Quality dimensions for activation and participation in language-responsive mathematics classrooms

Kirstin Erath and Susanne Prediger

Introduction

Inspired by Flanders’ (1970) seminal work on interaction analysis, researchers in mathematics education and general education have tried to capture the quality of classroom interaction, first by assessing mainly surface structures (e.g. talk time of teachers and students), and, since the 1980s, also by deep qualitative analysis of the interaction pattern and their thematic focus (e.g. Bauersfeld, 1988). Since then, the quality of classroom interaction has repeatedly been identified as being highly relevant to students’ access to mathematics, and it has been shown that it is not pervasively established (Walshaw & Anthony, 2008). Although in classroom practices different quality aspects are often intertwined, mathematical aspects (conceptual focus or cognitive demand) and talk-related aspects of interaction quality are different in nature; for instance, a high student rate of talking-time does not automatically coincide with high cognitive demand. Little is known so far about how different quality aspects interact in detail, partly because they are not yet systematically disentangled in different dimensions.This chapter intends to contribute to their disentanglement and identification.

For the specific quality dimension of cognitive demand, Henningsen and Stein (1997) have suggested two perspectives for their conceptualization: (1) by teachers’ choices of tasks and their ways of enacting the cognitive activation in the interaction; and (2) by students’ ways of participation. These two perspectives, teachers’ activation and students’ participation in classroom interaction, have also proven suitable for other dimensions such as the discursive dimension and for the specific group of language learners, i.e. all children with low language proficiency in the language of instruction, with or without a migration background.

Qualitative studies have elaborated that classroom interaction is a crucial learning opportunity for language learners only when they are engaged in rich discourse practices (Barwell, 2012; Erath, Prediger, Quasthoff, & Heller, 2018; Moschkovich, 2013, 2015). In current teaching practices, however, the opportunity gap occurs with respect to both activation and participation: Language learners are often exposed to teaching practices with lower degrees of teacher activation (Gresalfi, Martin, Hand, & Greeno, 2009). A second limitation of learning opportunities for language learners can occur with respect to their participation, when teacher activation is provided, but not accompanied by additional support (de Araujo, Roberts, Willey, & Zalmer, 2018; Gibbons, 2002; Moschkovich, 2013; Smit, van Eerde, & Bakker, 2013).

So far, this research on quality of interaction in mathematics classrooms has mainly adopted qualitative approaches. In order to also strengthen the quantitative research base for discourse practices, this mainly theoretical chapter (which is an extended version of the conference contribution Erath & Prediger, 2018) aims at systematizing existing approaches for conceptualizing the quality of classroom interaction. Furthermore, it contributes to refining the construct of quality of interaction in a way that allows a later operationalization also for quantitative research approaches, which disentangle several dimensions and always coordinate both perspectives, teacher activation and student participation.This chapter therefore pursues responses to the following question: How can the quality of interaction in mathematics classrooms for language learners be disentangled into distinguishable dimensions which are measurable in scale?

The first section provides an overview of existing approaches, systematized within the supply-use model (Briihwiler & Blatchford, 2011; Fend, 1998; Helmke, 2009) according to their focus on teachers’ activation (supply) or students’ participation (use).The next section suggests four dimensions, the talk-related, conceptual, discursive and lexical dimensions, which are each conceptualized with respect to supply and use. A short transcript is presented to illustrate how these dimensions can be distinguished and how they are intertwined. The outlook briefly presents first suggestions for operationalizing the four dimensions and two perspectives for quantitative video-ratings.

Developing a theoretical framework in four dimensions and the supply and use perspective

 
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