Mathematics Learning Support in Ireland in 2015

The provision of mathematics learning support in higher-level institutions on the island of Ireland has developed rapidly in recent times with the number of institutions providing some form of support doubling in the past seven years. The Irish Mathematics Learning Support Network aims to inform all mathematics support practitioners in Ireland on relevant issues. Consequently it was decided that a detailed picture of current provision was necessary. A comprehensive online survey was conducted to amass the necessary data. The ultimate aim of the survey is to benefit all mathematics support practitioners in Ireland, in particular those in third-level institutions who require further support to enhance the mathematical learning experience of their students. The survey reveals that the majority of Irish higher-level institutions provide mathematics learning support to some extent, with 65% doing so through a support centre. Learners of service mathematics are the primary users: first-year science, engineering and business undergraduates, with non-traditional students being a sizeable element. Despite the growing recognition for the need to offer mathematics learning support almost half of the centres are subject to annual review. Further, less than half the support offerings have a dedicated full-time manager, while 60% operate with a staff of five or fewer. The elevation of mathematics support as a viable and worthwhile career in order to attract and retain high quality staff is seen by many respondents as the crucial next phase of development.

Mathematical prerequisites for learning statistics in Psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates.

This study sought to extend earlier work by Mulhern and Wylie (2004) to investigate a UK-wide sample of psychology undergraduates. A total of 890 participants from eight universities across the UK were tested on six broadly defined components of mathematical thinking relevant to the teaching of statistics in psychology - calculation, algebraic reasoning, graphical interpretation, proportionality and ratio, probability and sampling, and estimation. Results were consistent with Mulhern and Wylie's (2004) previously reported findings. Overall, participants across institutions exhibited marked deficiencies in many aspects of mathematical thinking. Results also revealed significant gender differences on calculation, proportionality and ratio, and estimation. Level of qualification in mathematics was found to predict overall performance. Analysis of the nature and content of errors revealed consistent patterns of misconceptions in core mathematical knowledge , likely to hamper the learning of statistics.

A heterosynaptic learning rule for neural networks

In this article we intoduce a novel stochastic Hebb-like learning rule for neural networks that is neurobiologically motivated. This learning rule combines features of unsupervised (Hebbian) and supervised (reinforcement) learning and is stochastic with respect to the selection of the time points when a synapse is modified. Moreover, the learning rule does not only affect the synapse between pre- and postsynaptic neuron, which is called homosynaptic plasticity, but effects also further remote synapses of the pre-and postsynaptic neuron. This more complex form of synaptic plasticity has recently come under investigations in neurobiology and is called heterosynaptic plasticity. We demonstrate that this learning rule is useful in training neural networks by learning parity functions including the exclusive-or (XOR) mapping in a multilayer feed-forward network. We find, that our stochastic learning rule works well, even in the presence of noise. Importantly, the mean leaxning time increases with the number of patterns to be learned polynomially, indicating efficient learning.

Accurate image capturing control of bottle caps based on iterative learning control and Kalman filtering

This paper investigates camera control for capturing bottle cap target images in the fault-detection system of an industrial production line. The main purpose is to identify the targeted bottle caps accurately in real time from the images. This is achieved by combining iterative learning control and Kalman filtering to reduce the effect of various disturbances introduced into the detection system. A mathematical model, together with a physical simulation platform is established based on the actual production requirements, and the convergence properties of the model are analyzed. It is shown that the proposed method enables accurate real-time control of the camera, and further, the gain range of the learning rule is also obtained. The numerical simulation and experimental results confirm that the proposed method can not only reduce the effect of repeatable disturbances but also non-repeatable ones.

Is Our Students Learning - QuestionMark: Extending E-Assessment Systems for Adapative Marking and Feedback

Our key contribution is a flexible, automated marking system that adds desirable functionality to existing E-Assessment systems. In our approach, any given E-Assessment system is relegated to a data-collection mechanism, whereas marking and the generation and distribution of personalised per-student feedback is handled separately by our own system. This allows content-rich Microsoft Word feedback documents to be generated and distributed to every student simultaneously according to a per-assessment schedule.

The feedback is adaptive in that it corresponds to the answers given by the student and provides guidance on where they may have gone wrong. It is not limited to simple multiple choice which are the most prescriptive question type offered by most E-Assessment Systems and as such most straightforward to mark consistently and provide individual per-alternative feedback strings. It is also better equipped to handle the use of mathematical symbols and images within the feedback documents which is more flexible than existing E-Assessment systems, which can only handle simple text strings.

As well as MCQs the system reliably and robustly handles Multiple Response, Text Matching and Numeric style questions in a more flexible manner than Questionmark: Perception and other E-Assessment Systems. It can also reliably handle multi-part questions where the response to an earlier question influences the answer to a later one and can adjust both scoring and feedback appropriately.

New question formats can be added at any time provided a corresponding marking method conforming to certain templates can also be programmed. Indeed, any question type for which a programmatic method of marking can be devised may be supported by our system. Furthermore, since the student’s response to each is question is marked programmatically, our system can be set to allow for minor deviations from the correct answer, and if appropriate award partial marks.