ABSTRACT

We argue that the distinction between dialogue (after Bakhtin) and dialectics (after Hegel, Marx, Vygotsky), is of key importance to learning-teaching and to mathematics education. Some followers of Bakhtin have argued that these concepts are irreconcilable, or incompatible, since dialectics implies and dialogism implicitly denies the requirement of telos (i.e., a targeted endpoint). On the contrary, we argue for compatibility; dialogism can allow for the progress implied by dialectics, but its teleology is inherent in its efficacy in practice rather than in any pre-defined endpoint. We show how a mathematical or professional dialogue can involve dialectical negations and supersession, thus providing for progress or development, without loss of dialogism. Our case is taken from a lesson study in which progress emerging from classroom and staffroom dialogues is interpreted in dialectical terms as developmental. The connection with Vygotsky’s theory of concepts in learning-teaching and the possible generalization of the argument are discussed. We conclude that the key moments on which concept development turns are: (1) the negation by multiple, lived practices, and (2) the creative, speculative, supersession of inadequate concepts, in appropriate dialogues.

摘要

我们认为对话（在巴赫金之后）与辩证法（在黑格尔，马克思，维果斯基之后）之间的区别对于学习教学和数学教育至关重要。巴赫金的一些追随者认为，这些概念是不可调和的，或不兼容的，因为辩证法暗示性和对话性含蓄否认的需求终极目的（即目标端点）。相反，我们主张兼容性。对话可以允许辩证法所隐含的进步，但是它的目的论是其在实践中的效力所固有的，而不是在任何预定的终点中所固有的。我们展示了数学或专业对话如何包含辩证法否定和超级对话，从而在不丧失对话性的情况下为进步或发展提供了条件。我们的案例来自于一项课程研究，其中课堂和员工间对话中出现的进步被辩证地解释为发展性的。讨论了与维果斯基的理论教学理论的联系以及该论证的可能概括。我们得出结论，概念发展的关键时刻是：（1）多种实践经验的否定；（2）创造性的，投机性的，