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Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations -- one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration -- and a look at how collaborations built with that intentionality and acknowledgment can be impactful for students and institutions and be personally and professionally rewarding for the collaborators. [ABSTRACT FROM AUTHOR]

In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, descriptions of mathematical practices for making build upon prior everyday mathematical practices and open up a new landscape of inquiry. [ABSTRACT FROM AUTHOR]

The situation of doctoral students is a complex ethical issue. They are not really students any more, but they are not yet full members of the Academy, so they are excluded from it. PhD students focus primarily on research, since if they do not publish in quality scientific journals, their future (both career and financial) is very much in question. As most of the doctoral student's capacity is taken up by research and publication during the training period, another important task is relegated to the background: learning to teach and to supervise research. Will the student have the ambition to become a good teacher and research supervisor as well as a researcher? What ethical factors can influence the personality development of a doctoral student? What experiences and perspectives will the newly graduated doctoral student bring to their academic career? Here I raise these questions both in general and in relation to graduate studies in mathematics. [ABSTRACT FROM AUTHOR]