Mathematics Discourse in Instruction (MDI): A Discursive Resource as Boundary Object Across Practices

Abstract

Linked research and development forms the central pillar of the Wits Maths Connect Secondary (WMCS), a project working with secondary mathematics teachers in one province in South Africa. A key outcome is a sociocultural analytic framework-a discursive resource that has been developed and refined through our work in and across three inter-linked practices. Named Mathematics Discourse in Instruction (MDI), we have used the framework as a planning and reflection tool in professional development and we have operationalised it as an analytic framework for research. MDI enables a description of mathematics made available to learn in a lesson, and an interpretation of shifts in practice across lessons and over time. MDI is both process and product of the WMCS. I describe and reflect on our use of MDI to build a case for embracing a discursive resource as a boundary object that moves productively across multiple practices.

Levering change: the contributory role of a mathematics teaching framework

“…-The pre and post video study of teachers in the 2012 TM1 course As noted above, we embarked on pre and post video study over 2012 and 2013 meeting significant methodological challenges-first at the level of the data gathered, and then in the analysis of the les-sons and interpretation of this. I mention this study here despite not publishing its results beyond project reports and descriptive presentations of the project (see Adler, 2017). Limitations included: obtaining only one lesson per teacher in each year; a number of teachers were not teaching similar content or grades in the 2 years, let alone the same lesson topic.…”

“…The details of the project and its intervention have been described elsewhere (Adler, 2017;Adler & Pillay, 2017a, 2017b. Briefly, we knew that any potential success of our intervention would depend on whether and how the project connected with teachers in their schools and classrooms, and this included their current practices and the materials with which they were required to work.…”

“…1 i.e., teachers' mft with structured opportunities in the course sessions for teachers to participate with mathematics and the framework to which I now turn. moved between: the practices of teacher education 4 and the practices of mathematics teaching on the one hand, and the practices of research 5 on the other (Adler, 2017). The mathematics teaching framework (MTF) is the teaching version, and it was developed as a resource for teachers' use in their interaction with other resources as they went about their work of teaching.…”

Teachers’ Involvement in Designing MERLO Items: Boundary Crossing

“…The introduction and creation of new boundary objects require different learning to enable the members of each community to cross boundaries, negotiate common boundary objects, develop new cognitive tools at the boundaries and reflect on how boundary objects could be adapted by and for each community. This new learning of communities has been studied in mathematics education research by different scholars (Adler 2017;Goos and Benisson 2017;Kynigos and Kalogeria 2012;Rasmussen et al 2009;Robutti et al 2019).…”

“…Interactions among researchers and teachers have been studied in mathematics education research by different scholars (Adler 2017;Aldon et al 2017;Goos and Benisson 2017;Kynigos and Kalogeria 2012;Rasmussen et al 2009;Robutti et al 2019) or in a wider context of research in education (Monod-Ansaldi et al 2019;Nizet et al 2019). We place ourselves in this stream of research to analyze the effects of these interactions in the specific case of MERLO items.…”