Development of numerical concepts observed in children's utterances in kindergartens and elementary schools and its relationship to mathematical education

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Children's conversations and utterances obtained during the participant observation were analyzed focusing on the comprehension of numerical concepts. There were lots of utterances concerning various kinds of numerical concepts that would be related to informal mathematics. It was revealed that numerical concepts were utilized as cues to construct children's plays as well as to develop children's various activities. On the other hand, the utterances observed in the class of mathematics in elementary schools also seemed to reflect children's knowledge of informal mathematics. It was indicated that there were some processes that relate their informal mathematics to formal knowledge. These results were considered important in a sense that abundant plays of preschoolers should be secured in order to develop their informal mathematics.