Specifically, the functions of CMES include the following: (1) providing cognitive tools with typical characteristics for the relationships among OAG (2) offering a general normalized open system on which sustainable in-depth research can be conducted and a conversion tool through which the complete textbook unit of the basic mathematics education can be converted to reveal the relationships among OAG and (3) presenting a set of cognitive theories, methods, and a system of basic mathematics education to further explore the relationships among OAG. Therefore this project attempts to construct a Children’s Mathematics Exploring System (CMES), which integrates with cognition theory, method, and contents of basic mathematics education to query the essence of the relationships among OAG. Thus, it is difficult for students to develop a systematic understanding of mathematics. In recent years, basic mathematics education cognitive tools have undergone rapid development, whereas the lack of a common normalization method for continued in-depth inquiry of the relationships among Objects, Algebra, and Geometry (OAG) has led to the fragmentation of students’ mathematical knowledge. It is believed that the main reason for this is the lack of an efficient cognitive tool or system that supports students’ study and exploration and correspondingly covers the whole curriculum of children’s math education. In terms of the leap-forward development for education experiment, both the Chinese and English educational experiment have been very successful, while the progress of the children’s mathematics education experiment in China has been relatively slow.
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