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Abstract: The article discusses the importance of combinatorial system in formalthinking and the necessity to take it directly as the object of study. Theinadiquacy to prove the existence of the combinatorial system with Piaget'sclassical experiment, and the difficulties to identify the existence of thecombinatorial system with tautological reasoning or language criteria areanalysed. On such a base, a new method is proposed to study the combin-atorial system by working out test questions according to the logical mea-ning of each binary operation implied in the combinatorial system. Thefocus of the article is on methodology rather than concrete experimentalresults. The result of the test has to some extent suggested that the binaryoperations of combinatorial system can be mastered by some of the teenagers.It has also proved the existence of INRC-group. But for lack of adequateproof of the universality of combinatorial system, the difficulties ofusing it as the structural model of formal thinking remains a problem.

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