Read this article to learn about theories of intelligence.
Intelligence Theory #1. Spearman's Two-Factor Theory of Intelligence:
Spearman gave his two-factor theory of intelligence in 1904."No event in the history of mental testing has proven to be as important as his famous two-factor theory"— (Guilford psychometric methods).
According to Spearman, mental traits are not independent; there is a common element in all our cognitive capacities. This is the basis of his famous two-factor theory of intelligence: the theory that every different intellectual activity involves a general factor, which it shares with all other intellectual activities, and a specific factor, which it shares with none.
Spearman refuses to designate this general factor as general intelligence, which seems to him to be“a word with so many meanings that in the end it has none.”He prefers to denote it with the letter “g” and the specific factor with “s”. It's true that Spearman's 'g' is often equated with what we commonly call "general intelligence", but it should be remembered that it is primarily a mathematical quantity derived from mathematical processes on measured data.
Mathematically, Spearman's theory, in short, is that each individual measure of each intellectual capacity can be broken down into two factors, one of which is a "general factor" (g) common to all measured capacities and the other a " specific factor". ”(s) peculiar to each particular skill. This statement can be translated into mathematical form by representing an individual's score (S) on a mental test given by the simple equation
S = one1g + one2S,
where the letters "a1" is a2” represent the “weights” or “loads” of the two factors 'g' and 's', respectively.
Intelligence Theory#2. Mathematical basis of Spearman's theory:
The full mathematical proof of Spearman's theory is quite complicated and difficult to follow, but the main line of the argument can be easily understood from a simple example. Let's start, as Spearman did, by correlating the results of a series of tests and organizing the coefficient or correlation systematically into what is known as a "correlation matrix."
Let's take 5 tests: a, b, c, d, e, with the titles given below and arrange their "intercorrelations" in the form of a matrix:
We can also express this in an equivalent algebraic form:
The beginning of Spearman's research was "a curious observation" that the cross products of any square block of four coefficients were approximately equal. For example, from the set of coefficients
we obtain by cross multiplication (0.48 x 0.35) = (0.40 x 0.42) or (0.48 x 0.35) – (0.40 x 0.42) =0;
or from another set, (0.56 x 0.30) – (0.40 x 0.42) = 0. Spearman called a square block of four coefficients a tetrad, and the equation that expresses the equality of the products crossed, the tetrad equation.
In algebraic terms, the first of the above tetrad equations would be:
tABS.CD= rC.A.rbd– radverts.rBC= 0; And the second
tABS.CD= rABS.rCD– radverts.rBC= 0
The rest of the argument consisted in demonstrating that if intellectual abilities are due to the presence of two factors, one 'general' and the other 'specific', that is, if the equation S = a1g + one2s holds, then the tetrad equation rABS.rCD– radverts.rBC= 0 must be true; and, conversely, if the tetrad equation is satisfied for four abilities a, b, c, d, then the equation S = a1g + one2s must be true, and consequently these abilities are divisible into two factors, one of which is a"generally"common factor to four abilities.
Spearman and Holzinger then provided a method for determining whether any deviation from the zero requirement of the tetrad equation is due to a "true" difference or "sampling error". The two-factor theory now rests on a solid mathematical foundation. The amount of correlation between two tests is determined by the extent to which the two tests are loaded with G. Another intercorrelation plot of 6 tests is given below, arranged in hierarchical order.
The graph shows the weights:
More clearly, in this table the variables have been arranged in order of sums. In each column, the coefficients are ordered from highest to lowest. This is called a pecking order by Spearman. Tests A and B are relatively highly correlated, that is, they have a lot in common with G, while tests A and C are poorly correlated, as they have small loadings with G.
Spearman and his followers later admitted the existence of some group factors such as“verbal ability, numerical ability and possible factor of mental speed, mechanical ability, attention and imagination”. “Tests G and H have a higher correlation than that attributable to G alone. An additional common factor like that of the G and H tests became known as the group factor.
Thorndike vehemently criticized Spearman's two-factor theory. E. L. Thorndike devised a test, the C A V D (Completeness, Arithmetic, Vocabulary, and Comprehension of Instructions and Speech), as the basis for the theory that intelligence is a composite of many different interconnected abilities in the brain. Thorndike proposed three types of intelligence: social, concrete, and abstract. This was probably the first multifactorial theory of intelligence, although it was not based on the results of a factor analysis of ability tests.
Intelligence Theory#3. Godfrey Thomson's theory of sampling:
In Britain, Spearman's most active critic was Godfrey Thomson. He claims that the two-factor theory is not the only possible explanation of the events. According to him, these facts can be explained by the hypothesis that there are multiple or group factors in intellectual capacities, each of which is common to a limited number of different intellectual capacities and, therefore, less restricted in scope than any of them. Spearman's studies. specific factors, and not yet universal in scope as is his G factor.
G. H. Thomson's theory is known as sampling theory. According to the sampling theory, each test shows a certain range of elementary human abilities; some with a wide range, some with a narrow range. He believes in a "g" factor or general ability, but it is not a basic entity. It is a constant combination of skill elements.
Similarly, group factors are more or less stable combinations of more limited collections of items, while specific factors are made up of items that restrict their appearance to individual tests (G. H. Thomson: The Factorial Analysis of Human Ability).
Intelligence Theory#4. Multifactorial theory:
The multifactorial theory holds that performance on a given test depends on one or more common factors, each weighted according to its importance to the success of the task.
The theory is based on various methods of factor analysis:
Although Charles Spearman has been considered the father of factor analysis, he and his followers were unwilling to admit the importance of group factors. They played the role of the 'G' factor. This was especially true of Cyril Burt, Philip Vernon and R. B. Cattell.
“It was Thurstone who popularized multifactorial theory and methods in psychology. Geometrically, the multifactor model is a set of dimensions or vectors that extend from the same origin, each vector representing a common factor.
“The closer a test vector is to a given factor vector, the higher the test's involvement with that factor, the higher its 'load' on that factor. A factor loading is also the correlation between a test (an empirical variable) and the factor (a purely ideal variable).
In short, he applied the centroid method of factoring and oblique rotation of correlations between many different cognitive measures. Thurstone deduced seven primary abilities. Her deduction was based on an analysis of the experiences of the Fitness Research Project. The skills or factors found are“Space, perceptual speed, numerical facility, verbal comprehension, rote memory, induction, word fluency, deduction and general reasoning”.
Intelligence Theory#5. Hierarchical theories:
British psychologists such as Cyril Burt (1949) and Vernon (1960) presented an alternative scheme for organizing factors. At the top of the hierarchy, Vernon places the 'G' factor, or the general cognitive factor. At the next level, he places two large groups of factors, corresponding to verbal-educational (v: ed) and practical-mechanical (k: m.) aptitudes. These main factors can be further subdivided.
The verbal educational factor can be subdivided into verbal and numerical subfactors, and the practical mechanical factor into mechanics, spatial information, and psychomotor skills. At the lowest level of the hierarchy are the special factors. "This hierarchical structure resembles an inverted family tree, with 'g' factors at the top, 's' factors at the bottom, and progressively narrower group factors in the middle."
The graphical representation of Spearman's bifactorial theory (A), multifactorial theory (B) and hierarchical theory (C), showing correlated tests, is presented below:
Vernon's theory is a compromise formula between Spearman's two factors and Thurstone's multifactorial theory. It retains the G factor and relegates the intellectual structure of Thurstone and Guilford to a subordinate level.
Intelligence Theory#6. R. B. Cattell's theory of fluid and crystallized intelligence:
According to R. B. Cattell, general intelligence is made up of two factors: fluid intelligence (G) and crystallized intelligence (Gc). This is similar to Vernon's distinction of A intelligence, which is a product of heredity, and B intelligence, which is due to environment. Fluid intelligence, such as “A-intelligence,” is more dependent on heredity and crystallized ability from the environment.
Both types of ability are related to the ability to perceive relationships, the ability to flow is general to many fields, and crystallized intelligence is specific to certain fields, such as school learning. Fluid intelligence is used more in tasks that require adaptation to new situations, while crystallized intelligence is used for tasks where habits have become fixed. He applied oblique rotations in his factor analysis. These two factors, fluid and crystallized intelligence, are distinct but interrelated.
Jean Piaget gave a theory of intelligence (cognitive development) not based on factor analysis. He believes that cognitive development occurs in a series of four stages: sensorimotor stage (up to age 2) when the child learns to exercise simple reflexes and coordinate various perceptions, leading to the general operational stage (ages 11 to 15). During adolescence the child can perform more abstract operations. Intelligence increases until the age of 15, it is the achievement that increases after the age of 15, intelligence, according to him, is the ability to solve new problems.
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