Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches PDF
Preview Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches
CONTEMPORARY ENVIRONMENTAL AND MATHEMATICS EDUCATION MODELLING USING NEW GEOMETRIC APPROACHES Geometries of Liberation Edited by Susan Gerofsky Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches Susan Gerofsky Editor Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches Geometries of Liberation Editor Susan Gerofsky Department of Curriculum & Pedagogy University of British Columbia Vancouver, BC, Canada ISBN 978-3-319-72522-2 ISBN 978-3-319-72523-9 (eBook) https://doi.org/10.1007/978-3-319-72523-9 Library of Congress Control Number: 2018944475 © The Editor(s) (if applicable) and The Author(s) 2018 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover illustration: Pattern adapted from an Indian cotton print produced in the 19th century Printed on acid-free paper This Palgrave Pivot imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland C ontents 1 Introduction: Geometries of Liberation 1 Susan Gerofsky 2 Shaped by the Places We Reason? Contrasting the Rectilinearity of Western Educational Thought with Other Possibilities 9 Brent Davis 3 Ecofractal Poetics: Five Fractal Geometries for Creative, Sustainable, and Just Educational Design 29 Marna Hauk 4 Always an Abundance: Interstitial/Liminal Space, Time, and Resources that Are Invisible to the Grid 47 Susan Gerofsky 5 The Curricular Geometries of *SAMBA* Schools: Fractal Dimensions, Surface, Depth, and Recursion 67 Peter Appelbaum v vi CoNTENTS 6 Of Grids and Gardens: School Gardening and the Unsettling Attachments of Teaching Beside the Grid 81 Julia ostertag 7 Off the Grid 101 Edward Doolittle Index 123 n C otes on ontributors Peter Appelbaum is Professor of Education at Arcadia University. He has a doctorate from the University of Michigan, Ann Arbor, in Educational Foundations, Policy and Administration, and Master’s degrees in Curriculum & Psychological Studies (Michigan) and in Mathematics (ABD at Duke University). Appelbaum’s books include Popular culture, educational discourse and mathematics (1995); Multicultural and diversity education: A reference handbook (2002); (Post) modern science (education) (2001); Embracing mathematics: On becoming a teacher and changing with mathematics (2008)—co-authored with Arcadia graduate students; and Children’s books for grown-up teachers: Reading and writing curriculum theory (2009), which was awarded the American Educational Research Association outstanding Book Award for Curriculum Studies. His articles have appeared in journals such as the Journal of Curriculum Studies, Transnational Curriculum Inquiry, The Journal of Curriculum Theorizing, and For the Learning of Mathematics. He has been the President of the American Association for the Advancement of Curriculum Studies and is currently Vice President of the International Commission for the Study and Improvement of Mathematics Education. Appelbaum enjoys collaborating with others in such areas as curriculum theory and history, arts-based and hermeneutic research methods, mixed methods that combine quantitative approaches with qualitative approaches, interdisciplinary studies, education in and out of formal institutions, inter- national and global leadership, psychoanalysis and education, popular cul- ture studies, and anything related to equity and social justice. His own vii viii NoTES oN CoNTRIBUToRS educational path meandered from physics and mathematics, to ethnomusi- cology, to topology and mathematical logic, to cultural and post-colonial queer theory, and he enjoys looking at questions and topics from perspec- tives that don’t initially seem connected until they are brought together by research. Brent Davis was born and raised in northern Alberta, Canada, where he also taught secondary school mathematics and science through most of the 1980s. Upon completion of graduate studies in the mid-1990s, he began his university career at The University of British Columbia (UBC), then moved to York University, then the University of Alberta (where he was Canada Research Chair in Mathematics Education and the Ecology of Learning), then back to UBC (as David Robitaille Chair in Mathematics Education), and finally, to the University of Calgary (as Distinguished Research Chair in Mathematics Education). He holds a Werklund Professorship. Davis’s research is focused on the educational relevance of recent developments in the cognitive and complexity sciences. He has written books and articles in the areas of mathematics learning and teaching, curriculum theory, teacher education, epistemology, and action research. The principal foci of his research are teachers’ disciplinary knowledge of mathematics and the sorts of structures and experiences that might sup- port mathematics learning among teachers. He has authored or co- authored five books and his scholarly writings have appeared in Science, Harvard Educational Review, Journal for Research in Mathematics Education, and other leading journals. Edward Doolittle is Associate Professor of Mathematics at the First Nations University of Canada and at the University of Regina. Doolittle is a Mohawk from the Six Nations reserve in southern ontario and is one of the only First Nations research mathematicians in Canada. He earned his PhD in Pure Mathematics from the University of Toronto in 1997; has taught at the University of Toronto, York University, Queen’s University, and the University of Regina; and has been on the faculty of First Nations University since 2001. He is the recipient of numerous awards, including a Governor General’s Gold Medal. Doolittle’s research interests in mathematics, statistics, and mathemat- ics education include partial differential equations, dynamical systems, Indigenous mathematics, applications of mathematics and statistics to Indigenous knowledge and issues, and the relationships among Indigenous NoTES oN CoNTRIBUToR S ix mathematics and science and education. He researches and publishes in mathematics, statistics, and mathematics education, including publica- tions in the Journal of Ethnobiology and For the Learning of Mathematics. Doolittle’s insightful and highly engaging writing explores interfaces between mathematics and Indigenous thought. Susan Gerofsky is an Assistant Professor of mathematics education and environmental education at The University of British Columbia. She brings experience in a number of fields to bear in innovative and interdis- ciplinary approaches to curriculum theory. She holds degrees in languages and linguistics as well as mathematics education, and worked for many years in film post-production, adult education (including workplace and labor education), and as a secondary school teacher with the Vancouver School Board. Gerofsky has studied and taught in England, Brazil, Italy, Germany, and Cuba. She speaks several languages and is active as a musi- cian, filmmaker, and playwright. Gerofsky’s research interests are in embodied, multisensory, gestural, and movement-oriented learning in mathematics, in the analysis of peda- gogical genres, and in garden-based environmental education. Her cur- rent research foci include work with learners with blindness/visual impairment learning graphing in embodied, multisensory ways; pedagogi- cal intersections of mathematics and the arts (including mathematics and dance); and teacher education across the curriculum in outdoor class- rooms and gardens. Her previous book is A man left Albuquerque heading east: Word problems as genre in mathematics education (2004), and her articles have appeared in journals including For the Learning of Mathematics, Gesture, Discourse, JCT: Journal of Curriculum Theorizing, The Mathematical Intelligencer, On Sustainability and the Australian Journal of Environmental Education. Marna Hauk serves as a postdoctoral scholar, instructor, and graduate mentor at Prescott College in sustainability education, where she instructs and mentors graduate students and leads graduate courses. She also directs the graduate education programs for the Institute for Earth Regenerative Studies in Portland, oregon. Hauk is a 2014–2016 Community Climate Change Fellow of the North American Association of Environmental Education. Hauk’s areas of research include education for climate change and jus- tice, sustainability education, complex systems, regenerative biomimicry, ecopsychology, historical trauma and intergenerational place connection, x NoTES oN CoNTRIBUToRS bioculturally responsive curriculum, ecopreneurship and ecosocial incuba- tors, ecofeminism and feminist research, higher educational design, and advanced research methods. Her research is published in Ecopsychology, the Australian Journal of Environmental Education, the American Educational Research Association, the Association for the Advancement of Sustainability in Higher Education, and the Journal of Sustainability Education. Hauk is co-editor of the practitioner volume, Community Climate Change: A Mosaic of Approaches (2017). Julia Ostertag is an arts-based environmental educator interested in cul- tivating and querying connections to place through gardening practices, and specifically through teacher education and adult education in outdoor classrooms. She asks how conceptualizations of human/nature relation- ships shape education and the design of educational spaces/places. ostertag’s doctoral dissertation, School gardening, teaching, and a peda- gogy of enclosures: Threads of an arts-based métissage (2015), draws on mate- rial feminist and posthumanist scholarship to reconfigure what it means to become a teacher, using site-specific installation art. She lingers beside both the possibilities and impossibilities of teaching with gardens, responding to the difficult history of school gardens, particularly during Nazi Germany and in the Canadian residential school system, and the etymological knots that link gardens with material and discursive practices of enclosure. ostertag is currently teaching environmental education with Lakehead University and the University of ottawa. Her upcoming research plans include further exploration of notions of enclosures at prison farms, gar- dens, and other land-based prison education, through collaborations with students, gardeners, plants, and artists, and site-specific installation art.
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