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According to the theory published in 1971 by the psychologist Raymond Cattell,general intelligence (g) is subdivided into fluid intelligence (gf) and crystallized intelligence (gc). Fluid intelligence is the ability to solve novel reasoning problems and is correlated with a number of important skills such as comprehension, problem solving, and learning. Crystallized intelligence on the other hand is the ability to deduce secondary relational abstractions by applying primary relational abstractions to each other. But the deduced relations among relations must be checked by fluid intelligence.
Fluid intelligence depends on working memory capacity, localized in the prefrontal cortex. This region degenerates faster than other cortical regions in the course of aging and encephalopathies. Fluid intelligence peaks at around age 20, and then gradually declines.
Each type of crystallized intelligence is independent of the other (increasing a student's proficiency in Latin does not increase the student's proficiency in algebra), but to a high degree dependent on the individual's fluid intelligence (students proficient in Latin tend to be proficient in algebra, too, because people with a high gf tend to acquire more gc-knowledge and at faster rates), and, to a lesser degree, on the quality of the learning environment (e.g., the quality of available books).
Fluid intelligence generally correlates with measures of abstract reasoning and puzzle solving. Crystallized intelligence correlates with abilities that depend on knowledge and experience, such as vocabulary, general information, and analogies. Paul Kline identified a number of factors that shared a correlation of at least r=.60 with Gf and Gc. Factors with [clarify] of greater than 0.6 on Gf included induction, visualization, quantitative reasoning, and ideational fluency. Factors with median loadings of greater than 0.6 on Gc included verbal ability, language development, reading comprehension, sequential reasoning, and general information. It may be suggested that tests of intelligence may not be able to truly reflect levels of fluid intelligence. Some authors have suggested that unless an individual was truly interested in the problem presented, the cognitive work required may not be performed because of a lack of interest. These authors contend that a low score on tests which are intended to measure fluid intelligence may reflect more a lack of interest in the tasks rather than inability to complete the tasks successfully.
There are various measures that assess fluid intelligence. The Cattell Culture Fair IQ test, the Raven Progressive Matrices (RPM), and the performance subscale of the WAIS are measures of Gf. The RPM is one of the most commonly used measures of fluid abilities. 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. 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.
Standardized IQ tests such as those used in psychoeducational assessment also include tests of fluid intelligence. In the Woodcock-Johnson Tests of Cognitive Abilities, Gf is assessed by two tests: Concept Formation (Test 5) in the Standard Battery and Analysis Synthesis (Test 15) in the Extended Battery. On Concept Formation tasks, the individual has to apply concepts by inferring the underlying "rules" for solving visual puzzles that are presented in increasing levels of difficulty. Individuals at the preschool level have to point to a shape that is different from others in a set. As the level of difficulty increases, individuals increasingly demonstrate an understanding of what constitutes a key difference (or the "rule") for solving puzzles involving one to one comparisons, and on later items identifying common differences among a set of items. For more difficult items, individuals need to understand the concept of "and" (e.g. 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 has worked with previously.
Concept Formation tasks assess inductive reasoning ability. 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 is presented with 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 present puzzles that require two or more sequential mental manipulations of the key to derive a final solution. Increasingly difficult items involve a mix of puzzles that require fluid shifts in deduction, logic, and inference. Analysis Synthesis tasks assess general sequential reasoning.
In the Wechsler Intelligence Scale for Children-IV (WISC IV), the Perceptual Reasoning Index contains two subtests that assess Gf: Matrix Reasoning, which involves induction and deduction, and Picture Concepts, which involves induction. In the Picture Concepts task, children are presented 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. Matrix Reasoning also tests 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 are presented a series or sequence of pictures with one picture missing. Their task is 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 are considered to be non-verbal tests of Gf.
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 Jacques Stratified Systems Theory.
Fluid intelligence, like reaction time, typically peaks in young adulthood and then steadily declines. This decline may be related to local atrophy of the brain in the right cerebellum. Other researchers have suggested that a lack of practice, along with age-related changes in the brain may contribute to the decline. Crystallized intelligence typically increases gradually, stays relatively stable across most of adulthood, and then begins to decline after age 65. The exact peak age of cognitive skills remains elusive, depending on the skill measurement as well as on the survey design. Cross-sectional data shows typically an earlier onset of cognitive decline in comparison with longitudinal data. The former may be confounded due to cohort effects while the latter may be biased due to prior test experiences.
According to David Geary, Gf and Gc can be traced to two separate brain systems. Fluid intelligence involves both 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.
Some researchers question whether the results of training are long lasting and transferable, especially when these techniques are used by healthy children and adults without cognitive deficiencies. A meta-analytical review conducted by researchers from the University of Oslo in 2012 concluded that "memory training programs appear to produce short-term, specific training effects that do not generalize."
In a study using four individual experiments, 70 participants (36 of them female, all with a mean age of 25.6) recruited from the University of Bern community, Susanne M. Jaeggi and her colleagues at the University of Michigan found that healthy young adults who practiced a demanding working memory task (dual n-back, a task that has strong face validity, has received some criticism regarding its construct validity and is in widespread use as a measure of working memory) approximately 25 minutes per day for between 8 and 19 days had statistically significant increases in their scores on a matrix test of fluid intelligence taken before and after the training than a control group who did not do any training at all.
A further examination of these findings was published in 2008 in the Proceedings of the Nation Academy of Sciences of the United States of America. Summarizing findings in the study as evidence that demonstrates that "fluid intelligence is trainable to a significant and meaningful degree."
Attention is drawn to the limitations of these results and the need for specific follow up inquiry. Robert J. Sternberg comments that "it is unclear to what extent the results can be generalized to other working-memory tasks" and states "it would be useful to show that the training transfers to success in meaningful behaviours that extend beyond the realm of psychometric testing". Sternberg asserts that ability level of the test participants is not necessarily examining a wide range of ability levels, or "address whether the training is durable over extended periods of time [and not only] "fleeting."
A second study conducted at the University of Technology in Hangzhou, China, supports Jaeggi's results independently. After student subjects were given a 10-day training regimen based on the dual n-back working memory theory, the students were tested on Raven's Standard Progressive Matrices. Their scores were found to have increased significantly.
Subsequent studies on n-back, namely by Chooi & Thompson and Redick et al., do not support the findings of the Jaeggi study. 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.