tify the amount of interactive instruction occurring in each
classroom. From each instructor’s responses, we calculated a
nominal percentage of time, called the Interactive Assessment
Score (IAS), spent on interactive learning strategies during the
term. The scores ranged from 0 to 49%, suggesting that our
questionnaire was successful at distinguishing different
amounts of interactive instruction, and that instructors were
not inflating estimates of their classes’ interactivity. If they had
been, we would surely have seen many estimates of over 49%
and none near 0%. Nonetheless, the IAS is only a first-order
indicator of allotted time. It provides no details as to the quality
of the implementation or engagement in the classroom.
In figure 4, we plot g versus IAS for the 52 Astro 101
classes in our study with at least 25 students. We excluded
smaller classes because we believe that the teaching and
learning in classes with a very small number of students can
be a special case, bordering on personalized instruction. Although
the plot shows no simple relationship between learning
gain and the level of interactivity, it is notable that no class
with an IAS below 25% achieved a gain above 0.30.
By contrast, classes with an IAS above 25% had gains
ranging from about 0.05 to 0.5. The average learning gain for
those classes was 0.29, more than twice the average gain of
0.13 found for classes with an IAS below 25%. This result is
almost identical with that found by Hake for introductory
physics. To determine if this dependence on IAS is real, we
conducted a statistical-significance test (a t-test) and concluded
that there is less than a 10–5 chance that the recorded
difference in learning gain between the two groups is just a
statistical fluke. If this were a medical study of two treatment
strategies for a disease, the study would be stopped at this
point for ethical reasons, so that every patient could be given
the more effective treatment immediately!
To further probe the relationship between interactivity
and learning gain, we conducted a multivariate regression
analysis to determine how individual differences (for example,
personal and family characteristics, academic achievement,
and student major) might be correlated with learning
gain.14 The results show that the use of interactive learning
strategies is the single most important variable in accounting