in certain situations, such as plotting data on graphs, calculating statistics, or
interpreting misleading graphs. In addition, if students do not have prior ex-
perience with graphs, a focus on the new stimuli, which Fiedler (2000) sug-
gested is associated with negative moods, should facilitate learning. In this
case, it is not necessary to link the new information to prior information, as
students may not have relevant prior information to which they would link
the new information. However, our research suggests that negative affect is
negatively related to reading and interpreting graphs (Linnenbrink & Pin-
trich, 2003, study 2). As noted previously, however, our tasks were rather
complex and occurred over a 6-week period, which may help to explain why
our findings our not consistent with the theoretical predictions.
Finally, similar to our results for conceptual change in science (Linnen-
brink & Pintrich, 2002b), we found that while positive affect did not enhance
performance in mathematics, it was related to high levels of effort and cogni-
tive regulation during the solving of number sequences and during graphing.
This provides further support for the notion that positive affect does not sig-
nal a lack of motivation (Bless, 2000).
It is also important to consider how the storage and retrieval of informa-
tion is linked to affect for mathematics learning. Based on Forgas’ (2000a)
model, we would expect affect to be relevant to long-term memory under cer-
tain conditions. For instance, it seems likely that computation tasks, where
students are simply retrieving strategies or number facts from long-term
memory and applying them, should not be influenced by affect. That is, this
type of processing involves direct retrieval, a type of processing in which af-
fect should not infuse thinking. In contrast, other mathematical tasks such as
problem solving, graphing, and shape discrimination may involve more sub-
stantive processing. Students engaged in these tasks may be learning new in-
formation or trying to link new information to prior knowledge. In these situ-
ations, it is likely that the affective state is encoded along with the relevant
mathematical material. Therefore, this may be a situation in which a congru-
ency between the encoding and retrieval states will facilitate recall. However,
none of the studies reviewed in this section tested this idea.
In summary, the research relating affect to cognitive processing in mathe-
matics presents a varied and complex view of the way in which affect influences
performance and learning. This is due in part to the wide variety of tasks that
fall under the domain of mathematics. Nevertheless, even within a type of task,
the results are not consistent, making it difficult to clearly analyze the findings
based on the proposed social psychological models of affect and cognitive
processing. We have suggested that part of the discrepancy in the findings may
be due to the duration of the task, in that affect may have different effects on
students’ processing depending on whether they must work on the task for a
long or short period of time. Other possible sources for the discrepant findings
are the complexity of the task (whether it requires both heuristic and detail-
- AFFECT AND COGNITIVE PROCESSING 81