Autobiographical Accounts of Students' Experiences Learning Mathematics: A Review

ABSTRACT

In this article, we review published literature that draws on autobiographical accounts of students' experiences learning mathematics. We summarize the main findings of the target literature and present recommendations for further research that will extend this field. Our review indicates that autobiographical and narrative methodological approaches have the potential to occasion important advances in our knowledge of students' experiences learning mathematics. However, relative to accounts of preservice teacher learning, there is a paucity of published research that documents the mathematics learning experiences of kindergarten to Grade 12 students.     

Optical scintillations and fade statistics for a satellite-communication system

Estimates of the scintillation index, fractional fade time, expected number of fades, and mean duration of fade time associated with a propagating Gaussian-beam wave are developed for uplink and downlink laser satellite-communication channels. Estimates for the spot size of the beam at the satellite or the ground or airborne receiver are also provided. Weak-fluctuation theory based on the log-normal model is applicable for intensity fluctuations near the optical axis of the beam provided that the zenith angle is not too large, generally not exceeding 60°. However, there is an increase in scintillations that occurs with increasing pointing error at any zenith angle, particularly for uplink channels. Large off-axis scintillations are of particular significance because they imply that small pointing errors can cause serious degradation in the communication-channel reliability. Off-axis scintillations increase more rapidly for larger-diameter beams and, in some cases, can lead to a radial saturation effect for pointing errors less than 1 μrad off the optical beam axis.     

Measurement-based modeling of contact forces and textures for haptic rendering

Haptic texture represents the fine-grained attributes of an object's surface and is related to physical characteristics such as roughness and stiffness. We introduce an interactive and mobile scanning system for the acquisition and synthesis of haptic textures that consists of a visually tracked handheld touch probe. The most novel aspect of our work is an estimation method for the contact stiffness of an object based solely on the acceleration and forces measured during stroking of its surface with the handheld probe. We establish an experimental relationship between the estimated stiffness and the contact stiffness observed during compression. We also measure the height-displacement profile of an object's surface enabling us to generate haptic textures. We show an example of mapping the textures on to a coarse surface mesh obtained with an image-based technique, but the textures may also be combined with coarse surface meshes obtained by manual modeling.     

Scalability issues with using FSMWeb to test web applications

Web applications are fast becoming more widespread, larger, more interactive, and more essential to the international use of computers. It is well understood that web applications must be highly dependable, and as a field we are just now beginning to understand how to model and test Web applications. One straightforward technique is to model Web applications as finite state machines. However, large numbers of input fields, input choices and the ability to enter values in any order combine to create a state space explosion problem. This paper evaluates a solution that uses constraints on the inputs to reduce the number of transitions, thus compressing the FSM. The paper presents an analysis of the potential savings of the compression technique and reports actual savings from two case studies.     

Creating corroborated crisis reports from social media data through formal concept analysis

During a crisis citizens reach for their smart phones to report, comment and explore information surrounding the crisis. These actions often involve social media and this data forms a large repository of real-time, crisis related information. Law enforcement agencies and other first responders see this information as having untapped potential. That is, it has the capacity extend their situational awareness beyond the scope of a usual command and control centre. Despite this potential, the sheer volume, the speed at which it arrives, and unstructured nature of social media means that making sense of this data is not a trivial task and one that is not yet satisfactorily solved; both in crisis management and beyond. Therefore we propose a multi-stage process to extract meaning from this data that will provide relevant and near real-time information to command and control to assist in decision support. This process begins with the capture of real-time social media data, the development of specific LEA and crisis focused taxonomies for categorisation and entity extraction, the application of formal concept analysis for aggregation and corroboration and the presentation of this data via map-based and other visualisations. We demonstrate that this novel use of formal concept analysis in combination with context-based entity extraction has the potential to inform law enforcement and/or humanitarian responders about on-going crisis events using social media data in the context of the 2015 Nepal earthquake.     

A Linear Variational System for Modelling From Curves

We present a linear system for modelling 3D surfaces from curves. Our system offers better performance, stability and precision in control than previous non‐linear systems. By exploring the direct relationship between a standard higher‐order Laplacian editing framework and Hermite spline curves, we introduce a new form of Cauchy constraint that makes our system easy to both implement and control. We introduce novel workflows that simplify the construction of 3D models from sketches. We show how to convert existing 3D meshes into our curve‐based representation for subsequent editing and modelling, allowing our technique to be applied to a wide range of existing 3D content.     

Parallel Algorithms for Maximum Matching in Complements of Interval Graphs and Related Problems

Given a set of n intervals representing an interval graph, the problem of finding a maximum matching between pairs of disjoint (nonintersecting) intervals has been considered in the sequential model. In this paper we present parallel algorithms for computing maximum cardinality matchings among pairs of disjoint intervals in interval graphs in the EREW PRAM and hypercube models. For the general case of the problem, our algorithms compute a maximum matching in O( log ³ n) time using O(n/ log ² n) processors on the EREW PRAM and using n processors on the hypercubes. For the case of proper interval graphs, our algorithm runs in O( log n ) time using O(n) processors if the input intervals are not given already sorted and using O(n/ log n ) processors otherwise, on the EREW PRAM. On n -processor hypercubes, our algorithm for the proper interval case takes O( log n log log n ) time for unsorted input and O( log n ) time for sorted input. Our parallel results also lead to optimal sequential algorithms for computing maximum matchings among disjoint intervals. In addition, we present an improved parallel algorithm for maximum matching between overlapping intervals in proper interval graphs. Received November 20, 1995; revised September 3, 1998.     

Predicting Interfacial Loads between the Prosthetic Socket and the Residual Limb for Below-Knee Amputees – A Case Study

Abstract:  In this study, an artificial neural network (ANN) was deployed as a tool to determine the internal loads between the residual limb and prosthetic socket for below-knee amputees. This was achieved by using simulated load data to validate the ANN and captured clinical load data to predict the internal loads at the residual limb–socket interface. Load/pressure was applied to 16 regions of the socket, using loading pads in conjunction with a load applicator, and surface strains were collected using 15 strain gauge rosettes. A super-position program was utilised to generate training and testing patterns from the original load/strain data collected. Using this data, a back-propagation ANN, developed at the University of the West of England, was trained. The input to the trained network was the surface strains and the output the internal loads/pressure. The system was validated and the mean square error (MSE) of the system was found to be 8.8% for 1000 training patterns and 8.9% for 50 testing patterns, which was deemed an acceptable error. Finally, the validated system was used to predict pressure-sensitive/-tolerant regions at the limb–socket interface with great success.     

Assessing Positive and Negative Changes in the Aftermath of Adversity: Psychometric Evaluation of the Changes in Outlook Questionnaire.

The Changes in Outlook Questionnaire (CiOQ; S. Joseph, R. Williams, & W. Yule, 1993) is a 26-item self-report measure that was designed to assess positive and negative changes in the aftermath of adversity. This article had 3 aims: 1st, to investigate the factor structure of the CiOQ; 2nd, to test for internal consistency reliability and convergent and discriminant validity; and, 3rd, to investigate the association between positive and negative changes in outlook, posttraumatic stress, and psychological distress. Three studies are reported. Study 1 provides evidence that positive and negative changes are statistically separable and that the 2-factor model is a better fit than the 1-factor model. Studies 2 and 3 provide evidence for internal consistency reliability, convergent and discriminant validity of the CiOQ, and its associations with posttraumatic stress and psychological distress. In conclusion, the CiOQ has much promise for research on responses to stressful and traumatic events. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Programming models for hybrid CPU/FPGA chips

Designers of embedded and real-time systems are continually challenged to meet tighter system requirements at better price-performance ratios. Best-practice methods have long promoted the use of commercial-off-the-shelf components to reduce design costs and time to market, but creating COTS components that are reusable in a wide range of applications remains difficult. In part, the challenge lies in satisfying the contradictory design forces of generalization and specialization. Systems designers are all too familiar with the tension these opposing forces cause in trying to balance cost versus performance. Adopting COTS components reduces costs and time to market but often fails to meet the most demanding performance requirements; custom-designed components can achieve significantly higher performance but at greater development costs and longer times to market. Emerging hybrid chips containing both CPU and field-programmable gate array (FPGA) components are an exciting new development. They promise COTS economies of scale while also supporting significant hardware customization. Components that combine a CPU and reconfigurable logic gates need a programming model that abstracts the computational hardware.