A fact-aligned corpus of numerical expressions

We describe a corpus of numerical expressions, developed as part of the NUMGEN project. The corpus contains newspaper articles and scientific papers in which exactly the same numerical facts are presented many times (both within and across texts). Some annotations of numerical facts are original: for example, numbers are automatically classified as round or non-round by an algorithm derived from Jansen and Pollmann (2001); also, numerical hedges such as 'about' or 'a little under' are marked up and classified semantically using arithmetical relations. Through explicit alignment of phrases describing the same fact, the corpus can support research on the influence of various contextual factors (e.g., document position, intended readership) on the way in which numerical facts are expressed. As an example we present results from an investigation showing that when a fact is mentioned more than once in a text, there is a clear tendency for precision to increase from first to subsequent mentions, and for mathematical level either to remain constant or to increase

A modified Galerkin/finite element method for the numerical solution of the Serre-Green-Naghdi system

A new modified Galerkin / Finite Element Method is proposed for the numerical solution of the fully nonlinear shallow water wave equations. The new numerical method allows the use of low-order Lagrange finite element spaces, despite the fact that the system contains third order spatial partial derivatives for the depth averaged velocity of the fluid. After studying the efficacy and the conservation properties of the new numerical method, we proceed with the validation of the new numerical model and boundary conditions by comparing the numerical solutions with laboratory experiments and with available theoretical asymptotic results

Preschool predictors of mathematics in first grade children with autism spectrum disorder

AbstractUp till now, research evidence on the mathematical abilities of children with autism spectrum disorder (ASD) has been scarce and provided mixed results. The current study examined the predictive value of five early numerical competencies for four domains of mathematics in first grade. Thirty-three high-functioning children with ASD were followed up from preschool to first grade and compared with 54 typically developing children, as well as with normed samples in first grade. Five early numerical competencies were tested in preschool (5–6 years): verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Four domains of mathematics were used as outcome variables in first grade (6–7 years): procedural calculation, number fact retrieval, word/language problems, and time-related competences. Children with ASD showed similar early numerical competencies at preschool age as typically developing children. Moreover, they scored average on number fact retrieval and time-related competences and higher on procedural calculation and word/language problems compared to the normed population in first grade. When predicting first grade mathematics performance in children with ASD, both verbal subitizing and counting seemed to be important to evaluate at preschool age. Verbal subitizing had a higher predictive value in children with ASD than in typically developing children. Whereas verbal subitizing was predictive for procedural calculation, number fact retrieval, and word/language problems, counting was predictive for procedural calculation and, to a lesser extent, number fact retrieval. Implications and directions for future research are discussed