Social Justice Mathematical Modeling for Teacher Preparation

Today’s math teachers face significant social and political challenges for which they receive little preparation. Mathematics content courses can potentially provide additional preparation in this regard by providing future teachers with experiences to mathematically explore social justice issues. This provides them with opportunities to increase their awareness and sensitivity to social justice issues, develop greater empathy for their future students, and serve as examples for high quality instruction that they can emulate in their future careers. This dissertation recounts the development and revision of three social justice mathematical modeling projects, and shares evidence from student work samples of the ways in which the experience impacted students’ lives. The implications of this work for teacher preparation and modeling education are discussed

How To Touch a Running System

The increasing importance of distributed and decentralized software architectures entails more and more attention for adaptive software. Obtaining adaptiveness, however, is a difficult task as the software design needs to foresee and cope with a variety of situations. Using reconfiguration of components facilitates this task, as the adaptivity is conducted on an architecture level instead of directly in the code. This results in a separation of concerns; the appropriate reconfiguration can be devised on a coarse level, while the implementation of the components can remain largely unaware of reconfiguration scenarios. We study reconfiguration in component frameworks based on formal theory. We first discuss programming with components, exemplified with the development of the cmc model checker. This highly efficient model checker is made of C++ components and serves as an example for component-based software development practice in general, and also provides insights into the principles of adaptivity. However, the component model focuses on high performance and is not geared towards using the structuring principle of components for controlled reconfiguration. We thus complement this highly optimized model by a message passing-based component model which takes reconfigurability to be its central principle. Supporting reconfiguration in a framework is about alleviating the programmer from caring about the peculiarities as much as possible. We utilize the formal description of the component model to provide an algorithm for reconfiguration that retains as much flexibility as possible, while avoiding most problems that arise due to concurrency. This algorithm is embedded in a general four-stage adaptivity model inspired by physical control loops. The reconfiguration is devised to work with stateful components, retaining their data and unprocessed messages. Reconfiguration plans, which are provided with a formal semantics, form the input of the reconfiguration algorithm. We show that the algorithm achieves perceived atomicity of the reconfiguration process for an important class of plans, i.e., the whole process of reconfiguration is perceived as one atomic step, while minimizing the use of blocking of components. We illustrate the applicability of our approach to reconfiguration by providing several examples like fault-tolerance and automated resource control

Corequisite Mathematics: A Program Analysis at the College Level

Many incoming college freshmen who do not meet minimum standardized exam cut-score requirements are often determined to be not ready for college-level coursework and registered for pre-requisite, multi-semester, remedial course sequences. The goal of pre-requisite courses is to prepare students for college-level courses prior to enrollment in college-level classes. However, based on multiple studies, traditional, pre-requisite developmental education has become a barrier to student success. In contrast, the co-requisite instructional model enrolls students into their college-level, credit-bearing course in their first semester on a college campus, improving the likelihood of success in those courses and beyond. The purpose of this study was to determine the effectiveness of implementing a corequisite curriculum into a college algebra course. To help with this determination, the study compared student success in a corequisite college algebra course to student success in a non-corequisite college algebra course, a traditional college algebra course, and success in subsequent precalculus classes. Another purpose was to examine faculty perceptions of their experiences teaching non-corequisite college algebra courses and corequisite college algebra courses. Faculty perceptions on initial transition preparedness, implementation of evidence-based teaching theories, and continued improvements were collected using interviews. This study showed corequisite mathematics benefitted students typically labeled developmental. This study also confirmed that academically at-risk students are capable of learning complex ideas and concepts at the college-level, and can be successful without slow-paced, extended remediation. Faculty benefitted from the training, collaboration, and resources provided for the implementation of new course curricula like the corequisite model. It was evident from this study, with the corequisite model, faculty continue to support students as they progress in their mathematics courses

From the constructs and methods of the philosophers to a model for improved discourse between disciplines

We have problem areas which are beyond the scope of a discipline, but we are generally educated in just a single discipline. I explored our philosophy of work to see how we became disciplinary, where the disciplines came from, what philosophy underlies our way of working, and what philosophy underpins work that is beyond the scope of a discipline. The underlying philosophy leads to the research question. My hypothesis is that a systems engineer can create a model which networks the disciplines using constructs from philosophy, the tiers of disciplines in transdisciplinarity, and systemic and holistic thinking. This will provide a way of working on problem situations which transgress the boundary of a discipline. Using constructs from philosophy, the methods of the philosophers, hermeneutics, systems thinking and soft systems methodology I proceeded to create a conceptual model and showed conceptual examples of how to use the model. The client for the model is the interdisciplinary researcher who is seeking a way of working to manage problem areas that transgress disciplinary boundaries. The recommendation is made for using critical, systemic and holistic thinking and a network model of disciplines to manage our approach to problem situations which are beyond the scope of a discipline. The model is developed in the incremental sequence: disciplinary, multidisciplinary, interdisciplinary, transdisciplinary and gets as far as catering for tiers of disciplines (one aspect of the large and complex field of transdisciplinarity). Therefore, the model is suitable for interdisciplinary research, but can be developed further in future projects. The importance of the model is that it provides a practical way of working to manage problem situations which transgress disciplinary boundaries whilst accessing the expertise of disciplined practitioners. The model can find wide applicability. It is not necessary for the user of the model to be comfortable with the abstract philosophy used to create it. Users will need the will for uncoerced mutual understanding or free communication, along with their disciplinary expertise. The reader of the dissertation however should be comfortable with abstractions such as ideas about reality and actuality, form and class, subject and object, truth and justice, truthfulness and functional fit. Future work may reduce the method to practice in the academy and extend the method to bridging silos in learning organisations in the workplace. The work was conducted independently, and an original model was created

Upper Urinary Tract Stone: Clinical, Experimental and Biochemical Studies

Clinical, biochemical and experimental studies in upper urinary tract stone have been carried out in more than one thousand patients. The investigation has been conducted during the last eight years in the Urological Department of the Victoria Infirmary. A broad picture of the general incidence and diagnostic findings has been presented with reference to the complete series, the numbers receiving operative and expectant treatment proving to be almost equal. A general increase in the incidence of the disease over the last thirty years has been noted. The purely clinical approach to aetiology has been disappointing, and a satisfactory cause has been shown in a very small proportion of all patients. The factors of possible and doubtful significance have been stated. lack of information about aetiology has been felt at all times to be the main obstacle to progress in prevention and treatment. The natural history of upper urinary tract stone has been studied to provide a standard or "control" series by which the results of operation may be judged, and to fill a gap which clearly exists in our understanding of the disease. The clinical progress of all stones originating in the kidney has been followed to its termination, either in operative removal or natural expulsion. Obstructive potential has been shown to be more important than size per se. Early removal of the obstructive stone has been considered to be its most conservative treatment. A plea, however, has been made for an expectant attitude, with careful supervision in a Stone Clinic in the case of (l) small symptom-free, calyceal stones with normal pyelograms, (2) large symptomless bilateral branched stones, and (3) small ureteric calculi which are making satisfactory progress in the absence of hydronephrosis. It has been shown that more than 80 per cent, of all stones which enter the ureter eventually pass, and that there is therefore no particular virtue in claiming similar results from treatment by endoscopic or open surgical procedures (if these are applied to every case encountered). The late results of operative treatment indicate a depressingly high recurrence rate. Recurrences have been graded as "mild" and "severe", depending on whether or not secondary operation has been necessary. In round figures, one out of every four patients undergoing operative treatment has developed severe recurrence, and the total figure for recurrence has been shown to be somewhere between thirty and fifty per cent. False recurrence, which has not been included in these figures, has been detected in one out of eight patients examined. The factors responsible for, or related to, recurrence have been studied at some length. Nephrolithotomy has been shown to be undesirable on account of its higher mortality rate, the incidence of pseudo- and true recurrence associated with it, and its harmful effect on renal function. Ablation of the kidney has proved to be no guarantee of immunity from recurrence on the opposite side, since the incidence of contralateral recurrence has been the same after nephrectomy and conservative procedures. There has been a steady decrease in recurrence rates in the last three decades. Urinary infection, hyperparathyroidism, hypercal-curia and uncorrected pelvi-ureteric obstruction all have much in common with recurrence, and attention to their treatment, together with complete removal of the stones, give the patient the best early chance of escaping this complication. Long-term preventive measures have been shown to depend, in our present incomplete state of knowledge, on the chemical analysis of the stone, the aim being the production of the maximum solubility of the main crystalloid present. Clinical trials on stone patients and experimental work in animals have failed to confirm that hyaluronidase is valuable in preventing recurrent stone or in reducing the size of those already present in the urinary tract. The place of oestrogens, aluminium hydroxide gel, and salicylates in the prevention of recurrence has been discussed. Comparative studies have indicated that bilateral stone is more serious than the unilateral condition, principally in respect of the post-operative mortality and the late results. (Abstract shortened by ProQuest.)

Public Systems Modeling

This is an open access book discusses readers to various methods of modeling plans and policies that address public sector issues and problems. Written for public policy and social sciences students at the upper undergraduate and graduate level, as well as public sector decision-makers, it demonstrates and compares the development and use of various deterministic and probabilistic optimization and simulation modeling methods for analyzing planning and management issues. These modeling tools offer a means of identifying and evaluating alternative plans and policies based on their physical, economic, environmental, and social impacts. Learning how to develop and use the mathematical modeling tools introduced in this book will give students useful skills when in positions of having to make informed public policy recommendations or decisions

Using diffusion of innovation theory to understand how technology is adopted in mathematics at a South African higher education institution

The issue of students enrolling who are ill prepared in mathematics for university studies has been an area of concern for some time in South Africa. Various universities tried different interventions to address this problem. One example is the establishment of a bridging programme at an institution of higher learning. Technology has been discussed as support that can be provided to students. This study therefore sought to understand the adoption of technology in the teaching of mathematics at an institution of higher education in South Africa. Using Roger's diffusion of innovation theory, this study sought to understand how technology is adopted by mathematics teachers in the bridging programme. Whilst the results of the study show that some teachers have adopted technology at different scales to provide access, to supplement instruction and to encourage interaction, the results also show that some teachers are uncertain of the benefits that technology has to teaching and learning in the programme. The current talk and chalk method is seen as being essential as it is tried and tested. The study also showed that teachers did not receive support from the institution resulting in them seeking assistance from outside of the university. The study recommends that higher education institutions should provide instructional design support to ensure that teachers are not overburdened with developing technology interventions where they have little or no expertise in

Current, August 20, 1990

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