Abstract
The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective exploration. We use the construct of instrumental orchestration to conceptualize a teacher’s intentional and systematic organization and use of digital technology to guide math-talk in terms of a collective instrumental genesis. We consider math-talk as a matter of inferential reasoning, taking place in the Game of Giving and Asking for Reasons (GoGAR).The combination of instrumental orchestration and inferential reasoning laid the foundation of a design experiment that addressed the research question: How can collective inferential reasoning be orchestrated in a technology-enhanced learning environment? The design experiment was conducted in lower-secondary school (students 14–16 years old) and consisted of three lessons on pattern generalization. Each lesson was tested and refined twice by the research team. The design experiment resulted in the emergence of the FlexTech orchestration, which provided teachers and students with opportunities to utilize the flexibility to construct, switch and mark in the orchestration of an instrumental math-GoGAR.
Highlights
Reform mathematics teaching calls attention to mathematics classroom talk (Brodie, 2013; Conner et al, 2014; Hufferd-Ackles et al, 2004; Walshaw & Anthony, 2008)
Instead, following Drijvers and colleagues’ notion of a collective instrumental genesis, we look at how artefacts take a position and are used as instruments in a social and pragmatic practice of reasoning and meaning-making in mathematics
This study was motivated by the need to further our understanding of orchestrating math-talk with technology that moves beyond a teaching practice of show-and-tell (Stein et al, 2008) and observational reports (Nilsson, 2019)
Summary
Reform mathematics teaching calls attention to mathematics classroom talk (hereafter, math-talk) (Brodie, 2013; Conner et al, 2014; Hufferd-Ackles et al, 2004; Walshaw & Anthony, 2008). In mathematics classrooms where teachers take the social and interactive nature of meaning-making seriously (Lerman, 2000), students are supposed to participate actively in a collective process of investigation, and analyse and reason, rather than wait to answer leading questions from the teacher (Hufferd-Ackles et al, 2004). In such teaching, the teacher is positioned as an orchestrator in supporting student participation. The teacher’s supporting role entails encouraging students to expand on their ideas and to make connections between ideas (Manouchehri & Enderson, 1999). Staples (2007) identified three interrelated thematic actions a teacher can take in supporting math-talk: supporting students in making contributions, establishing and monitoring common ground and guiding the mathematics
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