Year 6 students' idiosyncratic notions of unitising, reunitising and regrouping decimal number places

Having flexible notions of the unit (e.g., 26 ones can be thought of as 2.6 tens, 1 ten 16 ones, 260 tenths, etc.) should be a major focus of elementary mathematics education. However, often these powerful notions are relegated to computations where the major emphasis is on "getting the right answer" thus procedural knowledge rather than conceptual knowledge becomes the primary focus. This paper reports on 22 high-performing students' reunitising processes ascertained from individual interviews on tasks requiring unitising, reunitising and regrouping; errors were categorised to depict particular thinking strategies. The results show that, even for high-performing students, regrouping is a cognitively complex task. This paper analyses this complexity and draws inferences for teaching.

Devising a scenographic approach in Jonzi D's Hip Hop theatre

Jonzi D, one of the leading Hip Hop voices in the UK, creates contemporary theatrical works that merge dance, street art, original scored music and contemporary rap poetry, to create theatrical events that expand a thriving sense of a Hip Hop nation with citizens in the UK, throughout southern Africa and the rest of the world. In recent years Hip Hop has evolved as a performance genre in and of itself that not only borrows from other forms but vitally now contributes back to the body of contemporary practice in the performing arts. As part of this work Jonzi’s company Jonzi D Productions is committed to creating and touring original Hip Hop theatre that promotes the continuing development and awareness of a nation with its own language, culture and currency that exists without borders. Through the deployment of a universal voice from the local streets of Johannesburg and the East End of London, Jonzi D creates a form of highly energized performance that elevates Hip Hop as great democratiser between the highly developed global and under resourced local in the world. It is the staging of this democratised and technologised future (and present), that poses the greatest challenge for the scenographer working with Jonzi and his company, and the associated deprogramming and translation of the artists particular filmic vision to the stage, that this discussion will explore. This paper interrogates not only how a scenographic strategy can support the existence of this work but also how the scenographer as outsider can enter and influence this nation.

Association between migraine and a functional polymorphism at the dopamine β-hydroxylase locus

Migraine is a common neurological disorder with a significant genetic component. Although a number of linkage and association studies have been undertaken, the number and identity of all migraine susceptibility genes has yet to be defined. The existence of dopaminergic hypersensitivity in migraine has been recognised on a pharmacological basis and some studies have reported genetic association between migraine and dopamine-related gene variants. Our laboratory has previously reported association of migraine with a promoter STR marker in the dopamine beta hydroxylase (DBH) gene. In the present study, we analysed two additional DBH markers in two independent migraine case–control cohorts. These two markers are putative functional SNPs, one within the promoter (−1021C→T) and another SNP (+1603C→T) in exon 11 of the DBH gene. The results showed a significant association for allelic and genotypic frequency distribution between the DBH marker in the promoter and migraine in the first (P = 0.004 and P = 0.012, respectively) and the second (P = 0.013 and P = 0.031, respectively) tested cohorts. There was no association observed between either genotype and/or allelic frequencies for the DBH marker located in exon 11 and migraine (P ≥ 0.05). The promoter DBH marker, reported associated with migraine in this study, has been shown to affect up to 52% of plasma DBH activity. Varying DBH activity levels have been postulated to be involved in migraine process with an increase of dopamine, resulting from a lower DBH activity shown positively correlated with migraine severity. It is plausible that the functional promoter variant of DBH may play a role in the migraine disorder.

Assessment of inflammatory burden contralateral to the symptomatic carotid stenosis using high-resolution ultrasmall, superparamagnetic iron oxide-enhanced MRI

BACKGROUND AND PURPOSE It is well known that the vulnerable atheromatous plaque has a thin, fibrous cap and large lipid core with associated inflammation. This inflammation can be detected on MRI with use of a contrast medium, Sinerem, an ultrasmall superparamagnetic iron oxide (USPIO). Although the incidence of macrophage activity in asymptomatic disease appears low, we aimed to explore the incidence of MRI-defined inflammation in asymptomatic plaques in patients with known contralateral symptomatic disease. METHODS Twenty symptomatic patients underwent multisequence MRI before and 36 hours after USPIO infusion. Images were manually segmented into quadrants, and the signal change in each quadrant was calculated after USPIO administration. A mixed mathematical model was developed to compare the mean signal change across all quadrants in the 2 groups. Patients had a mean symptomatic stenosis of 77% compared with 46% on their asymptomatic side, as measured by conventional angiography. RESULTS There were 11 (55%) men, and the median age was 72 years (range, 53 to 84 years). All patients had risk factors consistent with severe atherosclerotic disease. All symptomatic carotid stenoses had inflammation, as evaluated by USPIO-enhanced imaging. On the contralateral sides, inflammatory activity was found in 19 (95%) patients. Contralaterally, there were 163 quadrants (57%) with a signal loss after USPIO when compared with 217 quadrants (71%) on the symptomatic side (P=0.007). CONCLUSIONS - This study adds weight to the argument that atherosclerosis is a truly systemic disease. It suggests that investigation of the contralateral side in patients with symptomatic carotid stenosis can demonstrate inflammation in 95% of plaques, despite a mean stenosis of only 46%. Thus, inflammatory activity may be a significant risk factor in asymptomatic disease in patients who have known contralateral symptomatic disease. Patients with symptomatic carotid disease should have their contralateral carotid artery followed up.

How critical is fibrous cap thickness to carotid plaque stability? A flow-plaque interaction model

Background and Purpose Acute cerebral ischemic events are associated with rupture of vulnerable carotid atheroma and subsequent thrombosis. Factors such as luminal stenosis and fibrous cap thickness have been thought to be important risk factors for plaque rupture. We used a flow-structure interaction model to simulate the interaction between blood flow and atheromatous plaque to evaluate the effect of the degree of luminal stenosis and fibrous cap thickness on plaque vulnerability. Methods A coupled nonlinear time-dependent model with a flow-plaque interaction simulation was used to perform flow and stress/strain analysis in a stenotic carotid artery model. The stress distribution within the plaque and the flow conditions within the vessel were calculated for every case when varying the fibrous cap thickness from 0.1 to 2 mm and the degree of luminal stenosis from 10% to 95%. A rupture stress of 300 kPa was chosen to indicate a high risk of plaque rupture. A 1-sample t test was used to compare plaque stresses with the rupture stress. Results High stress concentrations were found in the plaques in arteries with >70% degree of stenosis. Plaque stresses in arteries with 30% to 70% stenosis increased exponentially as fibrous cap thickness decreased. A decrease of fibrous cap thickness from 0.4 to 0.2 mm resulted in an increase of plaque stress from 141 to 409 kPa in a 40% degree stenotic artery. Conclusions There is an increase in plaque stress in arteries with a thin fibrous cap. The presence of a moderate carotid stenosis (30% to 70%) with a thin fibrous cap indicates a high risk for plaque rupture. Patients in the future may be risk stratified by measuring both fibrous cap thickness and luminal stenosis.

On the probability of dizygotic twins being concordant for two alleles at multiple polymorphic loci

Accurate determination of same-sex twin zygosity is important for medical, scientific and personal reasons. Determination may be based upon questionnaire data, blood group, enzyme isoforms and fetal membrane examination, but assignment of zygosity must ultimately be confirmed by genotypic data. Here methods are reviewed for calculating average probabilities of correctly concluding a twin pair is monozygotic, given they share the same genotypes across all loci for commonly utilized multiplex short tandem repeat (STR) kits.

Higher-resolution structure of the human insulin receptor ectodomain: Multi-modal inclusion of the insert domain

Insulin receptor (IR) signaling is critical to controlling nutrient uptake and metabolism. However, only a low-resolution (3.8 Å) structure currently exists for the IR ectodomain, with some segments ill-defined or unmodeled due to disorder. Here, we revise this structure using new diffraction data to 3.3 Å resolution that allow improved modeling of the N-linked glycans, the first and third fibronectin type III domains, and the insert domain. A novel haptic interactive molecular dynamics strategy was used to aid fitting to low-resolution electron density maps. The resulting model provides a foundation for investigation of structural transitions in IR upon ligand binding.