Contribution of intelligence and memory to mathematical ability among adolescents and adults with intellectual disability : correlations and developmental trajectories (Hebrew)

The main aim of the present study was to test the developmental trajectories of mathematical ability (basic concepts, arithmetic operations and problem-solving) among adolescents (CA=16-20) and adults (CA=22-50) with non-specific intellectual disability (ID) (N=56, IQ=50-75). Another aim was to test the contribution of background variables (age, gender, general intelligence), crystallized and fluid intelligence, working memory and long-term memory to the participants’ mathematical ability. The developmental trajectory of mathematical ability was tested in light of three possible trajectories for the development of cognitive ability in the population with ID (Fisher & Zeeman, 1970; Lifshitz, 2020): impaired, parallel and continuous-compensatory.

Mathematical ability is the ability to learn and master mathematical concepts and skills (Koshy et al., 2009). It is crucial for academic and occupational success, for social inclusion and for performing routine everyday tasks (such as managing money, managing time, measurements) (Faragher & Brown, 2005; Schnepel & Aunio, 2021). Mathematical ability is important for the quality of life of people with ID as it enables them to independently perform daily tasks, develop autonomy and avoid exploitation (Goya et al., 2019; Neveu et al., 2025).

The participants included adolescents (N=28; CA=16-20) and adults (N=28; CA=22-50) with mild and moderate non-specific ID (IQ=50-75). Crystallized and fluid intelligence and working memory were tested using six Wechsler subtests (WMS-III, 1997; WAIS-IIIHEB, 2001). Long-term memory was tested using the Verbal Rey Test (RAVL, Vakil & Blachstein, 1997). Mathematical ability was tested using the Key-Math 3 test (Connolly, 2007) that includes three domains: basic concepts, arithmetic operations and problem-solving.

The research findings will be presented with reference to its aims:

Differences in mathematical ability between adolescents and adults with ID

We hypothesized that the scores in tasks assessing mathematical ability (basic concepts, arithmetic operations, problem-solving) will be higher among adults with non-specific ID compared to adolescents with non-specific ID. This hypothesis was partially confirmed. Mann-Whitney analyses showed that the scores of adults were higher than the scores of adolescents in the mental computation and estimation, addition and subtraction, and measurement subtests. These measures were found to follow a continuous developmental trajectory. The findings support the Compensation Age Theory (Lifshitz-Vahav, 2015; Lifshitz, 2020), which posits that the developmental delay during the first years of life in individuals with ID is compensated in later years and their cognitive ability continues to develop also at adult ages (45-50). No differences between the scores of adolescents and adults were found in the remaining mathematical ability subtests, indicating a stable developmental trajectory that can indicate preservation of mathematical ability at adult ages.

Hierarchy of mathematical abilities among the participants (adolescents and adults)

Friedman analyses showed a hierarchy of mathematical abilities among the participants (adolescents and adults). The scores in basic concepts and problem-solving were higher than the scores in arithmetic operations. The basic concepts domain included five subtests (numeration, algebra, geometry, measurement, data analysis and probability). The scores in the geometry test were higher than the scores in the other subtests and the scores in algebra were lower than the scores in the other subtests. The arithmetic operations domain included three subtests (mental computation and estimation, addition and subtraction, multiplication and division). The scores in the addition and subtraction subtest were higher than the scores in multiplication and division. In the problem-solving domain, the scores on the foundation of problem-solving were higher than the scores on applied problem-solving. The operations domain appears to be more difficult for the participants due to the absence of solving strategies. Geometry is a field which relies more on visual-spatial ability, and these scores were therefore higher compared to algebra which requires a higher abstract ability level (unknowns, inference, generalization) already in its first stages. The low mastery of multiplication and division operations apparently stems from the absence of a sufficient learning emphasis, combined with the cognitive complexity of these operations. The participants tended to identify the required operation in simple verbal problems but had difficulty applying calculational and conceptual knowledge for solving the problem.

Correlations between the components of intelligence, memory and mathematical ability

We hypothesized that a correlation will be found between crystallized intelligence, fluid intelligence, working memory, and long-term memory and mathematical ability (basic concepts, arithmetic operations, problem-solving) among the participants (adolescents and adults). The hypothesis was partially confirmed. Kendall’s tau correlations indicated a correlation between the general intelligence score and all mathematics subtest scores (r=.20-.47). The correlations between fluid intelligence and mathematical ability included more mathematics domains and were higher (r=.25=.52) compared to correlations between crystallized intelligence and mathematical ability (r=.20-.29). More correlations were found between verbal working memory and mathematics domains than between visual-spatial working memory and the mathematics domains. No correlation was found between long-term memory and the mathematics subtests (except for a correlation between learning rate and algebra). The correlation between general intelligence and working memory and mathematics is compatible with findings in the population with typical development. Intelligence influences the basic cognitive processes necessary for mathematical tasks such as logical thinking, problem-solving, inference ability and use of prior knowledge. Working memory enables simultaneous retention and processing of information and is required for simple mathematical tasks (such as counting) as well as for complex tasks (such as verbal problems, algorithms). The numerous correlations between fluid ability and mathematical ability may indicate that the participants invest higher cognitive resources (fluid intelligence) and rely less on prior knowledge (long-term memory and crystallized intelligence) when performing mathematical tasks. The involvement of visual-spatial working memory was found in tasks with a visual-spatial component (measurement, algebra that included series of shapes, etc.). The correlation between visual-spatial ability and addition/subtraction may indicate the participants’ use of concrete manipulations (tangible aids) for solving the exercises.

Contribution of background variables (age, gender, general intelligence), crystallized and fluid intelligence, working memory and long-term memory to mathematical ability

We hypothesized that a contribution to mathematical ability will be found for age, general intelligence, crystallized and fluid intelligence, working memory and long-term memory. The hypothesis was partially confirmed. Hierarchical regression analyses showed that general intelligence and verbal working memory explain 42.8% of the general mathematical ability score, 49.8% of the basic concept score, and 36% of the problem-solving score. Regarding the arithmetic operations score, age contributed 14.3% and general intelligence and visual-spatial working memory contributed 22.3%. With reference to the unique contribution of crystallized and fluid intelligence to mathematical ability, fluid and crystallized intelligence contributed to the general mathematics score and to the problem-solving and basic concepts domains. The main contribution to the general mathematical ability and basic concepts score was attributed to fluid intelligence (26.5% out of 46.6% and 31.5% out of 54.1%, respectively). No contribution of crystallized intelligence was found in the arithmetic operations domain. The contribution of fluid ability stems from the fact that mathematical thinking includes the ability to process symbolic and abstract representations and involves application of rules and the ability for integration of information and inference. The contribution of crystallized ability in the basic concepts and problem-solving domains stems from the fact that these tasks were based on linguistic ability (reading/writing comprehension, understanding and using concepts, etc.). The participants apparently did not rely on prior verbal knowledge (basic facts) in the arithmetic operations domain. Rather, they solved each exercise anew. The contribution of age to the operations domain affords further support for the Compensation Age Theory.

Theoretical contribution: The research findings support the Compensation Age Theory (Lifshitz, 2020), according to which the cognitive ability of the population with ID continues to develop also during adulthood as a result of maturation and life experience. The research expands on the understanding of how cognitive variables contribute to mathematical ability among adolescents and adults with non-specific ID. The research also contributes to understanding the structure of mathematical knowledge among people with non-specific ID, by drawing a profile of areas of strengths and weaknesses – a non-uniform profile in the different mathematical domains.

Practical contribution: The research findings indicate that mathematical abilities among people with ID can continue to develop during adulthood. Due to the importance of mathematics in daily life, the mathematical ability of this population should be nurtured also during adulthood. The hierarchy of mathematical abilities found in this study enables professionals to understand what needs to be strengthened, and what strengths can be exploited in order to develop mathematical abilities. The contribution of fluid intelligence and verbal working memory to mathematical ability points to the need for using remembering aids and imparting strategical schemas to advance mathematical ability in the population with ID.