Knowledge decomposability hypothesis
The knowledge decomposability hypothesis is that human acquisition of academic competencies can be decomposed into units, called knowledge components, that yield predictions about student task performance and the transfer of learning.
Task performance predictions have the following fundamental character: If task T1 requires knowledge component K1 and task T2 requires knowledge components K1 and K2, then task T2 is predicted to be harder than T1 and students will make more errors on average on T2 then T1. Further, students can correctly perform T2 will likely be successful on T1, but not necessarily the reverse. Those students who are successful on T1 may only know K1 and thus fail on T2 because they do not know K2.
Transfer predictions have the following fundamental character: If task T1 requires K1, task T3 also requires K1, but task T4 requires K3 then repeated instructional events involving T3 (e.g., a worked example or a practice problem) will yield better subsequent performance (transfer) on T1, but repeated instructional events involving T4 will not. This prediction is essentially Thorndike's "identical elements of transfer" notion where the elements are, in our case, knowledge components (see also Singley & Anderson). This prediction is also related to the "smooth learning curve" criteria used to validate student models in intelligent tutoring systems (Corbett & Anderson; Ohlsson & Mitrovic).
The knowledge representation version of the knowledge component hypothesis suggests that a knowledge component (KC) model can be identified for a domain in a way that makes accurate predictions that generalizes across students. The KC hypothesis does not reject the possibility of individual differences, but makes the strong claim that student differences can be predicted as variations from the core KC model and do not need to be accounted for separately for each student.
An instructional consequence of the knowledge decomposability hypothesis is the knowledge component hypothesis.