Cognition: Memory, Attention, and Learning - Foundations for Designing User-Centered Systems - page 144

(a) (b)

Fig. 5.9 Time to perform a simple task (pushing a combination of buttons) on a linear plot
(a) and log-log plot (b) as well as a power law fit to the data shown as the solid line on each plot
(adapted from Seibel 1963 , and previously used in Ritter and Schooler 2001 , reproduced here
with permission)

been seen in tasks ranging from pushing buttons, reading unusual fonts or inverted
text, doing arithmetic, typing, using a computer, generating factory schedules, all
the way up to writing books (Ohlsson 1992 ). These improvement curves are also
found when large groups work together, for example, building cars.
There are huge improvements initially, although users rarely report satisfaction
with these improvements. The improvements decrease with time, however, fol-
lowing a monotonically decreasing curve. This is shown in Fig. 5.9 for the Seibel
task, a task where you are presented with a pattern of ten lights and you push the
buttons for the lights that are on. Each point represents the average for doing 1,000
patterns. Notice that with extended practice, performance continues to improve,
but by smaller and smaller increments. Over a wide variety of tasks and over more
than seven orders of magnitude (hundreds of thousands of trials), people get faster
at tasks.
With data with changes this wide and with small changes becoming important
later in the curve it becomes difficult to see the improvements. This is why the data
are plotted using logarithmic axes: the difference between two points is based on
their logarithms, as shown in Fig. 5.9 . Typically, on these log-log plots, learning
curves follow pretty much a straight line.
The mathematical representation of this curve is currently somewhat disputed.
Some believe that the learning curve is an exponential curve, and others think it is
a power equation (thus, called the power law of learning) of the form shown in
Eq. ( 5.1 ):

Time of a trial ¼ Constant1 ð Number of trial þ PP Þ a þ Constant2 ð 5 : 1 Þ

where Constant1 is the base time that decreases with practice, PP is previous
practice on the task, a (alpha) is a small number typically from 0.1 to 0.5, and
Constant2 is the limitation of the machinery or external environment (reviewed in
Newell 1990 , Chap. 1; see also Anderson 1995 , Chap. 6).