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The purpose of this chapter is to preface, and introduce, the content of this book, but also to help clarify concepts and terms addressed, set the stage by summarising our previous work, and issue some caveats about our limitations. We will close with a discussion of the mathematics in (IdME), which we see as a lacuna in the literature, and even in this book.

This section introduces interdisciplinarity in theory, and its conceptualization for policy and practice, with a view to developing the research in this subfield as a cumulative, scientific enterprise. The three chapters are outlined. Then I appeal to theory, policy and practice to re-think the notion of school discipline, and to unleash the learner, teachers, and the schools from discipline.

In this chapter, we develop in broad strokes the concept and history of the ‘disciplines’, a prerequisite for understanding disciplinary and interdisciplinary activity, since activity is always mediated by the cultural artefacts history leaves us. We develop the social and cultural theories of activity, practice, and discourse to offer further insights into both academic and professional ‘disciplines’, and their interrelationships, both in the academy, and in practical, joint, ‘interdisciplinary’ activity in everyday, workplace and professional life. The aim is to provide the foundations of a comprehensive theory for researchers of interdisciplinary activity. We build the analysis first of all on classical activity theory and modern developments in this tradition (a) of Vygotsky’s group and their Western interpreters, and (b) of those inspired by Bakhtin who have particularly developed multivoicedness and hybridity in dialogism. We additionally draw on Bourdieu and Foucault to consider the nature of the power structures in the disciplinary fields and discourses respectively, and how they might be resisted. We argue for a new conceptualisation of meta-disciplinary mathematics education that is a requirement of a critical mathematics education, concluding that meta-knowledge of disciplinarity is necessary for negating and becoming, to some extent, free from the discipline. We reflect on the adequacy of this theoretical battery, and its proposed synthesis for researchers in the field.

Since one of the keywords in the interdisciplinary discourse is integration, the aim of the study was to describe the actions of participants that could be considered as part of an integration process involving mathematical and musical discourses. Based on the commognitive perspective developed by Anna Sfard, which argues that communication is a collectively performed patterned activity, here integration is a way to develop a new type of communication. Music and mathematics students participated in an experience, where it was possible to observe how line graphics of random data were interpreted through actions from a musical discourse and how the students developed a new form of communication when talking about chords, which they called “baggies”.

There are increasing calls for the teaching of STEM within inter-disciplinary settings, as a way of engaging students in authentic tasks and innovation. However there have been concerns raised about the impact of inter-disciplinary curricula on mathematics learning particularly, with a concomitant need to conceptualise how mathematics might productively interact with other disciplines in STEM settings. This chapter explores cases of interdisciplinary STEM activity that arose as part of two major Australian STEM professional learning initiatives. It focuses on the variety of curriculum structures that occurred, the challenges for schools and teachers in implementing such structures, and teacher perceptions of their experiences including student engagement. Cases of inter-disciplinary tasks/investigations are presented to explore the different ways in which mathematics is transacted, and to develop a set of principles that should govern the inclusion of mathematics in inter-disciplinary settings. The cases show evidence of increased engagement and enthusiasm of students for STEM project and investigative work, but indicate the challenge for teachers of generating productive and coherent mathematics learning in inter-disciplinary settings. The results also point to institutional and systemic barriers to the wider take-up of interdisciplinary STEM activities.

The three chapters in this section each exemplify authentic practical problems addressed in learning situations. In so doing they point to the implied questions of scaling up problems so that a wider range of learners and teachers might engage with practical STEM. How can the work of inspirational and creative teachers with high levels of mathematical understanding be extended for wider participation? This part of the book draws out these issues by considering the slipperyness of STEM in a generalised, selective and examination-focused curriculum. In so doing, technology-afforded practice highlights specific areas for teacher development and curriculum liberation. In this section the authors of the chapters are grappling with some difficult issues. The work is all to a greater or lesser extent empirically driven. The studies to which the chapters refer are smaller scale, and although one (Mayes) draws on a project with 20 schools, the other two are set in the context of a single group of students working on a single project.

An interdisciplinary laboratory activity involved modelling and interpreting the motion of a rolling ball through the lens of algebraic representation. It was conducted with a group (N = 24) of high school mathematics students. The participants used scientific methods to formulate an algebraic representation of a position for a rolling object on a horizontal surface. While traditional mathematical modelling activities are usually driven by provided data, the technique applied in this study is driven by the phenomenon itself, which serves as a means to verify if the derived algebraic function adheres to the observed behaviour. The results of the study showed that including scientific methods in mathematics interdisciplinary activities may serve as a means to activate, and stimulate, students’ reasoning skills, and thus help them integrate the concepts of science and mathematics into a single coherent inquiry. While the study revealed benefits of using hypotheses in interdisciplinary activities, it also opened possibilities of utilizing interdisciplinary laboratories to improve students’ mathematical thinking. Suggestions for instructional strategies, as well as suggestions for mathematics curriculum policy makers, are discussed.

The Real Science, Technology, Engineering Mathematics (STEM) Project was conducted in middle schools and high schools in Georgia, USA. The project supported the development of interdisciplinary STEM modules and courses in over 20 schools. A project focus was development of five 21st century STEM reasoning abilities. In this chapter, I provide classroom activities from the Real STEM project that exemplify each form of reasoning: complex systems; model-based; computational; engineering design-based; and quantitative reasoning. Quantitative reasoning plays a critical rôle in authentic real-world interdisciplinary STEM problems, providing the tools to construct data informed arguments specific to the problem context, which can be debated, verified or refuted, modelled mathematically and tested against reality. Yet quantitative reasoning is often misrepresented, underdeveloped, and ignored in STEM classrooms. The chapter finishes with a discussion of the impact of Real STEM.

Whilst Science, Technology, Engineering and Mathematics (STEM) interdisciplinary teaching and learning in the USA K-12 education still needs greater promotion, middle school students demonstrated that they can, using low-cost, single board computers that promote the teaching of computer science (in this case Raspberry Pis), successfully engage with computer programming of digital images and videos. The context for these students’ engagement was the Advancing Out-of-School Learning in Mathematics and Engineering (AOLME) Project. This chapter describes how the processes of design, model, and implement, supported 40 Latinx middle school students’ development of computational thinking in an out-of-school setting, and how these processes promoted the genuine integrated practice and learning of technology, engineering, and mathematical concepts.

The five case study chapters in this section are introduced and contextualised in relation to previous case study work in Interdisciplinary Mathematics Education. Alongside the benefits which come from interdisciplinary work, a common theme which emerges from the case studies is that of a potential for mathematics to disappear, or to become a mere tool, within such activities. Appealing to Vygotsky’s theory of scientific concepts, it is argued that there is a crucial role for generalisation within interdisciplinary mathematics, and that the connections within mathematics require attention alongside the connections between mathematics and real world experience if mathematics is to more fully benefit from, and bring benefit to, interdisciplinary work.