A study of Multi-World Paradigm in Mathematics Learning

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Lately, the mathematical education is under significant influence of three thoughts including radical constructivism, interactionism, and socioculturism and a lot of studies are being conducted on the mathematical education based on each of such paradigms or combinations thereof.They have a common aspect : all of three thoughts view that children's activities play very important roles in mathematical learning, and they position social interaction as an important means in learning. On the other hand, they have distinct differences in any of the views of cognition, language, and learning.However, in the observations and analyses of children's practical activities in mathematical learning, various phases which could be explained by each of the three thoughts are frequently seen at the same class.While radical constructivism, interactionism and socioculturirm, are mutually conflicting theoretically, it is considered unavoidable to integrate and coordinate the three thoughts in order to explain the realities of learning in fair manner. A flexible paradigm is required from a practical point of view that would coordinate them, be mutually complementing, and be beyond common notions.The authors constructed such paradigm and call it the multi-world paradigm in mathematical learning. It contains the three worlds of the radical constructivism, interactionism, and socioculturism. We have tried to study theoretical as well as practical study of mathematical learning based on the multi-world paradigm.