In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and learning of statistics through real contexts. We also report the development of a corresponding assessment regime and how this works in the classroom.Controversially, in September 2006 the UK government announced that coursework was to be dropped for mathematics exams sat by 16-year-olds. A consequence of this decision is that areas of the curriculum previously only assessed via this method will no longer be assessed. These include the stages of design, collection of data, analysis and reporting which are essential components of a statistical investigation. The mechanism outlined here could provide some new and useful ways of coupling new teaching methods with learning and doing assessment -in short, they could go some way towards making up for the educational loss of not doing coursework. Also, our findings have implications for teaching, learning and assessing statistics for students of the subject at all ages.
Two mathematical models for tumour anti-angiogenesis, one originally formulated by Hahnfeldt et al. (1999, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res., 59, 4770-4775) and a modification of this model by Ergun et al. (2003, Optimal scheduling of radiotherapy and angiogenic inhibitors. Bull. Math. Biol., 65, 407-424) are considered as optimal control problem with the aim of maximizing the tumour reduction achievable with an a priori given amount of angiogenic agents. For both models, depending on the initial conditions, optimal controls may contain a segment along which the dosage follows a so-called singular control, a time-varying feedback control. In this paper, for these cases, the efficiency of piecewise constant protocols with a small number of switchings is investigated. Through comparison with the theoretically optimal solutions, it will be shown that these protocols provide generally excellent suboptimal strategies that for many initial conditions come within a fraction of 1% of the theoretically optimal values. When the duration of the dosages are a priori restricted to a daily or semi-daily regimen, still very good approximations of the theoretically optimal solution can be achieved.
Within the context of likelihood and Bayes approaches to inference in autoregressive moving-average (ARMA) time series models, previous ideas on parameter transformation and numerical integration for implementing Bayesian procedures are reviewed. Some novel transformation ideas are introduced and their role in an efficient numerical integration approach is examined. Some comparisons of the effectivesness of different numerical integration strategies are made.
The massive expansion of the internet into every aspect of our lives creates a challenge for social researchers: can they simply transfer their traditional methods and techniques online or do they need to reinvent research methods for the new environment? As online research becomes increasingly prevalent it becomes more important for researchers to have an answer to these questions and an approach to conducting research online. This book is a straightforward, accessible introduction to social research online. It covers the key issues and concerns for social scientists: online surveys, focus groups, interviews, ethnographies and experiments, as well as discussing the implications of social media, and of online research ethics. It provides a detailed, up-to-date glossary and bibliography for those new to the area. Short, clear case studies throughout allow students to see examples of the research in practice. Wide-ranging and interdisciplinary, What is Online Research? shows social scientists of all levels - from undergraduates to established researchers - how to engage in the online environment in appropriate ways, and points the way forward for future research.
International audienceThe analysis of the contrast problem in NMR medical imaging is essentially reduced to the analysis of the so-called singular trajectories of the system modeling the problem: a coupling of two spin 1/2 control systems. They are solutions of a constraint Hamiltonian vector field and restricting the dynamics to the zero level set of the Hamiltonian they define a vector field on B1 x B2, where B1 and B2 are the Bloch balls of the two spin particles. In this article we classify the behaviors of the solutions in relation with the relaxation parameters using the concept of feedback classification. The optimality status is analyzed using the feedback invariant concept of conjugate points
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