PASS theory of cognitive processing

The focus of this article is on the relations between the learning of mathematics by students with math learning difficulties and the cognitive processes included in the Planning, Attention, Simultaneous, and Successive (PASS) theory. It is known that relations exist between certain cognitive processes and math learning, and between PASS processing and effective mathematics instruction (Naglieri & Johnson, 2002). However, these relations are not without controversy, particularly with respect to the abilities of students with learning disabilities (LD). In addition to the many questions regarding the relations between cognition and mathematics (or mathematics learning disabilities), there are also questions regarding the role of intelligence and the role of intelligence testing in the diagnosis of learning disabilities (Kaufman & Kaufman, 2001).

Intelligence tests are mostly used to measure a student’s general ability level. In the identification of learning disabilities, IQ tests are also commonly used to compare a student’s ability to his or her actual achievement. Unless the discrepancy is beyond some pre-determined value, a learning disability has not been indicated (Mercer, 1997). However, the use of an IQ-achievement discrepancy has been under attack for some time (e.g., Siegel, 1999; Stanovich, 1999). One reason is that the cut-off points for the general intelligence scores used to define learning disabilities are often based, at least in part, on tests that have a clear achievement component (Kaufman & Kaufman, 2001; Naglieri, 1999). Another reason is that intelligence cannot always be measured exactly; there is always some kind of error, which complicates the use of an IQ score in, for example, a LD discrepancy formula. Some authors (e.g., Siegel, 1999) argue that the identification of LD should be based on achievement scores alone and simply encompass those students who consistently score in the 25th percentile, for example, without any consideration of intelligence whatsoever.

Conceptually, intelligence tests are not only used to measure the IQ-achievement discrepancy, they can also be used to map children’s cognitive strengths and weaknesses. Although findings generally do not support using IQ tests in this way (Kavale & Forness, 2000; Naglieri, 1999), recent research on cognitive processing has yielded promising results (Naglieri, 1999, 2000). The development of new approaches to intelligence testing, such as the Kaufman Assessment Battery for children (K-ABC; Kaufman & Kaufman, 1983) and the Cognitive Assessment System (CAS; Naglieri & Das, 1997a), is of obvious relevance for both diagnostic (Naglieri, 1999) and instructional purposes (Naglieri & Gottling, 1995, 1999; Naglieri & Johnson, 2000). Because these theory based tests measure ability as a multidimensional perspective, they may provide greater information on specific components and processes than a test designed to measure general intelligence (such as the WISC-III; Wechsler, 1991). And the specific information provided by these tests may be particularly useful during the diagnostic process, the design of instructional programs, and the development of specific interventions.

An example of such a new intelligence test is the Cognitive Assessment System (CAS; Naglieri & Das, 1997a), which is based on a theory of cognitive processing that has redefined intelligence in terms of four basic psychological processes: Planning, Attention, Simultaneous, and Successive (PASS) cognitive processes. The CAS provides information on students’ strengths and needs. In addition, CAS scores have been found to be strongly related to achievement (r= .70; Naglieri, 2001; Naglieri & Das, 1997b), which is quite remarkable as the test does not contain the verbal and achievement components found in other measures of IQ (i.e., the WISC). These and other reasons have led researchers in the Netherlands (Kroesbergen & Van Luit, 2002; Kroesbergen, Van Luit, Van der Ben, Leuven, & Vermeer, 2000) to study the validity of the CAS when used in that country. This study is an example of one that examines the relations between the CAS and math learning difficulties with particular intent to examine the potential of PASS theory, on which the CAS is based, for the remediation of math learning difficulties.

Naglieri and Das (1997b) have found each of the four sets of PASS processes to correlate with specific types of achievement in math and other academic areas as well. Although all of the PASS processes related to achievement, particular processes such as planning appear to be specifically related to particular aspects of academic performance, such as math calculation (Das, Naglieri, & Kirby, 1994). This specific example is theoretically logical because planning processes are required for making decisions with regard to how to solve a math problem, monitor one’s performance, recall and apply certain math facts, and evaluate one’s answer (Naglieri & Das, 1997b). Simultaneous processes are particularly relevant for the solution of math problems as these often consist of different interrelated elements that must be integrated into a whole to attain the answer. Attention is important to selectively attend to the components of any academic task and focus on the relevant activities. Successive processes are also important for many academic tasks but in mathematics, probably most important when the children leave the sequence of events and for the memorization of basic math facts. For example, when the child rehearses the math fact 8 + 7 = 15, the child learns the information as a serially arranged string of information that makes successive processing especially important. Successive processing is also important for the reading of words that are not known by sight and may therefore be particularly important for the solution of math word problems.

CAS scores have been found to correlate strongly with achievement scores (Naglieri & Das, 1997b). The overall correlation with the Woodcock-Johnson Revised Tests of Achievement (WJ-R; Woodcock & Johnson, 1989) Skills cluster has been found to be .73. The correlations with mathematics skills have been found to range from .67 to .72, with the highest subscale correlations occurring for Simultaneous processes and Math (.62) and Planning and Math (.57). These correlations are quite high when compared to research with other intelligence tests (e.g., WISC-R, Raven’s SPM), where the correlations between intelligence and math performance have been found to range from .30 to .50 (Ruijssenaars, 1992). These findings thus suggest that the CAS may be a good predictor of academic achievement in general and math achievement in particular. Research has also suggested that a child’s PASS profile is related to the effectiveness of particular intervention programs. Naglieri and Gottling (1995, 1999) and Naglieri and Johnson (2000), for example, have shown students to differentially benefit from instruction depending on their PASS cognitive profiles. The implication is that instruction can be made more effective when clearly matched to the cognitive characteristics of students. Along these lines, Naglieri and Johnson (2000) found the math computation of children with a planning weakness to benefit considerably from a cognitive strategy instruction that emphasized planning; those children with no planning weakness but nevertheless receiving the same planning-based instruction also did not show the same level of improvement in math computation as the other children. Similar insights into the relations between the intelligence profiles of students and the effectiveness of particular intervention programs may also aid the planning of remedial education programs and therefore call for further investigation.