Intelligence is an ability to act directionally, think rationally, and face the environment effectively. In generally it can be concluded that intelligence is a mental ability include thinking process rationally. Therefore, intelligence cannot perceive directly, but must be concluded from various real actions that represent by manifestation of rational thinking process.
Overview about Theories of Intelligence
1.Scientific Versus Lay Definitions
The meaning of intelligence is understood differently by psychologists and lay persons. Recent research shows that most lay persons think of intelligence as comprised of verbal ability, practical problem-solving ability, and social competence, example being fair with others, having a social conscience.
In contrast, experts define intelligence as including verbal ability, problem-solving ability, and practical intelligence but not the social competence that most laypersons apparently value.
2.Spearman's General factor
At the beginning of the 20th century British psychologist Charles Spearman theorized that every aptitude of people is caused by two factors, they are:
General factor is factor as basis of the people aptitude. But special factor has function in special aptitude. Factor g has function in every people aptitude and factor s has function in different aptitude. He also give opinion that factor g appropriate on base and factor s appropriate on experiences(environment, education, etc. )
3.Thurstone's Primary Mental Abilities
The American psychologist L.L. Thurstone (1887 -1955) relied on the finding so fairly intelligence testing to develop his idea of primary mental abilities. According to Thurstone, there are seven such abilities necessary for high-level test performance, they are spatial ability; perceptual speed; numerical ability; verbal meaning; memory; word fluency; and reasoning.
4.Guilford's Three-Dimensional Model
About of J.P. Guilford
He was born on Nebraska, March 7, 1897, and died in Los Angeles on November 26, 1987. In 1924 Guilford entered the psychology Ph.D. program at Cornell University and was awarded in 1927. After short periods of time on the faculties of the universities of Illinois and Kansas, Guilford returned in 1928 to the University of Nebraska as professor of psychology, where he achieved an international reputation as one of America’s foremost psychologist. In 1940 he moved to the University of Southern California. Guilford was a psychologist involved during the World War II in developing tests to select candidates for training as pilots. As he expanded his interests into testing various other specific thinking skills, he developed a model to guide his research and to organize his thinking about all the various skills he was testing.
J.P. Guilford developed the idea of specific intelligence factors into a very detailed model beginning in the 1950s. Guilford(1967) conceives of intelligence as being a combination of three dimensions, they are:
With each specific intellectual ability being one specific combination of these three factors. Since there are 5 operations, 5 contents, and 6 products in Guilford’s model. This means that there are 150 different mental abilities that could conceivably be measured. Although only about 100 have been measured to date, Guilford’s model is an important advance in understanding intelligence.
a.Cognition is the ability to recognize various forms of information and to understand information.
Example: A child who can separate a mixed pile of squares and triangles into separate piles of squares and triangles is exercising a degree of cognition.
b.Memory is the ability to store information in the mind and to call out stored information in response to certain stimuli. Two kinds of memory:
Memory retention is contain memory related to daily life
Memory recording is fresh memories
Example: A student who immediately answer 1 when asked to give the sine of 90° is using his or her memory.
c.Divergent is the ability to view given information in a new way so that unique and unexpected conclusions are the consequence.
Example: A mathematician who discovers and proves a new and important mathematical theorem is exhibiting considerable ability in divergent production.
d.Convergent is the ability to take a specified set of information and draw a universally accepted conclusion or response based upon the given information.
Example: In algebra lesson, student who finds the correct solution to a set of three linear equations have used his or her convergent production ability.
e.Evaluation is the ability to process information in order to make judgments, draw conclusion and arrive at decisions.
Example: If we want to solve mathematics problem we think hard to solve it by simple method
a.Visual is information in visual form such as are shape or color.
example: triangle, cubes, parabola, etc.
b.Auditory involves information in auditory form, such as spoken words or music
c.Symbolic are symbol or codes representing concrete object or abstract concepts.
Example: + is the mathematical symbol for the operation of addition.
d.Semantic of learning are those words and ideas which evoke a mental image when they are presented as stimuli.
Example: sun, car, white, moon, etc. are word which evoke image in people’s minds when they hear or read them.
e.Behavioral contents of learning are the manifestations of stimuli and responses in people can be also obtained through facial expression or voice.
a.Unit is a single symbol, figure, word, object, or idea.
Example: each real number.
b.Classes is sets of items grouped by virtue of their common properties
Example: set of real numbers.
c.Relations are connections between items of information
Example: equality and inequality are relation in the set of real numbers.
d.A systems is a composition of units, classes, and relationship into a larger and more meaningful structure.
Example: the set of real numbers together with the operations of addition, subs traction, multiplication, and division and the algebraic properties of these operations.
e.Transformation is the process of modifying, reinterpreting, and restructuring existing information into new information. The transformation ability is usually thought to be characteristic of creative people.
Example: functions defined on the real number system.
f.An implication is a prediction or a conjecture about the consequences of interactions among units, classes, relations, systems, and transformations.
Example: each theorem about function on the real numbers.
Application of Guilford Theory in Math Education
Example task of creativity that was developed by Guilford in applied starting at the kindergarten level, they are recognizing numbers, drawing plane and space. At the elementary and secondary school level even in the university level, there are some essential materials allows children to make them creative such as the geometry material.
Examples of material to determine the creativity of student
Factors that Influence Intelligence
1. Robert R Reilly/Ernest L. 1981. Lewis. Educational Psychology. New York : Macmillan Publishing Co
2. Arno F. Witting and Gurney Williams III. 1984. Psychology an Introduction. Mc Graw Hill Book Co