Beginning at the end of the nineteenth century, systematic scientific abstracting played a crucial role in reconfiguring the sciences on an international scale. For mathematicians, the 1931 launch of the Zentralblatt für Mathematik and 1940 launch of Mathematical Reviews marked and intensified a fundamental transformation, not just to the geographic scale of professional mathematics but to the very nature of mathematicians’ research and theories. It was not an accident that mathematical abstracting in this period coincided with an embrace across mathematical (...) research fields of a distinctive form of symbolic and conceptual abstraction. This essay examines the historical, institutional, embodied, and conceptual bases of mathematical abstracting and abstraction in the mid-twentieth century, placing them in historical context within the first half of the twentieth century and then examining their consequences and legacies for the second half of the twentieth century and beyond. Focused on scale, media, and the relationship between mathematical knowledge and its forms of articulation, my analysis connects the changing social structure of modern mathematical research communities to their changing domains of investigation and resources for representation and collective understanding. (shrink)

This paper follows recent debates on the ontological turn in the social sciences and humanities to exemplify how this turn creates important openings of methodological and political potential in education. In particular, the paper makes an attempt to show two things: first, the new questions and possibilities that are opened from explicitly acknowledging the methodological and political consequences of the ontological turn in education—e.g. concerning agency, transformation, materiality and relations; and second, the importance of being clear about how educators and (...) educational researchers conceptualize ontology and engage with debates on the ontological turn in related disciplines. The paper sketches some of the methodological and political implications of the ontological turn for education, focusing in particular on the concept of learning. (shrink)

This paper takes an embodied and extended cognition perspective to ER integration – a cognitive process through which a learner integrates external representations in a domain, with her internal model, as she interacts with, uses, understands and transforms between those ERs. In the paper, I argue for a theoretical as well as empirical shift in future investigations of ER integration, by proposing a model of cognitive mechanisms underlying the process, based on recent advances in extended and embodied cognition. I present (...) this new model in contrast to the still dominant classical cognitivist approaches to ER integration, and the educational technology intervention designs such approaches inspire. I then exemplify this distinction between the information processing model and the new model through a case of arithmetic problem solving. Corroborative neuroscience evidence presented in relation to this case provides empirical support for the new model by showing how bodily actions are critical to ER integration and learning. Finally, as educational implications of the new model, I demonstrate the need for: re-viewing the development of ER integration and expertise as fine-tuning of the learner's action or sensorimotor system, and a shift of focus in new-media intervention design principles based on this newer understanding of ER integration in science, technology, engineering and mathematics. (shrink)