Relations between mathematics learning difficulties and cognition - PASS

Whether students with math learning difficulties exhibit cognitive profiles that are different from the cognitive

profiles of their normally achieving peers was first examined. Students with math learning difficulties were indeed found to show relatively lower scores on the four PASS scales and therefore on the CAS Full Scale as well. The group of students with math learning difficulties performed highest on the Simultaneous processing scale although the reference group also performed higher on this scale than the norm, which means that this result should be taken as tentative until further testing is undertaken. 

It appeared that, in accordance with the theory (Naglieri & Das, 1997b), students who encounter difficulties

with the learning of basic multiplication facts perform, in general, lower on successive processing. Students who encounter difficulties with the automatization of basic facts show problems with not only successive processing but also planning and attention. The latter processes are particularly important for the automaticity test because a time limit requires the efficient production of correct answers. Finally, those students who encounter difficulties with the solving of math word problems showed relatively weak attention and successive processes and relatively strong planning and simultaneous processes. Although both planning and simultaneous processes are important for the solution of math word problems, these findings suggest that attention and successive processing, which play an important role in reading, also play a key role in this type of math. The present results show that the PASS profiles of students with math learning difficulties differed from those of students with no such difficulties and thus demonstrate the diagnostic value of the CAS, especially in conjunction with other relevant information.

It was also found that more of the students in the group of students with math learning difficulties had a cognitive weakness in planning or successive processing . According to Naglieri , Planning is, an important process in mathematics along with the simultaneous processes. It was found that those students with simultaneous weaknesses have, on average, greater difficulties with word problem solving although the reverse was not found: Students who encounter difficulties  with word problem solving do not produce lower simultaneous processing scores. In solving math word problems, the successive processes also play a critical role, which may explain the lower scores on this scale for the group of students with specific difficulties solving math word problems. Given that a large part of the any math curriculum consists of word problems, it is very understandable that students with a successive weakness may encounter difficulties. However,

the present results suggest that the group of students with math learning difficulties is heterogeneous and being comprised of students with a specific planning weakness, with a specific successive processing weakness, with generally low processing scores, and even a few students with attention and/or simultaneous weaknesses. The results also suggest that a child’s PASS profile alone is not sufficient to diagnose math learning difficulties, a child’s PASS profile can, however, help identify specific cognitive weaknesses and thereby facilitate both diagnosis and treatment. The relations between specific PASS cognitive profiles and the effectiveness of a special math intervention devoted to the learning of basic multiplication facts, the automatization of these facts, and word problem solving skills were carefully examined in the next set of analyses. Previous research showed students with a cognitive planning weakness to benefit from a cognitive intervention with specific attention to planning more than students without a cognitive weakness and more than students with other cognitive weaknesses (Naglieri & Johnson, 2000). Although these results for the present study, the group of students with an attention weakness showed a tendency to improve the most on the (automatized) mastery of basic multiplication facts while the group of students with a simultaneous weakness showed a tendency to improve most on word problem solving. An explanation for the discrepancy in the results of these different studies may lie in the fact that the intervention utilized in the present study was less focused on planning than the interventions used in previous research (e.g., Naglieri & Johnson, 2000). The intervention described here was mainly concerned with the acquisition of the basic math facts and the adequate use of strategies. Although planning is certainly part of strategy use, it was not explicitly taught. Nevertheless, the intervention appeared to be particularly effective for those with a simultaneous cognitive weakness.

To conclude, some important relations between PASS cognitive processes and math learning difficulties  the relations were not very strong, the findings nevertheless highlight the importance of particular cognitive processes for the functioning of students within certain areas of the mathematics curriculum. Simultaneous and successive processes appear to be of particular importance for the solution of math word problems, for example, and attention appears to play a role in the automatization of basic facts. Previous research has also shown the CAS to be a valuable diagnostic instrument and also useful for the planning of special instruction or intervention. We therefore encourage further research along these lines. Future research might also address the specific difficulties that students encounter with the mathematics curriculum in connection with the development of special instructional methods based on the PASS cognitive processing theory and specific weaknesses.