Abstract
The present study was designed to throw light on the logical thinking of children. On it are analyzed logical operations into three aspects on the basis of the logical dispositions of the task: form, content, and complexity.
192 subjects from the 2nd grade in primary school to the 3rd grade in secondary school were tested in the first experiment. In the training experiment 120 of them were examined and formed into three groups on the basis of the result of the first experiment the first was the experietial group who were trained under an experiential program, the second was the symbolical group who were trained under an symbolical program, and the third was the control group.
The 36 calculi of propositions used as the task had three levels of difficulty at the three above mentioned aspects; on form: basic conditional, contrapositive or converse of contrapositive, on content; experiential, symbolical or hypothetical, on complexity; the number of propositions which forms one “Sentential Calculus” were 2, 3, 4 or 6.
Findings are:
1) Logical operations had clear developmental traits from the lowest grade to the highest grade. However, statistically significant stagnations were found at the 5th grade in primary school and the 2nd grade in secandary school.
2) The three tapes of the form had distinctly different developmental traits; basic conditional gave the most steep slope from the lowest grade to the highest grade, and contrapositive gave slightly lower but almost sams type slope. But the last one, converse of contrapositive, showed statistically significant increase from the 5th to the 6th grade, and thus before the 5th and after the 6th grade, no deelopmetal trait was found. Generally it was concluded that about the 5th grade was the period of the preparation for the progress from the lower stage to the higher in thinking.
3) On the content, the experiential tasks were most easy and the hypothetical was most difficult, thus there seemed to be a close relation between the verbal ability and the logical operations.
4) On the degree of the complexity, it was revealed that the task became more and more difficult from 2 to 6, and yet after the training there was no distinction in performance level by complexity, except for the certain gap between 4 and 6.
5) On the of effects of training, the experiential program was most of effective for the subjects in the “stage of preconcrete operations” (2nd-3rd grade), and the symbolically program was most of effective in the “stage of concrete operations” (4th-6th grade). In the “stage of formal operations”, both programs had almost equivalent of effect. From this, it was suggested that children in the given stage of logical operations would require training programs with the mode of operation which would be predominant in the next stage.
6) Analysis of errors found to be available in attempting to reveal the process of the development of logical thinking.
