1) Psychometric theories try to answer the questions what forms intelligence takes and what its parts are. Important examples of such theories, mostly based on data collected from paper-and-pencil tests are: the Standford-Binet and the Wechsler Intelligence Scales (both for adults and children). Using data from such tests, psychologists developed different theories. The British psychologist Charles E. Spearman (1863-1945) suggested two major forms of intelligence: a general intelligence (g) and specific intelligence (s). L. L. Thurstone (1887-1955) considered Spearman's g-intelligence as statistical artefact and suggested seven "primary mental abilities": verbal comprehension, verbal fluency, numeracy, spatial visualisation, inductive reasoning, memory, and perceptual speed.
The Canadian Philip E. Vernon (1905-1987) and the American Raymond B. Cattell (1905-1998) tried to bring the two theories together by suggesting that intellectual abilities are hierarchical with g-intelligence at the top and s-intelligence at the bottom. Later on Cattell suggested that g-intelligence can be divided into fluid and crystallized intelligence: Whereas fluid intelligence is represented by reasoning and problem solving, crystallized intelligence is the knowledge acquired over the years.
Not everybody agreed on intelligence having a hierarchical structure: J. P. Guilford (1897-1988) postulated 120 different abilities in his Structure-of Intellect theory. He arrived at that number by combining multiplicatively five kinds of operations, four kinds of content and six kinds of products. Later he increased the number to 150 abilities.
Because the number of abilities which had to be measured in tests got out of hand, and because the psychometric theories couldn't explain the processes underlying intelligence, some researchers tried to study the mental processes important for intelligence directly.
2) Cognitive psychology assumes that intelligence comprises a set of mental representations of information and a set of processes operating on them. A more intelligent person therefore will have a better representation of information and can operate on them faster. Whether processes are executed serially or parallel hasn't been decided yet. The use of computer models for intelligence had less of an impact on intelligence theories but proofed hugely influential in computer science itself. However, cognitive psychology didn't answer the question of why a certain behaviour is considered as intelligent. Thus, Michael E. Cole argued that the description of intelligence may differ from one culture to another: to know what intelligence is the context in which cognition operates would have to be taken into account.
3) Contextualism looks at how cognitive processes operate in various environmental contexts. The two most influential theories with this approach are Sternberg's Triarchic Theory of Human Intelligence and Gardner's Multiple Intelligences. Gardner went a step further than earlier researchers who suggested intelligence comprises several abilities. He argued that there is no single intelligence.
Even though Sternberg agreed with Gardner that intelligence as measured in IQ-tests was to narrow a concept, he disagreed with other aspects, because he understands some abilities rather as talent than intelligence. Sternberg also considered the automatization of cognitive processes very important: Only a person who has automatized daily life's task, can use enough mental powers to cope with newly arising situations.
4) Biological science tries to understand the neural bases of intelligence and not, like the other three approaches, hypothetical constructs. This reductionistic way of looking at the brain, made possible by newest technology, might sound like the ultimate tool to build a model upon. Yet, because it looks at such narrow details, so far it can't be handled successfully to understand higher concepts such as critical thinking. Some yet unproved theories suggest that intellect could be a result of either more efficiently connected brain-cells (neurons) or the fast transmition of information through the axons of neurons. Also, very recently the role of the glia-cells, formerly considered as less important, has come into the limelight. Another new interesting approach is the simulation of very small parts of the human brain with massively parallel computer networks.
Despite all these different ideas about what intelligence could be, IQ-tests play an important role in the identification of the gifted. But today, most people in the field would probably agree with the American psychologist Howard E. Gruber that to measure giftedness merely in terms of a single test core would be a trivialization of the concept. Also, through the work of James Flynn from New Zealand who discovered that IQ test scores are rising in the general population and other researchers, today intelligence is considered as a result of nature and nurture and therefore malleable to an extent. Or in other words, the intelligence of a person can be influenced through education.