Exploring the episodic structure of algebra story problem solving

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attampts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction

Exploring the episodic structure of algebra story problem solving

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attempts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction

The effect of multiple knowledge sources on learning and teaching

Current paradigms for machine-based learning and teaching tend to perform their task in isolation from a rich context of existing knowledge. In contrast, the research project presented here takes the view that bringing multiple sources of knowledge to bear is of central importance to learning in complex domains. As a consequence teaching must both take advantage of and beware of interactions between new and existing knowledge. The central process which connects learning to its context is reasoning by analogy, a primary concern of this research. In teaching, the connection is provided by the explicit use of a learning model to reason about the choice of teaching actions. In this learning paradigm, new concepts are incrementally refined and integrated into a body of expertise, rather than being evaluated against a static notion of correctness. The domain chosen for this experimentation is that of learning to solve "algebra story problems." A model of acquiring problem solving skills in this domain is described, including: representational structures for background knowledge, a problem solving architecture, learning mechanisms, and the role of analogies in applying existing problem solving abilities to novel problems. Examples of learning are given for representative instances of algebra story problems. After relating our views to the psychological literature, we outline the design of a teaching system. Finally, we insist on the interdependence of learning and teaching and on the synergistic effects of conducting both research efforts in parallel

Environment Crises

Report consists of three different parts(print) 91 p. ; 28 cm.Preface -- List of Tables -- Part A: Dimensions of Community Leadership and the Definition of Water Resources Problems -- Part B: Factors in the Community Perception of Water Resource Problems -- Part C: A Sociologist Looks at Water Resources Researc

A radiologic classification of talocalcaneal coalitions based on 3D reconstruction

Talocalcaneal coalitions can be difficult to detect on plain radiographs, despite obvious clinical findings. The purpose of this study is two-fold: (1) to delineate the benefits of thin-cut computed tomography (CT) and 3D reconstructions and (2) to develop a classification scheme for talocalcaneal coalitions that will provide valuable information for surgical planning. From 2005 to 2009, 54 feet (35 patients) with a talocalcaneal coalition were evaluated with thin-cut (1 mm) CT, using multi-planar 2D and 3D reconstructions. The talocalcaneal coalitions were classified into five types based on the cartilaginous or bony nature, location, and facet joint orientation. Bilateral coalitions were found in 22/35 patients. Types I and II were fibrocartilaginous coalitions, which was the most common type, comprising 40.7 and 16.7% of the coalitions, respectively. Of the patients, 14.8% had a shingled Type III coalition, while 11.1% of the feet examined had a complete bony coalition (Type IV). Small peripheral posterior bony coalitions (Type V), which are heretofore not described, were found in 16.7% of feet. CT scans can provide valuable information regarding the bony or cartilaginous nature of coalitions, as well as the facet orientation, which is helpful in diagnosis and treatment. In this study, the 2D and 3D reconstructions revealed previously unreported peripheral posterior bony coalitions (Type V), as well as coalitions that are in the same plane as the standard CT cuts or Harris view radiographs (Type I). The CT scan also improved the crucial pre-operative planning of the resection in the more complex vertical and combined horizontal and vertical fibrocartilaginous coalitions (Type I and II). Additionally, the complete bony coalitions (Type IV) can be sized accurately, which is helpful in decision-making on the resectability of the coalition

Ecosystem services of collectively managed urban gardens : exploring factors affecting synergies and trade-offs at the site level

Collective management of urban green space is being acknowledged and promoted. The need to understand productivity and potential trade-offs between co-occurring ecosystem services arising from collectively managed pockets of green space is pivotal to the design and promotion of both productive urban areas and effective stakeholder participation in their management. Quantitative assessments of ecosystem service production were obtained from detailed site surveys at ten examples of collectively managed urban gardens in Greater Manchester, UK. Correlation analyses demonstrated high levels of synergy between ecological (biodiversity) and social (learning and well-being) benefits related to such spaces. Trade-offs were highly mediated by site size and design, resulting in a tension between increasing site area and the co-management of ecosystem services. By highlighting synergies, trade-offs and the significance of site area, the results offer insight into the spatially sensitive nature of ecosystem services arising from multi-functional collectively managed urban gardens

Iron depletion suppresses mTORC1-directed signalling in intestinal Caco-2 cells via induction of REDD

Acknowledgements This work was supported by grants from the Biotechnology and Biological Science Research Council (BB/I007261/1 and BB/N002342/1) and The Scottish Government's Rural and Environment Science and Analytical Services Division (RESAS 854/11).Peer reviewedPublisher PD

Development and evaluation of tools and an intervention to improve patient- and carer-centred outcomes in Longer-Term Stroke care and exploration of adjustment post stroke: the LoTS care research programme

Background: Evidence-based care pathways are required to support stroke patients and their carers in the longer term. Aims: The twofold aim of this programme of four interlinking projects was to enhance the care of stroke survivors and their carers in the first year after stroke and gain insights into the process of adjustment. Methods and results: We updated and further refined a purposely developed system of care (project 1) predicated on a patient-centred structured assessment designed to address areas of importance to patients and carers. The structured assessment is linked to evidence-based treatment algorithms, which we updated using a structured protocol: reviewing available guidelines, Cochrane reviews and randomised trials. A pragmatic cluster randomised controlled trial evaluation of the clinical effectiveness and cost-effectiveness of this system of care was undertaken in 29 community-based UK stroke care co-ordinator services (project 2). In total, 15 services provided the system of care and 14 continued with usual practice. The primary objective was to determine whether the intervention improved patient psychological outcomes (General Health Questionnaire-12) at 6 months; secondary objectives included functional outcomes for patients, outcomes for carers and cost-effectiveness, as measured through self-completed postal questionnaires at 6 and 12 months. A total of 800 patients and 208 carers were recruited; numbers of participants and their baseline characteristics were well balanced between intervention and control services. There was no evidence of statistically significant differences in primary or secondary end points or adverse events between the two groups, nor evidence of cost-effectiveness. Intervention compliance was high, indicating that this is an appropriate approach to implement evidence into clinical practice. A 22-item Longer-term Unmet Needs after Stroke (LUNS) questionnaire was developed and robustly tested (project 3). A pack including the LUNS questionnaire and outcome assessments of mood and social activity was posted to participants 3 or 6 months after stroke to assess acceptability and validity. The LUNS questionnaire was re-sent 1 week after return of the first pack to assess test–retest reliability. In total, 850 patients were recruited and the acceptability, validity and test–retest reliability of the LUNS questionnaire as a screening tool for post-stroke unmet need were confirmed. This tool is now available for clinical use. An in-depth qualitative investigation was undertaken with 22 patients (and carers) at least 1 year after stroke (project 4) to gain further insights into the experience of adjustment. This included initial semistructured interviews, limited observations and solicited diaries with a follow-up interview 3–4 months after the initial interview and highlighted a range of different trajectories for post-stroke recovery. Conclusions: The programme has been completed as planned, including one of the largest ever stroke rehabilitation trials. This work highlights that successfully addressing the needs of a heterogeneous post-stroke population remains problematic. Future work could explore stratifying patients and targeting services towards patients (and carers) with specific needs, leading to a more specialised bespoke service. The newly developed LUNS questionnaire and the qualitative work will help inform such services