Dynamic geometry software: the teacher's role in facilitating instrumental genesis

In the UK, teachers’ use of dynamic geometry software (DGS) has remained limited. The importance of the teacher’s role is often stated in dynamic geometry research but has been seldom elaborated. This study aims to address the apparent deficiency in research. The author conducted the research in the role of a practitioner-researcher with a high ability year 8 class. By analysing teacher/pupil interactions in a DGS context, elements of instrumental genesis are distinguished in pupils’ dialogue and written work which suggest strategies that teachers can employ to facilitate this process. Whilst these strategies are specific to a DGS context, they highlight general principles of mathematics teaching. This paper argues that the focus of research needs to shift away from the context, towards teachers and the strategies they employ

Galois coverings of weakly shod algebras

We investigate the Galois coverings of weakly shod algebras. For a weakly shod algebra not quasi-tilted of canonical type, we establish a correspondence between its Galois coverings and the Galois coverings of its connecting component. As a consequence, we show that a weakly shod algebra is simply connected if and only if its first Hochschild cohomology group vanishes.Comment: Some references were added. The proof of Lemma 6.5 was modifie

Mathematical Knowledge for Teaching Using Technology: a Case Study

This paper analyses data from a PhD pilot study to explore the nature of mathematical knowledge for teaching using technology, as represented by the central construct of the TPACK framework. The case study of teacher Alice is used as an illustrative example to suggest that the central TPACK construct may be better understood as a transformation and deepening of existing mathematical knowledge rather than as a new category of knowledge representing the integration of technology, pedagogical and mathematical knowledge

Detectability of Plasmodium falciparum clones.

BACKGROUND: In areas of high transmission people often harbour multiple clones of Plasmodium falciparum, but even PCR-based diagnostic methods can only detect a fraction (the detectability, q) of all clones present in a host. Accurate measurements of detectability are desirable since it affects estimates of multiplicity of infection, prevalence, and frequency of breakthrough infections in clinical drug trials. Detectability can be estimated by typing repeated samples from the same host but it has been unclear what should be the time interval between the samples and how the data should be analysed. METHODS: A longitudinal molecular study was conducted in the Kassena-Nankana district in northern Ghana. From each of the 80 participants, four finger prick samples were collected over a period of 8 days, and tested for presence of different Merozoite Surface Protein (msp) 2 genotypes. Implications for estimating q were derived from these data by comparing the fit of statistical models of serial dependence and over-dispersion. RESULTS: The distribution of the frequencies of detection for msp2 genotypes was close to binomial if the time span between consecutive blood samples was at least 7 days. For shorter intervals the probabilities of detection were positively correlated, i.e. the shorter the interval between two blood collections, the more likely the diagnostic results matched for a particular genotype. Estimates of q were rather insensitive to the statistical model fitted. CONCLUSIONS: A simple algorithm based on analysing blood samples collected 7 days apart is justified for generating robust estimates of detectability. The finding of positive correlation of detection probabilities for short time intervals argues against imperfect detection being directly linked to the 48-hour periodicity of P. falciparum. The results suggest that the detectability of a given parasite clone changes over time, at an unknown rate, but fast enough to regard blood samples taken one week apart as statistically independent

Measurement of Plasmodium falciparum transmission intensity using serological cohort data from Indonesian schoolchildren.

BACKGROUND: As malaria transmission intensity approaches zero, measuring it becomes progressively more difficult and inefficient because parasite-positive individuals are hard to detect. This situation may arise shortly before achieving local elimination, or during surveillance post-elimination to prevent reintroduction. Antibody responses against the parasite last longer than the infections themselves. This "footprint" of infection may thus be used for assessing transmission intensity. A statistical approach is presented for measuring the seroconversion rate (SCR), a correlate of the force of infection, from individual-level longitudinal data on antibody titres in an area of low Plasmodium falciparum transmission. METHODS: Blood samples were collected from 160 Indonesian schoolchildren every month for six months. Titres of antibodies against AMA-1 and MSP-1(19) antigens of P. falciparum were measured using ELISA. The distribution of antibody titres among seronegative and -positive individuals, respectively, was estimated by comparing the titres from the study data (a mixture of both seropositive and -negative individuals) with titres from a (unexposed) negative control group of Indonesian individuals. Two Markov-Chain models for the transition of individuals between serological states were fitted to individual anti-PfAMA-1 or anti-PfMSP-1 titre time series using Bayesian Markov-Chain-Monte-Carlo (MCMC). This yielded estimates of SCR as well as of the duration of seropositivity. RESULTS: A posterior median SCR of 0.02 (Pf AMA-1) and 0.09 (PfMSP-1) person(-1) year(-1) was estimated, with credible intervals ranging from 1E-4 to 0.2 person(-1) year(-1). This level of transmission intensity is at the lower range of what can reliably be measured with the present study size. A Bayesian test for seroconversion of an individual between two observations is presented and used to identify the subjects who have most likely experienced an infection. Furthermore, the theoretical limits of measuring transmission intensity, and how these depend on duration and size of a study as well as on transmission intensity itself, is illustrated. CONCLUSIONS: This analysis shows that it is possible to measure SCR's from individual-level longitudinal data on antibody titres. In addition, individual seroconversion events can be identified, which can be useful in assessing interruption of transmission. Analyses of further serological datasets using the present method are required to improve and validate it. This includes measurement of the duration of antibody responses, how it depends on host age or cumulative exposure, or on the particular antigen used

Documentation of a fully integrated epidemiological-demographic-macroeconomic model of Malaria: The case of Ghana

We develop a novel and fully integrated epidemiological-demographic-macroeconomic EDM-malaria simulation model framework for modelling of P. falciparum malaria transmission in Ghana. Our model framework represents a milestone, as the first fully integrated EDM model framework for any type of infectious disease. The complex specification and integration of regional epidemiological-demographic models within a malaria-focussed macroeconomic Computable General Equilibrium model is fully described and documented, and ideas are outlined for future applications to investigate the interplay between macroeconomic and health disease burdens, to measure the health and economic impacts of economic growth and malaria interventions, and to study the importance (or lack thereof) of the general omission of proper epidemiological underpinnings and integration of economic incentive feedback effects in the existing literature on macroeconomic assessment of infectious disease

The first Hochschild cohomology group of a schurian cluster-tilted algebra

Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã.Fil: Assem, Ibrahim. University of Sherbrooke; CanadáFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Normal forms of modules over admissible algebras with formal two-ray modules

The aim of the paper is to classify the indecomposable modules and describe the Auslander--Reiten sequences for admissible algebras with formal two-ray modules

Emotional Voice Areas: Anatomic Location, Functional Properties, and Structural Connections Revealed by Combined fMRI/DTI

We determined the location, functional response profile, and structural fiber connections of auditory areas with voice- and emotion-sensitive activity using functional magnetic resonance imaging (fMRI) and diffusion tensor imaging. Bilateral regions responding to emotional voices were consistently found in the superior temporal gyrus, posterolateral to the primary auditory cortex. Event-related fMRI showed stronger responses in these areas to voices-expressing anger, sadness, joy, and relief, relative to voices with neutral prosody. Their neural responses were primarily driven by prosodic arousal, irrespective of valence. Probabilistic fiber tracking revealed direct structural connections of these "emotional voice areas” (EVA) with ipsilateral medial geniculate body, which is the major input source of early auditory cortex, as well as with the ipsilateral inferior frontal gyrus (IFG) and inferior parietal lobe (IPL). In addition, vocal emotions (compared with neutral prosody) increased the functional coupling of EVA with the ipsilateral IFG but not IPL. These results provide new insights into the neural architecture of the human voice processing system and support a crucial involvement of IFG in the recognition of vocal emotions, whereas IPL may subserve distinct auditory spatial functions, consistent with distinct anatomical substrates for the processing of "how” and "where” information within the auditory pathway