Using tasks to explore teacher knowledge in situation-specific contexts

This article was published in the journal, Journal of Mathematics Teacher Education [© Springer] and the original publication is available at www.springerlink.comResearch often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning and teaching issues that previous research and experience have highlighted as seminal; are likely to occur in actual practice; have purpose and utility; and, can be used both in (pre- and in-service) teacher education and research through generating access to teachers’ views and intended practices. The Tasks have the following structure: reflecting upon the learning objectives within a mathematical problem (and solving it); examining a flawed (fictional) student solution; and, describing, in writing, feedback to the student. Here we draw on the written responses to one Task (which involved reflecting on solutions of x+x−1=0 of 53 Greek in-service mathematics teachers in order to demonstrate the range of teacher knowledge (mathematical, didactical and pedagogical) that engagement with these tasks allows us to explore

Bioluminescence intensity modeling and sampling strategy optimization

Author Posting. © American Meteorological Society 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Atmospheric and Oceanic Technology 22 (2005): 1267–1281, doi:10.1175/JTECH1760.1.The focus of this paper is on the development of methodology for short-term (1–3 days) oceanic bioluminescence (BL) predictions and the optimization of spatial and temporal bioluminescence sampling strategies. The approach is based on predictions of bioluminescence with an advection–diffusion–reaction (tracer) model with velocities and diffusivities from a circulation model. In previous research, it was shown that short-term changes in some of the salient features in coastal bioluminescence can be explained and predicted by using this approach. At the same time, it was demonstrated that optimization of bioluminescence sampling prior to the forecast is critical for successful short-term BL predictions with the tracer model. In the present paper, the adjoint to the tracer model is used to study the sensitivity of the modeled bioluminescence distributions to the sampling strategies for BL. The locations and times of bioluminescence sampling prior to the forecast are determined by using the adjoint-based sensitivity maps. The approach is tested with bioluminescence observations collected during August 2000 and 2003 in the Monterey Bay, California, area. During August 2000, BL surveys were collected during a strong wind relaxation event, while in August 2003, BL surveys were conducted during an extended (longer than a week) upwelling-favorable event. The numerical bioluminescence predictability experiments demonstrated a close agreement between observed and model-predicted short-term spatial and temporal changes of the coastal bioluminescence.This work has been supported by the Ocean Optics and Biology and Physical Oceanography Programs of the Office of Naval Research. Shulman’s support is through the NRL “Use of a Circulation Model to Enhance Predictability of Bioluminescence in the Coastal Ocean” project sponsored by the Office of Naval Research

Higher Structures in M-Theory

The key open problem of string theory remains its non-perturbative completion to M-theory. A decisive hint to its inner workings comes from numerous appearances of higher structures in the limits of M-theory that are already understood, such as higher degree flux fields and their dualities, or the higher algebraic structures governing closed string field theory. These are all controlled by the higher homotopy theory of derived categories, generalised cohomology theories, and $L_\infty$-algebras. This is the introductory chapter to the proceedings of the LMS/EPSRC Durham Symposium on Higher Structures in M-Theory. We first review higher structures as well as their motivation in string theory and beyond. Then we list the contributions in this volume, putting them into context.Comment: 22 pages, Introductory Article to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018, references update

Entry in the ADHD drugs market: Welfare impact of generics and me-toos

Recent decades have seen a growth in treatments for attention deficit hyperactivity disorder (ADHD) including many branded and generic drugs. In the early 2000's, new drug entry dramatically altered market shares. We estimate a demand system for ADHD drugs and assess the welfare impact of new drugs. We find that entry induced large welfare gains by reducing prices of substitute drugs, and by providing alternative delivery mechanisms for existing molecules. Our results suggest that the success of follow-on patented drugs may come from unanticipated innovations like delivery mechanisms, a factor ignored by proposals to retard new follow-on drug approvals

Differential electrophysiological response during rest, self-referential, and non-self-referential tasks in human posteromedial cortex

The electrophysiological basis for higher brain activity during rest and internally directed cognition within the human default mode network (DMN) remains largely unknown. Here we use intracranial recordings in the human posteromedial cortex (PMC), a core node within the DMN, during conditions of cued rest, autobiographical judgments, and arithmetic processing. We found a heterogeneous profile of PMC responses in functional, spatial, and temporal domains. Although the majority of PMC sites showed increased broad gamma band activity (30-180 Hz) during rest, some PMC sites, proximal to the retrosplenial cortex, responded selectively to autobiographical stimuli. However, no site responded to both conditions, even though they were located within the boundaries of the DMN identified with resting-state functional imaging and similarly deactivated during arithmetic processing. These findings, which provide electrophysiological evidence for heterogeneity within the core of the DMN, will have important implications for neuroimaging studies of the DMN

Newly qualified physical education teachers’ experiences of developing subject knowledge prior to, during and after a Postgraduate Certificate in Education course

Office for Standards in Education (OFSTED) inspections of secondary Postgraduate Certificate in Education (PGCE) physical education courses in England between 1996 and 1998 (OFSTED, 1999) were critical of student teachers' subject knowledge. The purpose of this study was to investigate the development of subject knowledge and influences on the development of that subject knowledge in a sample of three newly qualified teachers (NQTs) who had completed a PGCE physical education course in England. The research comprised semi-structured interviews and analysis of documentation. Among these three NQTs there were some similarities, but more differences in terms of the development of subject knowledge as well as different influences on the development of subject knowledge. These results suggest that teacher educators may need to be flexible in how they approach and support the development of student teachers' subject knowledge. Results also suggest that teacher educators should work more closely with colleagues teaching sports-related undergraduate degree courses to support the development of subject knowledge for those students who wish to progress to a PGCE physical education course

Suppressing qubit dephasing using real-time Hamiltonian estimation

Unwanted interaction between a quantum system and its fluctuating environment leads to decoherence and is the primary obstacle to establishing a scalable quantum information processing architecture. Strategies such as environmental and materials engineering, quantum error correction and dynamical decoupling can mitigate decoherence, but generally increase experimental complexity. Here we improve coherence in a qubit using real-time Hamiltonian parameter estimation. Using a rapidly converging Bayesian approach, we precisely measure the splitting in a singlet-triplet spin qubit faster than the surrounding nuclear bath fluctuates. We continuously adjust qubit control parameters based on this information, thereby improving the inhomogenously broadened coherence time from tens of nanoseconds to >2 μs. Because the technique demonstrated here is compatible with arbitrary qubit operations, it is a natural complement to quantum error correction and can be used to improve the performance of a wide variety of qubits in both meteorological and quantum information processing applications