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There are increasing calls for the teaching of STEM within interdisciplinary 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.

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There is evidence that spontaneous learning leads to relational understanding and high positive affect. To study spontaneous abstracting, a model was constructed by combining the RBC model of abstraction with Krutetskii's mental activities. Using video-stimulated interviews, the model was then used to analyse the behaviour of two Year 8 students who had demonstrated spontaneous abstracting. The analysis highlighted the crucial role of synthetic and evaluative analysis, two processes that seem unlikely to occur under guided construction.

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