A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In this paper, we mapped the blueprint of the whole curriculum with a brief section of "number" activities. We also compared this inquiry-based curriculum and instruction with the traditional mathematics teaching process in practical settings through a teaching experiment process, in which young children's mathematical learning performances were collected and analyzed as empirical evidence. Reflecting on the outcomes of this comparison, we presented exploratory findings of teaching experiments, and proposed relevant discussion for future works.