This paper investigated the positive integral number concept development status of young children who were attending senior or intermediate classes of a kindergarten, located in central Taiwan. The approach used included problem posing, observing young children’s’ behaviors and question solving approaches. We then could conjecture the number concepts the young children possess, then re-posing problems and verifying (or revising) estimates. Further, this paper attempted to elaborate the implications of the results for young children’s mathematics education: First, findings show the possible number concept developments of 4.5-5.0 year olds, 5.0-5.5 year olds, 5.5-6.0 year olds, and 6.0 year olds and above. Results indicate the development of female young children may not be faster. Parent guidance provides the opportunity for young children’s’ development but may not be beneficial. Development of young children’s’ solving comparison problems ability is slower than developments of abilities for compound problems and take-away problems. Second, this paper raises implications for young children’s mathematics education. Suggestions regarding the contents of young children’s’ mathematics education and 5 teaching principles for young children educators are proposed.