title: Processing mathematical thinking through digital pedagogical media: the spreadsheet

authors: Calder, Nigel Stuart

subjects: mathematics education

abstract: Abstract

This study is concerned with the ways mathematical understanding emerges when mathematical phenomena are encountered through digital pedagogical media, the spreadsheet, in particular. Central to this, was an examination of the affordances digital technologies offer, and how the affordances associated with investigating mathematical tasks in the spreadsheet environment, shaped the learning trajectories of the participants. Two categories of participating students were involved, ten-year-old primary school pupils, and pre-service teachers. 

An eclectic approach to data collection, including qualitative and quantitative methods, was initially undertaken, but as my research perspective evolved, a moderate hermeneutic frame emerged as the most productive way in which to examine the research questions. A hermeneutic process transformed the research methodology, as well as the manner in which the data were interpreted. The initial analysis and evolving methodology not only informed this transition to a moderate hermeneutic lens, they were constitutive of the ongoing research perspectives and their associated interpretations. The data, and some that was subsequently collected, were then reconsidered from this modified position.

The findings indicated that engaging mathematical tasks through the pedagogical medium of the spreadsheet, influenced the nature of the investigative process in particular ways. As a consequence, the interpretations of the interactions, and the understandings this evoked, also differed. The students created and made connections between alternative models of the situations, while the visual, tabular structuring of the environment, in conjunction with its propensity to instantly manage large amounts of output accurately, facilitated their observation of patterns. They frequently investigated the visual nature of these patterns, and used visual referents in their interpretations and explanations. It also allowed them to pose and test their informal conjectures and generalisations in non-threatening circumstances, to reset investigative sub-goals easily, hence fostering risk taking in their approach. At times, the learning trajectory evolved in unexpected ways, and the data illustrated various alternative ways in which unexpected, visual output stimulated discussion and extended the boundaries of, or reorganised, their interaction and mathematical thinking. An examination of the visual perturbations, and other elements of learning as hermeneutic processes also revealed alternative understandings and explanations.

Viewing the data and the research process through hermeneutic filters enhanced the connectivity between the emergence of individual mathematical understanding, and the cultural formation of mathematics. It permitted consideration of the ways this process influences the evolution of mathematics education research. While interpretive approaches are inevitably imbued with the researcher perspective in the analysis of what gets noticed, the research gave fresh insights into the ways learning emerges through digital pedagogical media, and the potential of this engagement to change the nature of mathematics education.

text: Processing mathematical thinking through digital pedagogical media: the spreadsheet Abstract

This study is concerned with the ways mathematical understanding emerges when mathematical phenomena are encountered through digital pedagogical media, the spreadsheet, in particular. Central to this, was an examination of the affordances digital technologies offer, and how the affordances associated with investigating mathematical tasks in the spreadsheet environment, shaped the learning trajectories of the participants. Two categories of participating students were involved, ten-year-old primary school pupils, and pre-service teachers. 

An eclectic approach to data collection, including qualitative and quantitative methods, was initially undertaken, but as my research perspective evolved, a moderate hermeneutic frame emerged as the most productive way in which to examine the research questions. A hermeneutic process transformed the research methodology, as well as the manner in which the data were interpreted. The initial analysis and evolving methodology not only informed this transition to a moderate hermeneutic lens, they were constitutive of the ongoing research perspectives and their associated interpretations. The data, and some that was subsequently collected, were then reconsidered from this modified position.

The findings indicated that engaging mathematical tasks through the pedagogical medium of the spreadsheet, influenced the nature of the investigative process in particular ways. As a consequence, the interpretations of the interactions, and the understandings this evoked, also differed. The students created and made connections between alternative models of the situations, while the visual, tabular structuring of the environment, in conjunction with its propensity to instantly manage large amounts of output accurately, facilitated their observation of patterns. They frequently investigated the visual nature of these patterns, and used visual referents in their interpretations and explanations. It also allowed them to pose and test their informal conjectures and generalisations in non-threatening circumstances, to reset investigative sub-goals easily, hence fostering risk taking in their approach. At times, the learning trajectory evolved in unexpected ways, and the data illustrated various alternative ways in which unexpected, visual output stimulated discussion and extended the boundaries of, or reorganised, their interaction and mathematical thinking. An examination of the visual perturbations, and other elements of learning as hermeneutic processes also revealed alternative understandings and explanations.

Viewing the data and the research process through hermeneutic filters enhanced the connectivity between the emergence of individual mathematical understanding, and the cultural formation of mathematics. It permitted consideration of the ways this process influences the evolution of mathematics education research. While interpretive approaches are inevitably imbued with the researcher perspective in the analysis of what gets noticed, the research gave fresh insights into the ways learning emerges through digital pedagogical media, and the potential of this engagement to change the nature of mathematics education.

year: 2008

title: ‘Troubling’ gender in virtual gaming spaces

authors: Todd, Cherie J.

subjects: Avatar

abstract: This article considers the relationship between gaming and gender, and explores how eight mature women gamers (30 years of age and older), living in the Waikato region of New Zealand negotiate their ‘real-life’ identities with their ‘virtual’ gaming identities. In particular, performances of ‘gender-bending’ in gaming are examined and Butler's notion of ‘gender trouble’ is drawn upon to look at the ways in which ‘gender-bending’ disrupts and/or reinforces hegemonic binary distinctions of gender – masculinity/femininity and man/woman. This article concludes by arguing that gender-switching within gaming spaces is a normative practice within gaming culture, and as such, acts of ‘gender-bending’ do very little to challenge or ‘bend’ dominant notions of gender within the spaces of mainstream gaming.

text: ‘Troubling’ gender in virtual gaming spaces This article considers the relationship between gaming and gender, and explores how eight mature women gamers (30 years of age and older), living in the Waikato region of New Zealand negotiate their ‘real-life’ identities with their ‘virtual’ gaming identities. In particular, performances of ‘gender-bending’ in gaming are examined and Butler's notion of ‘gender trouble’ is drawn upon to look at the ways in which ‘gender-bending’ disrupts and/or reinforces hegemonic binary distinctions of gender – masculinity/femininity and man/woman. This article concludes by arguing that gender-switching within gaming spaces is a normative practice within gaming culture, and as such, acts of ‘gender-bending’ do very little to challenge or ‘bend’ dominant notions of gender within the spaces of mainstream gaming.

year: 2012

title: Exploring synergies between Māori pedagogy and communicative language teaching

authors: Nock, Sophie

subjects: Māori pedagogy

abstract: The primary aim of this paper is to explore potential synergies between Māori pedagogy and what is known as ‘communicative language teaching’. A brief outline of some changes and developments in approaches to language teaching and learning over the last few decades is followed by a summary of some of the main characteristics of communicative language teaching (CLT) and of different approaches to the conceptualization of Māori pedagogy. Some of the primary characteristics of communicative language teaching are then explored in the context of Māori pedagogy and it is argued that there are some important synergies between the two.

text: Exploring synergies between Māori pedagogy and communicative language teaching The primary aim of this paper is to explore potential synergies between Māori pedagogy and what is known as ‘communicative language teaching’. A brief outline of some changes and developments in approaches to language teaching and learning over the last few decades is followed by a summary of some of the main characteristics of communicative language teaching (CLT) and of different approaches to the conceptualization of Māori pedagogy. Some of the primary characteristics of communicative language teaching are then explored in the context of Māori pedagogy and it is argued that there are some important synergies between the two.

year: 2009-02