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.     

Treating achalasia: from whalebone to laparoscope

Reports of bile duct injuries are from tertiary care institutions and, therefore, may not report the spectrum of management that these patients receive in the care of these injuries. From June 14,1990 (the first operation) to June 30, 1995, 2654 laparoscopic cholecystectomies (LCs) were reviewed at this community hospital medical center to determine risk factors contributing to the etiology of these injuries, time and symptoms at presentation, duration of illness, and management of these injuries. None of the 13 general surgeons practicing during this time period had laparoscopic training in a general surgical residency. There were six major bile duct injuries (0.25%), of which five were available for further review. All occurred in women with cholelithiasis and chronic cholecystitis. Two operations were routine and two were associated with biliary tract anomalies. In two patients, the injuries were detected at LCs and definitive biliary-enteric anastomoses were performed immediately. Three patients presented at 2, 15, and 42 days after LC. In two patients, one or more operative procedures were performed before definitive repair and these patients were referred to tertiary care centers. One patient was managed with sequential CT-guided drainage catheters after attempted closure of the defect. The length of illness for these five patients was 8, 69, 348, 402, and 435 days with a follow-up of 245, 345, 531, 575, and 1088 days. Laparoscopic experience before injury by the operating surgeon was 3, 26, 35, 77, and 333 operations. Major biliary tract injuries occurred during routine cholecystectomy, length of illness was substantial for most patients, and biliary-enteric anastomosis was definitive for four of the five patients. The operating surgeons' "learning curve" did not seem as important as in other studies.     

Extension of a typology of alcohol dependence based on relative genetic and environmental loading

Mild, severe, and dyssocial subtypes of alcohol dependence, previously identified among Caucasian men from the Epidemiologic Catchment Area study, were also identified among Caucasian men and women with DSM-IV alcohol dependence from the National Longitudinal Alcohol Epidemiologic Survey (n = 2,703; 1,746 respectively). These subtypes were not identified among African American and Hispanic American men or women with DSM-IV alcohol dependence. Among Caucasians with alcohol dependence, the subtypes were characterized by differential loading on three dimensions: genetic, general environmental, and dyssocial environmental symptom scales developed in a prior twin study. The mild subtype (60% of men and 66% of women) was distinguished by low mean scores on all three scales; the dyssocial subtype (24% of men and 20% of women) by low mean genetic and general environmental scores but high mean dyssocial environmental scores; and the severe subtype (16% of men and 14% of women) by high scores on the genetic and general environmental scales. These subtypes also showed the expected distinctions in clinical characteristics. The severe subtype showed greater comorbid drug dependence and major depression, more treatment seeking, and a higher prevalence of parental alcoholism. The severe subtype also showed significantly greater genetic influence adjusted for overall severity of alcohol dependence (genetic ratio). Only the severe subtype showed a pattern of scale scores and clinical characteristics suggestive of substantial genetic influence. The present study indicates a robustness of the typology originally developed among DSM-III alcohol-dependent Caucasian men by empirical extension of the subtypes to a different sample of Caucasian men and, separately, Caucasian women. The use of this typology may aid in distinguishing between Caucasian alcohol-dependent individuals on the basis of relative genetic influence, enabling genetic, behavioral, and epidemiological investigations to reduce genetic or environmental "noise" and better focus on specific aspects of alcohol dependence.     

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.     

Spinal neurilemmomas and neurofibromas: central dot sign in postgadolinium MRI

The MR studies of three histologically proven spinal neurilemmomas and neurofibromas were reviewed retrospectively. There were two benign neurilemmomas (schwannomas) and one neurofibroma. The common characteristic of these cases was a central low intensity focus ("dot") seen on postcontrast T1-weighted imaging. The low intensity foci corresponded histologically to a congeries of changes including edema, microcysts, foam cells, hyalinization of blood vessels, old hemorrhage, and dystrophic calcification.     

"Indianism" and MMPI scores of men alcoholics

Mean MMPI profiles of 40 Indian and 40 White veterans were similar, but "Indianism," as measured by the Indian Culturalization Test, was significantly related to scores on Hs, Hy, Pt and Sc scales. Caution is advised in using the MMPI in the diagnosis of Indians' psychiatric problems.     

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.