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The teacher's use of representations is a crucial aspect of instructional quality in mathematics education, given their pivotal role in facilitating mathematics learning. However, in our international research community, perspectives on what constitutes high-quality use of representations may vary. This cross-cultural study aims to explore whether the perspectives from Western literature, emphasizing the importance of explicit connections between symbolic and graphic representations, can be extended legitimately to the East Asian context. Using a situated approach, the study elicited norms of high-quality representation use from researchers in Germany and Taiwan. A total of 31 mathematics education professors from both countries evaluated the use of representations in three secondary mathematics classroom situations presented as text vignettes. The vignettes, designed by the German research team, each depicted a situation where from their perspective, a norm of high-quality representation use, specifically the explicit connection between symbolic and graphic representations, was violated. Qualitative analysis of the researchers' responses revealed that in each situation, at least half of the German researchers expected explicit connections between representations. Conversely, the majority of Taiwanese researchers only expected such connections in one situation, particularly when the graphic representation served as an independent learning objective rather than solely aiding conceptual understanding. These findings indicate easily unnoticed culture-specific differences regarding how a common aspect of instructional quality is expected to unfold in teaching. [ABSTRACT FROM AUTHOR]

As an important component of teaching expertise, teacher noticing is gaining growing attention in our intercultural mathematics education community. However, it is likely that in many cases the researchers' perspectives on what characterizes high instructional quality in mathematics classrooms shape what they expect teachers to notice. In particular, it is an open question how potentially different norms of instructional quality influence how teacher noticing is operationalized in East Asian and Western cultures. Consequently, in a first step, this bicultural research project on teacher noticing in Taiwan and Germany focuses on exploring the researchers' frames of reference for investigating teacher noticing. In this paper, we thus propose a concurrent process for developing vignettes and eliciting corresponding expert norms as a prerequisite to investigating teacher noticing in a way that is sensitive to different cultural contexts. In this process, the research teams in both countries developed in parallel, text vignettes in which, from their perspective, a breach of a norm regarding a specific aspect of instructional quality was integrated. In an online expert survey, these vignettes were then presented to German and Taiwanese researchers in mathematics education (19 from each country) to investigate whether these experts recognize the integrated breach of a norm. This approach allows researchers to identify potentially different norms of instructional quality in mathematics classrooms. In particular, by means of a specific representation of practice, it became visible how expert norms of responding to students' mathematical thinking can be different from a Taiwanese compared to a German perspective. [ABSTRACT FROM AUTHOR]