|Autocorrelation reveals a three-minute periodicity|
Digital learning tools such as computer games and CAD software emit a lot of temporal data about what students do when they are deeply engaged in the learning tools. Analyzing these data may shed light on whether students learned, what they learned, and how they learned. In many cases, however, these data look so messy that many people are skeptical about their meaning. As optimists, we believe that there are likely learning signals buried in these noisy data. We just need to use or invent some mathematical tricks to figure them out.
In Version 0.2 of our Visual Process Analytics
(VPA), I added a few techniques that can be used to do time series analysis
so that researchers can find ways to characterize a learning process from different perspectives. Before I show you these visual analysis tools, be aware that the purpose of these tools is to reveal the temporal trends of a given process so that we can better describe the behavior of the student at that time. Whether these traits are "good" or "bad" for learning likely depends on the context, which often necessitates the analysis of other co-variables.
|Correlograms reveal similarity of two time series.|
The first tool for time series analysis added to VPA is the autocorrelation function
(ACF), a mathematical tool for finding repeating patterns obscured by noise in the data. The shape of the ACF graph, called the correlogram
, is often more revealing than just looking at the shape of the raw time series graph. In the extreme case when the process is completely random (i.e., white noise), the ACF will be a Dirac delta function
that peaks at zero time lag. In the extreme case when the process is completely sinusoidal, the ACF will be similar to a damped oscillatory cosine wave
with a vanishing tail.
An interesting question relevant to learning science is whether the process is autoregressive
(or under what conditions the process can be autoregressive). The quality of being autoregressive means that the current value of a variable is influenced by its previous values. This could be used to evaluate whether the student learned from the past experience -- in the case of engineering design, whether the student's design action was informed by previous actions.
Learning becomes more predictable if the process is autoregressive (just to be careful, note that I am not saying that more predictable learning is necessarily better learning). Different autoregression models, denoted as AR(n) with n indicating the memory length, may be characterized by their ACFs
. For example, the ACF of AR(2) decays more slowly than that of AR(1), as AR(2) depends on more previous points. (In practice, partial autocorrelation function
, or PACF, is often used to detect the order of an AR model.)
The two figures in this post show that the ACF in action within VPA, revealing temporal periodicity and similarity in students' action data that are otherwise obscure. The upper graphs of the figures plot the original time series for comparison.