PedagogyModelsCert
The structure certifies that the inductive enumeration of pedagogy models has finite cardinality exactly five, fixing configDim D to 5 in the education depth of Recognition Science. Curriculum theorists mapping instructional methods to distinct recognition channels would cite the certificate when partitioning exposition, practice, exploration, synthesis, and enculturation. It is realized as a structure definition whose single field directly encodes the cardinality equality.
claimA certificate structure whose sole field asserts that the finite cardinality of the set of pedagogy models equals 5, where the models are the five enumerated cases of direct instruction, mastery learning, inquiry-based learning, project-based learning, and apprenticeship.
background
Recognition Science sets configDim D = 5 for education depth and enumerates five canonical pedagogy models. The inductive type lists them explicitly as direct instruction, mastery learning, inquiry-based learning, project-based learning, and apprenticeship, each tied to one recognition channel: exposition, practice, exploration, synthesis, enculturation. The module imports Mathlib to obtain the Fintype instance and Constants for framework parameters.
proof idea
The declaration is a structure definition containing only the field that states the finite cardinality of the pedagogy model enumeration equals five. No lemmas are applied and no tactics are used; the body is empty because the object is a pure definition.
why it matters in Recognition Science
The certificate supplies the finite count required by the downstream constructor that builds a concrete term of this type. It closes the education module's enumeration claim with zero sorry or axiom, aligning the five-model partition with the framework's deterministic assignment of configDim D = 5 to distinct recognition channels.
scope and limits
- Does not derive the five models from the forcing chain or J-uniqueness.
- Does not specify explicit mappings from each model to a recognition channel beyond the module comment.
- Does not address educational contexts outside the canonical five.
- Does not claim optimality or completeness of the model set.
formal statement (Lean)
29structure PedagogyModelsCert where
30 five_models : Fintype.card PedagogyModel = 5
31