Knowledge component

Knowledge Component

A knowledge component is a description of a mental structure or process that a learner uses, alone or in combination with other knowledge components, to accomplish steps in a task or a problem. A full description and taxonomy of knowledge components can be found in Koedinger, Corbett, & Perfetti (2012) . A knowledge component is a generalization of everyday terms like concept, principle, fact, or skill, and cognitive science terms like schema, production rule, misconception, or facet. When we say a student "has" a knowledge component, it might mean the student can describe it in words (e.g., "Vertical angles are congruent") or it might simply mean that the student behaves as described by the knowledge component, but may not be able to describe it themselves. In this second case, to say the student "has" the knowledge component "If angle A and B are vertical angles and angle A is X degrees, then angle B is X degrees" means the student will behave in accord with it even though they might not be able to state the rule. The first is an "explicit" knowledge component, like a fact or principle, and the second an "implicit" knowledge component , like a skill. Much of what first language learners know about their first language involves implicit knowledge components.

A knowledge component (KC) relates features to a response where both the features and response(s) can be either external, in the world, like cues in a stimulus and a motor response or internal, in the mind, like inferred features and a new goal.

KCs are "correct" when all of the features are relevant to making the response and none of them are irrelevant. In geometry, for example, the knowledge component "if angles look equal, then conclude they are equal" is incorrect because it includes an irrelevant feature "angles look equal" and is missing a relevant feature like "the angles are at the base of an isosceles triangle". See also feature validity and refinement.

An example of a knowledge component analysis (a kind of cognitive task analysis) can be found in the description of Julie Booth's study knowledge component construction vs. recall. In her case, the key knowledge components are concepts and skills for making decisions during problem solving in the domain of algebra equation solving. She identifies both incorrect knowledge components that students tend to acquire and correct knowledge components that good students eventually acquire.

A data mining approach to knowledge component analysis is support by LearnLab's DataShop.

Kinds of knowledge components

Mental representations of:

• Domain knowledge
  • Facts, concepts, principles, rules, procedures, strategies
• Prerequisite knowledge
  • Feature encoding knowledge (see examples in Algebra and Chinese radicals)
• Integrative knowledge
  • Schemas or procedures that connect other KCs
• Metacognitive knowledge
  • About knowledge, controlling use or acquisition of knowledge (see the help-seeking project)
• Beliefs & interests
  • What one likes, believes

Cross-cutting distinctions

• Correct vs. incorrect
• Verbal (explicit) vs. non-verbal (implicit)
• Probabilistic vs. discrete

Not knowledge components

• Any external representation of knowledge
  • Like textbook descriptions or an example
• Generic cognitive structures
  • Working memory
• Continuous parameters on knowledge representations
  • Strength, level of engagement, implicit value of a goal, affect

Other uses of "knowledge"

“Knowledge” in PSLC is used as in the Cognitive Science and AI traditions. The mind is a knowledge base stored in the brain’s hardware. All competencies and behaviors are determined by “knowledge” in this sense. "Knowledge" in philosophy is “justified true belief" whereas our use of knowledge components includes both incorrect (false) knowledge and implicit (no explicit belief or justification) knowledge. "Knowledge" in education is basic facts (1st level of Bloom’s (1956) taxonomy) whereas knowledge components can be procedures, integrating schemas, complex reasoning strategies, metacognitive skills …, that is, all levels of Bloom’s taxonomy.

References

• VanLehn, K. (2006). The behavior of tutoring systems. International Journal of Artificial Intelligence in Education, 16 (3), 227-265 Abstract&PDF

• Koedinger's PSLC Lunch Talk from August, 2006.

• Norma Chang's CMU Psychology PhD Thesis (2006) on surface vs. structural problem variations and resultant acquisition of relevant vs. irrelevant features ("spurious correlations" with surface features).

• Bloom, B. S. (Ed.). (1956). Taxonomy of educational objectives. Handbook 1: Cognitive domain. New York: McKay.