Thinking skills in the early years: a literature review

Since 1999, thinking skills have been included in the National Curriculum alongside ‘key skills’ such as those to do with communication and information and communications technology (ICT). Thinking skills are expected to be developed at all key stages and centre on: information-processing skills, reasoning skills, enquiry skills, creative thinking skills and evaluation skills. This literature review consisted of three phases based on the following research questions: 1. What pedagogical approaches to developing generic thinking skills currently exist for children between the ages of three and seven? 2. What are the generic thinking skills that children are able to demonstrate at this age? 3. What is the relationship between these thinking capabilities and those that the pedagogical approaches aim to develop? The review covered post-2000 literature in the area of thinking skills in the early years. It provides an update of the evidence base upon which thinking skills approaches have been established, suggests areas where more evidence is needed and makes some practical recommendations for researchers, policy makers and practitioners.

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

Are you thinking what I’m thinking? Peer group similarities in adolescent hostile attribution tendencies

A bias towards attributing hostile intent to others has been linked to aggression. In an adolescent sample, we investigated whether peer group homophily exists in the tendency towards attributing hostile intent. We assessed hostile attribution tendencies and self-reported aggressive behaviours in a normative sample of 910 adolescents, and computed average peer group scores based on nominated friend scores. Results indicated that adolescents showed significant correlations between their own level of hostile attributions and that of their peer group. Further analyses indicated that this effect occurred specifically in reciprocal friendships, and was retained even once own and peer group level of aggression were controlled.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Mathematical notation: help or hindrance?

In this article Geoff Tennant puts forward a range of reasons for using mathematical notation, emphasising the need to allow children learning it time and space to come to terms with it. Examples are given in furthering the argument that the time to introduce notation is after the concept is already fully understood.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

A simplified mathematical model for urban microclimate simulation

Techniques for modelling urban microclimates and urban block surfaces temperatures are desired by urban planners and architects for strategic urban designs at the early design stages. This paper introduces a simplified mathematical model for urban simulations (UMsim) including urban surfaces temperatures and microclimates. The nodal network model has been developed by integrating coupled thermal and airflow model. Direct solar radiation, diffuse radiation, reflected radiation, long-wave radiation, heat convection in air and heat transfer in the exterior walls and ground within the complex have been taken into account. The relevant equations have been solved using the finite difference method under the Matlab platform. Comparisons have been conducted between the data produced from the simulation and that from an urban experimental study carried out in a real architectural complex on the campus of Chongqing University, China in July 2005 and January 2006. The results show a satisfactory agreement between the two sets of data. The UMsim can be used to simulate the microclimates, in particular the surface temperatures of urban blocks, therefore it can be used to assess the impact of urban surfaces properties on urban microclimates. The UMsim will be able to produce robust data and images of urban environments for sustainable urban design.

The evolution of strategy: thinking war from antiquity to the present

Latin had no word for "strategy", but the East Romans, whom we call the Byzantines, did. This book tracks the evolution of the concept of warfare being subjected to higher political aims from Antiquity to the Present, using Greek, Latin, French, Spanish, Italian, English and German sources. It tracks the rise, fall, and resurrection of the belief in the Roman and later the medieval and early modern world that warfare was only legitimate if it pursued the higher goal of a just peace, which in the 19th century gave way to a blinkered concentration on military victory as only war aim. It explains why one school of thought, from Antiquity to the present, emphasised eternal principles of warfare, while others emphasised, in Clausewitz's term, the "changing character of war". It tracks ideas from land warfare to naval warfare to air power and nuclear thinking, but it also stresses great leaps and discontinuities in thinking about strategy. It covers asymmetric wars both from the point of view of the weaker power seeking to overthrow a stronger power, and from the stronger power dealing with insurgents and other numerically inferior forces. It concludes with a commentary of the long-known problems of bureaucratic politics, non-centralised command and inter-service rivalry, which since the 16th century or earlier has created obstacles to coherent strategy making.