Fluid and crystallized intelligence

Horn[7] provided the following example of crystallized and fluid approaches to solving a problem. Here is the problem he described:

"There are 100 patients in a hospital. Some (an even number) are one-legged but wearing shoes. One-half of the remainder are barefooted. How many shoes are being worn?"

The crystallized approach to solving the problem would involve the application of high school-level algebra. Algebra is an acculturational product.

${\displaystyle x+1/2*(100-x)*2}$ is the number of shoes worn, where x equals the number of one-legged patients. ${\displaystyle 100-x}$ equals the number of two-legged patients. The solution boils down to 100 shoes.

In contrast to the crystallized approach to solving the problem, Horn provided a made-up example of a fluid approach to solving the problem, an approach that does not depend on the learning of high school-level algebra. In his made-up example, Horn described a boy who is too young to attend secondary school but could solve the problem through the application of fluid ability: "He may reason that if half the two-legged people are without shoes, and all the rest (an even number) are one-legged, then the shoes must average one per person, and the answer is 100."

The Raven's Progressive Matrices (RPM)[10] is one of the most commonly used measures of fluid ability. It is a non-verbal multiple-choice test. Participants have to complete a series of drawings by identifying relevant features based on the spatial organization of an array of objects and choosing one object that matches one or more of the identified features.[11] This task assesses the ability to consider one or more relationships between mental representations or relational reasoning. Propositional analogies and semantic decision tasks are also used to assess relational reasoning.[12][13]

In the Woodcock–Johnson Tests of Cognitive Abilities, Third Edition (WJ-III), g_f is assessed by two tests: Concept Formation and Analysis Synthesis.[14] Concept Formation tasks require the individual to use categorical thinking; Analysis Synthesis tasks require general sequential reasoning.[15]

Individuals have to apply concepts by inferring the underlying "rules" for solving visual puzzles that are presented with increasing levels of difficulty. As the level of difficulty increases, individuals have to identify a key difference (or the "rule") for solving puzzles involving one-to-one comparisons. For more difficult items, individuals need to understand the concept of "and" (e.g., a solution must have some of this and some of that) and the concept of "or" (e.g., to be inside a box, the item must be either this or that). The most difficult items require fluid transformations and cognitive shifting between the various types of concept puzzles that the examinee had worked with previously.[15]

In the Analysis–Synthesis test, the individual has to learn and orally state the solutions to incomplete logic puzzles that mimic a miniature mathematics system. The test also contains some of the features involved in using symbolic formulations in other fields such as chemistry and logic. The individual has presented a set of logic rules, a "key" that is used to solve the puzzles. The individual has to determine the missing colors within each of the puzzles using the key. Complex items presented puzzles that require two or more sequential mental manipulations of the key to deriving a final solution. Increasingly difficult items involve a mix of puzzles that requires fluid shifts in deduction, logic, and inference.[14]

The Wechsler Intelligence Scales for Children, Fourth Edition (WISC-IV)[16] is used to have an overall measure in cognitive ability with five primary indexing scores. In the WISC-IV, the Perceptual Reasoning Index contains two subtests that assess g_f: Matrix Reasoning, which involves induction and deduction, and Picture Concepts, which involves induction.[17]

In the Picture Concepts task, children have presented with a series of pictures on two or three rows and asked which pictures (one from each row) belong together based on some common characteristic. This task assesses the child's ability to discover the underlying characteristic (e.g., rule, concept, trend, class membership) that governs a set of materials.[17]

Matrix Reasoning also assesses this ability as well as the ability to start with stated rules, premises, or conditions and to engage in one or more steps to reach a solution to a novel problem (deduction). In the Matrix Reasoning test, children have presented with a series or sequence of pictures with one picture missing. Their task requires the child to choose the picture that fits the series or sequence from an array of five options. Since Matrix Reasoning and Picture Concepts involve the use of visual stimuli and do not require expressive language, they have been considered to be non-verbal tests of g_f.[17]

Within the corporate environment, fluid intelligence is a predictor of a person's capacity to work well in environments characterised by complexity, uncertainty, and ambiguity. The Cognitive Process Profile (CPP) measures a person's fluid intelligence and cognitive processes. It maps these against suitable work environments according to Elliott Jaques's Stratified Systems Theory.[18] Fe et al. (2022) show that fluid intelligence measured in childhood predicts labor market earnings.[19]

Some authors have suggested that unless an individual is truly interested in a problem presented on an IQ test, the cognitive work required to solve the problem may not be performed owing to a lack of interest. These authors have contended that a low score on tests that are intended to measure fluid intelligence may reflect more of a lack of interest in the tasks than an inability to complete the tasks successfully.[20]

According to David Geary, g_f and g_c can be traced to two separate brain systems. Fluid intelligence involves the dorsolateral prefrontal cortex, the anterior cingulate cortex, and other systems related to attention and short-term memory. Crystallized intelligence appears to be a function of brain regions that involve the storage and usage of long-term memories, such as the hippocampus.[27]

Because working memory is thought to influence g_f, then training to increase the capacity of working memory could have a positive impact on g_f. Some researchers, however, question whether the results of training interventions to enhance g_f are long-lasting and transferable, especially when these techniques are used by healthy children and adults without cognitive deficiencies.[28] A meta-analytical review published in 2012 concluded that "memory training programs appear to produce short-term, specific training effects that do not generalize."[29]

In a series of four individual experiments involving 70 participants (mean age of 25.6) from the University of Bern community, Jaeggi et al. found that, in comparison to a demographically matched control group, healthy young adults who practiced a demanding working memory task (dual n-back) approximately 25 minutes per day for between 8 and 19 days had significantly greater pre-to-posttest increases in their scores on a matrix test of fluid intelligence.[30] There was no long-term follow-up to assess how enduring the effects of training were.

Two later n-back studies[31][32] did not support the findings of Jaeggi et al. Although participants' performance on the training task improved, these studies showed no significant improvement in the mental abilities tested, especially fluid intelligence and working memory capacity.

Thus the balance of findings suggests that training for the purpose of increasing working memory can have specific short-term effects but no effects on g_f.