I’ll Show You My Learning Curve, If You Show Me Yours

What does learning look like? No seriously, take a moment and think about how you would visualize the learning process. What shape would it be? How would it change over time? What variables would you include?

You might try to answer this question by thinking about some common visualizations claimed to depict the learning process. I’ve included a couple below that I frequently see associated with discussions of learning:

While highly simplified, these visualizations convey a particular view of the learning process — both in terms of what features are emphasized and which are excluded. Furthermore, I frequently find these visualizations influencing the thinking of learning designers both in terms of what an effective learning experience should look like and how its efficacy should be measured.

This is unfortunate because I believe these visualizations often do more harm than good, encouraging the design of suboptimal learning experiences. I am simply not a fan of these graphs.

Recently a colleague asked me, after listening to my latest diatribe about the continuing influence of these learning curve visualizations, what I thought a more accurate depiction of the learning process would look like. This is a fair question. And after taking some time to think about it I replied that I thought a better visualization of the learning process would look something more like this:

I realize this image is probably unhelpful. In fact, I can already hear learning designers saying, “What am I supposed to do with this?” So I want to try and break down my thought process. This is a valuable exercise because I am convinced that sharing what I believe is a more faithful visualization of the learning process (although by no means am I claiming it to be complete), informed by research in cognitive and learning sciences, will foment better thinking about the design of learning products.

In particular, traditional depictions of the learning process (e.g., learning curve) engender inferior learning designs because they encourage thinking about learning in a way that is both deeply misleading and crucially incomplete. In contrast, my hope is that a picture like the one above comes to mind when people think about learning and that a greater appreciation of the dazzling complexity of the learning process will result in more effective and powerful learning products.

So let’s get started!

A Picture Is Worth…

So we start simple enough with a couple axes. On the Y axis we have a generic high and low scale; meanwhile the X axis depicts passing time.

We start populating our visualization by adding two variables: learning potential and performance. Learning potential is a measure of the receptivity of our brain to encoding additional information for long-term storage. As we will see, learning potential fluctuates significantly during the learning process. Performance, also known as retrieval strength, is defined as ease of current access to information in memory (Roediger & Butler, 2011). At the beginning of a learning experience, as you might expect, our potential for learning is quite high while our performance level is low.

Also low at the beginning of the instructional process, but rarely distinguished in visualizations, is our level of learning, also known as storage strength. Storage strength is a measure of how entrenched, enduring, and transferable our knowledge is (Roediger & Butler, 2011). This is usually what we really care about when we talk about learning. It is important to note that storage strength is distinct from performance (i.e., retrieval strength). Furthermore, while performance can be measured during instruction or training, learning is a latent variable only measurable post instruction.

We’ve now begun the learning process. As you can see, performance typically rises quickly as a learner begins engaging with new information, whereas the learning potential curve drops in an inverse relationship. Our measure of learning, on the other hand, increases but at a much slower rate than performance.

As learning continues we see the learner is performing at a high level and starting to plateau — she is likely making few errors and are enjoying the memorial benefits of recent exposure to information and massed practice — the learning curve at the bottom, meanwhile, is also plateauing as the learning potential curve is now very low.

This inverse relationship between performance and learning is reflected in substantial research showing “gains in storage strength (learning) are a decreasing function of retrieval strength” (Bjork, 2011). In other words, we don’t learn very much when we are performing highly. So if we want to continue to increase our learning and not just maintain high, but transitory, performance levels, what must be done?

Before answering that question I want to point out something visible in the image above. In particular, we can see (the green dashed line) the familiar learning curve depicted in the earlier visualizations I shared. Hopefully, the impoverished and incomplete nature of this visualization, which we can already see is guilty of conflating performance with learning, will become increasingly evident as we continue our visual journey.

So how do we increase our brain’s receptivity to additional learning (since this is what we really care about) while remaining mindful not to be misled by our high, but fleeting, level of current performance?

It turns out that we increase our learning potential by, counterintuitively, forgetting what we’ve learned. Continued study or instruction at the peak of performance provides little long-term learning benefits.

Thus we continue making progress in learning by allowing our brain to forget information it has just acquired; that is, by making retrieval more effortful and difficult which results in lower near-term performance (Fritz, 2011). The critical role of forgetting explains much of the learning benefit associated with familiar studying strategies like the spacing effect: spacing out study gives our brain the opportunity to forget.

Of course we don’t want to forget everything we’ve learned so we need to reintroduce study and instruction before too long. The challenge is predicting the optimal point at which we’ve maximized our future learning potential while avoiding completely forgetting previously learned information.

Now stop and take a minute to look at the visualization that is emerging. We can now see one of the biggest problems with traditional learning curve visualizations: they fail to depict the symbiotic and cyclical relationship between performance and forgetting and how they function to mutually support learning over time. Focusing primarily on increasing learner performance, while neglecting the importance of inducing forgetting, engenders inferior learning design (see, Bjork & Bjork, 2011).

I’ve now extended this waxing and waning of performance and forgetting, attempting to illustrate the goal of decreasing variability in learner performance as the underlying storage strength (learning) of information increases.

An important thing to note is that each of the three curves displayed in this image (learning potential, performance, and learning) should be viewed as averages of underlying multidimensional constructs. Let me take a moment to explain what I mean by this.

We never learn something in isolation. Our brains are contextual devices and every successful learning event incorporates information not only about the target of our learning efforts but also our feelings, our environment, related ideas, etc. (Marcus, 2008). Initial learning, in particular, relies heavily on context and cues found in the environment. It is for reason that people are better able to recall information while in the setting or mood as when the information was originally learned (Godden & Baddeley, 1975). More stable learning outcomes requires practice across a diversity of settings, problems, and times.

So how do these considerations change our image? As mentioned previously, it means we should interpret each curve as an average which, when decomposed, reflects significant learning variability given different settings, cues, affective states, and intervening activities.

For instance, learner performance might be high in setting that matches study conditions but much lower if we removed cues present during study in a later testing situation. Consequently, we should be seeking less variability in both overall student performance as well as performance across settings/problems/contexts when evaluating the efficacy a learning intervention.

I’ve tried to illustrate this fact above by drawing highly variable waves at the beginning of the learning process (learning gains initially highly context/problem dependent) but eventually coalescing (learning more steady across contexts/problems).

Focusing on performance gains in a single context , with similar problem types and over a short period of time, will give a highly inaccurate indication of overall learning.

So that’s my final doodle. And despite my artistic limitations, I don’t think this visualization is too far from the one I originally shared! But more importantly, I think this visualization depicts the learning process with greater fidelity.

So I would encourage you to remember next time someone shows you a picture of a learning curve that the process of learning is more accurately depicted as a beautiful and fluid dance of many curves — in particular, the continuous ebb and flow of performance and forgetting that result in successful learning!

So I’ll ask you again, what does your visualization of learning look like?

References

Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. Psychology and the real world: Essays illustrating fundamental contributions to society, 56–64.

Bjork, R. A,. (2011). On the symbiosis of remembering, forgetting, and learning. In Aaron Benjamin (Ed.) Successful remembering and successful forgetting: A Festschrift in honor of Robert A. Bjork, 1–22.

Fritz, C. O., (2011). Testing, Generation, and Spacing Applied to Education: Past, Present, and Future. In Aaron Benjamin (Ed.) Successful remembering and successful forgetting: A Festschrift in honor of Robert A. Bjork, 1–22.

Godden, D. R., & Baddeley, A. D. (1975). Context‐dependent memory in two natural environments: On land and underwater. British Journal of psychology, 66(3), 325–331.

Marcus, G. (2008). Kludge: The Haphazard Construction of the Human Mind. New York, NY: Houghton Mifflin Company.

Roediger III, H. L., & Butler, A. C. (2011). Paradoxes of learning and memory. The Paradoxical Brain, Cambridge University Press, Cambridge, 151–176.