symbol-heavy logic), these patterns are still weakly helpful but can fail to distinguish genuine understanding from illusion-of-understanding unless traces also capture explicit cross-representation linking, symbol manipulation, or verbal justification.

More specifically:

• High-visualizability, tightly mapped domains (e.g., kinematics, circuits, basic probability, introductory calculus graphs): OVAT-with-dwell, revisits to informative contrast cases, and extended prediction–test–explanation cycles are strong and fairly robust predictors of durable learning and far transfer across topics.
• Moderate-visualizability or mixed domains (e.g., statistics modeling, multi-step pipelines, simple dynamical systems): the same patterns still predict durable learning, but they must involve composition (e.g., revisiting contrasts at key regime boundaries, chaining predictions across panels) to discriminate deep understanding from local, illusion-prone parameter tuning.
• Low-visualizability or symbol-anchored domains (e.g., abstract algebraic structures, formal logic, proof patterns): purely visual OVAT/contrast/prediction cycles can overestimate understanding; here, those trace patterns only reliably predict durable learning when they co-occur with evidence of cross-representation reasoning (e.g., mapping diagrams to formal rules, writing justifications) or symbol-level operations aligned with the visual behavior.

So, the form of the productive patterns generalizes across domains, but the diagnosticity of those patterns depends on how directly the visual encodes the underlying conceptual structure and whether traces also capture how learners connect the visual to non-visual representations.