Mathematics teacher educators’ navigational expertise when designing multimodal representations of practice: a semiotic analysis

Critical elements of the expertise of mathematics teacher educators (MTE) can be identified in the artifacts they design for working with prospective teachers (PT), specifically for engaging PT in the double role of practitioners and students of practice. While MTE are increasingly utilizing designed multimodal representations of practice (such as storyboards), theoretical frameworks and methods for analyzing these pedagogical artifacts and the meanings they support are still in early development. We utilize a semiotic framework, expanding systemic functional linguistics to encompass non-linguistic elements, to identify aspects of what we call navigational expertise—which supports PTs in engaging both as practitioners and students of the practice. We view this expertise as tacit knowledge-in-use, enacted through artifact production. The paper demonstrates MTE’s navigational expertise by showing how MTE design storyboards of practice to engage PT as fellow teachers experiencing the lesson taught by a peer and as university students who consider the artifact (including the represented lesson) as an object of study. The framework allows us to identify how MTE’s navigational expertise lies in seamlessly interweaving these two purposes and navigating between them, knowing when, how, and for what purposes to invoke each. Through analysis of storyboards from four MTE in diverse US settings, we uncover some of the nuanced tacit components of navigational expertise, highlighting linguistic and non-linguistic design choices and their potential meanings for transactions with PT.