Audit of mathematics learning support in Ireland in 2015 – the key findings

In 2015 the Irish Mathematics Learning Support Network (IMLSN) commissioned a comprehensive audit of the extent and nature of mathematics learning support (MLS) provision on the island of Ireland. An online survey was sent to 32 institutions, including universities, institutes of technology, further education and teacher training colleges, and a 97% response rate was achieved. While the headline figure – 84% of institutions that responded to the survey provide MLS – sounds good, deeper analysis reveals that the true state of MLS is not so solid. For example, in 25% of institutions offering MLS, only five hours per week (at most) of physical MLS are available, while in 20% of institutions the service is provided by only one or two staff members. Furthermore, training of tutors is minimal or non-existent in at least half of the institutions offering MLS. The results provide an illuminating picture, however, identifying the true state of MLS in Ireland is beneficial only if it informs developments in the years ahead. This talk will present some of the findings of the survey in more depth along with conclusions and recommendations. Key among these is the need for institutions to recognise MLS as a vital element of mathematics teaching and learning strategy at third level and devote the necessary resources to facilitate the provision of a service which can grow and adapt to meet student requirements.

A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

The control and learning of patterns of interlimb coordination: past and present issues in normal and disordered control

The present paper provides a historical note on the evolution of the behavioral study of interlimb coordination and the reasons for its success as a field of investigation in the past decades. Whereas the original foundations for this field of science were laid down back in the seventies, it has steadily grown in the past decades and has attracted the attention of various scientific disciplines. A diversity of topics is currently being addressed and this is also expressed in the present contributions to the special issue. The main theme is centered on the brain basis of interlimb coordination. On the one hand, this pertains to the study of the control and learning of patterns of interlimb coordination in clinical groups. On the other hand, basic neural approaches are being merged together with behavioral approaches to reveal the neural basis of interlimb coordination. (C) 2002 Elsevier Science B.V. All rights reserved.

Computational learning of the conditional phase-type (C-Ph) distribution: Learning C-Ph distributions

This paper presents a new algorithm for learning the structure of a special type of Bayesian network. The conditional phase-type (C-Ph) distribution is a Bayesian network that models the probabilistic causal relationships between a skewed continuous variable, modelled by the Coxian phase-type distribution, a special type of Markov model, and a set of interacting discrete variables. The algorithm takes a dataset as input and produces the structure, parameters and graphical representations of the fit of the C-Ph distribution as output.The algorithm, which uses a greedy-search technique and has been implemented in MATLAB, is evaluated using a simulated data set consisting of 20,000 cases. The results show that the original C-Ph distribution is recaptured and the fit of the network to the data is discussed.

A systematic review evaluating the impact of online or blended learning vs. face-to-face learning of clinical skills in undergraduate nurse education.

Aim: To determine whether the use of an online or blended learning paradigm has the potential to enhance the teaching of clinical skills in undergraduate nursing.

Background: The need to adequately support and develop students in clinical skills is now arguably more important than previously considered due to reductions in practice opportunities. Online and blended teaching methods are being developed to try and meet this requirement, but knowledge about their effectiveness in teaching clinical skills is limited.

Design: Mixed methods systematic review, which follows the Joanna Briggs Institute User guide version 5.

Data Sources: Computerized searches of five databases were undertaken for the period 1995-August 2013.

Review Methods: Critical appraisal and data extraction were undertaken using Joanna Briggs Institute tools for experimental/observational studies and interpretative and critical research. A narrative synthesis was used to report results.

Results: Nineteen published papers were identified. Seventeen papers reported on online approaches and only two papers reported on a blended approach. The synthesis of findings focused on the following four areas: performance/clinical skill, knowledge, self-efficacy/clinical confidence and user experience/satisfaction. The e-learning interventions used varied throughout all the studies.

Conclusion: The available evidence suggests that online learning for teaching clinical skills is no less effective than traditional means. Highlighted by this review is the lack of available evidence on the implementation of a blended learning approach to teaching clinical skills in undergraduate nurse education. Further research is required to assess the effectiveness of this teaching methodology.

Efficient Structure Learning of Bayesian Networks using Constraints

This paper addresses the problem of learning Bayesian network structures from data based on score functions that are decomposable. It describes properties that strongly reduce the time and memory costs of many known methods without losing global optimality guarantees. These properties are derived for different score criteria such as Minimum Description Length (or Bayesian Information Criterion), Akaike Information Criterion and Bayesian Dirichlet Criterion. Then a branch-and-bound algorithm is presented that integrates structural constraints with data in a way to guarantee global optimality. As an example, structural constraints are used to map the problem of structure learning in Dynamic Bayesian networks into a corresponding augmented Bayesian network. Finally, we show empirically the benefits of using the properties with state-of-the-art methods and with the new algorithm, which is able to handle larger data sets than before.