school children induced into a positive mood learned the shape-discrimi-
nation task more quickly than children in a negative or neutral mood, as did
those induced into an active rather than passive state. There was also an in-
teraction of valence and arousal, with children in the negative mood condi-
tion taking longer to master the task when they were induced into a passive
rather than active state. Taken together, these results suggest that positive
moods are beneficial for learning shape discrimination tasks whereas nega-
tive moods are detrimental, especially when arousal is high.
Finally, given the large emphasis on problem solving as part of the mathe-
matics curriculum, research relating problem solving and mood seems rele-
vant to this discussion. For instance, Isen et al. (1987) examined college stu-
dents’ performance on creative problem-solving tasks. In a series of studies,
participants completed two types of creative problems solving tasks,
Duncker’s (1945) candle task and the Remote Associates Test, both of which
lasted between 10 and 15 minutes under a variety of induced mood condi-
tions. The results from these studies suggest that positive mood facilitates cre-
ative problem solving in comparison to a neutral or negative mood, but there
are not differences in problem solving between negative and neutral moods.
Finally, some of the studies included an arousal condition (exercise). Stu-
dents in the positive mood condition scored higher than those in the arousal
condition, while there was no difference between the arousal condition and
the neutral mood condition. This suggests that valence, but not arousal, is
important in terms of students’ creative problem solving.
In summary, the research relating positive and negative affect to mathe-
matics learning is not consistent. This may be due in part, however, to the
broad range of tasks that fall under the purview of mathematics education as
well as the context of the study, including the duration of the task. Therefore,
in attempting to apply social psychological theories, we consider that the dif-
ferent tasks may require different processes and, accordingly, positive and
negative affect may hinder or enhance cognitive processing in different situa-
tions. We also discuss whether differences in the contexts and lengths of tasks
may help to account for the discrepancies in the results.
Bless (2000), Fiedler (2000), and Fredrickson (2001) all suggested that pos-
itive moods should result in broad, heuristic processing. Fiedler (2000) fur-
ther suggested that positive affect is beneficial when active generation occurs.
In terms of mathematics learning, we would therefore expect positive affect
to enhance learning and performance when tasks require a broad perspective
or active generation. For instance, learning and distinguishing shapes may re-
quire a broader perspective in that considering the whole shape rather than
focusing on details of particular aspects of the shape may enhance perform-
ance. Furthermore, this information needs to be linked to prior knowledge,
so Fiedler’s suggestion that positive affect helps to activate prior knowledge
78 LINNENBRINK AND PINTRICH