Logic develops in children over time

SUNY Plattsburgh elementary teacher education students and I fanned out each semester into local schools to gather data about the intellectual development of children, kindergarten through the sixth grade. More than 1,500 students were tested as part of the requirements of a course in foundations of education. We drew upon the concepts developed by Jean Piaget and accumulated the results of our research.

Jean Piaget’s “conservation experiments” determine the developmental level of capabilities for logic, which mature in a sequence beginning with an automatic motor response to input from our senses. Then comes uniquely creative pre-operational or pre-logical intellectual capabilities, followed by concrete operational or simple logic based on direct experience, and finally formal operational or full capabilities for logic with hypothetical situations.

One of these data-gathering “conservation experiments” we used is offered here in illustration.

Two identical beakers of water were presented to each child, who was asked to observe if there was the same amount of water in each. Adjustments were made until there was an agreement that each indeed contained the same amount of water. Then the water in one beaker was poured into a taller, skinnier beaker. The level of the water now appeared much higher in the taller beaker.

Each subject was then asked: “What about now? Is there the same amount of water in the original beaker and the skinnier one, or has the amount changed?”

The sensory/motor youngsters did not engage the experiment. The pre-operational youngsters insisted there was more water in the taller beaker, even though they just agreed a few moments before that the amounts of water were the same. Their judgments were based on perception or how the situation appeared to them. Judgments that appeared to be logical at this stage were considered coincidental.

The concrete operational youngsters said, “As long as no water was lost, the amounts remained the same regardless of how they appear.” Their judgments were based on simple logic: If there are equal amounts to begin with and nothing is lost in the process of pouring the liquid into the taller beaker, then the amounts have to be the same no matter how they appear. Their judgments are based on simple logic dependent upon concrete evidence from direct experience.

The formal operational youngsters will look at the seemingly empty beaker and observe a droplet of water in the bottom and claim there is not the same amount of water in the remaining and taller beaker because there is still a droplet left in the so-called empty beaker.

These individuals are basing their judgments on multiple discriminations – a more sophisticated logic. They can deal logically with hypothetical problems.

We found 85 percent of 5-year-olds functioned intellectually at a pre-operational, pre-logical level. The remaining 15 percent were only at the onset of concrete operations. Sixty percent of the 6-year-olds were pre-operational, 35 percent were at the onset of concrete operations, and 5 percent had reached a mature concrete operational level, capable of simple logic. Thirty-five percent of the 7-year-olds were pre-operational, 55 percent had reached the onset of concrete operations, and 10 percent had matured to a level of mature concrete operations. Thirty-five percent of 8-year-olds were pre-operational, 35 percent were at the onset of concrete operations, and only 5 percent were at a mature concrete operations level – meaning only 5 percent were capable of simple logic. Fifteen percent of 9-year-olds were pre-operational or pre-logical, 55 percent were at the onset of concrete operations, and 30 percent functioned at a mature concrete operations level. Twelve percent of 10-year-olds were pre-operational, 52 percent were at the onset of concrete operations, 35 percent were at mature concrete operations, and only 1 percent functioned at the onset of formal operations, just beginning to deal logically with hypothetical situations. Six percent of 11-year-olds were still pre-operational, 49 percent were at the onset of concrete operations, 40 percent were at mature concrete operations, and 5 percent at the onset of formal operations. Five percent of 12-year-olds were pre-operational, 32 percent were at the onset of concrete operations, 51 percent were at the mature concrete operations level, 12 percent were at the onset of formal operations, and none were at the formal operations level, exhibiting abilities required to perform with insight many requirements of the Common Core standards.

Age and grade levels have nothing to do with developmental readiness for logic. This readiness occurs in phases of biological development influenced, for better or worse, by experience or lack of experience.

When youngsters at each of these phases of development are confronted with legitimate test questions based on standards that require logic, pre-operational or pre-logical youngsters can only guess at an answer. Concrete operational youngsters (those who are logical about things they have directly encountered) will answer correctly provided the questions are within their direct experience. If the questions ask for hypothetical deduction, they will fail unless they guess correctly. The formal operational youngsters, mostly teenagers, will be capable of logic and hypothetical deduction, but if they have not experienced the secretive subject matter, they, too, will be forced to guess.

Advocates of standardization know about these findings but choose to ignore them. They have established a self-fulfilling prophesy that many youngsters will fail the new tests, thus proving the conventional public school is deficient.

Most so-called failing youngsters are just not ready developmentally to construct solutions to logical problems and therefore will fail to answer correctly many test questions. No amount of coercion or instruction will produce these capabilities. Logical capabilities develop naturally over time, guided by one’s genetics. These capabilities can be driven off course by mandated, developmentally inappropriate instruction.

To develop background on Piaget’s cognitive-developmental theory, the following sources are recommended:

Almy, M.C. (1979) “The Impact of Piagetian Theory on Education, Philosophy, Psychiatry, and Psychology.” Baltimore: University Park Press

Flavell, John (1963) The Developmental Psychology of Jean Piaget.” New York

Van Nostrand. Lowenfeld, Viktor (1947) “Creative and Mental Growth.” New York: Macmillan

Piaget, Jean and lnhelder (1958) “The Growth of Logical Thinking from Childhood to Adolescence.” New York: Basic Books.

Robert L. Arnold lives in Willsboro and is a professor emeritus of education at the State University of New York at Plattsburgh.