Exploring pedagogy with interactiue whiteboards in Australian schools

This research project investigated the use of interactive whiteboards (IWBs) in K-12 education. Exploration of the use of IWBs in six different school settings provided insights into the activities, approaches, roles and beliefs of students and teachers in a range of primary and secondary class contexts and discipline areas. The study was informed by socio-cultural theory and a major focus was on the interactions between the new technology, pedagogy and the social conditions of the classroom. The findings presented in this paper focus on the pedagogical aspects of using IWBs that emerged from the study

Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time

We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. The results from numerical simulations are in excellent agreement with our analytical predictions.Comment: 13 pages, 5 figures. Published in Journal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech. (2007) P10008, doi:10.1088/1742-5468/2007/10/P10008

An exactly solvable self-convolutive recurrence

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the $n$th coefficient is expressed as the $(n-1)$th moment of a measure, and also as the trace of the $(n-1)$th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics

Area distribution and the average shape of a L\'evy bridge

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the area A = \sum_{m=1}^n x_B(m) under such a L\'evy bridge and show that, for large n, it has the scaling form P_B(A,n) \sim n^{-1-1/\alpha} F_\alpha(A/n^{1+1/\alpha}), with the asymptotic behavior F_\alpha(Y) \sim Y^{-2(1+\alpha)} for large Y. For \alpha=1, we obtain an explicit expression of F_1(Y) in terms of elementary functions. We also compute the average profile < \tilde x_B (m) > at time m of a L\'evy bridge with fixed area A. For large n and large m and A, one finds the scaling form = n^{1/\alpha} H_\alpha({m}/{n},{A}/{n^{1+1/\alpha}}), where at variance with Brownian bridge, H_\alpha(X,Y) is a non trivial function of the rescaled time m/n and rescaled area Y = A/n^{1+1/\alpha}. Our analytical results are verified by numerical simulations.Comment: 21 pages, 4 Figure

Temporal-Difference Learning to Assist Human Decision Making during the Control of an Artificial Limb

In this work we explore the use of reinforcement learning (RL) to help with human decision making, combining state-of-the-art RL algorithms with an application to prosthetics. Managing human-machine interaction is a problem of considerable scope, and the simplification of human-robot interfaces is especially important in the domains of biomedical technology and rehabilitation medicine. For example, amputees who control artificial limbs are often required to quickly switch between a number of control actions or modes of operation in order to operate their devices. We suggest that by learning to anticipate (predict) a user's behaviour, artificial limbs could take on an active role in a human's control decisions so as to reduce the burden on their users. Recently, we showed that RL in the form of general value functions (GVFs) could be used to accurately detect a user's control intent prior to their explicit control choices. In the present work, we explore the use of temporal-difference learning and GVFs to predict when users will switch their control influence between the different motor functions of a robot arm. Experiments were performed using a multi-function robot arm that was controlled by muscle signals from a user's body (similar to conventional artificial limb control). Our approach was able to acquire and maintain forecasts about a user's switching decisions in real time. It also provides an intuitive and reward-free way for users to correct or reinforce the decisions made by the machine learning system. We expect that when a system is certain enough about its predictions, it can begin to take over switching decisions from the user to streamline control and potentially decrease the time and effort needed to complete tasks. This preliminary study therefore suggests a way to naturally integrate human- and machine-based decision making systems.Comment: 5 pages, 4 figures, This version to appear at The 1st Multidisciplinary Conference on Reinforcement Learning and Decision Making, Princeton, NJ, USA, Oct. 25-27, 201

Designing personalised, authentic and collaborative learning with mobile devices: Confronting the challenges of remote teaching during a pandemic.

This article offers teachers a digital pedagogical framework, research-inspired and underpinned by socio-cultural theory, to guide the design of personalised, authentic and collaborative learning scenarios for students using mobile devices in remote learning settings during this pandemic. It provides a series of freely available online resources underpinned by our framework, including a mobile learning toolkit, a professional learning app, and robust, validated surveys for evaluating tasks. Finally, it presents a set of evidence-based principles for effective innovative teaching with mobile devices

Innovative mobile learning: A scan of the literature

© 2019 IADIS Press. All rights reserved. This paper summarises findings from an initial study completed as the first phase of the Erasmus+ KA2 research project: Designing and Evaluating Innovative Mobile Pedagogies (DEIMP). The purpose of the scoping study was to inform the design and development of a multi-purpose mobile app that will support educators and pre-service teachers in designing and evaluating creative and innovative mobile learning episodes for their students. This first component of the DEIMP study involved the conduct of a Systematic Literature Review to identify innovative and effective practices in m-Learning. A set of 57 articles were identified as reporting on innovative mobile practices and these were further assessed for their level of innovation. The study showed that innovation lies on a continuum from sustaining innovation to disruptive innovation and that disruptive innovation is infrequent

Mobagogy- mobile learning for a higher education community

This paper reports on a project in which a learning community of higher educators was formed to investigate how best to use mobile technologies in their own learning and teaching. Activities of this group included investigating best practice approaches by interviewing experts in the field, exploring the literature on mobile learning and then initiating and testing some mobile learning pedagogies in the context of their own higher education subjects. The community met regularly to discuss emerging issues and applications. The paper shares some of the findings gained both from the expert interviews and from the experiences of members of the community, and discusses the challenges and constraints that were experienced. We conclude with recommendations for promoting mobile learning communities in higher education. © 2010 IADIS

Precise Asymptotics for a Random Walker's Maximum

We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum E[M_n] of the walk up to n steps behaves asymptotically for large n as, E[M_n]/\sigma=\sqrt{2n/\pi}+ \gamma +O(n^{-1/2}), where \sigma^2 is the variance of the step lengths. While the leading \sqrt{n} behavior is universal and easy to derive, the leading correction term turns out to be a nontrivial constant \gamma. For the special case of uniform distribution over [-1,1], Coffmann et. al. recently computed \gamma=-0.516068...by exactly enumerating a lengthy double series. Here we present a closed exact formula for \gamma valid for arbitrary symmetric distributions. We also demonstrate how \gamma appears in the thermodynamic limit as the leading behavior of the difference variable E[M_n]-E[|x_n|] where x_n is the position of the walker after n steps. An application of these results to the equilibrium thermodynamics of a Rouse polymer chain is pointed out. We also generalize our results to L\'evy walks.Comment: new references added, typos corrected, published versio