952 resultados para subtraction solving


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Collaborative networks have come to form a large part of the public sector’s strategy to address ongoing and often complex social problems. The relational power of networks, with its emphasis on trust, reciprocity and mutuality provides the mechanism to integrate previously dispersed and even competitive entities into a collective venture(Agranoff 2003; Agranoff and McGuire 2003; Mandell 1994; Mandell and Harrington 1999). It is argued that the refocusing of a single body of effort to a collective contributes to reducing duplication and overlap of services, maximizes increasingly scarce resources and contributes to solving intractable or 'wicked’problems (Clarke and Stewart 1997). Given the current proliferation of collaborative networks and the fact that they are likely to continue for some time, concerns with the management and leadership of such arrangements for optimal outcomes are increasingly relevant. This is especially important for public sector managers who are used to working in a top-down, hierarchical manner. While the management of networks (Agranoff and McGuire 2001, 2003), including collaborative or complex networks (Kickert et al. 1997; Koppenjan and Klijn 2004), has been the subject of considerable attention, there has been much less explicit discussion on leadership approaches in this context. It is argued in this chapter that the traditional use of the terms ‘leader’ or ‘leadership’ does not apply to collaborative networks. There are no ‘followers’ in collaborative networks or supervisor-subordinate relations. Instead there are equal, horizontal relationships that are focused on delivering systems change. In this way the emergent organizational forms such as collaborative networks challenge older models of leadership. However despite the questionable relevance of old leadership styles to the contemporary work environment, no clear alternative has come along to take its place.

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Introduction: Work engagement is a recent application of positive psychology and refers to a positive, fulfilling, work-related state of mind characterized by vigor, dedication and absorption. Despite theoretical assumptions, there is little published research on work engagement, due primarily to its recent emergence as a psychological construct. Furthermore, examining work engagement among high-stress occupations, such as police, is useful because police officers are generally characterized as having a high level of work engagement. Previous research has identified job resources (e.g. social support) as antecedents of work engagement. However detailed evaluation of job demands as an antecedent of work engagement within high-stress occupations has been scarce. Thus our second aim was to test job demands (i.e. monitoring demands and problem-solving demands) and job resources (i.e. time control, method control, supervisory support, colleague support, and friend and family support) as antecedents of work engagement among police officers. Method: Data were collected via a self-report online survey from one Australian state police service (n = 1,419). Due to the high number of hypothesized antecedent variables, hierarchical multiple regression analysis was employed rather than structural equation modelling. Results: Work engagement reported by police officers was high. Female officers had significantly higher levels of work engagement than male officers, while officers at mid-level ranks (sergeant) reported the lowest levels of work engagement. Job resources (method control, supervisor support and colleague support) were significant antecedents of three dimensions of work engagement. Only monitoring demands were significant antecedent of the absorption. Conclusion: Having healthy and engaged police officers is important for community security and economic growth. This study identified some common factors which influence work engagement experienced by police officers. However, we also note that excessive work engagement can yield negative outcomes such as psychological distress.

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The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

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Maternal behaviors and child mastery behaviors were examined in 25 children with Down syndrome and 43 typically developing children matched for mental age (24–36 months). During a shared problem-solving task, there were no group differences in maternal directiveness or support for autonomy, and mothers in the two groups used similar verbal strategies when helping their child. There were also no group differences in child mastery behaviors, measured as persistence with two optimally challenging tasks. However, the two groups differed in the relationships of maternal style with child persistence. Children with Down syndrome whose mothers were more supportive of their autonomy in the shared task displayed greater persistence when working independently on a challenging puzzle, while children of highly directive mothers displayed lower levels of persistence. For typically developing children, persistence was unrelated to maternal style, suggesting that mother behaviors may have different causes or consequences in the two groups.

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Computers not only increase the speed and efficiency of our mental efforts, but in the process they also alter the problem-solving tasks we are faced with and, in so doing, they alter the cognitive processes we use to solve problems. Computers are fundamentally changing our forms of thinking (Colc & Griffin, 1980). Therefore, the computer should be seen as not only having the potential to amplify human mental capabilities, but also of providing a catalyst for intellectual development.

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The Flinders Decision-Making Questionnaire (FDMQ) (Mann, 1982), which measures three decision-making styles and decision-making self-esteem, and the Self-Description Questionnaire III (SDQ HI) (Marsh & O'Neill, 1984), which measures 13 facets of self-concept; were administered to 475 university students to investigate some of the tenets of Janis and Mann's (1976, 1977) conflict model of decision-making and to further investigate the influence of self-concept on decision-making behaviours. The findings empirically validated Janis and Mann's (1977) link between decision-making self-esteem and decision-making style. Modest relationships, in the predicted direction, were found between decision-making self-esteem and the three decision-making styles (Vigilance, Defensive Avoidance, and Hypervigilance). In addition, specific facets of self-concept (General, Verbal, Academic, Honesty/Reliability and Problem-Solving Self Concepts) were related to self-reported decision-making behaviours.

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There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

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Online moderation meetings have the potential to support the collaborative professional development of teachers, and the formation of a common understanding of what denotes quality in student work in a standards based assessment system. In doing so systemic calls for consistency across education systems are also being met. In this paper a case for employing online moderation meetings is developed through recourse to the demands of learning in the twenty-first century and the place of assessment within those discourses. It is argued that empirical data is needed on the efficacy of online moderation meetings to guide future practice as the use of information and communication technologies increases in education systems. Online moderation is one way of gathering teachers across vast distances to share their understandings and develop common meanings of assessment. While it is suggested that online moderation is one possible procedure to meet systemic requirements and support teachers’ professional collaboration, the implementation of such a system also introduces new challenges for schools and teachers. Meeting online to discuss professional understandings is a new way of operating for teachers and involves technology that has not yet been fully utilised within education departments. Issues such as the types of interactions that are afforded within such an environment, as well as technical operating problems that occur when using technology impact on the employment of online meetings. Online moderation meetings while potentially solving the issue of developing common understandings across an entire department also pose new issues to be resolved. There is a need for research into the efficacy of online moderation meetings so that future policy decisions may be based on sound empirical data. It is imperative that as new ways of knowing and acting are incorporated into school curriculum and pedagogy, assessment practices are also aligned. Online moderation meetings can support such practices by enabling teachers to communicate with a wider and more diverse group of teachers to establish common understandings.

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This article presents one approach to addressing the important issue of interdisciplinarity in the primary school mathematics curriculum, namely, through realistic mathematical modelling problems. Such problems draw upon other disciplines for their contexts and data. The article initially considers the nature of modelling with complex systems and discusses how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then addressed, with reference to two mathematical modelling problems— one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. A reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems. The article concludes with suggested opportunities for generating multidisciplinary projects within the regular mathematics curriculum.

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This paper argues for a future-oriented, inclusion of Engineering Model Eliciting Activities (EngMEAs) in elementary mathematics curricula. In EngMEAs students work with meaningful engineering problems that capitalise on and extend their existing mathematics and science learning, to develop, revise and document powerful models, while working in groups. The models developed by six groups of 12-year students in solving the Natural Gas activity are presented. Results showed that student models adequately solved the problem, although student models did not take into account all the data provided. Student solutions varied to the extent students employed the engineering context in their models and to their understanding of the mathematical concepts involved in the problem. Finally, recommendations for implementing EngMEAs and for further research are discussed.

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Engineering education for elementary school students is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to use the data to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results provide evidence that engineering model-eliciting activities can be successfully integrated in the elementary mathematics curriculum. These activities provide rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

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Australia’s National Review of Visual Education (DEEWR, 2009) asserts the primacy of visual language ability, or ‘visuacy” in problem-solving. This paper reports on a recent university/schools research project with ‘at risk’ middle school students in which visuacy was promoted as a primary medium for obtaining data relating to issues of immediate concern to the students. Using a students-as-researchers approach, the project investigated middle school students’ perspectives on school engagement and disengagement. In this project, novice researchers used a variety of data gathering methods including photography, video interviews and drawn images as well as more traditional verbal methods, such as interviews, and quantitative methods, such as questionnaires. Engaging student imagination was a key focus of the approach taken by the project, acknowledging that student participants may be reluctant to enter dialogue with teachers and researchers on matters to which they have previously had little input. Students who have previously been marginalized and prevented from contributing their voices to educational forums often have difficulty in adjusting to the novelty of collaborative research with adults (Rudduck, 2003) and may be uncertain of their own place in the relationship that defines teacher/student interactions. It is argued that the project’s promotion of visuacy, alongside more traditional literacies and numeracy in education research, helped to overcome these concerns, engaged the imaginations of the student researchers, and provided a medium for the expression of the voices of marginalised young people.

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In the study of complex neurobiological movement systems, measurement indeterminacy has typically been overcome by imposing artificial modelling constraints to reduce the number of unknowns (e.g., reducing all muscle, bone and ligament forces crossing a joint to a single vector). However, this approach prevents human movement scientists from investigating more fully the role, functionality and ubiquity of coordinative structures or functional motor synergies. Advancements in measurement methods and analysis techniques are required if the contribution of individual component parts or degrees of freedom of these task-specific structural units is to be established, thereby effectively solving the indeterminacy problem by reducing the number of unknowns. A further benefit of establishing more of the unknowns is that human movement scientists will be able to gain greater insight into ubiquitous processes of physical self-organising that underpin the formation of coordinative structures and the confluence of organismic, environmental and task constraints that determine the exact morphology of these special-purpose devices.

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Poor student engagement and high failure rates in first year units were addressed at the Queensland University of Technology (QUT) with a course restructure involving a fresh approach to introducing programming. Students’ first taste of programming in the new course focused less on the language and syntax, and more on problem solving and design, and the role of programming in relation to other technologies they are likely to encounter in their studies. In effect, several technologies that have historically been compartmentalised and taught in isolation have been brought together as a breadth-first introduction to IT. Incorporating databases and Web development technologies into what used to be a purely programming unit gave students a very short introduction to each technology, with programming acting as the glue between each of them. As a result, students not only had a clearer understanding of the application of programming in the real world, but were able to determine their preference or otherwise for each of the technologies introduced, which will help them when the time comes for choosing a course major. Students engaged well in an intensely collaborative learning environment for this unit which was designed to both support the needs of students and meet industry expectations. Attrition from the unit was low, with computer laboratory practical attendance rates for the first time remaining high throughout semester, and the failure rate falling to a single figure percentage.

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The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.