What is abstract reasoning?

How people actually solve them

The most cited study of how people solve matrices is Carpenter, Just and Shell (1990). They analyzed solutions using verbal protocols, eye-fixation patterns and errors, and expressed their theory as two computer simulation models, one performing like the median college student in their sample and one like the best (Carpenter, Just & Shell, 1990).

Two findings stand out. First, everyone solved the matrices with the same incremental, step-by-step strategy of encoding the figures and inducing the regularities in each problem (Carpenter, Just & Shell, 1990). Second, what separated higher from lower scorers was mainly the ability to induce abstract relations and to manage many problem-solving goals in working memory (Carpenter, Just & Shell, 1990). Strong solvers are not using a secret trick; they keep more of the problem in mind at once and spot less obvious relations.

Later work describing the theory lists five rules in Raven's items (Lozano, Embretson & Revuelta, 2025):

• Constant in a row: a feature stays the same across a row. The easiest rule to induce.
• Quantitative pairwise progression: a feature grows or shrinks step by step.
• Figure addition or subtraction: two figures combine or cancel to make the third.
• Distribution of three values: three values each appear once in every row.
• Distribution of two values: the hardest rule under the theory.

Item difficulty depends on both the type of rule, which taxes finding correspondences, and the number of rules, which taxes goal management in working memory (Lozano, Embretson & Revuelta, 2025). That links abstract reasoning closely to memory: a reanalysis of 14 data sets found a median correlation of .72 between working memory capacity and fluid intelligence, while agreeing the two are not the same thing (Kane et al., 2005).

How much of intelligence a matrix test captures

Matrix tests are excellent, but not pure. Across several large samples, Raven's shared about 50% of its variance with g, about 10% with a separate fluid intelligence factor, and had about 25% test-specific reliable variance (Gignac, 2015). Gignac concluded that Raven's is not a pure measure of g and recommended a four-subtest Wechsler combination (g validity .93, 14 minutes) when a valid estimate of g is needed (Gignac, 2015). In plain terms: a matrix score tells you a lot, and a broader battery tells you more. The pattern recognition page covers the inductive skill matrices share with series and analogy items.

How abstract reasoning is measured

Clinical batteries give abstract reasoning its own score. The WAIS-5 split the old perceptual domain into separate Visual Spatial and Fluid Reasoning index scores (Pearson: WAIS-5), and its Fluid Reasoning index uses Matrix Reasoning and Figure Weights (Pearson: WAIS-5 overview). Raven's 2, the current clinical edition, builds its digital forms from an item bank to limit overlap between test takers (Pearson: Raven's 2). Hiring tests use it too: the PI Cognitive Assessment reports an Abstract Reasoning subscore next to Verbal and Numeric (Predictive Index: Cognitive Assessment). The Raven's test page covers forms, timing and scoring.

Research studies often give matrix tests under a time limit; Jaeggi and colleagues allowed 10 minutes and scored the number correct (Jaeggi et al., 2008). Scores spread widely even among university students: in 506 first-year students, scores on the 36-item Set II of the Advanced Progressive Matrices ranged from 6 to 35, with a mean of 22.17 (Bors & Stokes, 1998). The IQ Octopus test gives abstract reasoning its largest section, 9 of its 25 items, and reports an estimated IQ with a confidence range.

Can abstract reasoning be improved?

Some learning happens inside a single test. Within one matrix test, items using the pairwise progression and figure addition or subtraction rules got easier as test takers went along, a sign of rule learning, and that learning correlated with external measures of ability (Lozano, Embretson & Revuelta, 2025). Retesting adds more: average gains were 0.33 SD at the second sitting and 0.50 by the third (Scharfen, Peters & Holling, 2018).

Whether training can lift the underlying ability is a long-running debate. Jaeggi and colleagues (2008) reported that training on a demanding working memory task, the n-back, transferred to fluid intelligence tests (Jaeggi et al., 2008). A randomized, placebo-controlled follow-up with 20 training sessions found improvement on the trained tasks but no transfer to any of the cognitive ability tests (Redick et al., 2013). A 2015 meta-analysis of 20 studies found a small net effect (g = 0.24), but studies with passive control groups showed larger transfer (g = 0.44) than studies with active control groups (g = 0.06) (Au et al., 2015). Sala and Gobet report that a reanalysis puts the effect close to zero in studies with active controls (Sala & Gobet, 2019). The honest summary: practice makes matrices familiar, and there is no reliable shortcut to a higher fluid ability.

Try it

Take the free abstract reasoning test for ten timed grids, or browse the matrix puzzles by difficulty with full explanations.