ABSTRACT International comparisons of languages have shown how mathematical concepts can be expressed and conceptualised in different languages. For multilingual students, these findings raise the question of how the interplay of languages and conceptualisations shape multilingual learning processes. This paper presents an investigation of case studies of bilingual learning processes of Turkish–German speaking students in Grade 7. Investigating the conceptual learning pathways of 14 focus students reveals that multilingual students navigate between different conceptualisations of fractions across both languages. To account for how these multilingual resources can provide opportunities for deepening conceptual understanding of fractions, two bilingual modes are distinguished and empirically substantiated: (1) The complementarity mode, in which code switching occurs for combining different nuances of a conceptualisation, and (2) the connection mode, in which (a) nuances travel across the languages or (b) languages are locally combined in translanguaging practices. Both modes contribute to multiperspective views on the part-whole concept.

中文翻译：

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一种思想，两种语言——独立的概念化？学生处理与语言相关的分数概念化的双语模式的案例研究

摘要 语言的国际比较表明数学概念可以如何用不同的语言表达和概念化。对于多语言学生，这些发现提出了语言和概念的相互作用如何塑造多语言学习过程的问题。本文对 7 年级土耳其语-德语学生双语学习过程的案例研究进行了调查。调查 14 名重点学生的概念学习途径表明，多语种学生在两种语言的不同分数概念化之间导航。为了说明这些多语言资源如何为加深对分数的概念理解提供机会，区分并实证证实了两种双语模式：（1）互补模式，其中代码切换发生以组合概念化的不同细微差别，以及（2）连接模式，其中（a）细微差别跨越语言或（b）语言在跨语言实践中本地组合。这两种模式都有助于对部分整体概念的多视角视图。