Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

In this paper, we discuss the process of identifying and validating students' abilities to think proportionally. More specifically, we describe the methodology we used to identify these proportional reasoning attributes, beginning with the selection and review of relevant literature on proportional reasoning. We then continue with the…

Data from open modelling sessions for year 10 and 11 students at an extracurricular modelling event and from a year 9 class participating in a programme of structured modelling of real situations were analysed for evidence of Niss's theoretical construct, "implemented anticipation," during mathematisation. Evidence was found for all…

This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: "language of generalisation," "language of comparison," "language of proportional reasoning," and…

This investigation explored the challenges of creating meaningful mathematics practices for a community engaged in Distance Education (DE). Specifically, the study maps the influence of "new" technologies on the practices of a learning community where mathematics was taught remotely. The theoretical framework of this study utilised Bourdieu's work…

The explosion of Gaeilge (Irish)-medium primary and secondary schools has played a crucial role in the rebirth of our native language in Ireland. The popularity of attending Gaeilge-medium education is significant, and continues to increase annually ("Gaeilscoileanna Teo" 2008). However, the majority of Gaeilgeoiri (students who learn through the…

This article describes the implementation and outcomes, as perceived by the professional learning providers and school principals, of a professional learning (PL) model devised in response to recognition that models of PL that are effective in urban settings are not effective in rural and remote areas. Rather than expecting the teachers to travel…

In Australia, concerns about the quality of mathematics education that students experience are particularly salient in rural schools. These schools typically report great difficulty in attracting and retaining qualified teachers of mathematics. Teachers in non-metropolitan locations may also experience professional isolation if they have limited…

In the present study, I examine a modelling strategy as employed by a teacher in the context of an algebra lesson. The actions of this teacher suggest that a modelling approach will have a greater impact on enriching student learning if we do not lose sight of the need to manage associated cognitive loads that could either aid or hinder the…

Mathematics education researchers conducting instruction experiments using a design research methodology are challenged with the analysis of often complex and large amounts of qualitative data. In this paper, we present two case studies that show how multimedia analysis software can greatly support video data analysis and theory development in…

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school…

Although variability and structure are often considered as antonyms in many everyday settings, a mathematically disciplined view contradicts this opposition. To initiate fifth- (10 years old) and sixth-grade (11 years old) students in this disciplinary view, we engaged students in practices of modeling data. These practices included inventing and…

This research was conducted during an after-school partnership between a University and school district in an economically depressed, urban area. The school population consists of 99% African American and Latino students. During the informal after-school math program, a group of 24 6th-grade students from a low socioeconomic community worked…

When ethnomathematical ideas, that is, the mathematical ideas of different cultural groups, are included in mathematics curriculum texts they can become part of the learning experience in various ways. Once included in western classroom mathematics texts, the ethnomathematical ideas become transformed. The transformations involve changes in form…

One of most notable features of existing body of research in transition seems to be the absence of a theoretical model. The suggestion we present in this paper--to view and understand the high school to university transition in mathematics as a modern-day rite of passage--is an attempt at defining such framework. Although dominantly reflecting…