“Theory at the crossroads”: Mapping moments of mathematics education research onto paradigms of inquiry

In this essay, traveling through the past half-century, the authors illustrate how mathematics education research shifted, theoretical, beyond its psychological and mathematical roots. Mapping four historical moments of mathematics education research onto broader paradigms of inquiry, the authors make a case for the field to take up a theoretical “identity” that refutes closure and keeps the possibilities of mathematics teaching and learning open to multiple and uncertain interpretations and analyses

Molecular polarisation studies in relation to mesomerism in aromatic compounds

The dipole moments of a number of substituted anilines, in both benzene and dioxan, have been evaluated from measurements of the dielectric constants, densities and refractive indices of dilute solutions. In selecting the compounds for study attention was paid to the desirability of comparing, on the one hand, the effects of o-p and m-directing substituents and, on the other hand, the effects of the positions of the groups on the deviations from the moments to be expected from the simple vector addition theory. Hence, the dipol9 moments of m- and p-nitro- and bromo-, 2:4- and 3:5-dinitro- and dibromo- and 2:4:6-trinitroaniline, p-nitro- and 2:4-dinitromethyl-aniline and 2-methyl-4-nitroaniline have been measured in both solvents.The results have been interpreted in terms of the mesomeric and inductive effects of the substituents. In the absence of substituents in positions ortho to the amino-group the difference between the apparent moments of the amines in dioxan and benzene solutions increased progressively with increase in the interaction moment. The presence of methyl groups, bromine atoms or nitro-groups in both positions ortho to the amino-group decreased the dioxan increment although there appeared to be no appreciable interference when there was one nitro-group in such a position and only slight inhibition of the mesomeric effect when there was one bromine atom in the ortho-posit ion. The presence of one nitro-group in the ortho-position to a methylamino-group caused a decrease in the dioxan increment. All these results are attributable to steric effects in the molecules.<p

Affective productions of mathematical experience

In underscoring the affective elements of mathematics experience, we work with contemporary readings of the work of Spinoza on the politics of affect, to understand what is included in the cognitive repertoire of the Subject. We draw on those resources to tell a pedagogical tale about the relation between cognition and affect in settings of mathematical learning. Our interest is first captured in the way in which one teacher’s priority of establishing an inclusive learning community occasionally harboured what appeared to be pedagogically restrictive conceptions of mathematics. Yet, the classroom practices that produced these conceptions promoted the students’ motivation and provided meaningful access to mathematical learning within the classroom collectivity. In a second example, the postponement of scientific encapsulation in bodily imitations of planetary movement kept alive a shared dynamic sense of an elliptical orbit. In both of these cases, we draw on Spinoza’s work to show how the affectivity of classroom practice constituted conceptions of cognition and of mathematical activity crucially linked to the imperatives of participation

New Perspectives on Mathematics Pedagogy

“New Perspectives on Mathematics Pedagogy” represents a serious attempt to understand pedagogy within mathematics classrooms. To that end, this symposium will address the key questions and issues surrounding mathematics pedagogy presently confronting vast numbers of researchers, as well as educators, and policy makers. Organised around presentations, responses, discussion and debate, the symposium is intended not only to enhance understanding but also to stimulate fresh thinking and initiate ongoing critical dialogue about the practice of mathematics pedagogy within teaching and learning settings

Reconstructing Asian faunal introductions to eastern Africa from multi-proxy biomolecular and archaeological datasets

Human-mediated biological exchange has had global social and ecological impacts. In subS-aharan Africa, several domestic and commensal animals were introduced from Asia in the pre-modern period; however, the timing and nature of these introductions remain contentious. One model supports introduction to the eastern African coast after the mid-first millennium CE, while another posits introduction dating back to 3000 BCE. These distinct scenarios have implications for understanding the emergence of long-distance maritime connectivity, and the ecological and economic impacts of introduced species. Resolution of this longstanding debate requires new efforts, given the lack of well-dated fauna from high-precision excavations, and ambiguous osteomorphological identifications. We analysed faunal remains from 22 eastern African sites spanning a wide geographic and chronological range, and applied biomolecular techniques to confirm identifications of two Asian taxa: domestic chicken (Gallus gallus) and black rat (Rattus rattus). Our approach included ancient DNA (aDNA) analysis aided by BLAST-based bioinformatics, Zooarchaeology by Mass Spectrometry (ZooMS) collagen fingerprinting, and direct AMS (accelerator mass spectrometry) radiocarbon dating. Our results support a late, mid-first millennium CE introduction of these species. We discuss the implications of our findings for models of biological exchange, and emphasize the applicability of our approach to tropical areas with poor bone preservation

Confirmations and contradictions: Investigating the part that digital technologies play in students' everyday and school lives

Widespread change at the technological level brings a dimension into students' everyday life scarcely imagined in earlier times. This paper investigates the role that digitally mediated forms of activity play in the lives of young people. Using data drawn from a national survey, complemented with interviews undertaken with two students, the paper exposes confirmatory and contradictory practices at work, in relation to technology use in two different fields. Bourdieu's insightful analyses of social practice provide a means to reveal the ways in which a student's habitus, formed by the technology available in everyday life, is fostered, shaped and negotiated in schools

Confirmations and contradictions: Investigating the part that digital technologies play in students' everyday and school lives

Widespread change at the technological level brings a dimension into students' everyday life scarcely imagined in earlier times. This paper investigates the role that digitally mediated forms of activity play in the lives of young people. Using data drawn from a national survey, complemented with interviews undertaken with two students, the paper exposes confirmatory and contradictory practices at work, in relation to technology use in two different fields. Bourdieu's insightful analyses of social practice provide a means to reveal the ways in which a student's habitus, formed by the technology available in everyday life, is fostered, shaped and negotiated in schools