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264 Adaptation

strategy A
strategy B
strategy C
Frequency of use

Amount of experience
Figure 8.4. An in-principle representation of the multiple overlapping waves pattern.
After Siegler, 1996, Figure 4.4.

According to developmental psychologist Robert S. Siegler and his co-work-
ers, the relation between the successive strategies for a given task follows a
temporal pattern called multiple overlapping waves. Each strategy has a life
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cycle consisting of an initial phase with low probability of use, followed by a
period with steady increase in this probability, a peak and a final decline. A
graph of the probability of use over time therefore has the shape of a wave.
The starting points for different waves differ because the different strategies
are discovered at different times. Their peaks vary in height and the time from
the discovery of a strategy until it fades can be shorter or longer. At each
moment in time, multiple waves are in progress; see Figure 8.4 for an illus-
tration of this concept. In contrast to Figure 8.1, the vertical axis in Figure 8.4
is a measure of the probability or relative frequency of execution of a skill or
strategy, not a measure of performance. Each successive strategy is acquired
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through a negatively accelerated learning curve. The pattern in Figure 8.4 is
orthogonal to the shape of improvement of the individual strategies. Although
the multiple overlapping waves pattern has only been observed in the first 15
years of life, it is plausible that the same pattern characterizes skill acquisition
across the entire life span.
The theoretical challenge posed by the multiple waves pattern is not pri-
marily to understand why a new strategy increases its relative probability of use
at the beginning of its life cycle. A new strategy is presumably created for a good
reason; it might, for example, enable a task to be performed faster or with less
cognitive load. The challenge is to understand why the probability of use drops