Approximately 40% of the students were in Cluster 3 (n = 34,
39.5%); their frequency of exhibiting average learning behavior in
regard to the four main behaviors – analyze, explore, and manipulation behaviors (A, E, CM, IM) – lay between the other
two clusters. Similar to Cluster 2, these students also performed
a certain degree of the learning cycle of ‘manipulations after analysis’
and ‘analysis again after manipulations’ (i.e., A?CM, CM?A,
A?IM, IM?A). They also evaluated their status and chose to
‘restart the game after analyzing the clues or failed manipulation
by timely reflective process’ (i.e., A?R, IM?R). Compared with
Cluster 2, Cluster 3 lacked the additional sequences of ‘‘analyze
(A) to fail (F)’’ (A?F) and ‘‘incorrect manipulation to correct
manipulation’’ (IM?CM), but was boosted with the sequence of
‘‘incorrect manipulation (IM) to fail (F)’’ (IM?F) (z = 2.3, p < .05).
When compared with Cluster 2, this behavior pattern shows a lack
of ‘conservative trial-and-error analysis of fail situations in the
analyzing phase’ or ‘correcting errors in the manipulation phase’.
Cluster 3 was more prone to experiencing the entire game context
before applying the strategy of exercising incorrect manipulation
until failure (IM?F) to reflect upon and adjust their problemsolving
behaviors. The proportion of students from Cluster 3 having
prior knowledge was between the other two clusters; in contrast
to Cluster 2, the reflective strategy of Cluster 3 gravitated
toward the process of more students experiencing the game context
and clues (their average learning behavior frequency was
higher than that of Cluster 2), and they may tend to reflect upon
and adjust their behaviors by evaluating the fail situations caused
by incorrect manipulations directly in the manipulation phase
(IM?F). In terms of the mission completion rate, Cluster 3
achieved the highest percentage of 94.1%, slightly better than Cluster
2 and most students of Cluster 3 were able to complete the
tasks within the given game time.
There were only three students in Cluster 1 (n = 3, 3.5%). The
frequency of their average learning behavior regarding the four
main types – analyzing, exploring, and manipulating behaviors
(A, E, CM, IM) – accounts for the highest frequency, approximately
twice that of the other two clusters. In terms of the behavioral patterns,
students from Cluster 1 only showed the unidirectional
sequential behavioral patterns of ‘‘analyze to repeated incorrect
manipulations’’ (A?IM, IM?IM); they did not show the circular
and interactive reflective process patterns of ‘‘analyze-manipulation-
analyze’’ (e.g., A?CM, CM?A, IM?A) as Clusters 2 and 3
did. Because of their higher behavior frequency, the students of
Cluster 1 adopted a hastier problem-solving behavior, and their
sequential pattern of repeated incorrect manipulations (IM?IM)
did not appear in the other two clusters. In addition, Cluster 1 also
lacked the reflective behavior sequences of ‘‘analyze to restart’’
(A?R) and ‘‘incorrect manipulation to correct manipulation’’
(IM?CM). Moreover, we also found that the z-scores of the
sequence of A?CM (z = 2.88) was lower than 1.96 in Cluster
1, suggesting that this behavior seldom happened in Cluster 1. That
is, students in Cluster 1 less frequently adjusted their manipulation
into correct one after analysis. To some extent, it may illustrate
that students in Cluster 1 were less likely to reflect on the clues
in the game, compared with the other groups. The percentages of
the students who had prior knowledge and the mission completion
rate in Cluster 1 were both 33.3%, which was lower than that in the
other two clusters. Students in Cluster 1 appeared to be lacking a
deeper reflective process, which may have indirectly affected their performance.