Spanning tree methods for sampling graph partitions

In the last decade, computational approaches to graph partitioning have made a major impact in the analysis of political redistricting, including in U.S. courts of law. Mathematically, a districting plan can be viewed as a balanced partition of a graph into connected subsets. Examining a large sample of valid alternative districting plans can help us recognize gerrymandering against an appropriate neutral baseline. One algorithm that is widely used to produce random samples of districting plans is a Markov chain called recombination (or ReCom), which repeatedly fuses adjacent districts, forms a spanning tree of their union, and splits that spanning tree with a balanced cut to form new districts. One drawback is that this chain's stationary distribution has no known closed form when there are three or more districts. In this paper, we modify ReCom slightly to give it a property called reversibility, resulting in a new Markov chain, RevReCom. This new chain converges to the simple, natural distribution that ReCom was originally designed to approximate: a plan's stationary probability is proportional to the product of the number of spanning trees of each district. This spanning tree score is a measure of district "compactness" (or shape) that is also aligned with notions of community structure from network science. After deriving the steady state formally, we present diagnostic evidence that the convergence is efficient enough for the method to be practically useful, giving high-quality samples for full-sized problems within several hours. In addition to the primary application of benchmarking of redistricting plans (i.e., describing a normal range for statistics), this chain can also be used to validate other methods that target the spanning tree distribution

Towards a critical curriculum for mid-level community based rehabilitation training in South Africa.

Thesis (Ph.D.)-University of KwaZulu Natal, 2008.This study, conducted in Pietermaritzburg and surrounding rural and township areas, is a critical exploration of the training of mid-level Community Based Rehabilitation workers with a specific focus on the ability of course participants to understand and address the oppression and empowerment of people with disabilities. The aim of the study was to develop a conceptual framework for curriculum construction of a midlevel Community Based Rehabilitation course, through examining a Community Based Rehabilitation course and the changes that were made to it. The study was conducted within a critical theory paradigm. The social model of disability and an understanding of disability as a form of oppression were the key constructs that guided the research. Participatory action research was used in the initial phase of the research, followed by a second phase that adopted a life history approach. The initial phase of the study consisted of one cycle of action research, beginning with a reflection on the existing curriculum. The action research cycle then moved through stages of planning changes to the curriculum, implementing the changes, observing the effects of the changes and reflecting again. Data collection comprised interviews with staff members, students and community rehabilitation facilitators who had previously completed the Community Based Rehabilitation course, as well as focus groups with people with disabilities and parents of children with disabilities. Several participatory rural appraisal techniques were also used with the students. The action research cycle raised further questions about how the life experiences of the students influenced their responses to the changed curriculum. This stimulated the development of the second phase of the research which used life history methodology, comprising in-depth interviews with four students. The study found that several changes occurred in the students’ attitudes and understanding as well as in some of the activities they undertook. Some students worked with rather than for people with disabilities, indicating a change in the power relationship with their clients. The students were able to analyse their own oppression and that of people with disabilities, unlike previous students. The students also engaged in social action for the rights of people with disabilities. These findings cannot be solely attributed to the changes in curriculum. However, they raise the possibility that Community Based Rehabilitation personnel can work to address the oppression of people with disabilities rather than focusing entirely on technical rehabilitation, which is a common approach in the literature. An analysis of the life histories revealed that those students identified as ‘activists’, more willingly engaged in social action during the Community Based Rehabilitation course than other students. This challenges the dominant discourse in the literature of Community Based Rehabilitation personnel as rehabilitation workers rather than activists. One key contribution of this thesis is to research methodology through its combination of life history methodology and action research in the study. A second is its proposed framework for curriculum construction that incorporates findings from the action research and the life histories. This framework, with its macroenvironment, organisational and student influences on the curriculum, contributes to the under-theorised field of Community Based Rehabilitation training

Barriers to Advocacy and Litigation in the Equality Courts for Persons with Disabilities

The effective implementation of the Promotion of Equality and Prevention of Unfair Discrimination Act 4 of 2000 (PEPUDA) and the fulfilment of the South African state's obligations in terms of the Convention on the Rights of Persons with Disabilities (CRPD) are dependent on two fundamental tools, advocacy and litigation. This article discusses the outcome of three cases in the Equality Courts and how these cases promote accessibility and access to justice for persons with disabilities. The authors then consider the impact of CREATE, a KwaZulu-Natal NGO's advocacy initiatives to promote the rights of persons with disabilities and the utilisation of the Equality Court to realise those rights. Participants of ten workshops in KwaZulu-Natal identified three barriers to access to justice in accessing the Equality Courts. Firstly, some Equality Courts are geographically (and financially) inaccessible. Secondly, the negative and insensitive attitudes of front-line workers impact on the ability of persons with disabilities to bring equality claims to and access the services of the Equality Court. These barriers constitute discrimination and flout articles 9 and 13 of the CRPD, which require the provision of support for persons with disabilities to access the justice system and the promotion of accessibility to the physical environment, and the provision to them of transportation, information and other services. Thirdly, cultural norms and fears impede access to courts and the agency of persons with disabilities to bring these claims, for example the requirement that traditional leaders provide "permission" to persons with disabilities to sue and a similar requirement of permission from the in-laws of women with disabilities. The article analyses the three barriers identified as inhibiting advocacy and litigation, and explains the implication of these barriers for the state's obligations in terms of articles 5, 8, 9, 12 and 13 of the CRPD. Recommendations are made on overcoming these barriers.   &nbsp

Fifth Graders\u27 Enjoyment, Interest, and Comprehension of Graphic Novels Compared to Heavily-Illustrated and Traditional Novels

The comparative effectiveness of graphic novels, heavily illustrated novels, and traditional novels as reading teaching tools has been sparsely researched. During the 2011-2012 school year, 24 mixed-ability fifth grade students chose to read six novels: two traditional novels, two highly illustrated novels and two graphic novels. Students participated in discussion groups structured with thinking skills, and completed assignments during and after reading the books. Student comprehension and enjoyment were measured by rubric-graded assignments and rating scales. The numbers of student responses during discussions per type of novel were tabulated. The graphic novel received the highest scores in all categories. The researchers conclude that graphic novels be considered an engaging and effective method of teaching reading to fifth graders

Reading Nonfiction Science Literature with and without Arts Integration Activities

This study explores the integration of the arts into the teaching of science nonfiction texts during literacy instruction. Sixty-one elementary students (15 second graders, 25 third graders, and 21 fifth graders) attending schools of differing socio-economic levels participated in this study. The study examined the effects of artsintegration on student content knowledge, engagement level, and attitudes toward learning regarding science nonfiction texts. Throughout the eight-week study, students experienced both the traditional no-arts control condition and the experimental arts-integration condition in two-week segments for different science topics. Both conditions employed literacy strategies to teach comprehension of science nonfiction texts. The resulting pretests, posttests, and distal posttests, attitude surveys, and teacher observations indicated that students learned and retained content knowledge taught through both ways of teaching. The fifth-grade students evidenced greater learning during the experimental condition with very large effect sizes. Students’ overall attitudes and engagement were better when the arts were incorporated into daily instruction. The excitement for learning and academic abilities of the participants throughout the study supports the idea that different ways of creative teaching positively impact the way students learn in the classroom

A Content Analysis of Thirty Children’s Picture Books about Ecology

This study presents a content analysis of 30 ecology-themed children’s picture books published in English and Spanish from 1994 to the present. Books were analyzed for the following aspects: 1) Nature appreciation, 2) Interrelatedness of Nature, 3) Realistic ecology problem, 4) Differing perspectives, 5) Hope for a solution, 6) Reflection and responsibility, 7) Steps for a solution, 8) Positive tone, 9) Representation of diversity, 10) Appropriate illustrations, 11) Story appeal, and 12) Developmental appropriateness. Scoring guidelines are provided in an appendix. Content analysis results revealed that most books raise awareness about the impact of human action on the environment, although some titles lack important traits such as offering differing perspectives of ecological problems. Researchers encourage educators to incorporate picture books and art in science lessons to increase student engagement and scientific learning while meeting various standards. A companion practical paper in the same issue of the Journal provides example art projects connected to the books

Practical Art Projects Related to Children’s Picture Books about Ecology

This study presents art projects that reinforce scientific content presented in children’s picture books about ecology. Ten K-6 students from varying socioeconomic classes, and different cultural and language backgrounds from the United States and Spain participated. Next Generation Science Standards were identified and addressed in these art projects. Students’ understanding and engagement were evaluated through teacher observations, photographs, and a student attitude survey. Upper- and lower-elementary students evidenced increased understanding of environmental issues, and high level of enjoyment and engagement through these art projects integrated with science content. Researchers encourage educators to incorporate picture books and art in science lessons to increase student engagement and scientific learning while meeting various standards

Intersecting Disability and Poverty in the Global South: Barriers to the Localization of the UNCRPD

The UN Convention on the Rights of Persons with Disabilities (UNCRPD) remains in place as the major disability rights instrument recognising that all persons with disabilities must enjoy human rights and freedoms as every other person. However, the CRPD does not automatically confer realization of these rights. In practice, its implementation is met by multiple hurdles, most pronounced at the local level in the Global South, where disability and poverty intersect. This article reports on findings from a study in five countries (Kenya, Philippines, Jamaica, Guatemala, and South Africa) looking at the extent to which the CRPD is being implemented locally in contexts of poverty, and the factors and processes impacting this localization. The findings highlight multiple barriers, becoming more pronounced in local rural areas. These include weak and fragmented organisations of persons with disabilities (OPDs), political and legal issues, and a siloed approach where disability is marginalised in mainstream areas, including development. These barriers are accentuated as intersectional dimensions are factored in, including indigeneity, age, gender, race, and ethnicity. Overall, each local context is left to its own devices, with urban stakeholders, unknowing of what life in poverty is like and how this reframes the CRPD in discourse and practice at the forefront. Our study concludes that there is a profound need for an informed, contextualized, intersectional, and geopolitical analysis where poverty is kept sharply in focus. This is essential to move beyond unrealistic assumptions about disability rights frameworks and to work towards truly localized and transformative efforts

Challenging Elementary Learners with Programmable Robots during Free Play and Direct Instruction

Computer programming skills are important to many current careers; teaching robot coding to elementary students can start a positive foundation for technological careers, develop problem-solving skills, and growth mindsets. This study, through a repeated measures design involving students in two classrooms at two widelyseparated grade levels (first graders aged 6-7 years and fifth graders aged 10-11 years), determined if allowing students to challenge themselves with coding exercises in the experimental condition resulted in greater learning and more positive attitudes than a more structured set of exercises provided by the teacher in the control condition. Background instruction in coding and using robots occurred before the study began. Students experienced each condition twice for a two-week duration in the eight-week study; a robot performance, scored for technical and creative skills, was presented by students at the end of each two-week period. During the control condition, teachers used direct instruction to teach coding skills; during the experimental condition, students were asked to challenge themselves through free play and inquiry based learning. The results indicated that technical scores for robot performances showed the largest positive effects during the direct instructional portions of the study, while the creative score for robot performances indicated the largest positive effects during the free play rotations. Overall scores for robotic performances indicated a steady growth of skills week after week during the study. The attitudes of the participants remained positive throughout the study

Small Mammal Jointed Models to Make, Description Cards, and a Menu of Follow-on Activities in Different Intelligence Areas

Instilling an appreciation of nature in our youth is an important precursor to environmental protection and support for sustainability. Research has shown that involving students in environmental projects improves their motivation, skills, and achievement on standardized tests, This document contains images of the body parts of small mammals with directions for reproducing, cutting, gluing, and assembling them (with paper fasteners) into life-size jointed models of the animals. There are two distinct versions (different color phases and poses) of each of 11 small mammals that generally live in grasslands, along creeks/ponds, or woodland edges of Midwestern habitats: Eastern Chipmunk, Franklin’s Ground Squirrel, Eastern Mole, Plains Pocket Gopher, Thirteen Lined Ground Squirrel, Northern Short Tailed Shrew, Southern Bog Lemming, Meadow Vole, Meadow Jumping Mouse, Deer Mouse, and Northern Grasshopper Mouse. A set of card fronts and backs gives facts about each of the animals (to be matched to the corresponding jointed models) with an image of the correct animal on the reverse side for selfchecking. The main lesson activity is explained and presented as a learning cycle. A menu of authentic activities that would make meaningful follow-on activities in the last phase of the learning cycle, the expansion phase, is presented. These are sorted into different multiple intelligence areas to provide student choice and differentiation of instruction. Each activity is accompanied with objective, instructions, rationale of how the activity is an authentic task, criteria for evaluation and an example correct response to the activity. [50 Figures; 12 References; Appendix with 20 pages of additional figures