Mathematically gifted and talented learners: Theory and practice

This is an Author's Accepted Manuscript of an article published in International Journal of Mathematical Education in Science and Technology, 40(2), 213-228, 2009, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/00207390802566907.There is growing recognition of the special needs of mathematically gifted learners. This article reviews policy developments and current research and theory on giftedness in mathematics. It includes a discussion of the nature of mathematical ability as well as the factors that make up giftedness in mathematics. The article is set in the context of current developments in Mathematics Education and Gifted Education in the UK and their implications for Science and Technology. It argues that early identification and appropriate provision for younger mathematically promising pupils capitalizes on an intellectual resource which could provide future mathematicans as well as specialists in Science or Technology. Drawing on a Vygotskian framework, it is suggested that the mathematically gifted require appropriate cognitive challenges as well as attitudinally and motivationally enhancing experiences. In the second half of this article we report on an initiative in which we worked with teachers to identify mathematically gifted pupils and to provide effective enrichment support for them, in a number of London Local Authorities. A number of significant issues are raised relating to the identification of mathematical talent, enrichment provision for students and teachers’ professional development

Traumatic fracture of central venous catheter resulting in potential migration of distal fragment: a case report

We report a surgical retrieval of an indwelling portion of a traumatic rupture of the Central venous catheter following hair cutting by a confused patient secondary to Postoperative cognitive dysfunction. He had a dynamic compression screw for fixation of fractured neck of femur after previously failed surgical procedure. The second procedure was complicated with major blood loss, which required central venous and arterial line insertion for intra-operative and post-operative management. The patient was discharged to the ward following an uneventful stay on intensive care. While on the ward, he decided to trim his hair and in the process he inadvertently cut through the right internal jugular catheter. Complications and management resulting from embolisation of central line are reviewed

The Reform of Employee Compensation in China’s Industrial Enterprises

Although employee compensation reform in Chinese industrial sector has been discussed in the literature, the real changes in compensation system and pay practices have received insufficient attention and warrant further examination. This paper briefly reviews the pre- and post-reform compensation system, and reports the results of a survey of pay practices in the four major types of industrial enterprises in China. The research findings indicate that the type of enterprise ownership has little influence on general compensation practices, adoption of profit-sharing plans, and subsidy and allowance packages. In general, pay is linked more to individual performance and has become an important incentive to Chinese employees. However, differences are found across the enterprise types with regard to performance-related pay. Current pay practices are positively correlated to overall effectiveness of the enterprise

A novel nonparametric item response theory approach to measuring socioeconomic position: a comparison using household expenditure data from a Vietnam health survey, 2003

BACKGROUND: Measures of household socio-economic position (SEP) are widely used in health research. There exist a number of approaches to their measurement, with Principal Components Analysis (PCA) applied to a basket of household assets being one of the most common. PCA, however, carries a number of assumptions about the distribution of the data which may be untenable, and alternative, non-parametric, approaches may be preferred. Mokken scale analysis is a non-parametric, item response theory approach to scale development which appears never to have been applied to household asset data. A Mokken scale can be used to rank order items (measures of wealth) as well as households. Using data on household asset ownership from a national sample of 4,154 consenting households in the World Health Survey from Vietnam, 2003, we construct two measures of household SEP. Seventeen items asking about assets, and utility and infrastructure use were used. Mokken Scaling and PCA were applied to the data. A single item measure of total household expenditure is used as a point of contrast. RESULTS: An 11 item scale, out of the 17 items, was identified that conformed to the assumptions of a Mokken Scale. All the items in the scale were identified as strong items (Hi > .5). Two PCA measures of SEP were developed as a point of contrast. One PCA measure was developed using all 17 available asset items, the other used the reduced set of 11 items identified in the Mokken scale analaysis. The Mokken Scale measure of SEP and the 17 item PCA measure had a very high correlation (r = .98), and they both correlated moderately with total household expenditure: r = .59 and r = .57 respectively. In contrast the 11 item PCA measure correlated moderately with the Mokken scale (r = .68), and weakly with the total household expenditure (r = .18). CONCLUSION: The Mokken scale measure of household SEP performed at least as well as PCA, and outperformed the PCA measure developed with the 11 items used in the Mokken scale. Unlike PCA, Mokken scaling carries no assumptions about the underlying shape of the distribution of the data, and can be used simultaneous to order household SEP and items. The approach, however, has not been tested with data from other countries and remains an interesting, but under researched approach

Over-expression of lysophosphatidic acid receptor-2 in human invasive ductal carcinoma

INTRODUCTION: Lysophosphatidic acid (LPA) is a bioactive phospholipid with diverse effects on various cells. It interacts with at least three G-protein-coupled transmembrane receptors, namely LPA1, LPA2 and LPA3, whose expression in various tumours has not been fully characterized. In the present study we characterized the expression profile of LPA receptors in human breast cancer tissue and assessed the possible roles of each receptor. METHODS: The relative expression levels of each receptor's mRNA against β-actin mRNA was examined in surgically resected invasive ductal carcinomas and normal gland tissue using real-time RT-PCR. LPA2 expression was also examined immunohistochemically using a rat anti-LPA2 monoclonal antibody. RESULTS: In 25 cases normal and cancer tissue contained LPA1 mRNA at similar levels, whereas the expression level of LPA2 mRNA was significantly increased in cancer tissue as compared with its normal counterpart (3479.0 ± 426.6 versus 1287.3 ± 466.8; P < 0.05). LPA3 was weakly expressed in both cancer and normal gland tissue. In 48 (57%) out of 84 cases, enhanced expression of LPA2 protein was confirmed in carcinoma cells as compared with normal mammary epithelium by immunohistochemistry. Over-expression of LPA2 was detected in 17 (45%) out of 38 premenopausal women, as compared with 31 (67%) out of 46 postmenopausal women, and the difference was statistically significant (P < 0.05). CONCLUSION: These findings suggest that upregulation of LPA2 may play a role in carcinogenesis, particularly in postmenopausal breast cancer

Investigation of Semiconductor Quantum Dots for Waveguide Electroabsorption Modulator

In this work, we investigated the use of 10-layer InAs quantum dot (QD) as active region of an electroabsorption modulator (EAM). The QD-EAM is a p-i-n ridge waveguide structure with intrinsic layer thickness of 0.4 μm, width of 10 μm, and length of 1.0 mm. Photocurrent measurement reveals a Stark shift of ~5 meV (~7 nm) at reverse bias of 3 V (75 kV/cm) and broadening of the resonance peak due to field ionization of electrons and holes was observed for E-field larger than 25 kV/cm. Investigation at wavelength range of 1,300–1320 nm reveals that the largest absorption change occurs at 1317 nm. Optical transmission measurement at this wavelength shows insertion loss of ~8 dB, and extinction ratio of ~5 dB at reverse bias of 5 V. Consequently, methods to improve the performance of the QD-EAM are proposed. We believe that QDs are promising for EAM and the performance of QD-EAM will improve with increasing research efforts

Non-relativistic Matrix Inflation

We reconsider a string theoretic inflationary model, where inflation is driven by $n$ multiple coincident $D3$-branes in the finite $n$ limit. We show that the finite $n$ action can be continued to the limit of large $n$, where it converges to the action for a wrapped $D5$-brane with $n$ units of U(1) flux. This provides an important consistency check of the scenario and allows for more control over certain back-reaction effects. We determine the most general form of the action for a specific sub-class of models and examine the non-relativistic limits of the theory where the branes move at speeds much less than the speed of light. The non-Abelian nature of the world-volume theory implies that the inflaton field is matrix valued and this results in modifications to the slow-roll parameters and Hubble-flow equations. A specific small field model of inflation is investigated where the branes move out of an AdS throat, and observational constraints are employed to place bounds on the background fluxes.Comment: 25 page

Cyclooxygenase-2 inhibition: effects on tumour growth, cell cycling and lymphangiogenesis in a xenograft model of breast cancer

Cyclooxygenase-2 (COX-2) is associated with poor-prognosis breast cancer. We used a nude mouse xenograft model to determine the effects of COX-2 inhibition in breast cancer. Oestrogen receptor (ER)-positive MCF7/HER2-18 and ER-negative MDAMB231 breast cancer cell lines were injected into nude mice and allowed to form tumours. Mice then received either chow containing Celecoxib (a COX-2 inhibitor) or control and tumour growth measured. Tumour proliferation, apoptosis, COX-2, lymphangiogenesis and angiogenesis were assessed by immunohistochemistry (IHC), Western blotting or Q-PCR. Celecoxib inhibited median tumour growth in MCF7/HER2-18 (58.7%, P=0.029) and MDAMB231 (46.3%, P=0.0002) cell lines compared to control. Cyclooxygenase-2 expression decreased following Celecoxib treatment (MCF7/HER2-18 median control 65.3% vs treated 22.5%, P=0.0001). Celecoxib increased apoptosis in MCF7/HER2-18 tumours (TUNEL 0.52% control vs 0.73% treated, P=0.0004) via inactivation of AKT (median pAKTser473 57.3% control vs 35.5% treated, P=0.0001 – confirmed at Western blotting). Q-PCR demonstrated decreased podoplanin RNA (lymphangiogenesis marker) in the MCF7/HER2-18 – median 2.9 copies treated vs 66.6 control (P=0.05) and MDAMB231-treated groups – median 160.7 copies vs 0.05 control copies (P=0.015), confirmed at IHC. Cyclooxygenase-2 is associated with high levels of activated AKTser473 and lymphangiogenesis in breast cancer. Cyclooxygenase-2 inhibition decreases tumour growth, and may potentially decrease recurrence, by inactivating AKT and decreasing lymphangiogenesis