Flanagan and Schneider in a Meta-Analysis of the Relationship Between Cognitive Abilities and Mathematics

 Our old acquaintance Dawn Flanagan and Joel Schneider, together with several other researchers led by Niileksela, conducted a meta-analysis examining the relationships between cognitive abilities and mathematics tests. The article was published very recently, in July 2026.

The authors used data from the technical manuals of 122 cognitive test batteries.

In an earlier study by Amland and colleagues, published in 2025, correlations of .25 to .50 were found between language skills, visuospatial ability, and working memory, on the one hand, and various mathematical skills, on the other. Phonological awareness, verbal working memory, and visuospatial ability were associated with the ability to solve arithmetic problems, whereas language comprehension, visual working memory, and visuospatial ability were associated with the ability to solve mathematical word problems.

The present study examined correlations between individual tests only, rather than between indexes, which are composites of several tests. The samples included children and adults with typical mathematics achievement. Children and adults with mathematics difficulties were not included.

The meta-analysis included only tests that the researchers regarded as good indicators of broad or narrow cognitive abilities. In my opinion, this results in a substantial loss of information. The authors provide an example of a test that was excluded from the meta-analysis: nonword repetition. This is an excellent test that assesses both working memory and phonological awareness. Because it is a good measure of both abilities, rather than a pure measure of only one of them, it was excluded from the analysis. This is unfortunate, because it means that we receive much less information about the relationship between useful, high-quality tests and cognitive abilities. On the other hand, the researchers’ reasoning is understandable, because they wanted to obtain clean and precise estimates of the relationship between each individual cognitive ability and mathematical functioning.

The supplementary material accompanying the article is supposed to include the classification of every test according to broad and narrow cognitive abilities, as well as all the correlations between the tests. This could be a very important resource for us, but I was unable to open or download it. I hope the problem will be corrected.

Altogether, the meta-analysis included 47,000 correlations between tests. This is an almost unimaginable amount of data.

The mathematics tests assessed five main domains:

Mathematical calculation: The ability to solve arithmetic exercises involving the four basic operations.

Mathematics fluency: The ability to solve arithmetic exercises involving the four basic operations quickly and fluently, and to apply mathematical procedures efficiently, rapidly, and accurately.

Mathematics problem solving: The ability to solve mathematical word problems.

Mathematics knowledge: Knowledge of mathematical content and concepts, rather than mathematical procedures.

Number sense: The ability to compare large quantities of objects rapidly and without counting, to identify which group contains more objects, and to estimate large quantities. It also includes number-line estimation, such as placing a number on a number line marked only at its endpoints, and understanding the quantitative meaning of numbers. In this meta-analysis, number sense was assessed mainly using tests from the Woodcock-Johnson IV and V. These specific tests do not measure number sense in a pure form, but also assess other functions, such as counting and mental calculation.

All the correlations between the mathematics tests and the cognitive abilities were positive and statistically significant, and most were in the range of .30 to .50. The correlations can be seen in Table 1, which I prepared. Click to enlarge.

Table 1: Correlations Between Cognitive Abilities and Math Skills

The table shows that fluid reasoning, crystallized knowledge (comprehension-knowledge), and working memory capacity had the strongest correlations with mathematical calculation, mathematics problem solving, mathematics knowledge, and number sense.

Processing speed was particularly strongly associated with mathematics fluency.

Visual processing, auditory processing, learning efficiency, and retrieval fluency also made statistically significant contributions, although their relationships with the various mathematical functions were weaker.

The authors also conducted a structural equation modeling analysis, or SEM. This type of analysis examines whether a proposed network of relationships fits the observed data. It can reveal both direct and indirect effects between variables. An indirect effect means, for example, that Variable A influences Variable B through Variable C.

The standardized path coefficients in such an analysis indicate how much performance in a mathematical ability is expected to change, in standard-deviation units, when a particular cognitive ability increases by one standard deviation. For example, a path coefficient of .45 between crystallized knowledge and mathematical calculation means that an increase of one standard deviation in crystallized knowledge is associated with an expected increase of .45 standard deviations in mathematical calculation.

Suppose that mathematical calculation scores have a mean of 100 and a standard deviation of 15, as is the case for Woodcock-Johnson standard scores. An increase of one standard deviation in crystallized knowledge would then be associated with an expected increase of 6.75 points in mathematical calculation. Thus, theoretically, a child who initially scores 75 in crystallized knowledge and 80 in mathematical calculation, and whose crystallized knowledge score improves to 90, an increase of one standard deviation, might be expected to improve to approximately 86.75 in mathematical calculation.

Table 2 presents the path coefficients for the direct and indirect effects of cognitive abilities on mathematics. Strong effects are shown in brown, while weaker effects that remain statistically significant are shown in black.

Table 2: Path Coefficients Between Cognitive Abilities and Math Skills

The results show that crystallized knowledge, fluid reasoning, processing speed, and, to some extent, working memory capacity are strongly associated with the various mathematical skills.

Crystallized knowledge is associated with all mathematical skills except mathematics fluency. Its strongest relationships are with mathematical word-problem solving and with knowledge of mathematical content and concepts. To perform these two types of tasks, a child needs a well-developed mathematical vocabulary, including terms such as numerator, denominator, decimal fraction, prime number, parallelogram, and octagon. The child must also be able to extract mathematical meaning from the sentences presented in a word problem.

Fluid reasoning is likewise associated with all mathematical skills. It hardly needs to be stated that mathematical performance requires abstract reasoning. Examples include translating a word problem into mathematical language, developing a strategy for solving the problem, understanding abstract mathematical concepts, and manipulating those concepts.

Processing speed contributes to all mathematical functions by making calculation processes more efficient. It operates together with working memory capacity. The greater a person’s processing speed, the more likely they are to complete a calculation before the information held in working memory decays.

In addition to these four abilities, several other relationships were found between cognitive abilities and mathematical functioning.

Visual processing was particularly strongly associated with number sense. This may be related to tasks such as estimating a position on a number line, deciding which of two groups contains more objects, and deciding which of two numbers is closer to a third number. All these tasks probably also rely on visual processing.

Auditory processing was associated with mathematics problem solving, but also with mathematical calculation and mathematics fluency. Auditory processing underlies a child’s ability to count aloud. The child initially learns the sequence of number words almost as though it were a nonword or a continuous phonological sequence, such as “onetwothreefourfive.” The child gradually segments this sequence and connects each number word with its quantitative meaning.

The ability to count backward automatically from ten is also related to phonological processing. The same is true of the ability to count automatically in twos from an even number, for example, four, six, eight, ten, twelve, and so forth. These automatic phonological sequences provide a foundation for learning to count and, later, for learning arithmetic operations, particularly addition and multiplication.

Retrieval fluency was associated with mathematics fluency. This finding highlights the relationship between rapid-naming tests such as RAN, in which the child must quickly and fluently retrieve the word corresponding to a visual stimulus, and the ability to retrieve solutions to simple arithmetic problems involving the four basic operations quickly and fluently.

Learning efficiency showed a relatively weak relationship with mathematical skills.

Overall, the meta-analysis found that cognitive abilities explained 53% of the variance in mathematical calculation scores, 35% of the variance in mathematics fluency scores, 67% of the variance in mathematics problem-solving scores, and 43% of the variance in number-sense scores.

On average, mathematical skills showed the strongest correlation with fluid reasoning, , followed by crystallized knowledge, , working memory, , and visual processing, .

The authors also found significant correlations between mathematical skills and narrow abilities within crystallized knowledge, fluid reasoning, working memory, and visual processing. I will not discuss those findings in detail here. One finding that is worth mentioning, however, is the relationship between verbal working memory and mathematics knowledge, and between visual working memory and mathematical calculation. These relationships have repeatedly been reported in the professional literature. One possible explanation is that mathematical calculations depend partly on movement along a mental number line.

Niileksela, C. R., Hajovsky, D. B., Cocar-Montenegro, F. P., Schneider, W. J., Flanagan, D. P., & Alfonso, V. C. (2026). Cognitive–Mathematics Relations: A Meta-Analysis of Norm-Referenced Standardized Test Batteries. Journal of Intelligence. doi:10.3390/jintelligence14070142