Understanding Linear Function: A Comparison of Selected Textbooks from England and Shanghai

This study describes a comparison of how worked examples in selected textbooks from England and Shanghai presented possible learning trajectories towards understanding linear function. Six selected English textbooks and one Shanghai compulsory textbook were analysed with regards to the understanding required for pure mathematics knowledge in linear function. Understanding was defined as being at five levels: Dependent Relationship, Connecting Representations, Local Properties Noticing, Object Analysis and Inventising. These levels were developed by examining the most prominent theories from the existing literature on understanding function. Findings suggested that the English textbooks constrained the structural aspect of understanding linear function due to a point-to-point view of function, while the Shanghai textbook which focussed on a variable view of function overemphasised the algebraic approach. The discussion explored the drawbacks to each approach and what teachers or textbook writers could do to balance these two approaches in order to facilitate students’ understanding towards a structural view of linear function

Developing the use of diagrammatic representations in primary mathematics through professional development

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in primary classrooms, through introducing primary teachers to the research literature in this area, and researching the subsequent impact on children and teachers. A professional development programme was designed, involving three one-day training sessions for mathematics co-ordinators. They were asked to implement the ideas from the training back in their schools. Sample: Mathematics co-ordinators from eight primary schools attended the professional development programme. The study focussed on Year 3 pupils (aged seven–eight) and Year 5 pupils (aged nine–10). Design and methods: In this paper, we report the qualitative findings from the larger project looking at the overall impact of the professional development programme. The paper focuses on semi-structured interviews carried out with the mathematics co-ordinators attending the professional development sessions, and the Year 3 and Year 5 class teachers who subsequently worked with the co-ordinators on their use of diagrammatic representations in their teaching of mathematics. Lesson observations involving the class teachers were also carried out in order to explore further the possible impact of the project on classroom practice. Results: The qualitative results identified the impact of the project on mathematics co-ordinators and class teachers’ knowledge and practice. However, the nature of this impact was complex, with a variety of facilitating and hindering factors identified for the transfer of the professional development ideas on the use of diagrammatic representations. In addition, different levels of sophistication of class teachers’ use of diagrammatic representations were identified. Conclusions: Implications for the development of professional development programmes to facilitate the transfer of research into practice were identified. Recommendations for the use of diagrammatic representations are also put forward

Uncharted Waters: Treating Trauma Symptoms in the Context of Early Psychosis.

Psychosis is conceptualized in a neurodevelopmental vulnerability-stress framework, and childhood trauma is one environmental factor that can lead to psychotic symptoms and the development of psychotic disorders. Higher rates of trauma are associated with higher psychosis risk and greater symptom frequency and severity, resulting in increased hospitalization rates and demand on outpatient primary care and mental health services. Despite an estimated 70% of individuals in the early stages of psychosis reporting a history of experiencing traumatic events, trauma effects (post-traumatic anxiety or depressive symptoms) are often overlooked in psychosis treatment and current interventions typically do not target commonly comorbid post-traumatic stress symptoms. We presented a protocol for Trauma-Integrated Cognitive Behavioral Therapy for Psychosis (TI-CBTp), an approach to treating post-traumatic stress symptoms in the context of early psychosis care. We provided a brief summary of TI-CBTp as implemented in the context of Coordinated Specialty Care and presented preliminary data supporting the use of TI-CBTp in early psychosis care. The preliminary results suggest that individuals with comorbid psychosis and post-traumatic stress symptoms can be appropriately and safely treated using TI-CBTp within Coordinated Specialty Care

Radiometer offsets and count conversion coefficients for the Earth Radiation Budget Experiment (ERBE) spacecraft for the years 1984, 1985, and 1986

A compendium is presented of the ground and inflight scanner and nonscanner offsets and count conversion (gain) coefficients used for the Earth Radiation Budget Experiment (ERBE) production processing of data from the ERBS, NOAA-9, and NOAA-10 satellites for the 1 Nov. 1984 to 31 Dec. 1986

Systems leadership in practice: thematic insights from three public health case studies.

BACKGROUND: 'Systems leadership' has emerged as a key concept in global public health alongside such related concepts as 'systems thinking' and 'whole systems approaches.' It is an approach that is well suited to issues that require collective action, where no single organisation can control the outcomes. While there is a growing literature on the theory of systems leadership in a number of fields, there remains a lack of published empirical studies of public health systems leadership for professionals to learn from. The aim of the current project was to conduct cases studies in UK public health to provide empirical evidence on the nature of effective systems leadership practice. METHODS: Three system leadership case studies were identified in the key domains of public health: health protection, healthcare public health and health improvement. A total of 27 semi-structured interviews were conducted. Data were thematically analysed to identify the components of effective systems leadership in each case and its impact. RESULTS: The thematic analysis identified themes around 'getting started,' 'maintaining momentum' and 'indicators of success' in systems leadership. In terms of getting started, the analysis showed that both a compelling 'call to action' and assembling an effective 'coalition of the willing' are important. To maintain momentum, the analysis identified themes relating to system structure, culture and the people involved. Regarding culture, the main themes that emerged were the importance of nurturing strong relationships, curiosity and a desire to understand the system, and promoting resilience. The analysis identified three components that could be used as indicators of success; these were a sense of enjoyment from the work, resource gains to the system and shifts in data indicators at the population level. CONCLUSIONS: This study has provided insight into the nature of systems leadership in public health settings in the UK. It has identified factors that contribute to effective public health systems leadership and offers a thematic model in terms of establishing a systems leadership approach, maintaining momentum and identifying key success indicators

The illusion of competency versus the desirability of expertise: Seeking a common standard for support professions in sport

In this paper we examine and challenge the competency-based models which currently dominate accreditation and development systems in sport support disciplines, largely the sciences and coaching. Through consideration of exemplar shortcomings, the limitations of competency-based systems are presented as failing to cater for the complexity of decision making and the need for proactive experimentation essential to effective practice. To provide a better fit with the challenges of the various disciplines in their work with performers, an alternative approach is presented which focuses on the promotion, evaluation and elaboration of expertise. Such an approach resonates with important characteristics of professions, whilst also providing for the essential ‘shades of grey’ inherent in work with human participants. Key differences between the approaches are considered through exemplars of evaluation processes. The expertise-focused method, although inherently more complex, is seen as offering a less ambiguous and more positive route, both through more accurate representation of essential professional competence and through facilitation of future growth in proficiency and evolution of expertise in practice. Examples from the literature are also presented, offering further support for the practicalities of this approach