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Anderson, J. R. (1982). Acquisition of cognitive skill. Psychological Review, 89, 369-406.

Author of the summary: David Zach Hambrick, 1998, gt8781a@prism.gatech.edu

Anderson sketches a quantitative formulation of Fitts and Posner's stage theory of skill acquisition. The theory consists of three stages: 1) declarative, 2) knowledge compilation, and 3) procedural. During the declarative stage, performance is characterized by frequent errors and verbal mediation. Working memory load is high because declarative facts about the skill must be rehearsed, and a crude approximation of the skill is produced through the action of general-purpose productions (e.g., working backwards strategy) on the declarative data base. An important implication of this postulate is that declarative knowledge affects behavior only through productions: "declarative knowledge can have impact on behavior, but that impact is filtered through an interpretative system that is well oiled in achieving the goals of the system" (p. 380).


The conversion of declarative knowledge to procedural knowledge occurs during the second stage, knowledge compilation. The qualitative characteristics of knowledge compilation are 1) speedup, 2) unitary application of productions, and 3) dropout of verbal mediation. Procedural knowledge is a collection of "productions," or if-then statements that operate on facts stored in the declarative data base. Each production consists of a cognitive contingency, defined by an IF statement, and an action, defined by a THEN statement. In addition, each production has variable slots. The values that occupy these slots can vary from situation to situation, or can become fixed through the second process of knowledge compilation, proceduralization. The following are examples of productions:


IF the goal is to dial LVtelephone-number

And LVdigit1 is the first digit of LVtele-


THEN dial LVdigit1


IF the goal is to dial LVtelephone-number

And Lvdigit1 has just been dialed

And Lvdigit is after LVdigit1 in LVtele-


THEN dial LVdigit2


In this example, the telephone numberódeclarative informationómust be held in working memory for the production to operate. The strength of a production is determined by the frequency with which it is applied.


Hierarchical organization of task sub-goals, which define subroutines, is an important aspect of a production system. Anderson states that, "In achieving a hierarchical subroutine structure by means of a goal-subgoal structure, I am accepting the claim that the hierarchical control of behavior derives from the structure of problem solving" (p. 372). A further implication of hierarchical organization of the production system is that only subroutine can be executed at a time. This, as Anderson explains, "forces a considerable degree of seriality into the behavior of the system" (p. 372).




How does knowledge compilation occur? Two mechanisms are responsible for knowledge compilation: composition and proceduralization. Composition is the collapsing of successive productions into a single production, and accounts for speedup and unitary application of productions. An important feature is that knowledge compilation only acts on successful productions. The following production illustrates how the two productions above can be collapsed into a single production:


IF the goal is to dial LVtelephone-number

and LVdigit1 is the first digit of LV-


and LVdigit2 is after LVdigit1,

THEN dial LVdigit1 and then LVdigit2.




Collapsed productions still require representation of that information in working memory, and the limit on the number of productions that can be collapsed is imposed by the capacity of working memory. That is, the amount of information in the production's condition (e.g., LVtelephone number) must not exceed the capacity of working memory. By contrast, the second knowledge compilation process, proceduralization, builds productions that no longer require representation of declarative information in working memory. Declarative information is instantiated in productions. Working memory load is thereby decreased, and verbal mediation drops out. The following illustrates:


IF the goal is to dial Mary's number,

THEN dial 432-2815.




Learning does not stop with knowledge compilation. During the third stage of skill acquisition, the search for alternate solution paths (of which there are many) becomes more selective. That is, "the problem solver becomes much more judicious in his choice of paths and may fundamentally alter his method of search" (p. 390). Three learning mechanisms are involved in tuning. First, generalization extracts common elements from two or more productions, and creates a new production based on these commonalities. For example, the following productions


IF the goal is to indicate that a coat belongs to me,

THEN say "My coat."

IF the goal is to indicate that a ball belongs to me

THEN say "My ball."


can be combined into a single production for producing sentences indicating possession of an object:


IF the goal is to indicate that LVobject belongs to me

THEN say "My LVobject."


Productions can become overgeneralized. The second tuning mechanism, discrimination, therefore restricts the application of productions, and depends on information about the correct and incorrect application of particular productions. Consider the following example:


IF the goal is to indicate the relation in

(LVsubject LVrelation LVobject)

THEN say "LVrelation + s."


This production would apply only in cases where the subject is singular (e.g., girl hits ball). Application of the production to plural subjects would be an overgeneralization (e.g., girls hits ball). The discrimination process thus "tries to restrict the range of application of productions to just the appropriate circumstances" (p. 392).


Strengthening is the final tuning mechanism. The strength of a production is augmented each time it is successfully applied, and decremented each time it is unsuccessfully applied. In addition, general productions are strengthened for each application of the more specific productions they subsume. This latter strengthening rule addresses an a paradox: productions cannot be strengthened unless they are applied, and cannot apply unless they are strong.


The Power Law


Anderson argues that learning occurs in successive stages. How does this assertion fit with the finding that learning is characterized by a smooth function? That is, the ubiquitous power-law, or log-linear, phenomenon "would seem to contradict the ACT theory of skill acquisition because it first seems that a theory that proposes changing mechanisms of skill acquisition would not predict the apparent uniformity of the speedup" (p. 398).




In Anderson's model, learning occurs in three stages. In Stage 1, the declarative stage, the learner produces a crude approximation of the skill by using general-purpose problem solving strategies to interpret facts about the skill. Performance is slow, error prone, and working memory load is high because facts about the skill (e.g., the correct sequence of movements) must be actively rehearsed. Stage 2 is characterized by speedup, more seamless performance, and dropout of verbal mediation. During this phase, declarative facts about the skill are converted into procedural knowledge through knowledge compilation. Procedural knowledge is a collection of productions, or if-then statements that specify a cognitive condition and an action that will be performed if that condition is met. Two mechanisms underlie knowledge compilation: composition and proceduralization. Composition collapses successive productions into single productions, and produces speedup and more seamless performance. The extent to which composition can occur is determined by the capacity of working memory because the conditions specified in a production must be represented in working memory. Through proceduralization, declarative facts are instantiated in productions, thereby eliminating the need to represent declarative information in working memory. Proceduralization is responsible for the dropout of verbal mediation. In the final phase, tuning, search of alternate solution paths becomes more selective. Generalization, discrimination, and strengthening are the three learning mechanisms responsible for proceduralization.



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