where S corresponds to the smoothed attention value produced
using an EWMA, t is time, A is the median-filtered index, and
c is a regularization constant that is inversely proportional to
the relative weighting of less recent events (a value of .2 was
used in this study based on pre-test results).
Using the smoothed attention index, the system is able to infer
student attention levels during the presentation of educational
material, provided that the presentation contains sections delineated
a priori. To determine the student attention level for
a given module of educational content, the supervisor calculates
the mean of the attention indices recorded during the
presentation of that section. This information can be passed
to computer systems or even human instructors to help them
gauge the effectiveness of lessons. In our proof-of-concept
design, the supervisor component uses attention information
to select review topic by choosing the lesson module with the
lowest average attention values (Figure 4).