Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

Taking as its starting point that the adjective international is an inadequate, but unavoidable, label to describe the content of a contemporary international education, this article sets out to explore some of the issues facing international education in a post-international world. It draws mainly on writings in French as a deliberate…

This article attempts to trace the evolution of the concept of international mindedness from the 17th century until the present, using four aspects to focus the discussion: education and other trends, ease of interaction across frontiers, determinants of international mindedness, and international mindedness in practice. Education trends start…

A comparison of the proof validation behavior of beginning undergraduate students and research-active mathematicians is explored. Participants' eye movements were recorded as they validated purported proofs. The main findings are that (a) contrary to previous suggestions, mathematicians sometimes appear to disagree about the validity of even short…

Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsak, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

This paper provides analytic focus on the productive and editorial contexts of children and young people's image-making, making visible its implications for the analysis of photographs. Drawing on participatory research in which children and young people worked alongside researchers to create a visual narrative of their lived experiences of…

This brief research report gives an overview of a visually based methodology that has recently been used to shed light on situated decision-making in a high stakes educational assessment environment. Looking carefully at the feedback interactions taking place between senior and less senior examiners, the project aim was to gain insight into the…

This article centres on a research project in which freehand drawings provided a richly creative and colourful data source of children's imagined, ideal learning environments. Issues concerning the analysis of the visual data are discussed, in particular, how imaginative content was analysed and how the analytical process was dependent on an…

This article addresses the under-theorization of visual techniques for social science research applications through the cultural-historical activity theory (CHAT). The "problem" of "the visual" in research is given an ontological framing by highlighting the ways in which the use of visual techniques as research tools--designed to elicit…

In an attempt to address minority issues with Israeli Arab English-as-a-foreign-language ninth-grade students, I as a teacher researcher introduced picture books on the issue and invited students to respond in different modes, one of which was artistic. In one of the lessons, students created collages to represent their identities. In this…

In this article, we set out to explore what we describe as the use of video in various modalities. For us, modality is a synthesizing construct that draws together and differentiates between the notion of "video" both as a method and as a methodology. It encompasses the use of the term video as both product and process, and as a data collection…

The context of the study reported in this paper is the difficulties of transition from nonformal primary schools to formal secondary schools in Bangladesh. The difficulties affecting a smooth school transition relate not only to the making of new relationships and adapting to new norms in a new environment, but also to a very different approach to…

Although primary source accounts provide students with direct access to the experiences of historical participants, they can reinforce the dominant culture historical narrative if misrepresented by teachers, curriculum publishers, or scholars. The author demonstrates the importance of adhering to guidelines presented by critical Indigenous…