Mechanism map
Designed directly from the paper’s transitions and instructional drivers.
Embodied manipulation
Turn a reversible, order-sensitive cube and observe visible state change.
Relational encoding
Notice inverses, preserved structure, cycles, and local–global dependence.
Algebraic abstraction
Compress patterns into notation such as R, U, R′, order, and identity-like relations.
Transfer
Apply the same structural ideas to cryptography, robotics, and symmetry-aware AI.
What matters more than the raw move list here: inverse, preserved structure, periodicity, or local–global dependence?
Can the learner describe an algorithm as a whole relation rather than as isolated turns?
Can the learner explain how R and R′ undo one another?
Can the learner identify what stays fixed under a sequence?
Can the learner notice periodic return, such as U⁴ = identity?
“This algorithm changes one part of the cube while preserving another relation.”
R U R′ U′ ; U⁴ = e ; R · R′ = e ; sequence order = 4.
Notation is not decorative. It lets learners name, compare, compress, and justify the relations first noticed through cube action.
The app scores whether the explanation emphasizes relations (inverse, order, preserved structure) rather than procedure alone.
What relation is preserved across two apparently different algorithms?
Can you express the same cube idea more compactly with notation?
Which part changed locally, and what remained globally constrained?
What would remain true if the stickers changed but the move structure stayed the same?