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Lee and Anderson (2001) published an article in which they argued that learning a complex skill can be understood in terms of learning various component skills. They did this by performing a hierarchical task analysis on the Kanfer-Ackerman Air Traffic Control Task. They then re-analysed a dataset where participants performed the task over repeated trials. By examining key logs, they were able to extract out the speed with which overall goals were achieved (e.g., landing planes) as well as subtasks (e.g., moving planes through the hold patterns, etc.). They then analysed the relationship between practice and performance (i.e., the learning curve) for both the overall task and the subtasks. Specifically, they fit three parameter power functions.

I'm currently doing some research exploring similarities and differences between overall and subtask learning curves, and I'm keen to identify other papers that have modelled subtask and overall task performance. However, the learning and performance literature is pretty broad and crosses multiple disciplines, and thus, somewhat challenging to search. I've also tried the cited by link for the article on Google Scholar.


  • What, if any, other studies have been published that have modelled the relationship between both practice and subtask performance, and practice and overall task performance?

My preference is for studies where the dependent variable is task/subtask completion time, but any dependent variable representing performance would be interesting.


  • Lee, F. J. and Anderson, J. R. (2001). Does learning a complex task have to be complex?: A study in learning decomposition. Cognitive Psychology, 42(3):267-316. FREE PDF

2 Answers 2

up vote 4 down vote accepted

I've been interested in this issue from another direction, namely, in how to model the acquisition of hierarchically decomposeable behaviors of the type you describe; and how these behaviors, once acquired, can be used as 'high order primitives' to bootstrap other learning. This is an important issue for artificial intelligence and machine learning, in particular, as a way to address the combinatorial explosion involved with learning complex tasks in realistic domains.

Barto et al. (2004) provide a nice overview that amends the standard reinforcement learning paradigm to take these hierarchical ideas into account, and includes an algorithmic implementation for a simple but non-trivial domain. Oudeyer et al. (2007) expand on how hierarchicality can make behavior acquisition more efficient, and implement their algorithm in a robot in a developmental setting. Botvinick et al. (2009) provide a more recent review of the state of this work, as well as an overview of possible neural correlates of some of the processes.

Taken together, these references may possibly be useful to you as dispatches from domains other than the one you're exactly interested in. I've found such disparate formulations to be fertile sources of inspiration and synthesis.


Based on the Anderson cite, I'm assuming you've looked a bit more at the ACT-R literature-- task analysis is a common prerequisite for creating ACT-R models and you'll find lots of tasks modeled as a series of sub-tasks in a goal hierarchy. Offhand, though, I don't know any ACT-R articles that look specifically at your question of interest...

On a different note, Catrambone (1998) may be of interest to you-- in this article, he looks out how breaking down math problems into sub-goals helps students learn the material better. One claim is that breaking a problem down into smaller components helps transfer when a novel problem is made up of some (but not necessarily all) of the components. It eliminates reliance on rote performance, which often requires cues from previous steps in order to transition into subsequent steps.

Catrambone, R. (1998). The subgoal learning model: Creating better examples so that students can solve novel problems. Journal of Experimental Psychology: General, 127, 355-376. FREE PDF

+1, Thanks. I guess the challenge is finding studies that have measured subtask and overall task performance and then reported changes in performance at both levels with practice. –  Jeromy Anglim Feb 1 '12 at 0:19

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