Excellent definitions from Kevin S. McGrew in Intelligence 37 (2009) 1–10. You can’t get much more up-to-date than this.

Fluid intelligence (Gf): The use of deliberate and controlled mental operations to solve novel problems that cannot be performed automatically. Mental operations often include drawing inferences, concept formation, classification, generating and testing hypothesis, identifying relations, comprehending implications, problem solving, extrapolating, and transforming information. Inductive and deductive reasoning are generally considered the hallmark indicators of Gf. Gf has been linked to cognitive complexity which can be defined as a greater use of a wide and diverse array of elementary cognitive processes during performance.

Tests include: General sequential (deductive) reasoning, Inductive reasoning, quantitative reasoning, speed of reasoning

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Crystallized intelligence (Gc): The knowledge of the culture that is incorporated by individuals through a process of acculturation. Gc is typically described as a person’s breadth and depth of acquired knowledge of the language, information and concepts of a specific culture, and/or the application of this knowledge. Gc is primarily a store of verbal or language-based declarative (knowing what) and procedural (knowing how) knowledge acquired through the investment of other abilities during formal and informal educational and general life experiences.

Tests include: Language development, Lexical knowledge, Listening ability, General (verbal) information, Information about culture, Communication ability, Oral production and fluency, Grammatical sensitivity, Foreign language proficiency, Foreign language aptitude.

Whenever scientists discuss or write about ‘intelligence’, they will often have one of these four theories in mind. Different scientists have different theoretical preferences.

1. Unitary intelligence – g.  Spearman’s theory of unitary intelligence, or g.  Spearman (1923) argued that underlying all cognitive abilities was a single general intelligence factor (g) that all the abilities draw on, and which individuals differ in – in a bell curve (normal) distribution.  From a statistical standpoint, all tests of cognitive ability are correlated positively and in factor analysis load highly on one higher-order general factor that shares variance with them all. When people talk about ‘IQ level’ this is generally the underlying ability that people have in mind. Spearman (1904) argued  that the variance of performance between individuals on ANY given cognitive task (spelling, arithmetic, inductive reasoning, mental rotation, verbal analogies, etc), could be attributed to two underlying factors: g and  s – the domain-specific skill accounting for the variance unique to that type of task. On this theory, g is the more crucial factor, and the most useful in describing individual differences, and explaining differences in cognitive ability. Recent studies have argued that differences in g are due to differences in working memory: that working memory capacity and processing efficiency underly the g factor.

2. Fluid intelligence (Gf or gF) and crystallized intelligence (Gc or gC). This is the theory favoured in this blog. It was originally proposed by Cattell back in 1943, and and later revised by Horn and Cattell in 1967. It holds that cognitive ability is best understood by two discrete factors: fluid intelligence (Gf) and crystallized intelligence (Gc). Fluid g is defined as the ability to reason and problem solve with novel tasks or in unfamiliar contexts (measured by tests of spatial and inductive reasoning), while crystallized g is defined as acquired knowledge and is measured using tests of general knowledge, mathematics, reading comprehension, and vocabulary knowledge.  From an instructional perspective, this two-factor model allows domain-specific knowledge to possibly compensate for limitations in capacity and processing (fluid intelligence). One may succeed due to knowledge about a task or domain (crystallized g), or due to sheer ‘horsepower’ (fluid g).

3. Speed vs capacity. According to Fry and Hale (1996) faster information processing speed allows for more efficient working memory processes that translates into improved performance on the demanding cognitive tasks that are found in intelligence tests. A number of developmental studies show that increases in processing speed at younger ages is followed by increases in working memory, and that these appear to be directed by a unified biological system (Kail, 2000). Reading disabilities may be the result of a domain-general deficit in speed of processing, and speed is associated with more effective imagery that, in turn, was associated with spatial memory span and performance on some sub-tests of intelligence batteries.

As for the capacity factor in this theory, Just and Carpenter (1992) have proposed an acount of capacity for language comprehension (a good measure of IQ) in which individual differences in performance can be accounted for in terms of the total amount of activation that is available in working memory for both processing and storage demands.

4. Verbal, spatial, working memory, and processing speed. This is another hierarchical theory  in the individual difference psychometric tradition. There is consensus that there is a general cognitive factor (g) that accounts for about 50% or so of the variance in a broad range of mental tests given to a large sample of the population. The general factors from different batteries of mental tests show very high correlations, often well above 0.9. When that variance is taken into account, there is still variance attributable to separable  ‘level 2’ factors of intelligence, each of which accounts for under 10% of the variance. On this account those factors are verbal, spatial/perceptual organisation, working memory and processing speed. These factors provide a very good fit to performance on the 13 WAIS-III intelligence scale subtests (Deary, 2001), and the separate indices of ability that you get on WAIS-IV are based on this factor analytic model.

We have discussed speed and working memory in the context of the speed vs capacity theory. As for ‘verbal’ vs ‘spatial’, Paivio’s (1971) dual coding theory, states that incoming information is coded into a verbal-based code, spatial/ imagery-based code, or both in long-term memory. Paivio claimed that the two codes are independent of one another but information that is coded via both codes can establish a more enriched memory structure, with multiple retrieval routes to access the information. These different codes are associated, on this model, with different sub factors of intelligence that can vary independently of each other.

The literature supporting each of these theories of intelligence is deep and well-supported.

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In a recent study by Nietfeld and colleagues in the psychometric tradition, theories 1, 2 and 3 – and the verbal vs spatial componentsof theory 4, were directly tested against each other in a confirmatory factor analysis study. The fluid vs crystallized hierarchical model came out to be the best fitting to the data. This structure is also consistent with Carroll’s (1993) proposed hierarchial structure of intellectual abilities based on his comprehensive meta-analysis of more than 450 independent datasets on intelligence testing. On his account, fluid intelligence and crystallized intelligence factors showed the closest relationship to g of all the broad factors at the second level of his hierarchy.

As theoretical constructs, fluid g and crystallized g are coming through strong!

Reference

Nietfeld et al. (2007). A test of theoretical models that account for information processing demands. Contemporary Educational Psychology, 32, 3, 499-515.

Fluid intelligence (Gf or gF!) broadly captures our general reasoning ability. To quote from Jonassen &  Hopkins (1993): “Gf represents different forms of reasoning including abstracting, forming and using concepts (classification), perceiving and using relations, identifying correlates, maintaining awareness in reasoning, and abstracting ideas, especially from figural and nonverbal… content” (p. 53). It has been described as the source of intelligence that an individual uses when he or she doesn’t already know what to do.

Crystallized intelligence (Gc) describes abilities depending on specific, acquired knowledge or expertise – the result of learning and acculturation. It is measured in tests of expert knowledge, general information, use of language (vocabulary) and is reflected in a wide variety of acquired, specific skills (Horn & Cattell, 1967). Educational and cultural opportunities are central to its development. Working memory capacity is closely related to fluid intelligence, and there is strong evidence that training working memory can improve fluid intelligence (Jaeggi et al, 2008).

People with a high capacity of Gf tend to acquire more Gc knowledge and at faster rates, and this has been called Gf  investment.