[Adele: Please change to "Headroom" to "Cognitive Headroom"]
One hypothesized pathway to accelerated future learning and transfer of higher level knowledge components (KCs) is through the development of fluency in lower level foundational skills. Students without such fluency must grapple with the basic lower level KCs while trying to use and acquire higher level KCs. Student with fluency in basic KCs have the more available cognitive capacity, more "headroom", to use and acquire higher level KCs.
For example, Haverty et al. (2000) found that basic number knowledge separated good from poor inductive reasoners and Haverty (1999) followed up with an experimental study showing that basic instruction on number knowledge (e.g., 17 vs. 19 facts) transfered to better higher level reasoning (e.g., discovering the function consistent with a table of x-y pairs).
In the terms of the cognitive load theory elaborated by Sweller and colleagues, lack of basic fluency may produce a kind of "extraneous cognitive load". A PSLC goal is to not simply label learning events as involving "extraneous cognitive load", which is done post-hoc in past research, but to develop predictive models to guide designers a priori in avoiding the design of such learning events. Such models involve knowledge component analysis and, in particularly, when a learning event involves student processing of knowledge components that are either under-learned (thus, no cognitive headroom) or irrelevant and unnecessary to meeting instructional objectives (e.g., keyboard vs. hand written entry of equations in Anthony's PSLC project).
Haverty, L. A., Koedinger, K. R., Klahr, D., & Alibali, M. W. (2000). Solving induction problems in mathematics: Not-so-trivial pursuit. Cognitive Science, 24(2), 249-298.
Haverty, L. A. (1999). The Importance of Basic Number Knowledge to Advanced Mathematical Problem Solving. Doctoral dissertation. Psychology Department, Carnegie Melon University.