Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

Promoting interdisciplinarity through mathematical modelling

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.

Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Economics and preventing healthcare acquired infection

The evolution of organisms that cause healthcare acquired infections (HAI) puts extra stress on hospitals already struggling with rising costs and demands for greater productivity and cost containment. Infection control can save scarce resources, lives, and possibly a facility’s reputation, but statistics and epidemiology are not always sufficient to make the case for the added expense. Economics and Preventing Healthcare Acquired Infection presents a rigorous analytic framework for dealing with this increasingly serious problem. ----- Engagingly written for the economics non-specialist, and brimming with tables, charts, and case examples, the book lays out the concepts of economic analysis in clear, real-world terms so that infection control professionals or infection preventionists will gain competence in developing analyses of their own, and be confident in the arguments they present to decision-makers. The authors: ----- Ground the reader in the basic principles and language of economics. ----- Explain the role of health economists in general and in terms of infection prevention and control. ----- Introduce the concept of economic appraisal, showing how to frame the problem, evaluate and use data, and account for uncertainty. ----- Review methods of estimating and interpreting the costs and health benefits of HAI control programs and prevention methods. ----- Walk the reader through a published economic appraisal of an infection reduction program. ----- Identify current and emerging applications of economics in infection control. ---- Economics and Preventing Healthcare Acquired Infection is a unique resource for practitioners and researchers in infection prevention, control and healthcare economics. It offers valuable alternate perspective for professionals in health services research, healthcare epidemiology, healthcare management, and hospital administration. ----- Written for: Professionals and researchers in infection control, health services research, hospital epidemiology, healthcare economics, healthcare management, hospital administration; Association of Professionals in Infection Control (APIC), Society for Healthcare Epidemiologists of America (SHEA)

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Creative clusters and universities : the cluster concept in economics and geography

This paper considers the history of the cluster concept in urban economic geography, and its relationship to recent debates about creative cities. It then looks at the role that universities can play in the development of a creative cluster, as well as some of the potential pitfalls.

Obesity in pregnancy : outcomes and economics

Maternal obesity is an important aspect of reproductive care. It is the commonest risk factor for maternal mortality in developed countries and is also associated with a wide spectrum of adverse pregnancy outcomes. Maternal obesity may have longer-term implications for the health of the mother and infant, which in turn will have economic implications. Efforts to prevent, manage and treat obesity in pregnancy will be costly, but may pay dividends from reduced future economic costs, and subsequent improvements to maternal and infant health. Decision-makers working in this area of health services should understand whether the problem can be reduced, at what cost; and then, what cost savings and health benefits will accrue in the future from a reduction of the problem.

Mixing colours : an ICT tool based on a semiotic framework for mathematical meaning-making about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.