从数学微身份到宏身份：数学权威如何在逐时逐刻的定位中生成

摘要

本文旨在更好地理解学生逐时逐刻的微身份如何“增厚”为宏身份，并特别聚焦于一名学生 Tia 作为数学权威的形成过程。本文的分析包括识别学生所提出的观念、这些观念如何被回应，以及在这些互动中发挥作用的数学微身份（Wood，2013）。研究发现：（1）揭示了这位教师－研究者及其学生提出与回应观念的方式，与他们被定位为何种数学微身份之间的关系；（2）印证了 Wood（2013）关于微身份定位性质的发现；（3）在 Wood 的框架之上作出拓展，描述了微身份如何可以被细化或专门化。本文的发现有助于解释逐时逐刻的定位如何促成一名学生作为数学权威的宏身份的发展。

Abstract

This paper aims to better understand how students' moment-to-moment micro-identities thicken into macro-identities, focusing specifically on one student, Tia, as a mathematical authority. Our analysis involved identifying the ideas that students proposed, how they were responded to, and the mathematical micro-identities (Wood, 2013) at play during these interactions. Findings (1) reveal the relationship between how this teacher-researcher and her students proposed and responded to ideas and how they were positioned into mathematical micro-identities; (2) confirm Wood's (2013) findings regarding the nature of positioning into micro-identities; and (3) build on Wood's framework to describe how micro-identities can be nuanced, or specialized. Our findings help explain how moment-to-moment positioning contributes to the development of one student's macro-identity as a mathematical authority.