A study of Multi-World Paradigm in Mathematics Learning

近年来，数学教育受到激进建构主义、互动主义和社会文化主义三种思想的影响，基于这三种范式或它们的组合，对数学教育进行了大量的研究，它们有一个共同点：这三种思想都认为儿童的活动在数学学习中起着非常重要的作用，他们把社会交往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，这三种思想都可以解释的不同阶段往往出现在同一个班级，而激进的建构主义、互动主义和社会文化主义在理论上是相互冲突的，因此，它们在理论上是相互对立的。这三种思想的整合与协调，对于公正地解释学习的现实是不可避免的。从实践的角度看，需要一种灵活的范式，使它们相互协调、相互补充、超越常规概念，作者构建了这种范式，称之为数学学习的多世界范式。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。我们试图在多世界范式的基础上对数学学习进行理论研究和实践研究。

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.