When you are cleaning out your closet, you generally start by pulling everything out and spreading it all over the floor before you start putting it back in a much more organized way. If you were to plot the messiness as a function of time, it would start out relatively organized, then head downwards as you spill your belongings onto the floor, but then turn back upwards as the reorganization phase began. In other words, the organization vs. time graph is U-shaped. Hopefully, it ends up higher than when you started. But, its unusual to organize a mess without making things a little worse for a short period of time before ultimately making things better.
It turns out, a similar thing seems to be true of your mind as you try to learn complicated ideas or tasks. It is common to think of learning as a monotonic progression in learning a new skill. The more you have practiced, the better you expect to be. But, there is evidence from a diverse array of cognitive tasks (language, art, facial perception, social cognition, music, science, etc.) that show that your performance on the task has a U-shaped dependence on time. In other words, for complex tasks, you may experience yourself getting worse before you actually get better.
We don’t know the cognitive reasons for this dip in performance yet, but a recent paper by Paul J. Camp proposes a thoughtful hypothesis for why this might happen with students learning Newtonian reasoning.
But as they move on from this initial burst of experience into other problems and different contexts, they must rely on remembering the correct Newtonian reasoning and recall is seriously complicated by the fact that their older phenomenological reasoning patterns are much, much better indexed and easily accessible than their newer Newtonian ones. They must experience failure of those memories and be reminded of what they have learned more recently. This produces a dip in performance.
According to the evidence, even while a learner’s performance is dipping, the actual understanding is not. The performance dip comes despite an increase in understanding.
So, how should a person go about learning something?
If skill acquisition is characterized by increments followed by decrements in performance as the mental representation of that knowledge is reorganized, and if shifting context is critical to the reorganization process, then curtailing that process after observing the first peak in performance runs the risk of losing access to that knowledge altogether. This directly implies that an iterative structure should be central, not peripheral.
In other words, learning should not be done linearly. Textbooks and curricula which lead students through a series of topics, always moving on to new material without constantly returning to previous materials is likely not the most efficient way to enable learning. In fact, it may leave students with a fragmented, poorly organized set of ideas that they are likely to forget and need to relearn later on. However, these students may still pass the exams and teachers will view them as success stories strengthening their confidence in linear teaching methods.
Moreover, the traditional method of testing may not be a good measure of student understanding.
The data above shows not only that performance development is U-shaped but also that it is at best only partially synchronized between students. If, say, a midterm exam is scheduled at a time when one student is at the first peak of performance and another is in the valley between peaks, the more knowledgeable student can actually receive the lower grade.