On an IQ scale for which the mean is 100 and standard deviation 15, a person with an IQ of 140 is in the 99.616957th percentile. This means that they have scored higher than 99.6% of the population on the test, an achievement equalled or bettered by only 1 in 261 people.
A person with such an IQ learns easily, can problem-solve at very high levels, and indulge in sophisticated abstract thought. This means that with sufficient work they can learn virtually any academic subject in the natural and social sciences. For such a person, virtually all career choices, except those that require special athletic or musical aptitudes will be available. Furthermore, the learning will be easier than for most people and can be acquired through books or computers with a minimum of external help.
One of the most comprehensive studies of mathematical giftedness was conducted in the Soviet Union between 1955 and 1966, by a team of researchers headed by psychologist Vadim Krutetskii. Since the Soviet philosophy rejected a genetic component of intelligence, Krutetskii and his team acknowledged that some students are intellectually gifted, but they were careful not to suggest a genetic link. They asserted*: (See references at the end of this post)
The difference between capable, average, and incapable pupils, as our research permits us to conclude, comes down to the following. In able pupils, associations can be formed “on the spot”; in this sense they are “born,” if one can so express it, already generalized, with a minimal number of exercises. In average pupils these associations are established and reinforced gradually, as a result of a whole series of exercises. They form isolated, concrete associations, related only to a given problem, “on the spot.” Through single-type exercises these associations are gradually transformed into generalized associations. In incapable pupils, even the isolated, concrete associations are formed with difficulty, their generalizations are still more difficult, and sometimes such generalizations do not occur at all.
In their studies, Krutetskii’s research group presented a comprehensive variety of problems to students in grades 5 through 8 and examined their thinking processes. One such problem is the following:
The figures below, viewed from left to right form a series.
Which of the figures, A, B, C, D, or E (below) represents the next figure in the series to maintain the same pattern?
They found that some students were unable to determine a pattern until it was explained to them. They suffered the same difficulties on similar sequencing problems. Other students were able to discern patterns in simple problems of this type, but required help when the sequences were more sophisticated. Still other students, designated as “gifted” were able to quickly identify answer B as the natural successor in the sequence. In yet other sequence problems, they were able to identify alternative generating patterns that could lead to a different answer. In essence, the research showed that students differed significantly in their ability to abstract from single “concrete” examples to general representations.
Competence in solving such problems could be easily dismissed as a “silly” or irrelevant skill that has no bearing on intelligence. Yet, it is this ability to see related patterns that’s at the heart of connecting concepts and ideas, because it is related to the ability to deal with abstraction. That’s why there is a high correlation between performance on IQ tests and success in professional careers. The ability to identify similar patterns in structure is vital to understanding metaphor in literature, to extracting trends from an examination of history and to making connections between disparate fields in science.
In essence, a person of IQ 140 has the ability to “see the forest rather than the trees” enabling them to see patterns in disparate pieces of information and make connections. This was the cognitive skill that enabled Isaac Newton to invent calculus and formulate the Law of Universal Gravitation. It was also evident in Einstein’s ability to identify inconsistencies in electromagnetic theory, enabling him to challenge the concept of absolute time.
*Krutetskii’s description of the difference between capable and non-capable students is taken from Krutetskii, Vadim A. 1976. The Psychology of Mathematical Abilities in Schoolchildren. Chicago: Chicago University Press. p. 262.
