The aim of this study was to model the most crucial numerical factors to the development of mathematical skills among children aged five to eight years (ie kindergarten, preschool, first and second graders) We categorised numerical skills into four main groups based on the results of longitudinal studies A series of analyses of test batteries designed to measure the development of mathematical skills in children yielded results in support of this construct Based on our findings we propose a working model for teachers of core numerical skills that focuses on four major factors: (1) symbolic and non-symbolic number sense; (2) understanding mathematical relations (early mathematical-logical principles, arithmetic principles, mathematical operational symbols, place-value and base-ten system); (3) counting skills (knowledge of number-symbols, number word-sequence, enumeration with concrete objects); and (4) basic skills in arithmetic (arithmetic combinations, addition and subtraction skills with number sy

Core numerical skills for learning mathematics in children aged five to eight years – a working model for educators

We describe how multimedia scenarios delivered online can be used in instruments for the study of professional knowledge. Based on our work in the study of the knowledge and rationality involved in mathematics teaching, we describe how the study of professional knowledge writ large can benefit from the capacity to represent know-how using multimedia representations of practice and alternatives to it. These instruments can be used to study what professionals notice and decide to do in practice in ways that improve upon earlier uses of written representations of professional scenarios or videorecorded episodes. In particular, storyboards and animations of nondescript cartoon characters can be used to explore professional knowledge variables systematically while the multimodal representation of human activity in context ensures the face validity of questions.

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Studying professional knowledge use in practice using multimedia scenarios delivered online

In this paper we consider the phenomenon of the growth of collective mathematical understanding and explore its dependence on the particular way that a group of learners work together collaboratively. We label this group process as improvisational coaction. In an earlier paper (Martin, Towers and Pirie, 2006) we drew on the theoretical work of Becker (2000), Sawyer (2001, 2003, 2004), and Berliner (1994) in improvisational jazz and theatre, to characterise the growth of collective mathematical understanding as a creative and emergent improvisational process. Here, we extend that conceptual analysis to a yet-finer grain to explore one element of that framework, improvisational coaction, and its relationship to the growth of mathematical understanding at the level of the group. In particular we identify improvisational coaction as a particular form of interaction, and through using data extracts we derive four characteristics of the phenomenon and consider how these occasion the growth of collective mathema...

Improvisational coactions and the growth of collective mathematical understanding

The paper describes a comprehensive approach to problems of performance measurement that can be used to tackle a wide range of situations, including designing monthly board and leadership reports in enterprises, assessing research quality and monitoring the efficiency and effectiveness of government programmes. It provides a review of various methods for tackling these problems and outlines some current areas of research. Although technical statistical issues are buried somewhat below the surface, statistical thinking is very much part of the main line of argument, meaning that performance measurement should be an area attracting serious attention from statisticians.

A comprehensive approach to problems of performance measurement

Self-injurious behaviors (SIBs) are increasing in the general adolescent population, giving rise to concerns about the impact these behaviors have on gifted and talented youth. Educators of the gifted may not have adequate understanding of these behaviors, limiting their effectiveness in supporting gifted students engaging in SIB. This article provides an overview of definitions, demographics, and influencing factors, which may enlighten teachers of gifted students about how best to work with those who are struggling with this behavior. The article concludes with a set of suggested best practices for educators of the gifted that can be implemented in schools and classrooms to support students who are self-injuring and to potentially prevent other gifted students from engaging in SIB.

Self-Injurious Behavior in Gifted and Talented Youth What Every Educator Should Know

Thinking and Learning

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