This research is supported in part by EU grant FP7-
ICT-2011-9 no. 600854 and by Israeli Science Foun-
dation grant no. 1276/12. Reuth Dekel was support-
ed in part by a grant from the Israeli Chief Scientist
for advancing the role of women in science.
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(AVG = 12. 47 minutes, SD = 6. 6). Additional analysis
reveals that the total number of actions in a student’s
interaction (AVG = 39. 65, SD = 11. 79) was signifi-
cantly lower than the total number of actions in the
list condition (AVG = 57.069, SD = 32.628). The ratio
of redundant actions of the plan condition ( 28 per-
cent) was significantly lower than the ratio of redun-
dant actions for students in the list condition ( 46 per-
cent). Although the number of total actions in the
plan condition (AVG = 47, SD = 12.01) was slightly
higher than in the list condition (AVG = 43. 66, SD =
18. 11), the ratio of redundant actions in the plan
condition ( 33 percent) was lower than the ratio of
redundant actions in the list condition ( 43 percent).
This indicates that visualizing the hierarchical aspect
of the example facilitates students’ ability to general-
ize mathematical and structural concepts across new
problems (in our case, the use of expectation to rea-
son about events in the sample space).
Finally, there were striking differences in the way
students explained the solution to the COIN problem
based on their respective visualization condition.
Overall, 75 percent of the students in the plan condition used and referred to subgoals when describing
the solution to the COIN problem, as compared to 66
percent of the list students. In our study, subgoals
represent higher-level activities such as generating
and running a sampler, projecting the results to a
plot, and computing the average sum of a random
variable. These activities recur in all three of the problems in the study, and recognizing and internalizing
these concepts may have contributed to the success
of the plan visualization. The students in the list condition were far less likely to use such concepts when
describing the problem.
Conclusion and Future Work
This article proposed new algorithms for recognizing
students’ plans in exploratory learning environ-
ments, which are open-ended and flexible educa-
tional software. Our algorithm is shown to outper-
form (or perform comparably with) the
state-of-the-art plan-recognition algorithms for two
different ELEs for teaching chemistry and statistics. It
is also the first recognition algorithm that is shown to
generalize successfully to several ELEs. It demon-
strates that using hierarchical visualizations of expert
solutions positively affects students’ problem solving
in ELEs. We are currently applying these results in
several directions. First, we are designing plan-recog-
nition algorithms for ELEs that do not depend on a
predefined grammar. Second, we are designing intel-
ligent tutors in ELEs that use plan recognition to
guide their interactions with students. Finally, we are
designing automatic methods for aggregate analysis
of students’ activities that is based on students’ plans.