The concept of scaffolding refers to temporary and adaptive support, originally in dyadic adult–child interaction. It has become widely used, also in whole‐class settings, but often in loose ways. The aim of this paper is to theoretically and empirically ground a conceptualisation of whole‐class scaffolding so that it remains close to the origin of the scaffolding concept, but also provides scope for features not salient in one‐to‐one interaction. Drawing an analogy with Vygotsky's concept of Zone of Proximal Development we argue why the extension to whole‐class settings is justified. We further distinguish three key characteristics for whole‐class scaffolding—diagnosis, responsiveness and handover to independence—and illustrate these with examples from a teaching experiment focusing on whole‐class scaffolding language in a multilingual mathematics classroom (age 10–12). The empirical data led to a metaphorical distinction between online and offline enactment of key characteristics, during respectively outside whole‐class interaction. Diagnoses can namely also be made outside lessons, for instance by reading pupils' work; responsiveness can also be realised in adapting instructional activities; and handover to independence can also be fostered in the design of lessons. In addition to this layered nature (online vs. offline), whole‐class scaffolding is often distributed over time. Finally, whole‐class scaffolding is cumulative with pupils' independence emerging as the cumulative effect of many diagnostic and responsive actions over time. We suggest these three features are at the core of whole‐class scaffolding that is deliberately employed to foster long‐term learning processes.

This article has two purposes: firstly to introduce this special issue on scaffolding and dialogic teaching in mathematics education and secondly to review the recent literature on these topics as well as the articles in this special issue. First we define and characterise scaffolding and dialogic teaching and provide a brief historical overview of the scaffolding metaphor. Then we present a review study of the recent scaffolding literature in mathematics education (2010)(2011)(2012)(2013)(2014)(2015) based on 21 publications that fulfilled our criteria and 14 articles in this special issue that have scaffolding as a central focus. This is complemented with a brief review of the recent literature on dialogic teaching. We critically discuss some of the issues emerging from these reviews and provide some recommendations. We argue that scaffolding has the potential to be a useful integrative concept within mathematics education, especially when taking advantage of the insights from the dialogic teaching literature.

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In this paper, we argue that dual design research (DDR) is a fruitful way to promote and trace the development of a mathematics teacher's expertise. We address the question of how a teacher participating in dual design research can learn to scaffold students' development of the language required for mathematical learning in multilingual classrooms. Empirical data were collected from two teaching experiments (each with 8 lessons, and 21 and 22 students, aged 11-12 years), for which lesson series about line graphs were co-designed by the researchers and the teacher. The teacher's learning process was promoted (e.g. by conducting stimulated recall interviews and providing feedback) and traced (e.g. by carrying out 5 pre-and post-interviews before and after the teaching experiments). An analytic framework for teachers' reported and derived learning outcomes was used to analyse preand post-interviews. The teacher's learning process was analysed in terms of changes in knowledge and beliefs, changes in practice and intentions for practice. Further analysis showed that this learning process could be attributed to the characteristics of dual design research, for instance the cyclic and interventionist character, the continuous process of prediction and reflection that lies at its heart, and the process of co-designing complemented with stimulated recall interviews.

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