Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

Characterising loss and damage from climate change

Policy-makers are creating mechanisms to help developing countries cope with loss and damage from climate change, but the negotiations are largely neglecting scientific questions about what the impacts of climate change actually are. Mitigation efforts have failed to prevent the continued increase of anthropogenic greenhouse gas (GHG) emissions. Adaptation is now unlikely to be sufficient to prevent negative impacts from current and future climate change1. In this context, vulnerable nations argue that existing frameworks to promote mitigation and adaptation are inadequate, and have called for a third international mechanism to deal with residual climate change impacts, or “loss and damage”2. In 2013, the United Nations Framework Convention on Climate Change (UNFCCC) responded to these calls and established the Warsaw International Mechanism (WIM) to address loss and damage from the impacts of climate change in developing countries3. An interim Executive Committee of party representatives has been set up, and is currently drafting a two-year workplan comprising meetings, reports, and expert groups; and aiming to enhance knowledge and understanding of loss and damage, strengthen dialogue among stakeholders, and promote enhanced action and support. Issues identified as priorities for the WIM thus far include: how to deal with non-economic losses, such as loss of life, livelihood, and cultural heritage; and linkages between loss and damage and patterns of migration and displacement2. In all this, one fundamental issue still demands our attention: which losses and damages are relevant to the WIM? What counts as loss and damage from climate change?

The Japanese Probation Service: a third sector template?

The use of probation in Japan is similar in some respects to probation in England and Wales (E&W) and unrecognizable in others. This article provides an outline of the structure and operation of probation in Japan and draws comparisons and contrasts with probation in England and Wales. It is intended to provide an overview for those who know little about Japanese criminal justice in general and about Japanese probation in particular. The focus in on accessible English language sources that will enable readers to follow up their interest and deepen their knowledge.