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The power law of practice states that the
logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...
of the
reaction time
Mental chronometry is the scientific study of processing speed or reaction time on cognitive tasks to infer the content, duration, and temporal sequencing of mental operations. Reaction time (RT; sometimes referred to as "response time") is meas ...
for a particular task decreases linearly with the logarithm of the number of practice trials taken. It is an example of the
learning curve
A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have. Proficiency (measured on the vertical axis) usually increases with increased experience (the ...
effect on performance. It was first proposed as a psychological law by Snoddy (1928), used by Crossman (1959) in his study of a cigar roller in Cuba, and played an important part in the development of Cognitive Engineering by Card, Moran, & Newell (1983). Mechanisms that would explain the power law were popularized by Fitts and Posner (1967), Newell and Rosenbloom (1981), and Anderson (1982).
However, subsequent research by Heathcote, Brown, and Mewhort suggests that the power function observed in learning curves that are averaged across participants is an artifact of aggregation. Heathcote et al. suggest that individual-level data is better fit by an exponential function and the authors demonstrate that the multiple exponential curves will average to produce a curve that is misleadingly well fit by a power function.
The power function is based on the idea that something is slowing down the learning process; at least, this is what the function suggests. Our learning does not occur at a constant rate according to this function; our learning is hindered. The exponential function shows that learning increases at a constant rate in relationship to what is left to be learned. If you know absolutely nothing about a topic, you can learn 50% of the information quickly, but when you have 50% less to learn, it takes more time to learn that final 50%.
Research by Logan suggests that the instance theory of
automaticity
Automaticity is the ability to do things without occupying the mind with the low-level details required, allowing it to become an automatic response pattern or habit. It is usually the result of learning, repetition, and practice. Examples of tas ...
can be used to explain why the power law is deemed an accurate portrayal of reaction time learning curves. A skill is automatic when there is one step from stimulus to retrieval. For many problem solving tasks (see table below), reaction time is related to how long it takes to discover an answer, but as time goes on, certain answers are stored within the individual's memory and they have to simply recall the information, thus reducing reaction time. This is the first theory that addresses the why of the power law of practice.
Power function:
:''RT'' = ''aP''
−''b'' + ''c''
Exponential function:
:''RT'' = ''ae''
−''b(P-1)'' + ''c''
Where
:''RT'' = trial completion time
:''P'' = trial number, starting from 1 (for exponential functions the P-1 argument is used)
:''a'', ''b'', and ''c'', are constants
Practice effects are also influenced by latency. Anderson, Fincham, and Douglass looked at the relationship between practice and latency and people's ability to retain what they learned. As the time between trials increases, there is greater decay. The latency function relates to the
forgetting curve
The forgetting curve hypothesizes the decline of memory retention in time. This curve shows how information is lost over time when there is no attempt to retain it. A related concept is the strength of memory that refers to the durability that m ...
.
[Anderson, J., Fincham, J., & Douglass, S. (1999). Practice and retention: A unifying analysis. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25(5), 1120-1136.]
Latency function:
latency = A + B*T
d
Where
A = asymptotic latency
B = latency that varies
T = time between introduction and testing
d = decay rate
See also
Portal: Psychology
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Learning curve
A learning curve is a graphical representation of the relationship between how proficient people are at a task and the amount of experience they have. Proficiency (measured on the vertical axis) usually increases with increased experience (the ...
*
Power law
*
Forgetting
Forgetting or disremembering is the apparent loss or modification of information already encoded and stored in an individual's short or long-term memory. It is a spontaneous or gradual process in which old memories are unable to be recalled from ...
Power Law
References
{{Reflist
Psychological theories
Learning theory (education)
Psychology of learning