Innovative teaching strategies: enhancing the soft-skilloriented approach through integrated onsite-online learning environments

ABSTRACT The integration of ICT in Higher Education requires reflective design by teachers. In particular, from recent international research on the subject, it emerges that the perspective of the TPCK framework (Technological, Pedagogical, Content Knowledge) can favour an effective design reasoning of teachers. Teaching practice requires the implementation of innovative organizational models for the creation of learning environments that offer continuity between classroom and distance learning (Hybrid Instruction Solution). The empirical mix-method research involved a group of volunteer teachers of different teachings. The objective was to design and implement innovative teaching solutions using ICT in onsite/online environments to enhance specific soft skills in students. The results of a questionnaire (CAWI) given to incoming and outgoing teachers from the experience of designing and conducting the didactic action will be presented. the TPCK perspective design of integrated learning environments and the reasoned choice of coherent methodologies seem to make a soft-skilloriented didactics feasible

Teacher education for effective technology integration

About a decade ago, several researchers used Shulman's (1986) framework about Pedagogical Content Knowledge (PCK) - a body of knowledge that constitutes a special amalgam of content, pedagogy, learners, and context - as a theoretical basis for developing TPCK or TPACK: a framework for guiding teachers' cognition about technology integration in teaching and learning (Angeli, Valanides, & Christodoulou, 2016). Different models of TPCK/TPACK are proposed in the literature, each with a different focus (on practice, instructional design, context, etc.) and with a different theoretical interpretation about the nature and development of the knowledge that teachers need to have to be able to teach with technology (e.g., Angeli & Valanides, 2005, 2009, 2013; Koehler & Mishra, 2008; Niess, 2005).In this direction, research is being carried out to identify TPCK design procedures for initial teacher education. In teaching, when transferring TPCK to design and methodological practices, there is a need to consider a number of factors, especially: the different modes of adopting technologies; the integration of tool affordances, content and pedagogy; the implementation of learning environments; the operationalization of knowledge; and detailed analysis of teaching models and approache

Hybrid spherical approximation

In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical harmonics as local approximants. Moreover, a spherical zone algorithm is efficiently implemented, which works well also when the amount of data is very large, since it is based on an optimized searching procedure. Numerical results show good accuracy of the method, also on real geomagnetic data

Saturation Assumption and Finite Element Method for a One-Dimensional Model

In this paper we refer to the hierarchical finite element method and stabilization techniques for convection–diffusion equations. In particular, the aim is to outline an application of saturation assumption to a posteriori error estimates for such problems. We consider here a simple one–dimensional model; the inequality is proved from an analitical point of view for the stabilized finite element solutions in two cases: artificial diffusion and SUPG stabilization techniques

A trivariate interpolation algorithm using a cube-partition searching procedure

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

Time-Varying Quantiles

A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. Quantiles estimated in this way provide information on various aspects of a time series, including dispersion, asymmetry and, for financial applications, value at risk. Tests for the constancy of quantiles, and associated contrasts, are constructed using indicator variables; these tests have a similar form to stationarity tests and, under the null hypothesis, their asymptotic distributions belong to the Cramér von Mises family. Estimates of the quantiles at the end of the series provide the basis for forecasting. As such they offer an alternative to conditional quantile autoregressions and, at the same time, give some insight into their structure and potential drawbacks

Quantiles, Expectiles and Splines

A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. It is shown that such time-varying quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Expectiles are similar to quantiles except that they are defined by tail expectations. Like quantiles, time varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties that generalize the moment conditions associated with fixed expectiles. Time-varying quantiles and expectiles provide information on various aspects of a time series, such as dispersion and asymmetry, while estimates at the end of the series provide the basis for forecasting. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be easily adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions

Efficient computation of partition of unity interpolants through a block-based searching technique

In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weight functions. In particular we present a new space-partitioning data structure based on a partition of the underlying generic domain in blocks. This approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points, leading to an optimized searching routine. Complexity analysis and numerical experiments in two- and three-dimensional interpolation support our findings. Some applications to geometric modelling are also considered. Moreover, the associated software package written in \textsc{Matlab} is here discussed and made available to the scientific community

Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data on the Sphere and Other Manifolds

We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the combination coefficients being incomplete Taylor expansions of the interpolated function at the interpolation points. The basis functions have the following features: (i) depend on the geodesic distance; (ii) are orthonormal with respect to the point-evaluation functionals; and (iii) have all derivatives equal zero up to a certain order at the interpolation points. Moreover, the construction of such interpolants, which belong to the class of partition of unity methods, takes advantage of not requiring any solution of linear systems

Local interpolation schemes for landmark-based image registration: a comparison

In this paper we focus, from a mathematical point of view, on properties and performances of some local interpolation schemes for landmark-based image registration. Precisely, we consider modified Shepard's interpolants, Wendland's functions, and Lobachevsky splines. They are quite unlike each other, but all of them are compactly supported and enjoy interesting theoretical and computational properties. In particular, we point out some unusual forms of the considered functions. Finally, detailed numerical comparisons are given, considering also Gaussians and thin plate splines, which are really globally supported but widely used in applications