What is a learning curve and what does it tell us?
In popular discourse, we sometimes say a learning curve is 'steep' or 'high' to mean that something is hard to learn. That shows a completely wrong understanding of what a learning curve represents.
Put simply, a learning curve is a line graph that plots of how much is learned in how much time. The degree of learning is the vertical axis of the graph, and time is the horizontal axis. Points on the graph show how much has been learned (and remains learned) after a particular time has passed since learning began. Data points high on the graph indicate that much has been learned.
Thus, a curve that rises sharply (a steep curve) indicates that much is learned in a short time, suggesting that the subject is easy to learn. A 'high' learning curve is sort of a meaningless expression, as the 'height' of a data point on the curve depends on the scale, which depends on the units of measurement for mastery and may be normalized as a percent. Using 'steep' or 'high' to mean 'difficult to learn' is incorrect, and may result from naively and ignorantly interpreting the curve as representing a wall that must be climbed, which it is not at all.
Defined better, a learning curve plots the measured degree of mastery of a task or a subject against a measure of the effort applied to the learning (the usual measure being time). In math, we say that the curve represents ability as a function of effort. So what truths a learning curve can tell us depends on how mastery is defined and how valid are the measures of mastery and effort.
A learning curve is measured for an individual learner and a particular task over a measured period of time. It is meant to say something about the ability of that learner to acquire and retain the skill needed to perform the task successfully.
If we take the learning curves of (preferably) very many learners for the same task obtained under the same conditions and somehow average them, we have a learning curve that might say something about the general learnability of the task itself (at least for the statistical population that is fairly represented by the sample of learners). That is to say, we can use it to predict how difficult the learning would be for an 'average' learner. When time is the measure of effort, we can predict how fast learning may happen and how fast forgetting or loss of skill may happen. We need to be very careful in making predictions from learning curves (or any statistics), because there are always assumptions.
Assumptions are the devil in science, and in our daily lives as well. They are necessary, but evil only if you are not aware of them and how they affect your results or if you fail to be very clear about them in your conclusions and explanations.
Examples of things to question when creating and using learning curves (and any statistical results preseted as graphs):
- How valid and reliable are the measurements of ability and time?
- How well does the sample represent the population? (the sample on which the curve is based and the sample or population for which predicion is made)
- Do the choice of scales in the graph suggest incorrect interpretation of the data?