Fundamentals of learning curves

In the introduction to yesterday's blog post, I alluded to the axiom that 'practise makes perfect' - the concept that the acquisition and improvement of new skills, knowledge or expertise are broadly predicated upon the learner's facility to rehearse and become more proficient in the tasks or activities being practised. This is not news - we have all experienced this process - and behaviorists would assert that perhaps we know it intuitively.

What is surprising is that the rate and shape of improvement is fairly common across learning.

The concept of the learning curve illustrates a simplified model of learning in which knowledge of a given subject is acquired through a progression of steps. Figure 1 shows a model of an idealized (and simplified, and in no way scientifically accurate) learning curve applied to Bloom's Taxonomy. At the lowest levels of the curve, the learner is a novice who then progresses through the various stages of cognitive development, where at each stage they increase in competency until (perhaps up to 10 years later) they reach an expert level of competency in the subject matter being tracked.

Figure 1. Bloom's Taxonomy charted on a learning curve

The learning curve has substantial implications for e-learning: it suggests that practice always helps improve performance, but that the most dramatic improvements happen first, with smaller and smaller incremental improvements being accrued over time. Another implication is that with sufficient practice people can achieve comparable levels of performance. For example, extensive practice on mental arithmetic (Staszewski reported in Delaney et al., 1998) and on digit memorization have turned average individuals into high performers.

The learning curve was devised from the historical observation that individuals who perform repetitive tasks demonstrate an improvement in performance as the task is repeated over time. First studied empirically in the 1930's by T. P. Wright's Factors Affecting the Cost of Airplanes, three conclusions were drawn upon which the current theory and practice surrounding learning curves are based:

1. The time required to perform a task decreases as the task is repeated
2. The amount of improvement decreases as more units are produced, and
3. The rate of improvement has sufficient consistency to allow its use as a prediction tool

In this study, Wright concluded

that consistency in improvement has been found to exist in the form of a constant percentage reduction in time required over successively doubled quantities of units produced. The constant percentage by which the costs of doubled quantities decrease is called the Rate of Learning.

More...

References:

Delaney, P. F., Reder, L. M., Staszewski, J. J., & Ritter, F. E. (1998). The strategy specific nature of improvement: The power law applies by strategy within task. Psychological Science, 9(1), 1-8.

Wright, T.P. (1936). Factors Affecting the Cost of Airplanes. Journal of Aeronautical Sciences, 3.4 : 122 -128.
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