Competence-Based KST (CB-KST)

CB-KST derives a knowledge structure from a skill map — the mapping from items to the skills required to solve them.

The model

Given:

• A set of items \(Q\) (problems/questions)

• A set of skills \(S\) (competencies)

• A skill map \(\mu: Q \to 2^S\) (each item requires a set of skills)

• A prerequisite relation on skills

The problem function maps a competence state \(C \subseteq S\) to the set of solvable items:

\[p(C) = \{q \in Q \mid \mu(q) \subseteq C\}\]

The knowledge structure is the image of all valid competence states:

\[\mathcal{K} = \{p(C) \mid C \in \mathcal{C}\}\]

Usage

High-level API

import knowledgespaces as ks

structure = ks.structure_from_skill_map(
    skill_map={
        "q1": ["s_add"],
        "q2": ["s_add", "s_carry"],
        "q3": ["s_mul", "s_add"],
    },
    skill_prerequisites=[("s_add", "s_carry")],
)

Low-level API

from knowledgespaces import SkillMap, derive_knowledge_structure
from knowledgespaces.structures import SurmiseRelation

skill_map = SkillMap(
    items=["q1", "q2", "q3"],
    skills=["s_add", "s_carry", "s_mul"],
    mapping={
        "q1": {"s_add"},
        "q2": {"s_add", "s_carry"},
        "q3": {"s_mul", "s_add"},
    },
)

skill_rel = SurmiseRelation(
    ["s_add", "s_carry", "s_mul"],
    [("s_add", "s_carry")],
)

result = derive_knowledge_structure(skill_map, skill_rel)

print(result.competence_structure.n_states)
print(result.knowledge_structure.n_states)
print(result.knowledge_structure.is_knowledge_space)

Skill-to-item conversion

You can also derive the item prerequisite relation from the skill map:

from knowledgespaces import skill_to_item_relation

item_rel = skill_to_item_relation(skill_map, skill_rel)
for a, b in item_rel:
    print(f"{a} → {b}")