解释学观照下数学对话的内涵与特征

Connotation and Characteristics of Mathematical Dialogue in Hermeneutics

数学具有＂对话＂的品质.对＂数学对话＂深层意涵的觉察和反省,使人们意识到真正的数学对话具有对话主体化、意义多元性和本质无止尽性的独特性格.真正的理解是一种接近诠释循环的对话历程,在视域融合的激荡过程中,人们可以不断地修正自己原先认识的意义与视域内容.在现今的知识社会背景下,深层反省＂数学对话＂背后的解释学立场,旨在以开放、包容的实践智慧来促成学生扎根于社会和文化的知识理念.数学对话是学生、文本与教师之间达成多重＂视域融合＂的理解性事件,视域融合应该成为检验数学对话有效性的重要维度.

Mathematics had the quality of ＂dialogue＂. The awareness and reflection of the deep meaning of ＂mathematics dialogue＂ made us realize that the real mathematical dialogue had a unique character of dialogue subjectivity, multi-meaning and non-exhaustive nature. The real understanding was a process of dialogue that was close to the cycle of interpretation. In the course of the fusion of horizons, we could constantly modify the original meaning and sight content. In the context of present knowledge society, the introspection of the ＂hermeneutic＂ position behind the ＂mathematical dialogue＂ aimed to promote students＇ rooting in the social and cultural knowledge and ideas through open and inclusive practical wisdom. Mathematical dialogue was an understanding event among students, texts and teachers to reach multiple fusions of horizons. Fusion of horizons should come to be an important dimension of checking validity of mathematical dialogue.