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In Transreform Radical Humanism: A Mathematics and Teaching Philosophy, a methodological collage of auto/ethnography, Gadamerian hermeneutics, and grounded theory is used to analyze a diverse collection of data: the author’s evolving relationship with mathematics; the philosophies of mathematics; the “math wars”; the achievement gap for Indigenous students in mathematics and some of the lessons learned from ethnomathematics; and risk education as an emerging topic within mathematics curricula. Foundational to this analysis is a new theoretical framework that envelops an Indigenous worldview…mehr
In Transreform Radical Humanism: A Mathematics and Teaching Philosophy, a methodological collage of auto/ethnography, Gadamerian hermeneutics, and grounded theory is used to analyze a diverse collection of data: the author’s evolving relationship with mathematics; the philosophies of mathematics; the “math wars”; the achievement gap for Indigenous students in mathematics and some of the lessons learned from ethnomathematics; and risk education as an emerging topic within mathematics curricula. Foundational to this analysis is a new theoretical framework that envelops an Indigenous worldview and the Traditional Western worldview, acting as a pair of voices (and lenses) that speak to the points of tension, conflict, and possibility found throughout the data. This analysis of the data sets results in the emergence of a new theory, the Transreform Approach to the teaching and learning of mathematics, and in the transreform radical humanistic philosophy of mathematics. Within these pages, mathematics, the teaching and learning of mathematics, hegemony, and the valuing of different kinds of knowledge and ways of knowing collide, sometimes merge, and most frequently become transformed in ways that hold promise for students, teachers, society, and even mathematics itself. As the assumed incommensurability of worldviews is challenged, so too new possibilities emerge. It is hoped that readers will not just read this work, but engage with it, exploring the kinds of knowledge and ways of knowing that they value within mathematics and the teaching and learning of mathematics and why.
Acknowledgements; Abbreviations; List of Figures and Tables; Introduction; Mathematics and Me: Re-Viewing of My Life with Mathematics; Preface: Speaking from Place; Contrasting Worldviews and the Emergence of a Theoretical Framework; An Introduction to Worldviews; The Traditional Western Worldview; An Indigenous Worldview; The Two Worldviews: Implications and Concerns; Concluding Thoughts on the Worldviews; Methodology and Methods; Auto/Ethnography; Gadamerian Hermeneutics; Grounded Theory: Methodology; My Research Methods; Analysis of My Story; “Long Before I Ever Entered School” Analysis; “My First Mathematical Memory” Analysis; “When I Started School” Analysis; “As It Came Time to Apply for University” Analysis; “After Eight Months of Being a Substitute Teacher and Volunteer” Analysis; “My Experiences as a Pilot Teacher and Implementation Leader” Analysis; “In the First Term of My PhD Program” Analysis; My Story: Summary of the Analysis and Moving Forward; Philosophies of Mathematics: Literature Review and Analysis; Neither Modern Nor Postmodern-Like Philosophies of Mathematics; Analysis of the Neither Modern-Like Nor Postmodern-Like Philosophies of Mathematics; Modern-Like Philosophies of Mathematics; Analysis of the Modern-Like Philosophies of Mathematics; Postmodern-Like Philosophies of Mathematics; Analysis of the Postmodern-Like Philosophies of Mathematics; Embodied Mathematics; Analysis of Lakoff and Núñez’s Embodied Mathematics; Mathematical Enculturation; Analysis of Bishop’s Mathematical Enculturation; Final Reflections on the Philosophies of Mathematics, Embodied Mathematics, and Mathematical Enculturation; The Math Wars; Analysis of the Math Wars; Indigenous Students in Relation to Mathematics and Ethnomathematics; Analysis of Indigenous Students in Relation to Mathematics and Ethnomathematics; Risk and Risk Education; Risk Education; Analysis of Risk Education, Risk Analysis, and Risk-Based Decision-Making; NavajoPlague, 1993; and Tsunami, 2004; Research Possibilities for My Theoretical Framework; Looking Inwards: Worldview Analysis of Mathematics and the Teaching and Learning of Mathematics; Examining and Challenging the Boundaries; A Catalyst for Change; The Emergence of a Theory; Potential of the Theory; Reflections on My Choice of Data Sources and Methodologies; Reflections; Moving Forward with the Transreform Approach; Asking Questions; Coda; References.
Acknowledgements; Abbreviations; List of Figures and Tables; Introduction; Mathematics and Me: Re-Viewing of My Life with Mathematics; Preface: Speaking from Place; Contrasting Worldviews and the Emergence of a Theoretical Framework; An Introduction to Worldviews; The Traditional Western Worldview; An Indigenous Worldview; The Two Worldviews: Implications and Concerns; Concluding Thoughts on the Worldviews; Methodology and Methods; Auto/Ethnography; Gadamerian Hermeneutics; Grounded Theory: Methodology; My Research Methods; Analysis of My Story; “Long Before I Ever Entered School” Analysis; “My First Mathematical Memory” Analysis; “When I Started School” Analysis; “As It Came Time to Apply for University” Analysis; “After Eight Months of Being a Substitute Teacher and Volunteer” Analysis; “My Experiences as a Pilot Teacher and Implementation Leader” Analysis; “In the First Term of My PhD Program” Analysis; My Story: Summary of the Analysis and Moving Forward; Philosophies of Mathematics: Literature Review and Analysis; Neither Modern Nor Postmodern-Like Philosophies of Mathematics; Analysis of the Neither Modern-Like Nor Postmodern-Like Philosophies of Mathematics; Modern-Like Philosophies of Mathematics; Analysis of the Modern-Like Philosophies of Mathematics; Postmodern-Like Philosophies of Mathematics; Analysis of the Postmodern-Like Philosophies of Mathematics; Embodied Mathematics; Analysis of Lakoff and Núñez’s Embodied Mathematics; Mathematical Enculturation; Analysis of Bishop’s Mathematical Enculturation; Final Reflections on the Philosophies of Mathematics, Embodied Mathematics, and Mathematical Enculturation; The Math Wars; Analysis of the Math Wars; Indigenous Students in Relation to Mathematics and Ethnomathematics; Analysis of Indigenous Students in Relation to Mathematics and Ethnomathematics; Risk and Risk Education; Risk Education; Analysis of Risk Education, Risk Analysis, and Risk-Based Decision-Making; NavajoPlague, 1993; and Tsunami, 2004; Research Possibilities for My Theoretical Framework; Looking Inwards: Worldview Analysis of Mathematics and the Teaching and Learning of Mathematics; Examining and Challenging the Boundaries; A Catalyst for Change; The Emergence of a Theory; Potential of the Theory; Reflections on My Choice of Data Sources and Methodologies; Reflections; Moving Forward with the Transreform Approach; Asking Questions; Coda; References.
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