NSTD.8:5.3 - Worked learning route: homotopy explanation
LearningNarrativeRoute@HomotopyIntro:
learnerUse: learner distinguishes intuitive deformation picture from formal definition and proof boundary
sourceSpineRefs:
- topological space
- path
- homotopy relation under constraints
- invariant
- example and counterexample
- proof-status return
learningStepOrder:
- image cue
- constraint marker
- formal definition return
- example
- counterexample
- reconstruction task
reconstructionTasks:
- mark where analogy stops
- state which deformations are not allowed
- return one claim to formal source
engagementBoundaryRef: vivid image cannot replace definition
evaluationRouteRef: `NSTD.6` rows for ordering, language-state precision, and source return
If learners can retell the loop picture but cannot state the required constraint, repair the connection to the definition. A suitable example, counterexample or worked comparison may supply that repair.