title: Processing mathematics through digital technologies: A reorganisation of student thinking?

authors: Calder, Nigel Stuart

subjects: mathematical thinking

abstract: This article reports on aspects of an ongoing study examining the use of digital media in mathematics education. In particular, it is concerned with how understanding evolves when mathematical tasks are engaged through digital pedagogical media in primary school settings. While there has been a growing body of research into software and other digital media that enhances geometric, algebraic, and statistical thinking in secondary schools, research of these aspects in primary school mathematics is still limited, and emerging intermittently. The affordances of digital technology that allow dynamic, visual interaction with mathematical tasks, the rapid manipulation of large amounts of data, and instant feedback to input, have already been identified as ways mathematical ideas can be engaged in alternative ways. How might these, and other opportunities digital media afford, transform the learning experience and the ways mathematical ideas are understood? Using an interpretive methodology, the researcher examined how mathematical thinking can be seen as a function of the pedagogical media through which the mathematics is encountered. The article gives an account of how working in a spreadsheet environment framed learners' patterns of social interaction, and how this interaction, in conjunction with other influences, mediated the understanding of mathematical ideas, through framing the students' learning pathways and facilitating risk taking.

text: Processing mathematics through digital technologies: A reorganisation of student thinking? This article reports on aspects of an ongoing study examining the use of digital media in mathematics education. In particular, it is concerned with how understanding evolves when mathematical tasks are engaged through digital pedagogical media in primary school settings. While there has been a growing body of research into software and other digital media that enhances geometric, algebraic, and statistical thinking in secondary schools, research of these aspects in primary school mathematics is still limited, and emerging intermittently. The affordances of digital technology that allow dynamic, visual interaction with mathematical tasks, the rapid manipulation of large amounts of data, and instant feedback to input, have already been identified as ways mathematical ideas can be engaged in alternative ways. How might these, and other opportunities digital media afford, transform the learning experience and the ways mathematical ideas are understood? Using an interpretive methodology, the researcher examined how mathematical thinking can be seen as a function of the pedagogical media through which the mathematics is encountered. The article gives an account of how working in a spreadsheet environment framed learners' patterns of social interaction, and how this interaction, in conjunction with other influences, mediated the understanding of mathematical ideas, through framing the students' learning pathways and facilitating risk taking.

year: 2011

title: Statistical representations of the housing problem in briefings to incoming ministers, 2008–2020: The politics of housing numbers

authors: Barrett, Patrick

abstract: An interpretive policy studies perspective on what is understood to be the ‘facts’ about the housing problem in New Zealand has potential to uncover the way statistical representations of problems are embedded in larger normative narratives, and the consequential implications for housing policy and governance. This paper analyses such representations as they are evident in policy briefings to incoming Ministers of Housing between 2008 and 2020 by Housing New Zealand (HNZ) and its successor Kāinga Ora, and the way these reflect and reinforce a neoliberal political rationality and an agenda to residualise and marketise state housing support. The briefings represent authoritative accounts by a key bureaucratic advisory agency of the significant issues and priorities in the housing portfolio. The period prior to 2017 saw the emergence of new articulations of housing problems relating to affordability, declining rates of home ownership, an increasing rental population, and increasing homelessness. In the briefings to ministers, these problems were routinely framed as issues of supply and demand and market adjustment, and this has continued following the change of government in 2017. The focus of the paper is on identifying statistical representations within the discursive context that give weight to particular policy choices.

text: Statistical representations of the housing problem in briefings to incoming ministers, 2008–2020: The politics of housing numbers An interpretive policy studies perspective on what is understood to be the ‘facts’ about the housing problem in New Zealand has potential to uncover the way statistical representations of problems are embedded in larger normative narratives, and the consequential implications for housing policy and governance. This paper analyses such representations as they are evident in policy briefings to incoming Ministers of Housing between 2008 and 2020 by Housing New Zealand (HNZ) and its successor Kāinga Ora, and the way these reflect and reinforce a neoliberal political rationality and an agenda to residualise and marketise state housing support. The briefings represent authoritative accounts by a key bureaucratic advisory agency of the significant issues and priorities in the housing portfolio. The period prior to 2017 saw the emergence of new articulations of housing problems relating to affordability, declining rates of home ownership, an increasing rental population, and increasing homelessness. In the briefings to ministers, these problems were routinely framed as issues of supply and demand and market adjustment, and this has continued following the change of government in 2017. The focus of the paper is on identifying statistical representations within the discursive context that give weight to particular policy choices.

year: 2021

title: "Thereness": Implications of Heidegger's "presence" for Māori

authors: Mika, Carl Te Hira

abstract: For Māori, the philosophical consequences of colonization are a hugely important issue, due to both the subtlety and the omnipresence of Western metaphysics. In this article I refer to the “meta-physics of presence” through one major Western thinker—Martin Heidegger—who identified “presence” as a problem for the West. He proposes that the metaphysics of presence underpins every perception in the West and that it is the fundamental mistake of philosophers since Plato but becoming ascendant with Aristotle. I identify the points of relevance within their claims and refer them to a Māori understanding of absence. I also consider the more affective nature of Western presence, which Heidegger refers to but which must be theorized by Māori. In the first instance I place particular emphasis on the ironies implicit in writing about metaphysics for the Māori writer in the academy and for the things being represented in that writing. Finally, the metaphysics of presence opens up possibilities for its own instability; this Heideggerean “saving power” is discussed in Māori terms.

text: "Thereness": Implications of Heidegger's "presence" for Māori For Māori, the philosophical consequences of colonization are a hugely important issue, due to both the subtlety and the omnipresence of Western metaphysics. In this article I refer to the “meta-physics of presence” through one major Western thinker—Martin Heidegger—who identified “presence” as a problem for the West. He proposes that the metaphysics of presence underpins every perception in the West and that it is the fundamental mistake of philosophers since Plato but becoming ascendant with Aristotle. I identify the points of relevance within their claims and refer them to a Māori understanding of absence. I also consider the more affective nature of Western presence, which Heidegger refers to but which must be theorized by Māori. In the first instance I place particular emphasis on the ironies implicit in writing about metaphysics for the Māori writer in the academy and for the things being represented in that writing. Finally, the metaphysics of presence opens up possibilities for its own instability; this Heideggerean “saving power” is discussed in Māori terms.

year: 2015