Mathematics Education

What is INTELLIGENCE?

Intelligence is an ability to act directionally, thinking 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

· Scientific Versus Lay Definitions

The meaning of intelligence is understood differently by psychologists and lay persons. Recent research shows that most laypersons think of intelligence as comprised of verbal ability, practical problem-solving ability, and social competence (e.g. being fair with others, having a social conscience).

In contrast, experts define intelligence as including verbal ability, problem-solving ability, and practical intelligence.

· Spearman's General Factor

At the beginning of the 20th century British psychologist Charles E. Spearman theorized that there is a general factor of intelligence, g, which functions as a source of energy for varied cognitive skills and performances. Many people also excel in particular areas of skill or talent, designated s. While s may be observed independently of a high level of g, g provides a richer foundation for s in people who have both kinds of ability.

· Thurstone's Primary Mental Abilities

The American psychologist L.L. Thurstone (1887 -1955) relied on the finding so fearly intelligence testing to develop his idea of primary mental abilities. According to Thurstone, there are seven such abilities necessary for high-level test performance: spatial ability; perceptual speed; numerical ability; verbal meaning; memory; word fluency; and reasoning.

· Guilford's Three-Dimensional Model

J. P. Guilford developed the idea of specific intelligence factor into a very detail model beginning in the 1950s. Guilford (1967) conceives of intelligence as being a combination of three dimensions :

1. Operations,
2. Content, and
3. Product

With each specific intellectual ability being one specific combination of these three factors. Since there are 5 operations, 5 content and 6 product 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.

STRUCTURE OF INTELLIGENCE

1. Operations

In Guilford’s model are major intellectual processes. He has identified five types :

1. 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 ½ when asked to give the cos of 30° is using his or her memory.

2. 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.

3. Evaluation is the ability to process information in order to make judgments, draw conclusion and arrive at decisions.

Example : When a member of a jury sits through a trial, deliberates in a closed session with other jury members and concludes that the defendant is guilty as charged, that person has used his or her mental ability of evaluation.

4. Convergent production is the ability to take a specified set of information and draw a universally accepted conclusion or response based upon the given information.

Example : An algebra student who finds the correct solution to a set of three linear equations in three unknowns has used his or her convergent production ability.

5. Divergent production is the creative ability to view given information in a new way so that unique and unexpected conclusions are the consequence.

Example : A mathematician who discover and proves a new and important mathematical theorem is exhibiting considerable ability in divergent production.

2. Content

Contents is categorizes the nature of the material being learned. Guilford identified four types of content involved in learning. There are consist of :

a. Visual, Visual information directly from the sence or from imaging

Example : triangle, cubes, parabola, etc.

2. Auditory, Auditory information directly from the sense or from images.
3. Symbolic, Symbolic items such as words and symbols which generally convey some meaning.

Example : (-) is the mathematical symbol for the operation of substraction.

4. Semantic content of learning are those words and ideas which evoke a mental image when they are presented as stimuli.

Example : Sun, Car, Blue, etc are the word which evoke image in people’s minds when they hear or read them.

e. Behavioral, are the manifestations of stimuli and responses in people can be also obtained through facial expression or voice.

3. Product

Product of learning refers to manner in which information is organized in the main. Guilford identified the six products of learning are consist of :

a. A unit is a single symbol, figure, word, object or idea

Example : Real number

b. Classes is sets of units and one mental ability is that of classifying unit.

Example : The entire set of real numbers.

c. Relations are connections among units and classes.

Example : Equation and inequality are relation in the set of real number.

d. A system is a composition of units, classes, and relation into a larger and more meaningful structure.

Example : The set of real numbers with the operations of addition, subtractions, multiplication, and division and the algebraic properties of these operations.

e. Transformation is process of modifying, reinterpreting, and restructuring existing information into new information. The transformation ability is usually thought to be characteristics of creative people.

Example : functions defined on the real number system.

f. An Implication is a prediction or conjecture about the consequences of interactions among units, clasess, relations, systems, and transformations.

Example : Each theorem about function on the real numbers.

ABOUT J.P. GUILFORD

Joy Paul Guilford 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.

Application of Guilford’s Theory in Mathematics Education

Example task of creativity that was developed by Guilford in applied starting at the kindergarten level, namely in recognizing numbers, space dimension. At the elementary and secondary school level and even at the college level there are some materials that essential that allows children to creativity such as the material geometry.

Examples Of Material To Determine The Creativity Of Student

1. Siswa di kelas diperkenalkan sebuah bangun ruang, yaitu kubus ABCD.EFGH yang disusun dari beberapa bidang sisi. Siswa diperkenalkan salah satu jaring-jaring kubus.

Siswa diberikan waktu untuk memikirkan berdasarkan contoh yang telah diberikan untuk menemukan sendiri susunan jaring-jaring kubus yang lain.

2. Dalam perlombaan pacuan kuda terdapat 15 lebih kaki kuda daripada ekornya. Berapa banyak kuda pada perlombaan itu?
3. Bagaimanakah cara mendapatkan 6 liter air dari suatu bak, bila hanya tersedia gelas ukuran 9 liter dan 4 liter?

FACTORS THAT INFLUENCE INTELLIGENCE

1. Nature – Genetic Factors

Intelligence is based on heredity. Our level of intelligence is determine by our genes and cannot improve.

2. Nurture – Environmental Factors

Intelligence is influenced by the environmental. The level of intellignece we are born with can be improved through exposure to a stimulating and healthy environmental.

3. Interaction between Environmental and Genetic Factors

Intelligence is determine by a complex interaction of heredity and the environment. Together, they contribute rougly equally to a person’s intellectual ability (Locurto 1991 : Plomin & Petril 1997 : Scarr 1997).

CONCLUSION

Intelligence is an ability to act directionally, think rationally, and face the environment effectively. There are overview about theories of Intelligence, they are Scientific Versus Lay Definitions, Spearman's General factor, Thurstone's Primary Mental Abilities, and Guilford's Three-Dimensional Model.

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 operations, contents, and Products.

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.

REFERENCES

● Robert R Reilly/Ernest L. 1981. Lewis. Educational Psychology. New York : Macmillan Publishing Co

● Arno F. Witting and Gurney Williams III. 1984. Psychology an Introduction. Mc Graw Hill Book Co

• www.drchrustowski.com/Intelligence.pdf