Entropy, correlation, or something else
Why?
What is the sign that a student is learning fruitfully in a given learning activity in which a set of parameters can be varied by the student?
One might rule out an effective learning if all knobs available are turned in a chaotic manner.
One might also rule out an effective learning if only one knob is turned and it is turned only by a minute amount or too few times.
If the pattern involves some initial exploration of all knobs, followed by a settling down on one knob, which is explored extensively and systematically, then this might be recognized easily as a great learning pattern by a human.
The question that we ask here is—can we develop a metric, or a set of metrics, that will automatically summarize these differences between these and other different learning patterns?
Entropy
Suppose that a student explores one axis in the full parameter space (which is four dimensional in the climate game).
The parameter variation is systematic.
The total range of the parameter variation is reasonably large.
The number of trials is reasonably large.
Note
How large is “reasonably large”? A priori, we may or may not know the answer. In the latter case, maybe we can determine the answer from the data, choosing something like “greater than the median.”