Maybe we are searching among branches for what only appears in the roots (Molavi, 1252). In this talk, I focus on a critical exploration of the philosophical and epistemological underpinnings of social, historical, and cultural (and intercultural) studies in the field of mathematics education. Specifically, I underline how epistemological assumptions, which I suggest fundamentally underlie the cultural assumptions, tend in the main to be largely unexamined in the studies of culture and cultural difference. I suggest that it is the careful examination of different epistemological assumptions that leads to the pursuit and achievement of a deeper understanding of the nuances and complexities of culturally saturated and constructed learning and teaching of mathematics.

Keywords:  Inter-cultural relationships, ways of knowing, non-western epistemologies.

I will elaborate on how certain ways of doing and talking about school mathematics can result in mathematical othering. Othering is regarded as a discourse in which certain wordings, choice of words, and practices dominate the communication. Pandey (2004) described othering as a manner in which dichotomies can be generated and represented through language, often in unintended ways, via binary oppositions as ‘them’ and ‘us’. This approach can be adapted to describe a potential division between mathematics and students, between ‘it’ and ‘us’. Mathematical othering concerns the relationship between students and mathematics, and represents a distance between students and mathematics. But what does mathematical othering look like? Moreover, what can create such othering?

In this talk, we look at reports about developmental work written by 23 lower-secondary school teachers who planned, implemented and reflected upon a lesson involving elements of exploration, argumentation and proving. We analyze the properties of the tasks that the teachers designed for their students, the scaffolding that was provided during the classroom implementation, and the challenges that the teachers experienced when leaving traditional teaching practice.

Keywords:  Proof, proving, argumentation.

For details about the presentation description, see the text by Toril Eskeland Rangnes and Tamsin Jillian Meaney http://www.laudim.no/conferences/LaUDiM/Rangnes_Meaney.pdf