It is argued in cognitive psychology that mental operations are domain-specific which have been generally believed to be universal. Y. Saeki, a cognitive psychologist, who is one of the most enthusiastic propagandists of this idea in Japan, gives three groups of evidences purporting to "support domain-specificity of mental operations, namely, recent cross-cultural researches, context effect on Piaget's tasks and experimental studies on hypothetico-deductive reasoning. In this article, the validity of these evidences and the credibility of his claim were examined. For this purpose, the following three tasks were analyzed, of which Saeki interprets the results as evidences for domain-specificity of mental operations. (1) a simple reasoning task in cross-cultural research (2) a number conservation task in an ecologically valid context (3) a.three-mountains problem in Borke's experiment The analysis of these tasks showed that the result of the simple reasoning task (1) has nothing to do with the problem of domain-specificity, and that the facilitation of the number conservation task (2) is not due to the meaningfulness of the context per se, but to a change in quality of the task, caused by introduction of the context and that Borke's task (3) is not isomorphic to Piaget's three-mountains problem. This is the first part of an article entitled "Understanding and Domain-specificity" Its second part will follow in the next issue.