Mentoring as professional development: ‘growth for both’ mentor and mentee

Teachers need professional development to keep current with teaching practices, although costs for extensive professional development can be prohibitive across an education system. Mentoring provides one way for embedding cost-effective professional development. This mixed-method study includes surveying mentor teachers (n = 101) on a five-part Likert scale and interviews with experienced mentors (n = 10) to investigate professional development for mentors as a result of the mentoring process. Quantitative data were analysed through a pedagogical knowledge framework and qualitative data were collated into themes. Survey data showed that although mentoring of pedagogical knowledge was variable, mentoring pedagogical knowledge practices occurs with the majority of mentors, which requires mentors to evaluate and articulate teaching practices. Qualitative data showed that mentoring acted as professional development and led towards enhancing communication skills, developing leadership roles (problem-solving and building capacity) and advancing pedagogical knowledge. Providing professional development to teachers on mentoring can help to build capacity in two ways: quality mentoring of preservice teachers through explicit mentoring practices, and reflecting and deconstructing teaching practices for mentors’ own pedagogical advancements.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

New Perspectives On Firm Growth

This insightful volume presents a collection of innovative works by two of the leading researchers of firm growth: Per Davidsson, Director, Australian Centre for Entrepreneurship Research and Professor of Entrepreneurship, Queensland University of Technology, Australia and Jönköping International Business School, Sweden and Johan Wiklund, Professor of Entrepreneurship, Syracuse University, US and Jönköping International Business School, Sweden. The studies extend previous research by providing stronger theoretical underpinnings and using longitudinal databases that can separate in time the firms’ growth from its presumed causes. They also break new ground by examining different modes of growth, such as sales growth vs. employment growth, and organic growth vs. acquisition-based expansion. Further, the studies investigate the drivers of firm growth and take a critical look at the effects, such as under what circumstances high growth is associated with high profitability. The issue of how firm growth is achieved and managed, and what consequences it has for different stakeholders is both theoretically interesting and practically important. The book will strongly appeal to academics of entrepreneurship, small business management and strategy.

Asset specificity and behavioral uncertainty as moderators of the sales growth-employment growth relationship in emerging ventures

New venture growth is a central topic in entrepreneurship research. Although sales growth is emerging as the most commonly used measure of growth for emerging ventures, employment growth has also been used frequently. However, empirical research demonstrates that there are only very low to moderately sized correlations between the two (Delmar et aL, 2003; Weinzimmer, et al., 1998). In addition) sales growth and employment growth respond differently to a wide variety of criteria (Baum et al., 2001; Delmar et al., 2003). In this study we use transaction cost economics (Williamson, 1996) as a theoretical base to examine transaction cost influences on the addition of new employees as emerging ventures experience sales growth. \\le theorize that transaction cost economics variables will moderate the relationship between sales growth and employment growth. W'e develop and test hypotheses related to asset specificity, behavioral uncertainty, and the influence of resource munificence on the strength of the sales growth/ employment growth relationship. Asset specificity is theorized to be a positive moderator of the relationship between sales growth and employment growth. When the behavioral uncertainty associated with adding new employees is greater than that of outsourcing or subcontracting, it is hypothesized to be a negative moderator of the sales growth/employment growth relationship. We also hypothesize that resource scarcity will strengthen those relationships.

Towards an integrative framework for future research on small firm growth

Our review has demonstrated that small firm growth is a complex phenomenon. The concept ‘growth’ denotes both a change in amount and the process by which that change is attained. Further, the growth can be achieved in different ways and with varying degrees of regularity, and it manifests itself along several different dimensions such as sales, employment, and accumulation of assets. This complexity has naturally led researchers to adopt different approaches to studying growth and to use different measures to assess it. Further, although our review shows that it can fruitfully be regarded as a growth issue, the research on small firms' internationalization has largely developed as a separate stream. Similarly, other relatively separate literatures have evolved, which effectively focus on different modes of growth although mostly without regarding the studies first and foremost as growth studies. This goes for topics such as mergers and acquisitions, diversification, and integration - research streams which have largely ignored the particularities of small firms and which in turn have been largely ignored among researchers focusing on small firm growth.

Organic and acquisitive growth : re-examining, testing and extending Penrose’s growth theory

The Theory of the Growth of The Firm by Edith Penrose, first published in 1959, is a seminal contribution to the field of management. Penrose's intention was to create a theory of firm growth which was logically consistent and empirically tractable (Buckley and Casson, 2007). Much attention, however, has been focused on her unintended contribution to the resource-based view (henceforth RBV) (e.g. Kor and Mahoney, 2004; Lockett and Thompson, 2004) rather than her firm growth theory. We feel that this is unfortunate because despite a rapidly growing body of empirical work, conceptual advancement in growth studies has been limited (Davidsson and Wiklund, 2000; Davidsson et ai., 2006; Delmar, 1997; Storey, 1994). The growth literature frequently references Penrose's work, but little explicit testing of her ideas has been undertaken. This is surprising given that Penrose's work remains the most comprehensive theory of growth to date. One explanation is that she did not formality present her arguments, favouring verbal exposition over formalized models (Lockett, 2005; Lockett and Thompson, 2004). However, the central propositions and conclusions of her theory can be operationalized and empirically tested.

Performance configurations over time: implications for growth-and profit-oriented strategies

Entrepreneurship research and practice places emphasis on company growth as a measure of entrepreneurial success. In many cases, there has been a tendency to give growth a very central role, with some researchers even seeing growth as the very essence of entrepreneurship (Cole, 1949; Sexton, 1997; Stevenson & Gumpert, 1991). A large number of empirical studies of the performance of young and/or small firms use growth as the dependent variable (see reviews by Ardishvili, Cardozo, Harmon, & Vadakath, 1998; Delmar, 1997; Wiklund, 1998). By contrast, the two most prominent views of strategic management – strategic positioning (Porter, 1980) and the resource-based view (Barney, 1991; Wernerfelt, 1984) – are both concerned with achieving competitive advantage and regard achieving economic rents and profitability relative to other competitors as the central measures of firm performance. Strategic entrepreneurship integrates these two perspectives and is simultaneously concerned with opportunity seeking and advantage seeking (Hitt, Ireland, Camp, & Sexton, 2002; Ireland, Hitt, & Sirmon, 2003). Consequently, both company growth and relative profitability are together relevant measures of firm performance in the domain of strategic entrepreneurship.

A potential role for lamellar insulin-like growth factor-1 receptor in the pathogenesis of hyperinsulinaemic laminitis

The reason why a sustained high concentration of insulin induces laminitis in horses remains unclear. Cell proliferation occurs in the lamellae during insulin-induced laminitis and in other species high concentrations of insulin can activate receptors for the powerful cell mitogen, insulin-like growth factor (IGF)-1. The first aim of this study was to determine if IGF-1 receptors (IGF-1R) are activated in the hoof during insulin-induced laminitis. Gene expression for IGF-1R and the insulin receptor (InsR) was measured using qRT-PCR, in lamellar tissue from control horses and from horses undergoing a prolonged euglycaemic, hyperinsulinaemic clamp (p-EHC), during the mid-developmental (24 h) and acute (46 h) phases of insulin-induced laminitis. Gene expression for both receptors was decreased 13–32-fold (P < 0.05) at both time-points in the insulin-treated horses. A second aim was to determine if the down-regulation of the receptor genes could be accounted for by an increase in circulating IGF-1. Serum IGF-1 was measured at 0, 10, 25 and 46 h post-treatment in horses given a p-EHC for approximately 46 h, and in matched controls administered a balanced, electrolyte solution. There was no increase in serum IGF-1 concentrations during the p-EHC, consistent with down-regulation of both receptors by insulin. Stimulation of the IGF-1R by insulin may lead to inappropriate lamellar epidermal cell proliferation and lamellar weakening, a potential mechanism for hyperinsulinaemic laminitis. Targeting this receptor may provide insights into the pathogenesis or identify a novel therapy for hyperinsulinaemic laminitis.

Insulin and the insulin-like growth factor system : a novel theory for hyperinsulinemic laminitis pathogenesis

Research into hyperinsulinemic laminitis has progressed significantly in recent years with the use of the prolonged-euglycemic, hyperinsulinemic clamp (p-EHC). Previous investigations of laminitis pathophysiology have focused on digital vascular dysfunction, inflammation, altered glucose metabolism within the lamellae, and lamellar basement membrane breakdown by metalloproteinases. The etiopathogenesis of laminitis occurring in association with hyperinsulinemia is yet to be fully characterized, but it may not involve these mechanisms. Insulin stimulates cellular proliferation and can also affect other body systems, such as the insulin-like growth factor (IGF) system. Insulin-like growth factor-1 (IGF-1) is structurally homologous to insulin and, like insulin, binds with strong affinity to a specific tyrosine kinase receptor on the cell surface to produce its effects, which include promoting cell proliferation. Receptors for IGF-1 (IGF-1R) are present in the lamellar epidermis. An alternative theory for the pathogenesis of hyperinsulinemic laminitis is that uncontrolled cell proliferation, mediated through both the insulin receptor (InsR) and IGF-1R, leads to lengthening, weakening, and failure of the lamellae. An analysis of the proliferative activity of lamellar epidermal cells during the developmental and acute phases of hyperinsulinemic laminitis, and lamellar gene expression of the InsR and IGF-1R was undertaken.

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

Layered silicates in Chondritic Porous Aggregate W7029*A : a case of primary growth

An important subset of extraterrestrial particles that reach the Earth's stratosphere include the so-called Chondritic Porous Aggregates (CPA's) [1-3]. In general, CPA's have a fluffy morphology and consist of numerous (>104)subparticles that are often <100A in size [4]. Mineral species in CPA's include Mg-rich pyroxene and olivine, Fe- and (Fe,Ni)-sulphides, taenite, Fe,Ni-carbides, magnetite, Ti-metal, a Bi-phase (metal or oxide), and variable amounts of carbonaceous material [1, 5-7]. Hydrated silicates are rare in CPA's and are limited to aggregates that have not been severely altered (thermo-metamorphosed) during atmospheric entry [8]. The presence of hydrated silicates in one cosmic dust particle was established by X-ray diffraction [2] and has been inferred in others by infra-red spectroscopy [8]. If CPA's are cometary, their mineralogy and morphology suggest that at least two episodes of aggregation occurred and that variations in porosity may be related to local differences in ice-to-dust ratio [3].

A novel numerical approximation for the space fractional advection-dispersion equation

In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

The analytical solution and numerical solution of the fractional diffusion-wave equation with damping

Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.