See also Pedagogy, Think-aloud interviews.
Cognitive task analysis is a way of improving our understanding of how students and experts perform tasks, so we can determine what specifically is lacking in student thinking and perhaps devise interventions to encourage students to think more like experts. It typically involves theorizing the steps involved in performing a task, then using think-aloud interviews with students and experts to determine what cognitive skills real people use.
Lovett, M. C. (1998). Cognitive task analysis in service of intelligent tutoring system design: A case study in statistics. In International conference on intelligent tutoring systems (pp. 234–243). Springer Berlin Heidelberg. doi:10.1007/3-540-68716-5_29
A good overview of cognitive task analysis. It can be theoretical (drawing a diagram of which steps we think should be involved in a specific task) or empirical (using think-alouds) to study how students or experts complete a task. Lovett gives examples of a study of exploratory data analysis, where students skip several steps (like identifying the types of the variables and the appropriate analyses) which experts perform routinely.
Feldon, D. F. (2007). The implications of research on expertise for curriculum and pedagogy. Educational Psychology Review, 19(2), 91–110. doi:10.1007/s10648-006-9009-0
Why is cognitive task analysis important? Basically: experts can’t articulate their actual problem solving strategies. Reviews research on the nature of expertise, showing that a lot of expert thinking is essentially automated, and experts “fabricate consciously reasoned explanations for their automated behaviors” which do not necessarily correlate with what they actually do. Gives an example from nursing, where careful interviews found that “more than one-third of the individual cues (25 out of 70) used to correctly diagnose infants across the most commonly reported form of infant distress were not listed in any of the existing medical research or training literature” – that is, expert nurses used reasoning which was sufficiently automated that it had never before been written down. However, when cognitive task analyses are used to elicit reasoning from experts in detail, the results can be used to teach novices much more effectively than had the experts taught without it.