{ "type": "Article", "identifiers": [], "references": [ { "type": "Article", "id": "bib-bib1", "authors": [], "title": "\nA. Gutiérrez, T. Lowrie and the IPC, The 26th ICMI Study: Discussion\ndocument. ICMI, Berlin, Germany (2024)\nhttps://www.mathunion.org/fileadmin/ICMI/ICMI%20studies/ICMI%20Study%2026/ICMI%20Study%2026%20Discussion%20Document.pdf", "url": "https://www.mathunion.org/fileadmin/ICMI/ICMI%20studies/ICMI%20Study%2026/ICMI%20Study%2026%20Discussion%20Document.pdf" }, { "type": "Article", "id": "bib-bib2", "authors": [], "title": "\nT. Lowrie,\nA. Gutiérrez and F. Emprin (eds.), Proceedings of the\ntwenty-sixth\nICMI\nStudy: Advances in Geometry Education.\nICMI, Berlin, Germany\n(2024)\nhttps://www.mathunion.org/fileadmin/ICMI/ICMI%20studies/ICMI%20Study%2026/Proceedings-ICMI%20Study26.pdf", "url": "https://www.mathunion.org/fileadmin/ICMI/ICMI%20studies/ICMI%20Study%2026/Proceedings-ICMI%20Study26.pdf" }, { "type": "Article", "id": "bib-bib3", "authors": [], "title": "\nC. Mammana and V. Villani (eds.), Perspectives on the teaching of\ngeometry for the\n21st century: An ICMI Study.\nKluwer Academic Publishers – Springer,\nDordrecht (1998)\n", "url": "https://doi.org/10.1007/978-94-011-5226-6" } ], "title": "Untitled", "meta": {}, "content": [ { "type": "Paragraph", "id": "p1", "content": [ "The Executive Committee of the International Commission on Mathematical\nInstruction (ICMI) established the foundations of the\n26th ICMI Study in 2022, the topic of the\nstudy being\nAdvances in Geometry Education. This is the first ICMI Study to focus on\ngeometry since 1998 (ICMI Study 9, Perspectives on the Teaching of\nGeometry for the 21st Century); it is aimed at reporting the current\nstate of the field of geometry education, focusing on the advances and\ncurrent challenges in the teaching and learning of geometry, and\nproposing guidelines for future research and innovation actions." ] }, { "type": "Paragraph", "content": [ "Angel Gutiérrez (University of Valencia, Spain) and Thomas Lowrie\n(University of Canberra, Australia) were appointed as co-chairs of the\nstudy by the ICMI Executive Committee. The ICMI\npresident, Frederick\nLeung (Hong Kong SAR), and the\nsecretary general, Jean-Luc Dorier\n(Switzerland), oversee the\nstudy for the ICMI\nexecutive. The\nInternational Program Committee (IPC) comprises the two co-chairs, the\nICMI\npresident and\nsecretary general (", { "type": "Emphasis", "content": [ "ex-officio" ] }, " members), and\nrepresentatives from five continents, with a diversity of expertise in\ndifferent areas of geometry education:" ] }, { "type": "Paragraph", "content": [] }, { "type": "List", "items": [ { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i1.p1", "content": [ "Cathy Bruce (Canada)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i2.p1", "content": [ "Fabien Emprin (France)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i3.p1", "content": [ "Keith Jones (United Kingdom)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i4.p1", "content": [ "Roza Leikin (Israel)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i5.p1", "content": [ "Michela Maschietto (Italy)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i6.p1", "content": [ "Lisnet Mwadzaangati (Malawi)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i7.p1", "content": [ "Oi-Lam Ng (Hong Kong SAR)\n" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i8.p1", "content": [ "Yukari Okamoto (United States)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i9.p1", "content": [ "Milton Rosa (Brazil)" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I1.i10.p1", "content": [ "Manuel Santos-Trigo (Mexico)" ] } ] } ], "order": "Unordered", "meta": { "listType": "bullet" } }, { "type": "Paragraph", "id": "p3", "content": [ "The IPC met at the University of Valencia in February 2023, with the\nobjective of starting the design of the\nstudy. We prepared the Study\nDiscussion Document [", { "type": "Cite", "target": "bib-bib1", "content": [ "1" ] }, "], which was distributed internationally in\nJune 2023, and planned the basis for the organization of the Study\nConference, to take place at the\nInstitut\nNational Supérieur\ndu\nProfessorat\net de\nl’Éducation\n(INSPÉ) of the University of Reims\nChampagne-Ardenne, in Reims (France) from\n23 to 26 April\n2024." ] }, { "type": "Paragraph", "content": [ "The activity of the\nstudy is organized around four focused topics, aimed\nto provide complementary perspectives and approaches to the teaching and\nlearning of geometry. Contributions to the topics were organized around\nsets of related sub-topics, each sub-topic focusing on a specific issue\nand stating a set of questions aimed to lead discussions, as defined in\nthe\ndiscussion document. The four topics were:" ] }, { "type": "Paragraph", "content": [] }, { "type": "List", "items": [ { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I2.i1.p1", "content": [ "theoretical perspectives,\n" ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I2.i2.p1", "content": [ "curricular and methodological approaches," ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I2.i3.p1", "content": [ "resources for teaching and learning geometry," ] } ] }, { "type": "ListItem", "content": [ { "type": "Paragraph", "id": "S0.I2.i4.p1", "content": [ "multidisciplinary perspectives." ] } ] } ], "order": "Ascending", "meta": { "listType": "order" } }, { "type": "Paragraph", "id": "p5", "content": [ "The Study Discussion Document also served as a call for papers for the\nStudy Conference. These topics and related sub-topics provided the basis\nfor inviting papers. Each submission was reviewed by at least two IPC\nmembers, and authors of accepted papers were invited to participate in\nthe Study Conference. Accepted papers were then revised (when necessary)\nby the authors, before being published in the conference proceedings [", { "type": "Cite", "target": "bib-bib2", "content": [ "2" ] }, "].\nThe conference proceedings contain 56 papers (see Table ", { "type": "Cite", "target": "S0-T1", "content": [ "1" ] }, "),\nwith contributions from 127 authors from\n28\ncountries across five\ncontinents: Argentina, Australia, Brazil, Canada, Chile,\nChina, Colombia, Costa Rica, Croatia, France, Germany, Greece, India,\nIran, Israel, Italy, Japan, Malawi, Mexico, New Zealand, Portugal,\nSerbia, South Africa, Spain, Sweden, Switzerland,\nthe United Kingdom, and\nthe United States." ] }, { "type": "Table", "id": "S0-T1", "caption": [ { "type": "Paragraph", "content": [ "Papers in Proceedings, by topic." ] } ], "rows": [ { "type": "TableRow", "cells": [ { "type": "TableCell", "content": [ "Topics" ] }, { "type": "TableCell", "content": [ "Number of papers" ] } ], "rowType": "Header" }, { "type": "TableRow", "cells": [ { "type": "TableCell", "content": [ "Theoretical perspectives" ] }, { "type": "TableCell", "content": [ "12" ] } ] }, { "type": "TableRow", "cells": [ { "type": "TableCell", "content": [ "Curricular and methodological approaches" ] }, { "type": "TableCell", "content": [ "17" ] } ] }, { "type": "TableRow", "cells": [ { "type": "TableCell", "content": [ "Resources for teaching and learning geometry" ] }, { "type": "TableCell", "content": [ "21" ] } ] }, { "type": "TableRow", "cells": [ { "type": "TableCell", "content": [ "Multidisciplinary perspectives" ] }, { "type": "TableCell", "content": [ "6" ] } ] }, { "type": "TableRow", "cells": [ { "type": "TableCell", "content": [ "Total" ] }, { "type": "TableCell", "content": [ "56" ] } ] } ] }, { "type": "Paragraph", "id": "p6", "content": [ "Figure ", { "type": "Cite", "target": "S0-F1", "content": [ "1" ] }, " captures participants after the closing ceremony of the Study\nConference in Reims." ] }, { "type": "Figure", "id": "S0-F1", "caption": [ { "type": "Paragraph", "content": [ "Participants of the ICMI Study Conference on Advances in Geometry Education." ] } ], "licenses": [ { "type": "CreativeWork", "url": "https://creativecommons.org/licenses/by/4.0/legalcode", "content": [ { "type": "Paragraph", "content": [] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F1.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Paragraph", "id": "p7", "content": [ "The map\nof Figure ", { "type": "Cite", "target": "Sx1-F2", "content": [ "2" ] }, " shows the distribution of contributions\naccording to the first author’s university affiliation." ] }, { "type": "Paragraph", "id": "p8", "content": [ "Paper coverage across the four topics was relatively balanced, including\nseveral studies on the role and function of visual tools and spatial\nreasoning in the development of geometric understanding; the importance\nof digital tools and manipulatives in teaching and learning; and the\ninfluence of cultural traditions and experiences on curriculum design.\nIn addition, the IPC invited two esteemed scholars to present plenary\nlectures, another five scholars to participate in a plenary panel on\ngeometry practices within diverse cultural settings, and five French\npractitioners to participate in another plenary panel on innovative\nmethodologies for teaching geometry used in French schools." ] }, { "type": "Heading", "id": "Sx1", "depth": 1, "content": [ "How the study was conducted" ] }, { "type": "Paragraph", "id": "Sx1.p1", "content": [ "The participants were welcomed at the Institut\nNational Supérieur\ndu\nProféssorat\net de\nl’Education, an institute responsible\nfor initial teacher training in France." ] }, { "type": "Paragraph", "id": "Sx1.p2", "content": [ "After a few traditional French songs from the “Le Tourdion” choir, guests\nwere welcomed by\nChristophe Clément,\npresident of the University of\nReims,\nFrederick Leung,\npresident of the International Commission on\nMathematical Instruction (ICMI),\nFrédéric Castel,\nassistant director\nof INSPÉ, representing\nthe director of the INSPÉ (French National Institute for\nHigher Education),\nNathalie Wach,\ndirector of IREM of Strasbourg,\nrepresenting ADIREM (Association of Directors of IREMs – Research\nInstitutes for Mathematics Education),\nAnne-Cécile Mathé,\nChristophe Clément, and\nFabien Emprin,\nhead of the Local Organizing\nCommittee and\nrepresenting\nthe director of the laboratory\nCEREP\n(Centre for Studies and Research on Jobs and Professionalization)." ] }, { "type": "Figure", "id": "Sx1-F2", "caption": [ { "type": "Paragraph", "content": [ "Author distribution by geographical location (map data © 2024 Google myMap)." ] } ], "licenses": [ { "type": "CreativeWork", "content": [ { "type": "Paragraph", "content": [ "© 2024 Google myMap / Alphabet" ] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F2bc.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Paragraph", "id": "Sx1.p3", "content": [ "The study took place over four days, with eight working sessions, two\nplenary lectures, two plenary round tables, and an introductory and\nconcluding session led by the two co-chairs." ] }, { "type": "Paragraph", "id": "Sx1.p4", "content": [ "Contributors were also able to sample local specialities and visit the\ncity of Reims and its famous Champagne\nhouses." ] }, { "type": "Heading", "id": "Sx2", "depth": 1, "content": [ "Content of the\nstudy" ] }, { "type": "Paragraph", "id": "Sx2.p1", "content": [ "The two plenary lectures were addressed by Nathalie Sinclair (Canada,\nsee Figure ", { "type": "Cite", "target": "Sx2-F3", "content": [ "3" ] }, ") and Patricio Herbst (United States, see Figure ", { "type": "Cite", "target": "Sx2-F4", "content": [ "4" ] }, ").\nSinclair presented results and reflections from her research experience\non teaching and learning with technology several curricular geometrical\ncontents in early primary grades. In her lecture, Sinclair linked recent\ntheorising about the role of geometry in contemporary mathematics,\nconsidered alternative curriculum approaches that challenge both Western\nand Piagetian progressions, and discussed pedagogical approaches that\ncentre making and acting. She presented task design principles employed,\nand theoretical constructs that were used to generate insights into the\nteaching and learning of geometry. Sinclair also discussed more recent\nexploratory work involving new digital technologies which is part of her\ncurrent research projects." ] }, { "type": "Figure", "id": "Sx2-F3", "caption": [ { "type": "Paragraph", "content": [ "Nathalie Sinclair plenary presentation." ] } ], "licenses": [ { "type": "CreativeWork", "url": "https://creativecommons.org/licenses/by/4.0/legalcode", "content": [ { "type": "Paragraph", "content": [] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F3.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Paragraph", "id": "Sx2.p2", "content": [ "Herbst presented a lecture on teaching knowledge in geometry for the\nteaching of proof in the United States. Herbst commented on a program of\ndescriptive research that seeks to understand what we call the practical\nrationality of mathematics teaching and how this rationality can make\nroom for instructional resources and practices that seek to improve\ninstruction. This program has focused on research on the teaching of\nmathematical proof in geometry, which is one of its core cases for\nempirical investigation developed over quite many years. The\npresentation went back and forth between theoretical ideas and specific\nresearch and development experiments involving teaching and learning\nproof and proving geometric contexts." ] }, { "type": "Figure", "id": "Sx2-F4", "caption": [ { "type": "Paragraph", "content": [ "Patricio Herbst plenary presentation." ] } ], "licenses": [ { "type": "CreativeWork", "url": "https://creativecommons.org/licenses/by/4.0/legalcode", "content": [ { "type": "Paragraph", "content": [] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F4.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Paragraph", "id": "Sx2.p3", "content": [ "The plenary panel examining the framing of geometric representations and\npractices in culturally diverse settings was co-ordinated by Thomas\nLowrie (Australia) and included Lisnet Mwadzaangati (Malawi), Natalia\nSgreccia (Argentina), Zara Gooya (Iran), and Milton Rosa (Brazil). The\npanel considered new directions for geometry education research framed\nwithin political, cultural, and contextual dimensions of practice (see\nFigure ", { "type": "Cite", "target": "Sx2-F5", "content": [ "5" ] }, "). Mwadzaangati presented the case of the teaching of\nmathematics and the advances that researchers in mathematics education\nand mathematics teachers are trying to undertake to improve the quality\nof education in Malawi. Teachers are urged to move from traditional\nteaching methods, characterized as “chalk and\ntalk,” to more\nparticipative methodologies promoting inquiry-based learning,\ncharacterized as “student-centred.” The problem of language of\nteaching was also raised. Sgreccia provided a snapshot of some\ncharacteristics of the Argentinian curriculum in geometry and\nmeasurement across primary and secondary contexts. She also provided\ninsights on the challenges of providing rich student learning of\ngeometry, since some topics are avoided due to the\nteacher’s insufficient content knowledge and school\nexperiences. Finally, Sgreccia commented on the presence of native\ncultures (Tobas, Guaraníes, etc.) and the possibilities of including\ntheir worldviews and conceptions in the teaching of geometry, in\nconnection with nature and about how geometry has been intrinsically\npresent in their practices. Gooya presented an overview of the evolution\nof geometry education in her country from the\n18th century to the\npresent day, characterizing each period in terms of their curricula and\ntextbooks. Rosa focused on the social Landless\nWorker’s Movement of\nBrazil, their agrarian culture, and their needs for geometry and\nmeasurement knowledge related to sustainability and planification. He\ninformed on the way the traditional method of ", { "type": "Emphasis", "content": [ "cubação of land" ] }, ", to\nmeasure the area of irregular pieces of land, has been used by the\nmembers of that social movement and transmitted orally in communities\nwith very low formal schooling and learning of mathematics. Rosa\ncompared the local traditional knowledge about this method of measuring\nsurfaces to the formal geometric knowledge." ] }, { "type": "Figure", "id": "Sx2-F5", "caption": [ { "type": "Paragraph", "content": [ "Plenary panel on geometric practices in culturally-diverse settings." ] } ], "licenses": [ { "type": "CreativeWork", "url": "https://creativecommons.org/licenses/by/4.0/legalcode", "content": [ { "type": "Paragraph", "content": [] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F5.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Figure", "id": "Sx2-F6", "caption": [ { "type": "Paragraph", "content": [ "Plenary panel by French classroom teachers." ] } ], "licenses": [ { "type": "CreativeWork", "url": "https://creativecommons.org/licenses/by/4.0/legalcode", "content": [ { "type": "Paragraph", "content": [] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F6.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Paragraph", "id": "Sx2.p4", "content": [ "Teachers’ voices were\nwell represented in the second plenary panel of\nthe\nconference (see Figure ", { "type": "Cite", "target": "Sx2-F6", "content": [ "6" ] }, "). Five French practitioners actively\ninvolved in collaborative geometry projects focused on different\nperspectives of their practices of teaching geometry from kindergarten\nto secondary levels. The panel was co-ordinated by Fabien Emprin and\nincluded Isabelle Audra, Mélanie Binet, Marie-Paul Foy, Lucie Jacotin,\nand Aurélie Marche. Each teacher provided an overview of their school\ncontext and their practices that promoted students learning of geometry,\nwhile posing questions to the group of researchers. They shared with the\naudience information about: the social context of their towns, schools,\nand classrooms; the place of geometry in their classes; examples of\ngeometry activities made in their classrooms (including pictures,\nvideos, sample students’ worksheets, manipulatives, technology, etc.);\ntheir teaching methodologies; the ways they care for their pupils with\nspecial needs; and problems and difficulties they face\nwhile teaching\ngeometry." ] }, { "type": "Heading", "id": "Sx3", "depth": 1, "content": [ "The\nworking groups" ] }, { "type": "Paragraph", "id": "Sx3.p1", "content": [ "The\nconference was organized around five working groups (WG) focused on\nspecific sets of the sub-topics defined in the\ndiscussion document, with\nthe intent of having strong synergies among the presentations in each\nWG. The WGs worked in parallel and were scheduled to meet for eight\n90-minute sessions. The first five sessions were mainly devoted to\npresenting and discussing the papers, with a range of\n10 to 14\npapers in each WG. In the last three sessions, the participants of each\nWG engaged in discussions focused on identifying the relevant issues\nraised in the previous presentations and making proposals to the IPC for\nthe design of a part of a book that will be part of the ICMI Study\nseries, which will be a culmination of the Study (see [", { "type": "Cite", "target": "bib-bib3", "content": [ "3" ] }, "] for the\nprevious Study\nseries book regarding geometry)." ] }, { "type": "Paragraph", "id": "Sx3.p2", "content": [ "WG1 paid attention to theoretical aspects of geometry education related\nto several main topics in the area: the teaching and learning of proof\nin geometric contexts (including DGS – dynamic geometry software) in\nthe light of new conceptions and approaches; roles of spatial reasoning\nin teaching and learning geometry; relationships between visualization\nand geometry reasoning; and connections between visualization and\nspatial reasoning." ] }, { "type": "Figure", "id": "Sx3-F7", "caption": [ { "type": "Paragraph", "content": [ "Working Group 2 participants." ] } ], "licenses": [ { "type": "CreativeWork", "url": "https://creativecommons.org/licenses/by/4.0/legalcode", "content": [ { "type": "Paragraph", "content": [] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F7.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Paragraph", "id": "Sx3.p3", "content": [ "WG2 (Figure ", { "type": "Cite", "target": "Sx3-F7", "content": [ "7" ] }, ") analysed characteristics of geometric thinking across different\neducational levels, students’ capacities – from those with learning\ndifficulties to mathematically gifted students – and curricula –\ninfluenced by local political and cultural characteristics. This group\nalso analysed the knowledge and competencies necessary to teach and\nlearn geometry and the design of learning environments, from several\npositions like interdisciplinarity,\nproblem solving/posing, contexts\ninfluencing the learning of geometry, and different types of tools." ] }, { "type": "Paragraph", "id": "Sx3.p4", "content": [ "WG3 discussed issues related to pre- and in-service teacher professional\ntraining, addressing issues like teachers’ content knowledge of\ngeometry, strategies for teacher training, and types of tasks suitable\nto be posed to teachers to promote their content and didactical\nknowledge for teaching geometry." ] }, { "type": "Paragraph", "id": "Sx3.p5", "content": [ "The participants in WG4 discussed burgeoning issues related to the use\nof ICT (Information and Communication Technology) in teaching and learning geometry, including: resources available\nthat are useful in the classrooms; characteristics of DGS like dynamism,\nembodiment, feedback; design of tasks to promote students’ understanding\nand learning of specific geometric topics; ways of supporting reasoning\nwith technology, like promoting deductive reasoning and proofs,\nsupporting visualization in\nproblem solving, or use of analogy to\npromote understanding of new constructs; and also constraints and\nlimitations due to the lack of ICT resources in classrooms." ] }, { "type": "Paragraph", "id": "Sx3.p6", "content": [ "Finally, WG5 (see Figure ", { "type": "Cite", "target": "Sx3-F8", "content": [ "8" ] }, ") worked on issues related to the use of\nmanipulatives and visual tools in teaching and learning geometry, in a\nkind of juxtaposition to the discussions in WG4. They dealt with the\nconcept of resources (physical, digital, tasks, etc.) as a starting\npoint to analyse issues like the specificities of resources for geometry\nclasses, resources for teachers, and kinds of manipulation from\nkindergarten to university." ] }, { "type": "Figure", "id": "Sx3-F8", "caption": [ { "type": "Paragraph", "content": [ "Working Group 5 participants." ] } ], "licenses": [ { "type": "CreativeWork", "url": "https://creativecommons.org/licenses/by/4.0/legalcode", "content": [ { "type": "Paragraph", "content": [] } ] } ], "content": [ { "type": "ImageObject", "contentUrl": "M208F8.jpg", "mediaType": "image/jpeg", "meta": { "inline": false } } ] }, { "type": "Heading", "id": "Sx4", "depth": 1, "content": [ "Next\nsteps" ] }, { "type": "Paragraph", "id": "Sx4.p1", "content": [ "The IPC is now working on the design of the Study Volume, which will be\npart of the ICMI Study\nseries. The chapters will cover, in more depth,\nthe content presented, and questions raised in the conference,\nhighlighting a diversity of issues and reflections related to the\nteaching and learning of geometry at the different educational levels,\ntogether with methodological and practical approaches to deal with them.\nThe volume will also provide guidelines for mathematics education\nresearch and innovation for the coming decades." ] }, { "type": "Heading", "id": "Sx5", "depth": 1, "content": [ "Final\nreflections" ] }, { "type": "Paragraph", "id": "Sx5.p1", "content": [ "This was a thought-provoking, energizing, and meaningful working group\nconference. We were able to assemble a cohort of geometry educators from\nacross the world – from diverse backgrounds and experiences – to work\nharmoniously and positively for a concentrated period. We appreciate\nthat such opportunities, where so many world-leading discipline\nspecialists gather for a common goal, seldom occur in one’s professional\nlife. The distinctness of this Study will be the way in which this\ncohort has been able to capture the nexus between geometry education\ntheory and practice, across the lifespan (from the early years of\nlearning to advanced multidisciplinary contributions of geometry)." ] }, { "type": "Paragraph", "id": "authorinfo", "content": [ "\nThomas Lowrie is a centenary professor and director of the STEM\neducation research centre (SERC) at the University of Canberra in\nAustralia. He holds a teaching degree and Master of Education degree\nfrom the University of Wollongong, and a PhD in geometry education from\nthe University of Newcastle. He is a recent recipient of Life Membership\nfrom the Mathematics Education Research Group of Australasia (MERGA). He\nwas an author of Australia’s Early Years Learning Framework and\ndeveloped several federally funded learning programs that utilize\ntechnologies in play-based learning. His research interests are in the\nareas of spatial reasoning and the use of visual representations in\nnovel\nproblem solving.\n", { "type": "Link", "target": "mailto:thomas.lowrie@canberra.edu.au", "content": [ "thomas.lowrie@canberra.edu.au" ] }, "\nAngel Gutiérrez is doctor in mathematics and professor of mathematics\neducation at the University of Valencia (Spain). His areas of expertise\ninclude geometry education, teaching and learning of mathematical proof,\nvisualization in mathematics, teaching of geometry with dynamic geometry\nsoftware, and mathematical giftedness.\nHe has been editor of\nEnseñanza de las Ciencias and associate editor of Educational Studies in\nMathematics. He is the leader of the “Group of research in geometry\neducation and mathematically gifted students” of the University of\nValencia.\n", { "type": "Link", "target": "mailto:angel.gutierrez@uv.es", "content": [ "angel.gutierrez@uv.es" ] } ] } ] }