Preliminary experimental findings suggest that a change of Piaget stage may be related to different developmental processes in boys and girls. At a somewhat later stage, the collaboration between the hemispheres increases.
1. Fitch and Denenberg (1995) suggest that age is a key parameter which intermediates to affect sex-related corpus callosum measurements (section V). Preliminary experimental findings (Fidelman, 1992a) may indicate that this suggestion is extendable to age dependent developmental processes of the hemispheres. In these developmental processes, children may have unexpected sex-related developmental differences.
2. The experiment is fully described in Fidelman (1992a; 1992b; 1995). The subjects were approximately six years old and were tested during their last three months of kindergarten before entering primary school. The experiment included a test regarding the conservation of cardinal numbers to determine each child's Piaget stage. This test involved increasing and diminishing the distances between objects presented to the subjects and asking them whether these operations changed the number of objects.
3. The experiment also included two independent tests for the right hemisphere, and two independent tests for the left. The first test for the right hemisphere was the enumeration of dots presented simultaneously during 120 milliseconds (MS) at the center of the visual field. The second test was a similar enumeration of nonsense figures.
4. The first test for the left hemisphere was the counting of dots presented one after another temporally for 120 MS each at different places on a computer monitor. The temporal intermissions between the presentations of the individual dots varied between 120 MS and 180 MS. The second test for the left hemisphere was a similar counting of dots presented at the same place at the center of the monitor. The relation between these four tests and the relevant hemispheres is discussed in Fidelman (1990). The subjects were tested three times using these tests.
5. The variable D is defined for each of the four hemispheric tests as the difference between the scores of an individual subject on the later and the earlier presentations of this test. During this study, the Piaget stage of 7 of the boys and 6 of the girls advanced to a higher stage. The difference between their scores on the hemispheric tests before and after this change was analyzed in Fidelman (1992a). A positive value of D indicates an increase in the efficiency of the related hemisphere, while a zero or negative value indicates a no-increase situation.
6. The left hemispheric D scores of 10 boys whose Piaget stage had not changed during the study were computed. Ten out of these 20 D scores for the two left hemispheric tests were positive. Similarly, six out of 12 left hemispheric D scores of the six girls whose Piaget stage had changed were positive. This may mean that the efficiency of the left hemisphere of these two groups of subjects did not change during the period between the hemispheric tests. However, 11 out of the 14 left hemispheric D scores of the boys whose Piaget stage had changed were positive. This last result is significant at p<0.058 in a 2-tailed binomial test.
7. Male hormones enhance the right hemisphere and damage the left one (Geschwind and Galaburda, 1985), while female hormones cause the opposite effect (Hampson, 1990). Therefore this result may imply that the influence of male hormones decreased, or the influence of female hormones increased, in the boys during the change of Piaget stage.
8. Two boys out of 7 and 4 girls out of 6 scored positive D scores on the test of simultaneous counting of nonsense forms. Two boys out of 7 and 5 girls out of 6 scored positive D scores on the test of simultaneous counting of dots. That is, the efficiency of the right hemisphere of girls, but not of boys, increased during the change of Piaget stage. Moreover, the mean score of boys on the two right hemispheric tests decreased, and that of girls increased, though these results are not significant statistically.
9. We observed that the influence of sex hormones is opposite on the two hemispheres. We also observed that the left hemisphere of boys became more efficient during the change of Piaget stage and their right hemisphere became less efficient. Moreover, the right hemisphere of girls became more efficient during the change of Piaget stage. We may formulate the following hypothesis: The change of Piaget stage regarding the conservation of cardinal numbers involves the development of the weaker hemisphere, that is, the left hemisphere of males and the right one of females. This development may involve increased activity of female hormones in boys, and male hormones in girls (or reduced activity of male hormones in boys and of female hormones in girls). Now we shall test this hypothesis regarding the right hemisphere.
10. The Piaget stage of 7 of the boys and 6 of the girls has changed, thus we have 26 independent scores on the right hemispheric tests before and after the change. We define a success as a positive D score for a girl, and a non-positive D score for a boy. There are 19 successes out of 26 trials. This result is significant at p<0.03 in a 2-tailed binomial test.
11. At the beginning of the study, 7 children (6 boys and one girl) were at the higher Piaget stage, and 30 children (19 boys and 11 girls) were at the lower stage. At this time, the mean scores of these two groups of children on all the four hemispheric tests were compared using a t-test. The result was significant only for the test of simultaneous enumeration of nonsense figures. The mean score of the children at the higher Piaget stage on this test was larger at p<0.02 in a 2-tailed t-test. An additional finding was that the sum of the means of the standardized scores on all the four hemispheric tests was larger for the higher Piaget stage group at p<0.05 in a 2-tailed t-test.
12. The test of enumerating nonsense figures may also be related to the collaboration between the hemispheres. The left hemisphere analyses the details of the unacquainted figures and transmits them to the right hemisphere for integration into forms. Then the forms are sent back to the left hemisphere for analysis as new details. Then the forms are sent again to the right hemisphere for integration into a set and for the determination of the cardinal number of this set. Therefore the higher scores on the test of counting nonsense figures obtained by the higher Piaget stage subjects may mean that their corpus callosum is more efficient. Another possible alternative or complementary explanation is that the higher Piaget stage subjects have a larger sum of hemispheric efficiencies (measured by the hemispheric tests), thus the accumulated better performances of both hemispheres count for the higher score on the test of enumerating nonsense figures. This second explanation is in line with the significant larger mean of the sum of the hemispheric tests obtained by the higher Piaget stage subjects.
13. There is an apparent contradiction between the advantage of the subjects who were at the higher Piaget stage at the beginning of the study in the test of enumerating nonsense figures and the observation that 6 out of 7 subjects of this group were males. The mean score on this test of the boys whose Piaget stage changed during the study decreased after the change, while the similar mean score of girls increased. This apparent contradiction may be resolved by assuming that most of the children who were at the higher Piaget stage at the beginning of the study had been at the higher Piaget stage for some time before the beginning of the study.
14. If we assume that the higher scores of the higher Piaget stage subjects on counting nonsense figures is due to their more efficient corpus callosum, we may assume that a relatively long time is required for the growth of new long axons of the corpus callosum, which counts for the delay in the accomplishing of the better scores on this test. If we assume that this effect is due to the larger efficiency of both hemispheres following the change of Piaget stage, we may assume that some time is required for the recovery of the right hemisphere of males and possibly also of the left hemisphere of females, after the detrimental influence of sex hormones on them during the change of Piaget stage.
15. The above experimental findings cannot decide between the two alternative (or complementary) solutions to the apparent contradiction. However, the conclusion of Fitch and Denenberg that the sex-related size differences of the corpus callosum may be age-dependent is in line with the theory that the efficiency of the corpus callosum increases following the change of Piaget stage. The quantity of sex hormones depends on age, and thus sex hormones and the size of the corpus callosum become related. We may assume that the neurons of the hemisphere which is enhanced during the change of Piaget stage grow new axons which create new synapses. Long new axons create new synapses later than short ones. Therefore we may expect that the last synapses which are created as a result of the changing of Piaget stage are the synapses created by the long interhemispheric commissures. These synapses may be created some time after the change of Piaget stage. The influence of sex hormones on the fibers of the corpus callosum may not be limited to the time of a change of Piaget stage. That is, we may hypothesize that male and female sex hormones enhance the growth of axons originated from right and left hemispheric neurons, respectively, in the corpus callosum.
16. If this hypothesis is correct, the male and female corpus callosum may differ not only in their size but also in the origin of their axons. The male corpus callosum may comprise more axons of right hemispheric neurons, while the female corpus callosum may comprise more axons of left hemispheric neurons. During the change of Piaget stage the numbers of these two kinds of axons may become more equal in both males and females.
Fidelman, U. (1990) Cerebral hemispheres, sex, handedness and the learning of arithmetic: A theory and initial experiments. Cybernetica, 33, 293-327.
Fidelman, U. (1992a) The role of hormones in cognitive and motor behavior: Piaget stages and the efficiency of the corpus callosum in children. In Proceedings of the 13th International Congress on Cybernetics: 334-338. Namur, Belgium: Association Internationale de Cybernetique.
Fidelman, U. (1992b) The hemispheres and arithmetic learning by children. In Proceedings of the 13th International Conference on Cybernetics: 339-343. Namur, Belgium: Association Internationale de Cybernetique.
Fidelman, U. (1995) The cerebral hemispheres and the learning of ordinal and cardinal arithmetic by kindergarten children. Cybernetica, 38 No. 2 (in press).
Fitch & Denenberg (1995) A Role for Ovarian Hormones in Sexual Differentiation of the Brain. PSYCOLOQUY 6(5) sex-brain.1.fitch.
Geschwind, N. & Galaburda, A.M. (1985) Cerebral lateralization, biological mechanisms, associations and pathologies: I. A hypothesis and a program for research. Archives of Neurology, 42: 428-459.
Hampson, E. (1990) Variations in sex-related cognitive abilities across the menstrual cycle. Brain and Cognition, 14: 26-43.