We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

It is generally believed that students should use multiple representations in solving certain physics problems, and earlier work in PER has begun to outline how experts and novices differ in their use of multiple representations. In this study, we build on this foundation by interviewing expert and novice physicists as they solve two types of…

This article describes a mathematics session in which students explored a challenging combinatorics task, a topic shown to be difficult for students when taught traditionally. The students developed a progression of personal representations, increasingly symbolic and abstract, which they used to find a solution and justification. (Contains 8…

While conceptualizations of giftedness have been broadened to include many forms of giftedness, a reconceptualization of gifted programs has not followed. The paper argues that the Reggio Emilia approach to early childhood education, combining important features of the fields of early childhood education and gifted education, is a good fit for…

Referential identification and resolution are considered the keys to help readers grasp the main idea of a text and solve lexical ambiguities. The goal of this study is to design a computer system for helping college students who learn English as a Foreign Language (EFL) develop mental maps of referential identification and resolution in reading.…

Whether two-digit numbers are represented holistically (each digit pair processed as one number) or compositionally (each digit pair processed separately as a decade digit and a unit digit) remains unresolved. Two experiments were conducted to examine the distance, magnitude, and SNARC effects in a number-matching task involving two-digit numbers.…

The use of "MapleTA"[R] in the assessment of engineering mathematics at Liverpool John Moores University (JMU) is discussed with particular reference to the design of questions. Key aspects in the formulation and coding of questions are considered. Problems associated with the submission of symbolic answers, the use of randomly generated numbers…

The purpose of this study was to describe how male, collegiate, certified athletic trainers (AT's) represent knowledge during 5 injury evaluation scenarios. A second purpose of the study was to identify what self-regulatory behaviors participants engaged in to improve or maintain their skills. Knowledge representation was studied as cue selection…

There is no agreement about the robustness of intuitive representations of the circulatory system and their susceptibility to change by instruction. In this paper, we analyse to what extent students with varying degrees of biology instruction and different ages (High School Health Science and Social Science students and first and final year…

The learning object remains an ill-defined concept, despite numerous and extensive discussion in the literature. This paper attempts to address this problem by providing a classification that potentially brings together various perspectives of what a learning object may be. Six unique types of learning objects are proposed and discussed:…

This paper explores the use of design patterns and anti-patterns in teaching human-computer interaction principles. Patterns are increasingly popular and are seen as an efficient knowledge transfer mechanism in many fields, including software development in the field of software engineering, and more recently in the field of human-computer…

This article explores the potential learning benefits of three-dimensional (3-D) virtual learning environments (VLEs). Drawing on published research spanning two decades, it identifies a set of unique characteristics of 3-D VLEs, which includes aspects of their representational fidelity and aspects of the learner-computer interactivity they…

Explores some of the constraints on knowledge development through a multi-perspective examination of a project in which there was an intention and enacted process to develop knowledge. Engaged with the generic question of what the conditions that facilitate knowledge creation in organizations are, considers data from three theoretical…

An educational assessment embodies an argument from a handful of observations of what students say, do or make in a handful of particular circumstances, to what they know or can do in what kinds of situations more broadly. This article discusses ways in which research into the nature and development of expertise can help assessment designers…

We review significant empirical studies of the arithmetic abilities of children with dyslexia. These studies suggest that the academic impairments of children with dyslexia are not limited to reading and spelling, but also include aspects of mathematics. A consistent finding across a number of studies is that children with dyslexia have difficulty…