This chapter concerns how three teachers in lower secondary school include climate change in school mathematics. Data was collected over a one-year period, where the teachers organised several teaching activities such as fieldwork, posters, contribution to an exhibition, and dialogue and debates, to facilitate students' critical mathematics competences through working with climate change. We apply a teacher perspective and focus on the role mathematics can play in formatting the understanding of climate change. A formatting power of mathematics is identified at three levels: (1) in teachers' meta-reflections, (2) when the teachers use mathematics to format students' understanding, and (3) when teachers facilitate students' awareness of the formatting power of mathematics. The findings suggest that a complex issue like climate change brings forth an awareness of the formatting powers of mathematics.

In this paper, the aim is to make a theoretical contribution by focusing on the origin, characteristics, and potential values of the concepts of instrumental and relational understanding. Five characteristics are identified to make it easier to operationalise the concepts and use them as an analytical framework. There is also a focus on how the concepts are closely related to two rationales for learning, the instrumental and the social rationale. The potential values of the concepts and their rationales are shown by using them to suggest a revision of the van Hiele framework and to analyse three empirical examples concerning young students’ understanding of triangles and a cylinder.

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