A study of Multi-World Paradigm in Mathematics Learning

近年来，数学教育受到了激进建构主义、互动主义和社会文化主义三大思潮的重大影响，基于这三种思潮或它们的组合对数学教育进行了大量的研究。它们有一个共同点：这三种思潮都认为儿童的活动在数学学习中起着非常重要的作用，都将社会互动作为学习的重要手段。然而，在对儿童数学学习实践活动的观察和分析中，三种思想可以解释的不同阶段经常出现在同一课堂上。虽然激进建构主义、互动主义和社会文化主义在理论上是相互冲突的，但为了公平地解释学习的现实，三种思想的整合和协调是不可避免的。从实践的角度出发，需要一个协调、互补、超越一般概念的灵活范式，作者构建了这种范式，称之为数学学习中的多世界范式。它包含了激进建构主义、互动主义和社会文化主义三个世界。我们尝试在多世界范式的基础上，对数学学习的理论研究和实践研究进行研究。

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.