ICME-13 Monographs Norma Presmeg Luis Radford Wolff-Michael Roth Gert Kadunz Editors Signs of Signification Semiotics in Mathematics Education Research ICME-13 Monographs Series editor Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität Hamburg, Hamburg, Germany Each volume in the series presents state-of-the art research on a particular topic in mathematics education and reflects the international debate as broadly as possible, while also incorporating insights into lesser-known areas of the discussion. Each volume is based on the discussions and presentations during the ICME-13 Congress and includes the best papers from one of the ICME-13 Topical Study Groups or Discussion Groups. More information about this series at http://www.springer.com/series/15585 Norma Presmeg Luis Radford (cid:129) Wolff-Michael Roth Gert Kadunz (cid:129) Editors fi Signs of Signi cation Semiotics in Mathematics Education Research 123 Editors Norma Presmeg Wolff-Michael Roth Illinois State University Faculty of Education Maryville, TN University of Victoria USA Victoria, BC Canada LuisRadford Faculty of Education GertKadunz UniversitéLaurentienne Fakultät für technische Wissenschaften, Sudbury,ON Institut für Mathematik Canada Alpen-Adria-Universität Klagenfurt Klagenfurt Austria ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN978-3-319-70286-5 ISBN978-3-319-70287-2 (eBook) https://doi.org/10.1007/978-3-319-70287-2 LibraryofCongressControlNumber:2017957196 ©SpringerInternationalPublishingAG2018 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart 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 orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 NormaPresmeg,LuisRadford,Wolff-MichaelRothandGertKadunz Part I Sociocultural Perspectives on Semiosis 2 Semiosis and Subjectification: The Classroom Constitution of Mathematical Subjects . . . . . . . . . . . . . . . . . . . . . . 21 Luis Radford 3 Birth of Signs: A (Spinozist-Marxian) Materialist Approach . . . . . 37 Wolff-Michael Roth 4 Relating Computational Cartesian Graphs to a Real Motion: An Analysis of High School Students’ Activity . . . . . . . . . . . . . . . . 55 Ulises Salinas-Hernández and Isaias Miranda 5 Joint Attention in Resolving the Ambiguity of Different Presentations: A Dual Eye-Tracking Study of the Teaching-Learning Process. . . . . . . . . . . . . . . . . . . . . . . . . . 73 Anna Shvarts 6 Attention Catching: Connection the Space of Joint Action and Togethering . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Debbie Stott Part II Language and Text Orientations 7 A Matter of Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Gert Kadunz 8 Using Social Semiotics to Explore Institutional Assumptions About Mathematics Students and Teachers . . . . . . . . . . . . . . . . . . 139 Candia Morgan v vi Contents 9 Semiotics, Epistemology, and Mathematics . . . . . . . . . . . . . . . . . . . 155 Michael Otte 10 A Semiotic-Conceptual Analysis of Conceptual Development in Learning Mathematics. . . . . . . . . . . . . . . . . . . . . . 173 Uta Priss Part III Peircean Semiotics, Including Semiotic Chaining and Representations 11 Iconicity and Diagrammatic Reasoning in Meaning-Making. . . . . . 193 Adalira Sáenz-Ludlow 12 Semiotic Representations: A Study of Dynamic Figural Register . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Jesus Victoria Flores Salazar 13 Progressive Visualization Tasks and Semiotic Chaining for Mathematics Teacher Preparation: Towards a Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Barbara M. Kinach 14 Primary Teachers’ Semiotic Praxis: Windows into the Handling of Division Tasks . . . . . . . . . . . . . . . . . . . . . . . . 257 Corin Mathews, Hamsa Venkat and Mike Askew Part IV Semiotic Resources Including Gesturing and Tools 15 Gradual Change of Perception: Signs, Tools, and Meaning-Making of Fractions . . . . . . . . . . . . . . . . . . . . . . . . . 279 Yasmine Abtahi 16 On the Role of Gestures for the Descriptive Analysis of ‘Grundvorstellungen’: A Case of Linear Functions . . . . . . . . . . 293 Christina M. Krause and Alexander Salle 17 DiagrammingandGesturingDuringMathematizing:Kinesthetic and Haptic Interactions Support Mathematical Ideation . . . . . . . . 315 Petra Menz and Nathalie Sinclair 18 Objectifying the Inclusion Relationship of Quadrilaterals in a Synchronic-Interactive and Collaborative Computer Supported Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 Osama Swidan and Naomi Prusak 19 Discussion and Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 NormaPresmeg,LuisRadford,Wolff-MichaelRothandGertKadunz Contributors Yasmine Abtahi University of Ottawa, Ottawa, ON, Canada; L’Université du Québec à Montréal, Montreal, Canada Mike Askew University of the Witwatersrand (WITS), Johannesburg, South Africa Gert Kadunz Department of Mathematics, Alpen-Adria Universitaet Klagenfurt, Klagenfurt, Austria Barbara M. Kinach Mary Lou Fulton Teachers College, Arizona State University, Mesa, AZ, USA Christina M. Krause Faculty of Mathematics, University of Duisburg-Essen, Essen, Germany Corin Mathews University of the Witwatersrand (WITS), Johannesburg, South Africa Petra Menz Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada Isaias Miranda Instituto Politécnico Nacional, CICATA-Legaria, Mexico City, Mexico Candia Morgan Department of Curriculum Pedagogy and Assessment, University College London Institute of Education, London, UK Michael Otte University of Bielefeld, Melle, Germany Norma Presmeg Mathematics Department, Illinois State University, Maryville, TN, USA Uta Priss Ostfalia University, Wolfenbüttel, Germany Naomi Prusak School of Education, The Hebrew University of Jerusalem, Jerusalem, Israel vii viii Contributors Luis Radford École des sciences de l’éducation, Université Laurentienne, Sudbury, ON, Canada Wolff-Michael Roth Applied Cognitive Science, UniversityofVictoria,Victoria, BC, Canada Jesus Victoria Flores Salazar Pontificia Universidad Catolica del Perú, Lima, Peru Ulises Salinas-Hernández Cinvestav-IPN, Mexico City, Mexico Alexander Salle Department of Mathematics/Computer Science, Institute of Mathematics, University of Osnabrück, Osnabrück, Germany Anna Shvarts Lomonosov Moscow State University, Moscow, Russia Nathalie Sinclair Faculty of Education, Simon Fraser University, Burnaby, BC, Canada Debbie Stott South African Numeracy Chair Project, Education Department, Rhodes University, Grahamstown, South Africa Osama Swidan Ben-Gurion University of the Negev, Beer-Sheva, Israel Adalira Sáenz-Ludlow Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, USA Hamsa Venkat University of the Witwatersrand (WITS), Johannesburg, South Africa Chapter 1 Introduction NormaPresmeg,LuisRadford,Wolff-MichaelRothandGertKadunz Abstract This introductory chapter presents an overview of the role of semiotic issuesintheteachingandlearningofmathematics,astheseissuesarecharacterized andelaboratedinthechaptersofthismonograph.Severalthreadsarerepresentedin thefoursectionsofthisbook:theevolvingsocioculturalperspectiveisaddressedin Sects. 1and4;Sect. 2addresseslinguisticandtextualaspectsofsignification,and Sect. 3 represents Peircean perspectives that were recognized as important in our field more than two decades ago, which continue to have relevance. (cid:1) (cid:1) (cid:1) (cid:1) Keywords Signs Semiotics Semiosis Signification Gesturing 1.1 Introduction All the chapters in this monograph grew out of presentations by the authors in Topic Study Group 54 (TSG 54), Semiotics in Mathematics Education, of the Thirteenth International Congress on Mathematics Education (ICME-13), held in N.Presmeg(&) MathematicsDepartment,IllinoisStateUniversity, 5160,CandlewoodCourt,Maryville,TN37804,USA e-mail:[email protected] L.Radford Écoledessciencesdel’éducation,UniversitéLaurentienne,Sudbury ONP3E2C6,Canada e-mail:[email protected] W.-M.Roth AppliedCognitiveScience,UniversityofVictoria,MacLaurinBuildingA567, Victoria,BCV8P5C2,Canada e-mail:[email protected] G.Kadunz DepartmentofMathematics,Alpen-AdriaUniversitaetKlagenfurt, Universitaetsstrasse65,9020Klagenfurt,Austria e-mail:[email protected] ©SpringerInternationalPublishingAG2018 1 N.Presmegetal.(eds.),SignsofSignification, ICME-13Monographs,https://doi.org/10.1007/978-3-319-70287-2_1