research on mathematics textbooks and teachers’ resources advances and issues

ICME-13 Monographs Lianghuo Fan Luc Trouche Chunxia Qi Sebastian Rezat Jana Visnovska Editors Research on Mathematics Textbooks and Teachers’ Resources Advances and Issues 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 conference 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 Lianghuo Fan Luc Trouche (cid:129) Chunxia Qi Sebastian Rezat (cid:129) Jana Visnovska Editors Research on Mathematics ’ Textbooks and Teachers Resources Advances and Issues 123 Editors Lianghuo Fan Sebastian Rezat Southampton Education School EIM—Institut für Mathematik University of Southampton UniversitätPaderborn Southampton Paderborn UK Germany LucTrouche JanaVisnovska Institut Français del’Education Schoolof Education ÉcoleNormale Supérieure deLyon TheUniversity of Queensland Lyon Brisbane, QLD France Australia ChunxiaQi Faculty of Education Beijing NormalUniversity Beijing China ISSN 2520-8322 ISSN 2520-8330 (electronic) ICME-13 Monographs ISBN978-3-319-73252-7 ISBN978-3-319-73253-4 (eBook) https://doi.org/10.1007/978-3-319-73253-4 LibraryofCongressControlNumber:2017962032 ©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. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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 authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Contents Mathematics Textbooks and Teachers’ Resources: A Broad Area of Research in Mathematics Education to be Developed .... ..... .... xiii Luc Trouche and Lianghuo Fan Part I Trends in Presentation of Mathematics in Textbooks and Other Resources 1 Open Educational Resources: A Chance for Opening Mathematics Teachers’ Resource Systems?. . . . . . . . . . . . . . . . . . . 3 Luc Trouche, Ghislaine Gueudet and Birgit Pepin 2 Textbook Use by Teachers in Junior High School in Relation to Their Role. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Chunxia Qi, Xinyan Zhang and Danting Huang 3 A Comparative Study on the Presentation of Geometric Proof in Secondary Mathematics Textbooks in China, Indonesia, and Saudi Arabia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Lianghuo Fan, Mailizar Mailizar, Manahel Alafaleq and Yi Wang Part II Teacher Interactions with Curricular and Other Learning Resources 4 Examining Teachers’ Interactions with Curriculum Resource to Uncover Pedagogical Design Capacity. . . . . . . . . . . . . . . . . . . . . . . 69 Janine T. Remillard 5 Disaggregating a Mathematics Teacher’s Pedagogical Design Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Moneoang Leshota and Jill Adler v vi Contents 6 Teachers’ Selection of Resources in an Era of Plenty: An Interview Study with Secondary Mathematics Teachers in England . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 Helen Siedel and Andreas J. Stylianides 7 Teachers as Designers of Digital Educational Resources for Creative Mathematical Thinking. . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Chronis Kynigos and Angeliki Kolovou Part III Teachers’ Collective Work Through Resources 8 Curriculum Support for Teachers’ Negotiation of Meaning: A Collective Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Hendrik Van Steenbrugge, Maria Larsson, Eva Insulander and Andreas Ryve 9 Mathematics Teachers’ Expertise in Resources Work and Its Development in Collectives: A French and a Chinese Cases . . . . . . 193 Chongyang Wang 10 Role of Context in Social Creativity for the Design of Digital Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Nataly Essonnier, Chronis Kynigos, Jana Trgalova and Maria Daskolia 11 UsesofOnlineResourcesandDocumentationalTrajectories:The Case of Sésamath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Katiane de Moraes Rocha Part IV Teachers’ and Students’ Interactions Through Resources 12 Instructional Activity and Student Interaction with Digital Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 Kenneth Ruthven 13 Resourcing Teachers in Transition to Plan for Interactions with Students’ Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Jana Visnovska and Jose Luis Cortina 14 Prospective Teachers’ Interactions with Interactive Diagrams: Semiotic Tools, Challenges and Well-Trodden Paths . . . . . . . . . . . 297 Elena Naftaliev 15 Teacher Decisions on Lesson Sequence and Their Impact on Opportunities for Students to Learn. . . . . . . . . . . . . . . . . . . . . . . . 315 Ok-Kyeong Kim Contents vii Part V Concluding Remarks 16 Present Research on Mathematics Textbooks and Teachers’ Resources in ICME-13: Conclusion and Perspectives . . . . . . . . . . . 343 Sebastian Rezat, Jana Visnovska, Luc Trouche, Chunxia Qi and Lianghuo Fan 17 Enhancing Teacher Learning with Curriculum Resources . . . . . . . 359 Birgit Pepin Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 375 Editors and Contributors About the Editors Lianghuo Fan obtained an M.Sc. from East China Normal University, Shanghai, and a Ph.D. fromtheUniversityofChicago,USA,andiscurrentlyProfessor(PersonalChair)inEducationand Director of the Mathematics, Science and Health Education Research Centre at Southampton Education School, University of Southampton. He has extensive experience in education and researchinChina,USA,Singapore,andnowtheUK,andhaspublishedwidelyinmathematics educationwithaparticularfocusonmathematics curriculum, classroominstruction,assessment, teacher professional development, and comparison of East and West. Among his numerous publications are Investigating the Pedagogy of Mathematics: How Do Teachers Develop Their Knowledge (author; Imperial College Press, 2014), Performance Assessment in Mathematics: Concepts,Methods,andExamplesfromResearchandPracticeinSingaporeClassrooms(editor; Pearson, 2011), and How Chinese Learn Mathematics (co-editor, World Scientific, 2004), and How Chinese Teach Mathematics (co-editor, World Scientific, 2015). He has served as editor, consultant, and mostly editor-in-chief of both primary and secondary school mathematics textbooks and instructional resources in the USA, Singapore, China, and the UK, including the latestseriesofShanghaiMathsProjectPracticeBookspublishedintheUKbyHarperCollinsand itsShanghaiEnglisheditionofShanghaiMathsOneLessonOneExercisebyEastChinaNormal UniversityPress.HewasChiefEditorofTheMathematicsEducator(2006–2010)andiscurrently SpecialtyChiefEditorofFrontiersinEducation(forSTEMEducation).Heorganized,asChair of the International Programme Committee (IPC), the inaugural International Conference on MathematicsTextbookResearchandDevelopment(ICMT-1)heldintheUK,2014.Hewasalso Co-ChairoftheIPCforICMT-2heldinBrazil,2017,andcontinuestoserveasCo-Chairofthe IPCforICMT-3tobeheldinGermany,2019. LucTrouche isProfessorofDidacticsofMathematicsintheFrenchInstituteofEducation,École normalesupérieuredeLyon,France. In previous years, his research was dedicated to studying ICT integration in Mathematics Education.Inparticular,hehasstudiedtheinterplaybetweeninstrumentationprocessesandcon- ceptualizationprocesses.Thisworkhasledhimtoanalysetheteacher’srole,introducingthenotion ofinstrumentalorchestrationformodellingthemanagementofavailableartefacts(forteachinga particularmathematicaltopic)intheclassroom.Hefocusesnowonresourcedesignandteacher professionaldevelopmentinthetimeofdigitalization.Thishasledhimtodevelop,inajointwork withGhislaineGueudetandBirgitPepin,thedocumentationalapproachtodidactics.Inthisper- spective, the notion of teacher resource system appears crucial in order to understand teacher’s (developing)knowledge andthecoherenceofhis/her activity.Investigating teachers’workwith ix x EditorsandContributors resourcesleadstoconsiderteachers’collectivework.Indeed,digitalizationfavourstheemergence ofmoreorlessformalcollectives:networks;teachinggroups;andlearningcommunitieswithinor out of schools. Studying the interactions between individual and collective teachers’ resource systemsgivesmeansforunderstandingthedynamicsofthesecollectives,andforrethinkingtheway ofsupportingteacherdevelopmentatatimeofthe“metamorphosis”ofteachingenvironments. He is currently involved in collaborative research at an international level, particularly with China,Brazil,orMexico.HeistheChairoftheInternationalConferenceRe(s)sources2018,tobe held in France in 2018. Among his publications: From Text to ‘Lived’ Resources: Mathematics Curriculum Materials and Teacher Development, co-edited with Birgit Pepin, and Ghislaine Gueudet(Springer,2012)andToolsandMathematics:InstrumentsforLearning,co-writtenwith JohnMonaghanandJonBorwein(Springer,2016). Chunxia Qi isaFullProfessorandDeputyHeadoftheInstituteofCurriculumandPedagogy, Faculty of Education, Beijing Normal University (BNU), China. She is an Associate Editor of EURASIAJournalofMathematics,ScienceandTechnologyEducation,amemberoftheEditorial BoardoftheEducationalReview,USA,andEditor-in-Chiefofproject-basedlearningmathematics textbooksforgrades7–9.SheisalsoanexecutivememberoftheCurriculumSub-commissionof ChineseSocietyofEducation.SheholdsadoctorateinComparativeMathematicsEducationfrom BNUandwasaFulbrightScholaratTeachersCollege,ColumbiaUniversity,from2006to2007. Her research interests include mathematics curriculum comparison and mathematics textbooks theoryandpractices.Shehaspublishedeightyarticles(inbothChineseandEnglish).Since2000, shehasservedasakeymemberontheNationalResearchandDevelopmentTeamforMathematics CurriculumStandardsattheCompulsoryEducationStage,theteamleaderforMacaoMathematics CurriculumStandardsatjuniorhighschool,andtheteamleaderforMacaoMathematicsCurriculum Standardsatseniorhighschool.SheisalsotheChiefExpertbothinCollaborativeInnovationCenter ofAssessmenttowardBasicEducationQuality,ChinaandBeijingAdvancedInnovationCenterfor FutureEducation,Beijing. Sebastian Rezat is a Full Professor of Mathematics Education at the Institute of Mathematics, PaderbornUniversity,Germany.Inhisresearch,heinvestigatestheuseoftraditionalanddigital mathematicstextbooksatprimaryandsecondarylevels.Heisparticularlyinterestedinstudents’ interactionswithtextbooksandtheinterplaybetweenstudents’andteachers’useoftextbooks.His doctoralthesisonstudents’useoftheirmathematicstextbookshasbeenawardedbytheGerman Society of Didactics of Mathematics (GDM). In collaboration with Rudolf Sträßer he has developed the socio-didactical tetrahedron that models the whole situation of textbook and resourceusefromanactivitytheoreticalperspectiveincludingthetwomainusers—teachersand students—as well as social and cultural factors. His current research also includes linguistic aspects of mathematics teaching and learning with a focus on subject-specific genres in mathematics education. Together with Sara Rezat he has developed a model for analysing the features of subject-specific genres and their implementation in mathematics textbooks and classrooms. As Chair of the International Programme Committee (IPC), he is going to host the ThirdInternationalConferenceonMathematicsTextbookResearchandDevelopment(ICMT-3), tobeheldinGermany,2019. Jana Visnovska is a Lecturer in Mathematics Education at the University of Queensland, Australia. Her research interests focus on the means of supporting mathematics teachers that empowertheminprovidingallstudentswithopportunitiestolearnmeaningfulmathematics.To thisend,sheexploresfeaturesofteachers’resourcesandformsofprofessionaldevelopmentthat are in particular effective in supporting the learning and instructional interactions of teachers in transition. In ongoing research collaboration with Jose Luis Cortina, she contributes to instructionaldesignresearchinareaoffractionsasmeasuresandhasbeenintriguedbytheroleof quantityinschoolmathematicseducation.Throughherresearch,sheseeksopportunitiestolearn about mathematics teaching and learning in different educational contexts, including severely

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Research on Mathematics Textbooks and Teachers' Resources: Advances and Issues (Icme-13 Monographs)

Description.

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level.

As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks?

As for the teachers, the book discusses the relationships between teachers' individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development?

As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students' use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

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This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. 

As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? 

As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? 

As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

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This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level.

As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks?

As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development?

As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

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Present Research on Mathematics Textbooks and Teachers’ Resources in ICME-13: Conclusion and Perspectives

by Jana Visnovska , Chunxia Qi , Luc Trouche

2018, Research on Mathematics Textbooks and Teachers’ Resources: Advances and issues. Springer

This chapter summarizes and discusses the state of the art of research on mathematics textbooks and other resources and their use as depicted in this volume. The discussion focuses on three questions: First, what are the theoretical and methodological tools used in order to conceptualize and investigate textbook and resource use? Second, what can we learn about the use of textbooks and resources by teachers from the chapters in this volume? Third, what do we learn from comparing teachers-resources interactions across different countries? Based on the discussion conclusions are drawn regarding perspectives of future research on mathematics textbooks and resources and their use.

Free Related PDFs

Luc Trouche , Fan L. , Jana Visnovska , Chunxia Qi

2018, Springer

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

Luc Trouche

This introduction aims to situate this monograph as a result of the work of the Topic Study Group (TSG) 38 at the 13th International Congress on Mathematical Education, held in Hamburg in July 2016. Beyond this goal, it aims to evidence the fact that, far from being an isolated work, the contributions received to this TSG, their number as well as their content, witness the emergence, at an international level, of a new field of research, dedicated to the teachers’ resources. After having set this scene, this introduction shortly overviews the chapters of this monograph, structured in five sections.

2019, The 'Resource' Approach to Mathematics Education

This chapter proposes a view from inside the DAD, starting from determining some essential resources missing of DAD, to proposing 10 programs of research/development for developing it. It could be considered as a follow-up of Chapter 1, where Ghislaine Gueudet situates the current state of DAD in looking back to its origin: chapter 12 proposes a possible future of this approach in analyzing its current state. It determines the missing resources of DAD in questioning current and past PhD students who have anchored their research in DAD. What did/do they learn in using DAD as a main theoretical resource; to which extent did/do they estimate that they have enriched DAD by their own work? Which are, according to them, the still missing resources of DAD? Which of these resources should be developed by DAD from itself, and/or in co-working with other theoretical framework? From this inquiry, this chapter proposes ten perspectives of research, aiming to develop some theoretical blind points of DAD, or to develop some methodological tools, or to deepen the cultural/social aspects of DAD in questioning the naming systems used by teachers when interacting with resources. This chapter echoes actually different perspectives of research already present, as promising germs, in previous chapters of the book.

Maryna Rafalska

Carole Le Hénaff

Our article examines how a science teacher, at high school, uses for her CLIL lessons some resources that she downloaded from Internet websites. For our analysis, we refer to two theoretical frameworks: the documentational approach of didactics, the Joint Action Theory in Didactics. We analyse the effects of the teacher's representations of “good” resources according to the language used in class, and of the use of such resources. We eventually produce recommendations for teacher training.

Jose Vieira DO Nascimento Junior , Luiz Marcio SANTOS FARIAS

2018, Creation of innovative teaching situation through instrumental genesis to maximize teaching specific content: acid-base chemical balance

This paper reports the creation of an innovative teaching situation for acid-base balance content. This “situation” occurred through instrumental genesis process. Here the computer is the artefact that becomes an instrument when a new element is introduced. The situation reported herein was observed during classes given to graduating student-teachers of Licentiate Course of Chemistry of Feira de Santana State University, Brazil. The theoretical framework is based on several concepts integrated: documental and instrumental genesis, instrumentation and instrumentalization, orchestration and anthropological theory of didactics.

2019, A lecture given in Beijing Normal University

The lecture (given at Beijing Normal University) propose to analyze teachers' work through their interactions with resources. It is based on the so called documentational approach to didactics, and exploites the PhD work of Chongyang Wang. It underlines the importance of teachers’ collective work with resources, an essential aspect of their professional development and evidences the necessity of designing new methodological tools. Contrasting Chinese and French cases, the lecture proposes a new approach to teachers' expertise in interacting with resources.

Birgit Pepin , Luc Trouche

The project of this book is to report on the emergence of a new field of research in mathematics education, which can be described as the study of “The ‘Resources’ Approach to Mathematics Education” (RAME) and to present to the reader a particular view on this field. In this introduction, we first present how and why this book is inserted within the “Advances in Mathematics Education” book series. Second, we attempt to characterize the RAME research field and to situate it in the landscape of mathematics education research. The Documentational Approach to Didactics (DAD) plays a particular role in this field; we discuss its links with other theoretical approaches in the third section. Fourth, we evoke the “Re(s)sources 2018 conference”, which took place in Lyon in May 2018 and has been a central source for this book. Fifth, we present the content of the book, and finally some perspectives for further research.

Katiane De Moraes Rocha

The goal of this conceptual paper is to develop enhanced understandings of mathematics teacher design and design capacity when interacting with digital curriculum resources. We argue that digital resources in particular offer incentives and increasing opportunities for mathematics teachers’ design, both individually and in collectives. Indeed they require increased design expertise because of the changing nature of the resources. Drawing on the literature we suggest ten questions providing a tool to study teacher design processes; and (2) we propose three components for exploring teacher design capacity. Building on two main theoretical areas (i.e. teaching as design; documentational approach to didactics) we propose to deepen understandings of the notions of “teacher design” and “teacher design capacity”. Drawing on two different collective environments and two individual teacher cases working within these environments, we investigate and illustrate teachers’ design processes and design capacity building across a range of contexts and curriculum formations, with the focus on how digital resources can help to develop teacher design capacity. We claim that the evolutions of digital resources in particular require an elaboration and refinement of the concept of teacher design capacity, which we develop and illustrate. Indeed, interacting with digital resources, it is claimed, might be a fruitful vehicle for developing teachers’ design capacity, in particular when working in collectives.

FREE RELATED PAPERS

Katiane De Moraes Rocha , Luc Trouche

This article contributes to the symposium coordinated by Janine Remillard, Hendrik Van Steenbrugge and Luc Trouche, that discusses teacher-resource use around the world. We address the following issue: how might we understand the processes by which teachers engage with curriculum resources to design instruction? We situate our work in the documentational approach to didactics and propose two new concepts: documentational experience and documentational trajectory, aiming to analyze teachers’ professional development over time through their interactions with resources. Our methodological choices are inspired by the reflective investigation leading teachers to reflect about their work. We analyze the case of two middle school teachers, Anna and Viviane. Our preliminary findings evidence that these teachers’ documentational experience developed quite differently. Anna’s documentation is strongly supported by her collective work outside of school, helping her to face new curricular changes. Viviane’s documentation work is strongly supported by her interactions with her colleagues and the use of institutional resources, helping her to face the same changes.

Prof Mdu Ndlovu

This particular paper reports on the investigation of (selected) French mathematics teachers’ interactions with and use of a commonly used mathematics e-textbook (Sesamath), individually and collectively. Using three recent studies on teachers’ work with Sesamath, and leaning on theoretical frames from the area of curriculum design and instructional design with technology, we identify several dimensions of “design”, that is mathematics teachers working as designers. Moreover, we claim that the affordances of digital resources are related to the opportunities for “design” by mathematics teachers, of their own curriculum materials in/for instruction; and for the development of teachers’ mathematics-didactical design capacity.

2011, From Text to 'Lived' Resources

Anita Messaoui

The number of available resources is increasing constantly. Teachers are both users and designers, and the activity of resource selection has become crucial. According to the documentational approach to didactics (Gueudet et al., 2012), we analyse teachers’ activity through their interactions with resources. This theoretical framework is based on an instrumental approach (Rabardel & Béguin, 2007) and on documentary engineering (Pédauque, 2006). We use the notions of documentation genesis and scheme to analyse how teachers develop their information literacy skills. The designing of learning resources is at the centre of documentation work. According to Vergnaud (2009), conceptualization comes from activity. For him, a scheme is an invariant organization of the activity undertaken to achieve a type of task. The aim of this contribution is to identify and characterize the scheme of selecting a resource, in the designing process. This study is part of a French national programme research (ANR-ReVEA), in which researchers study teachers’ interactions with resources in different subjects: mathematics, physics-chemistry, technology and English. In this contribution, we present a case study of an English teacher. Our methodology is based on the reflective investigation (Gueudet et al., 2012). After a first interview, the English teacher filmed herself as she was preparing a lesson plan on a new topic, and explained at the same time what she was doing. She did this again one year later for the same lesson. According to our analysis, the scheme of selecting a resource is led by different types of knowledge (didactic, curricular, experience). The evaluation and selection processes also are closely linked with goal representation, information needs, and evaluation. This is a significant part of the definition of documentation expertise.

Luc Trouche , ghislaine gueudet

2012, Mathematics curriculum material and teacher documentation: from textbooks to lived resources, 23-41

Chapter 2 and chapter 16 constitute two connected components of the presentation of a theoretical approach focusing on phenomena central in this book: the interactions between mathematics teachers and resources, and their consequences for professional growth. We name it documentational approach of didactics (Gueudet & Trouche 2009). We begin (section 2.1) with a discussion of the elementary concepts of this approach: documentation work, teachers’ documentation, resources/document dialectics, documentational genesis. We then elaborate (section 2.2) the methodology we use for studying teachers’ documentation, and the data we have collected using this methodology over two years. In section 2.3, we detail a case study, extracted from these data. Finally, we present the perspective on teachers’ professional growth yielded by this approach (section 2.4). We pay particular attention to digital resources, the constituting factors of major evolutions.

Chongyang Wang , Luc Trouche , Birgit Pepin

The boom of technology and a plethora of Internet resources are likely to enrich mathematics teachers' teaching resources and the forms for their collective work. This creates a new complexity for both the work of teachers and researchers who are interested in teachers' work and their professional development. Such situation has led to the emergence the Documentational Approach to Didactics (DAD) (Gueudet, Pepin & Trouche, 2012), which provides a perspective for investigating both teachers' individual and collective work with resources. With a particular interest in the knowledge aspect of teachers' interaction with resources, we propose the notion of Documentation Expertise (DE) based on the notion of documentation work in DAD, and selected methodology tools, such as Documentation-working Mate (DWM), for studying it. To contribute to the symposium topic " teacher-resource use in the world " , we situate our study in China, where teachers' collective work is part of teachers' daily work, which is evident in their various activities in the so-called Teaching Research Groups (TRG). We investigated two middle school mathematics teachers from the same school (one advanced teacher, and one novice teacher). We address (and compare) their individual work with their personal resources, and their collective work in the TRG. In terms of results, we develop insights into selected components of their DE, and how their DE is developed through collective work. This study is part of the first author's PhD project 1 (2014-2018).

Symposium "Mathematics Curriculum Contingencies: From Authoring to Enactment via Curriculum Resources", chaired by David Clarke, Kenneth Ruthven and Mary Kay Stein, in the frame of the AERA 2015 meeting

In this presentation/paper we report on a study of one case teacher’s (Vera) interaction with the French mathematics e- textbook Sesamath, drawing on the documentational approach of didactics. We link her interactions to the characteristics of the e-textbook, showing the different ways in which Vera used the e-textbook for her lesson preparations and the enactment of her percentage lessons (at grade 8). Moreover, we pay particular attention to the interplay between the e-textbook, the teacher and her grade 8 students, focusing on individualised work. It is claimed that the e-textbook, or parts of it, became a useful tool for enacting and assessing particular differentiated textbook activities that could meet the needs of different learners in Vera’s class. At the same time Vera used the e-textbook to create her own digital course material. Indeed, Vera proposed changes to selected content of the e-textbook, and hence became part of the authorship herself. Comparing these results with the literature, it became clear that the different, and ‘dynamic’, nature of e-textbooks not only provides opportunities for teachers, but also requires teachers to take more agency in selecting, designing and re-designing their curriculum resources. Hence, it is clear that this ‘differentness’ offers challenges, in particular for inexperienced teachers who may expect the textbook to provide defined learning trajectories and progressions. It is argued that the processes necessary to usefully work with interactive e-textbooks, and their associated resources, offer new opportunities for professional learning: learning to teach “with (and not by) the book”.

This chapter proposes a theoretical frame, the documentational approach to didactics (DAD), as a tool for analyzing the changes brought about by digitalization in the design and uses of mathematics teaching resources. One of the major changes appears to be initiated by the profusion of Open Educational Resources (OER), which provide new opportunities for the design and use of teaching resources. In order to analyze the effects of such opportunities, we focus on two cases: the French Sésamath association, providing OERs at a large scale; and a French mathematics teacher using OERs as a means for accomplishing her teaching. Through the lens of DAD, we investigate the implication of this provision of ‘resources-on-offer’ for teachers’ practices.

"This paper reviews the literature on the theme of mathematics teachers’ work and interactions with resources, taking a particular perspective, the so-called ‘collective perspective’ on resources, their use and transformation. The review is presented under three headings: (1) theoretical frameworks commonly used in this area of research; (2) teachers’ interactions with resources in terms of their design and use; and (3) teachers’ interactions with resources in terms of teacher learning and professional development. From the literature, and the collection of papers in this issue, we argue that the collective dimensions play an important role in mathematics teachers’ work with resources and in their professional learning/development. Further empirical investigations are likely to be needed on: how teachers may work in collectives and with resources, and in which ways ‘productive’ collectives may form and work together; which roles particular resources can play in these delicate constellations and how particular resources may support teachers in their work and learning; and which kinds of resources offer opportunities for community building."

Luc Trouche , ghislaine gueudet , Hussein Sabra

In this study, we investigated design processes in teacher collectives, which have been made possible by new ‘‘digital’’ opportunities: platforms, discussion lists, etc. The object of our study is the French Se ́samath teacher association and its design of a grade 10 e-textbook, more precisely the design of the ‘‘functions’’ chapter. We analysed it with two theoretical lenses: the documentational approach and cultural-historical activity the- ory. We studied the activity system of a community of teachers designing an e-textbook. At macro-level, we observed a change of objects of the activities: from designing a ‘‘toolkit’’ for mathematics teachers; to interactive exercises; and finally to a more ‘‘classical e-textbook’’. At micro-level, we analysed the development of collective documents by the community, combining resources and schemes.

Chongyang Wang

2018, Research on Mathematics Textbooks and Teachers Resources: Advances and issues

Designed as a case study, two mathematics teachers from two contrasting contexts, China and France, were selected and investigated. Looking through both the teachers' resource system and their resources work in collectives, it is hoped to develop a deeper understandings on teacher's expertise in working with resources, and the factors from collectives to develop it.

2012, Mathematics curriculum material and teacher documentation: from textbooks to lived resources 305-322

This chapter aims to deepen the documentational approach of mathematics didactics, whose main concepts have already been presented (Chap. 2); the documentational approach, as outlined in Chapter 2, illuminates the importance of the collective aspects of teachers’ documentation work. By nature, teaching involves aspects of collective work, but the development of digitalization fosters it. This chapter articulates the frames of communities of practice and of the documentational approach, defining the concept of community documentation genesis. We develop a case study, concerned with an online association of secondary school mathematics teachers, designing and sharing resources. Drawing on evidence from this case study, we explain the interactions between community geneses, community documentation geneses and professional geneses.

The MaTRiTT project answers to the Xu Guangqi call of the French Ministry of Foreign Affairs. It involves two researchers of the French Institute of Education (ENS de Lyon) in France, two researchers of the ECNU (East China Normal University in Shanghai), and three co-supervised PhD students. It aims to studying the evolution of mathematics teachers resources under the impact of two transitions: a curricular one, and a digital one.

Jeffrey Choppin

A B S T R A C T We conceptualize curriculum ergonomics as a field that studies the interactions between users and curriculum materials. We identify five themes that a curriculum ergonomics lens brings into sharper focus: (1) teachers' relationships with and capacity to use curriculum resources; (2) alignment between design intentions and patterns of curriculum use; (3) ways in which curriculum resources influence instruction; (4) ways in which curriculum features are purposefully designed to achieve an educative purpose; and (5) the dissolution of boundaries between design and use. We first summarize the literature in curriculum ergonomics and then show how key themes from that literature inform the discussion of curriculum ergonomics.

Luc Trouche , ghislaine gueudet , Daniel Chazan

In The Age of Discontinuity: Guidelines to Our Changing Society (1992), Professor of Management Peter Drucker lays out ways in which technologies are transforming, and will continue to transform, industries throughout the world economy; for many workers, what characterizes work life now is the continual need to adapt to technological change. Such changes are not limited to the world of work: technology is transforming interactions with media, and this also relates to books. This chapter focuses on one way in which technology may transform educa- tional processes and bring about new educational dynamics. Specifically we examine ways in which e-book technology might influence one genre of book, the (mathematics) textbook. This chapter’s focus on e-textbooks is a little different than the focus of many who do research on technology in mathematics education. For many years, technology in mathematics education has focused on support for student activity in classrooms. While two of the authors have written, in previous editions of this Handbook (Yerushalmy & Chazan, 2002, 2008), about curriculum development and technology, and the impact of various tools and approaches on teaching and learning, we explore in this chapter deep evolutions in the learning, teaching, and professional development processes that digital resources, in particular e-textbooks, may create as they potentially transform current educational practice. We suggest that these potential transformations in teaching and learning require new research perspectives (Gueudet, Pepin, & Trouche, 2012). Further, we suggest that there are interesting opportunities—and even an urgent need—to renew research perspectives on technology and teachers’ participation in the design phase of technology tools, in particular on e-textbooks used and designed by teachers. In this chapter, we present a synthesis of research and development studies on e-textbooks, and analyze the crucial evolutions connected with their design and use.

In this paper we study the collective dimensions of teachers’ work in their ordinary daily practice. We argue that teachers’ ordinary work comprises many collaborative aspects, and that the interactions with colleagues, often through resources, are crucial for teacher professional development. Using a theoretical framework based on teacher documentation work, we focused on interactions between teachers and resources to study two teachers’ work: one teacher in France and one teacher in Norway. For both teachers we identified collective dimensions in their work with resources. Contrasting these two cases enabled us to identify particular features, but also possible invariants, of teachers’ work with resources. Our results indicate that collective dimensions are always present in teachers’ work, but that true communities of practice, which could be considered as an achievement of collective teachers’ work, are scarce. We discuss the conditions for the emergence of such communities.

This work takes place in TSG 38, especially the second session "How does the digitalization of information and communication affect the role of resources?". In this moment of profusion of digital resources, we are interested in the development of teachers’ documentation work. We introduce the notion of documentational trajectory for explaining the different ways teachers are using and designing resources for preparing their lesson. This research happens at a crucial time in France, a period of curricular changes leading teachers to renew their resources, particularly their textbook. Focusing our analysis on the Sésamath resources, produced by teachers working collaboratively at a large scale, we look at both the design and the usages of these resources. This study presents here some preliminary results in studying how a teacher, whose students use Sésamath textbook, organize her own documentation work, and we try to relate this organization to this teacher’s documentational trajectory.

"""We study in this article mathematics teachers’ documentation work: looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, etc. We consider that this documentation work is at the core of teachers’ professional activity and professional development. We introduce a distinction between available resources and documents developed by teachers through a documentational genesis process, in a perspective inspired by the instrumental approach. Throughout their documentation work, teachers develop documentation systems, and the digitizing of resources entails evolutions of these systems. The approach we propose aims at seizing these evolutions, and more generally at studying teachers’ professional change."""

Luc Trouche , Veronica Gitirana , Takeshi Miyakawa , Birgit Pepin

2019, International Journal of Educational Research

In this study we explore the interactions between teachers and resources during lesson preparation from different perspectives. We ask in which ways the crossing of perspectives help to develop deeper understandings of teacher interactions with curriculum resources. For doing this, we have chosen the following three theoretical frames: (1) Documentational Approach to Didactics (DAD); (2) Anthropological Theory of the Didactic (ATD); and (3) Cultural-Historical Activity Theory (CHAT). We chose data concerning two experienced mathematics teachers (at lower secondary school level) working together, preparing lessons on the topic of " algorithmics " , a topic newly introduced in grade 6 of the French curriculum, and hence a topic they had never taught before.

Luc Trouche , eman shaaban , Iman Khalil

In this study teachers’ conceptions were analyzed as KVP interactions (K: knowledge; V: values; P: practices) during their documentary work. The persistent follow-up for two successive years of the documentary work of two Lebanese biology teachers, Tania and Maya, allowed the identification of the critical resources and critical situations related to their preparation/teaching practices of genetic determinism of phenotype. The analysis of these critical resources and the output of critical situations according to a specific grid allowed us to infer teachers’ conceptions about genetic determinism. The results showed that the updated scientific knowledge of Tania (K) due to her constant interactions with updated resources including digital resources, the social practices (P) of her school implementing updated French textbooks illustrating the environmental influence on gene expression in addition to collective and collaborative work among teachers and with the coordinator reinforced her epigenetics’ conception. While in the case of Maya the interaction with digital resources caused an evolution of her documentary work (P), in addition to an evolution in her scientific knowledge (K) leading to a non-stabilized evolution of her conceptions from hereditarianism to epigenetics. This study has important implications on teachers’ preparation and training programs.

Hussein Sabra

Jeffrey Choppin , Birgit Pepin

In this conceptual review paper we draw on recent literature with respect to digital curriculum resources (DCR); we briefly outline and explain selected theoretical frames; and we discuss issues related to the design, and the use (by teachers and students) of digital curricula and e-textbooks in mathematics education.

Luc Trouche , Hussein Sabra , Angela Maria Restrepo

2018, Int J of Sci and Math Educ (2018) 16:539–558

This paper is concerned with the development of e-textbooks. We claim that analysis (and design) of e-textbooks requires the development of a specific frame. Digital affordances provide particular opportunities (e.g. in terms of interactions between users) that require specific considerations for their analysis, as teachers and students use them for their individual and collective purposes. In this study, we develop a framework for mathematics e-textbook analysis, based on the notion of connectivity. We introduce criteria to assess the different aspects of connectivity and build an analysis grid for e-textbooks. We illustrate the framework proposed by analyzing 2 commonly used French grade 10 mathematics e-textbooks. The results of the analyses show that there are major differences between the 2 e-textbooks in terms of connectivity, which can be related to differences in their design. Beyond these 2 examples, we claim that focusing on connectivity is a useful and relevant way of analyzing e-textbooks, as it can provide a window into issues of interactivity, both practically and cognitively.

Luc Trouche , Birgit Pepin , Chongyang Wang

Regarding the notion of mathematics teaching expertise, there have been several studies investigating “expert” teachers’ characteristics as compared to those of “novice” teachers in Western countries (e.g. Berliner, 1987). More recently, possibly triggered by the success of Chinese Shanghai students in studies such as PISA and TIMSS (OECD, 2010), much attention has been given to studying mathematics teachers in mainland China and Shanghai (e.g. Li & Huang, 2008), and one of the particular areas of interest is the nature of their expertise in mathematics teaching (e.g. Ma, 1999). However, at a more general level there is insufficient knowledge of the nature of teacher expertise in mathematics education (e.g. Li & Kaiser, 2011), and hardly any relating such expertise to teachers’ resources and how they work with these resources in their daily practice. We define teachers’ resources as the curriculum/text, material and personal resources that teachers use and develop in their daily practice, in and for their teaching. As it is generally acknowledged that mathematics teaching is a cultural activity (e.g. Stigler & Hiebert, 1999), we assume that this is also likely to be the case with mathematics teaching expertise. At the same time research (e.g. Blömeke & Kaiser, 2012) suggests that teaching quality may be one of the most important factors in student learning, and Shanghai students have been recognized to perform outstandingly as compared to their Western counterparts. Hence, in order to develop deeper insights into the notion of mathematics teaching expertise, we have investigated three Chinese “expert teachers” through the lens of their resource systems aligned to their practice, and from different cultural and theoretical perspectives (Eastern and Western). The research questions are: (1) How do three Chinese “expert” mathematics teachers describe their resource systems; which kinds of resources do they use in/for their daily practice? (2) How do the three case teachers perceive expertise in teaching mathematics, and how to develop such expertise? (3) What are the characteristics of the three teachers’ resource systems, and in which ways do they characterize mathematics teaching expertise? After this general introduction, we propose, in the second section, a literature review focusing on the notion of mathematics teaching expertise. In the third section we detail the crucial notion of a resource system, drawing on the documentational approach of didactics (Gueudet & Trouche, 2009). The methodological considerations concerning the research design, the data collection strategies and analyses are presented in the fourth section. In the fifth section, we present our findings, and in the final section we conclude by developing deeper understandings of mathematics teaching expertise through the lens of resources, and by indicating the significance of this work for teacher professional development.

Activity theoretical approaches to technology enhanced mathematics learning orchestration

In this contribution, we expose and discuss a specific theoretical and methodological approach: the documentational approach to didactics (Gueudet & Trouche 2009). This approach has been developed for the study of mathematics teachers' activity and professional development, focusing on the interactions between teachers and various kinds of resources. These resources include technologies, and any kind of artefacts (in particular, traditional curriculum material); but resources are more general than artefacts, since we consider, as Adler (2000) does, that anything likely to re-source the teacher's practice can be considered as a resource. Our purpose here is not to expose the approach, but to discuss its links with activity theory, focusing in particular on two aspects: the system of resources that a teacher develops; and the collective work of teachers. Both aspects are indeed essential in particular for studying and for supporting the integration of technologies by teachers.

Our contribution to TWG 22 is dedicated to discussing teachers' interactions with resources for planning their classroom instruction, particularly in the context of collective work. Each teacher during his or her professional life uses and creates many resources. To analyse the history of teachers' work with resources, we propose the concept of the " documentational trajectory ". This idea is based on and aims to contribute to the development of the documentational approach to didactics. We will present a case study of one middle school teacher. The data related to this teacher's work will allowed us to consider her documentational trajectory. We then used the teacher's documentational trajectory to analyze her professional development. The teacher's documentational trajectory demonstrates a strong participation in collective work, in particular a collective named SESAMES, has an essential role. This participation contributes to the emergence of a particular resource, called a metaresource, to structure her documentation work.

Jana Visnovska , Chrystal Dean

2012, In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to 'lived' resources: Mathematics curriculum materials and teacher development (pp. 323-341).

In this chapter, we draw on a five-year interventionist professional development study that we conducted with a group of middle-school mathematics teachers in the USA. The fifth and final year of the study involved a performance assessment in which the teachers collectively designed an instructional unit on statistics that aimed both to build on what they learned in the professional development group and to address the objectives for middle-school statistics prescribed by the standards and objectives for mathematics in their State. This performance assessment provided a window into the teachers’ documentation work, especially on the resources they needed in order to engage in this type of design work effectively. We draw on this case to problematize the rhetoric of teachers as instructional designers. In doing so, we question the common assumption that groups of teachers are capable of designing coherent instructional sequences from provided materials immediately and without ongoing support. We illustrate that teachers becoming effective instructional designers and the associated professionalization of teaching are significant accomplishments.

Jana Visnovska

2018, In L. Fan, L. Trouche, C. Qi, S. Rezat & J. Visnovska (Eds.), Research on mathematics textbooks and teachers’ resources: Advances and issues (pp. 277-295)

Authors: Visnovska, J., & Cortina, J. L. . We explore how resources support teachers’ work broadly, and their preparation for interactions with students’ ideas specifically. We draw on data from two professional development design experiments aimed at supporting teachers in making students’ mathematical reasoning central to their instructional decisions. The forms of support that traditional resources and expectations provided were no longer present when teachers transitioned to proactively planning for classroom interactions. We identify new forms of support that designed instructional sequences can provide for teachers by (a) specifying simple initial goals for students’ reasoning, (b) supporting teachers’ design for classroom interactions, and (c) increasing the likelihood that these designs would do useful work in classrooms. . https://link.springer.com/chapter/10.1007/978-3-319-73253-4_13

chongyang wang

Aiming to contribute to session 3 of TSG 38, teachers' collective work through resources, this study works as a primary result of the author's PhD thesis, which aims to explore teachers' documentation expertise shown in their resource work in collectives. As a new notion, documentation expertise was introduced at the beginning of the study based on the literature review. Then through a case study on two teachers, as well as their entourage, from two contrasted situations, TRG in China and LéA in France, a deeper analysis on such a documentation expertise is hoped to be gained. Grounded in the theoretical frameworks of documentational approach of didactics and activity theory, this study uses a methodology of reflective investigation, beyond the traditional tools like interview or observation.

ghislaine gueudet

The abundant digital resources on the Internet are leading to profound changes in teachers' activity. We refer to the theoretical framework and methodology of the documentational approach to didactics to investigate these changes. We compare two case studies: an English teacher, and a mathematics teacher, both working in the same upper secondary school in France. We have observed significant use of digital resources in both cases, but of a different nature. We present and discuss these differences that shed light upon teachers' documentational work. We use these cases to draw more general conclusions on designing, using and sharing digital teaching resources. At all school levels and in all subjects, teachers work with a variety of resources: paper textbooks, software, lesson plans and so on. Recently available resources have dramatically increased: in many countries, teachers have access via the Internet to an abundance of open source material, free of charge. The national research project REVEA in France studies the consequences of these developments for teachers working in secondary education and teaching different school subjects: Biology, English, Mathematics, Physics and Technology. The work we present here comes from this project and builds on a particular didactical perspective. We maintain that analyzing the development of teachers' work within this context requires a specific theoretical approach. We have developed for this purpose the documentational approach to didactics (Gueudet, Pepin & Trouche, 2012), a theoretical approach (section 1) drawing on the instrumentation theory (Rabardel, 1995) and introducing the concepts of teachers' documentation work, resources and documents in particular. This theory is associated with a specific methodology called «reflexive investigation». In this paper, we develop this methodology further (section 2) notably by considering teachers teaching different subjects and by comparing their documentation work. We illustrate this method by using it to study two upper-secondary school teachers in France, one teaching English and the other mathematics (section 3). We discuss the Varia Investigating Teachers' Work with Digital Resources.

2014, Thèse Université libanaise

Cette étude comprend deux objectifs: premièrement, elle vise à étudier dans quelle mesure les enseignants de biologie du secondaire, au Liban, utilisent les ressources numériques dans leur enseignement en général et dans l'enseignement du génétique en particulier. Deuxièmement, elle vise à étudier les relations entre l’usage de ressources numériques par les enseignants et leurs conceptions concernant le déterminisme génétique du phénotype, en particulier de l’héréditarisme de l'épigénétique. Aux fins de cette étude, une combinaison entre deux cadres théoriques a été utilisée, à savoir, "l'approche documentaire" et le modèle de "KVP". Une méthodologie mixte a été conçue, combinant des études quantitatives et qualitatives: un questionnaire, des entretiens, des journaux de bords, des représentations schématiques de systèmes de ressources (RSSR) et des observations de classe. Le terrain de recherche a impliqué 116 enseignants de biologie du secondaire de diverses régions libanaises. Sur la base des réponses au questionnaire, quatre enseignants ont été sélectionnés pour des études plus approfondies et deux parmi eux ont été suivi pendant deux années consécutives. Les résultats ont mis en évidence que les enseignants intègrent des ressources numériques dans leur enseignement pour favoriser la compréhension, par les élèves, de concepts abstraits en génétique et pour enrichir et mettre à jour leurs connaissances scientifiques. En outre, les résultats ont indiqué que la disponibilité et l'accessibilité de la technologie, la disponibilité du temps, le travail collectif et collaboratif, la maîtrise technologique et les attitudes envers la technologie sont autant des facteurs qui affectent l'intégration, par les enseignants, de ressources numériques. Les résultats ont également montré que la relation entre les ressources et les conceptions est réversible : les conceptions des enseignants affectent leur choix des ressources et leur intégration d'une part (instrumentalisation) et le travail documentaire des enseignants affecte leurs conceptions d'autre part (instrumentation). Les implications pour la pratique et les futures recherches sont discutées.

Ana Isabel Sacristán , Luc Trouche

This paper considers the work carried out by online teacher educators and their professional development. We use the theoretical perspective of the documentational approach that focuses, in this case, on the interaction between teacher educators and the resources they use for their online training work. We thus study the following issues: (1) What kinds of resources do online teacher educators need, and how are such resources modified according to the educators’ specific skills and needs? (2) What specific skills are needed for setting up online training for mathematics teachers and how do these skills evolve as teacher education resources are used? We consider both questions simultaneously, while presenting results from a study within a specific teacher training programme in France that proposes ‘‘training paths’’ on a national platform. These ‘‘paths’’ are resources designed for teacher educators. We follow the appropriation of two training paths by two educator teams. The ways in which these educator teams were able to appropriate the paths give insights into the teacher educators’ skills and, as well, into the resources they need. By looking at their use of resources (as online mathematics teacher educators), we observe and analyse professional geneses, leading to the development of new skills.

2016, Tools and Mathematics: Instruments for Learning

The concept of connectivity, following the development of Internet resources, is more and more widely used, in the society in general, and in the mathematics education community in particular. This chapter aims to question the different meanings, and the potential, of this emergent concept. For this purpose, it lies first on the experience of the author, considering both connecting students as a support of their mathematics learning, and connecting teachers as a support of their professional development. Then it considers the views expressed in the connectivity panel occurring in the I7th ICMI study, dedicated to technology in mathematics education. Finally, it discusses the dynamics of the concept itself for the future of mathematics education.

Marko Lovric

Michiel Doorman , Paul Drijvers

ABSTRACT Digital resources offer opportunities to improve mathematics teaching and learning, but meanwhile may question teachers’ practices. This process of changing teaching practices is challenging for teachers who are not familiar with digital resources. The issue, therefore, is what teaching practices such so-called ‘mid-adopting’ mathematics teachers develop in their teaching with digital resources, and what skills and knowledge they need for this. To address this question, a theoretical framework including notions of instrumental orchestration and the TPACK model for teachers’ technological pedagogical content knowledge underpins the setting-up of a project with twelve mathematics teachers, novice in the field of integrating technology in teaching. Technology-rich teaching resources are provided, as well as support through face-to-face group meetings and virtual communication. Data include lesson observations and questionnaires. The results include a taxonomy of orchestrations, an inventory of skills and knowledge needed, and an overview of the relationships between them. During the project, teachers do change their orchestrations and acquire skills. On a theoretical level, the articulation of the instrumental orchestration model and the TPACK model seems promising.

Ulises Salinas-Hernández

In this article we report how a secondary school physics teacher in Mexico City used the Cartesian plane and gestures as resources to promote the understanding on the concept of reference frame among his students (between ages 16 and 18). The teacher’s use of resources arose from a question posed to him by one of his students while solving a problem linked to the concept of acceleration. This is a qualitative research supported by the theory of use of resources as a means of reflection during teaching practice in the classroom. This theory is linked to the documentational genesis (Gueudet & Trouche, 2009; 2012), and was used in the analysis of our data. The data collection was done by video-recording of the class when the physics teacher worked with his students. Our results suggest that even this physics teacher has difficulties understanding the concepts related with the movement of objects.

Paul Drijvers

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Research on Mathematics Textbooks and Teachers’ Resources

Advances and issues, publisher description.

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level.  As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks?  As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development?  As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

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9783319732527

ICME-13 Monographs

Lianghuo Fan

Springer International Publishing

13 February 2018

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This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. 

As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? 

As for the teachers, the book discusses the relationships between teachers' individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? 

As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students' use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

• © 2018

Research on Mathematics Textbooks and Teachers’ Resources

Advances and Issues

• Lianghuo Fan 0 ,
• Luc Trouche 1 ,
• Chunxia Qi 2 ,
• Sebastian Rezat 3 ,
• Jana Visnovska 4

Southampton Education School, University of Southampton, Southampton, United Kingdom

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Institut Français de l’Education, École Normale Supérieure de Lyon, Lyon, France

Faculty of education, beijing normal university, beijing, china, eim—institut für mathematik, universität paderborn, paderborn, germany, school of education, the university of queensland, brisbane, australia.

Discusses the role of textbooks and other curricular or learning resources in mathematics teaching, learning, and assessment

Considers different types of textbooks, which are suited for project-based, inquiry-based, or problem-based learning

Includes research on the effects of modern ICT (information and communications technology) on students’ use of resources, and their design

Part of the book series: ICME-13 Monographs (ICME13Mo)

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Table of contents (17 chapters)

Front matter, trends in presentation of mathematics in textbooks and other resources, open educational resources: a chance for opening mathematics teachers’ resource systems.

• Luc Trouche, Ghislaine Gueudet, Birgit Pepin

Textbook Use by Teachers in Junior High School in Relation to Their Role

• Chunxia Qi, Xinyan Zhang, Danting Huang

A Comparative Study on the Presentation of Geometric Proof in Secondary Mathematics Textbooks in China, Indonesia, and Saudi Arabia

• Lianghuo Fan, Mailizar Mailizar, Manahel Alafaleq, Yi Wang

Teacher Interactions with Curricular and Other Learning Resources

Examining teachers’ interactions with curriculum resource to uncover pedagogical design capacity.

• Janine T. Remillard

Disaggregating a Mathematics Teacher’s Pedagogical Design Capacity

• Moneoang Leshota, Jill Adler

Teachers’ Selection of Resources in an Era of Plenty: An Interview Study with Secondary Mathematics Teachers in England

• Helen Siedel, Andreas J. Stylianides

Teachers as Designers of Digital Educational Resources for Creative Mathematical Thinking

• Chronis Kynigos, Angeliki Kolovou

Teachers’ Collective Work Through Resources

Curriculum support for teachers’ negotiation of meaning: a collective perspective.

• Hendrik Van Steenbrugge, Maria Larsson, Eva Insulander, Andreas Ryve

Mathematics Teachers’ Expertise in Resources Work and Its Development in Collectives: A French and a Chinese Cases

• Chongyang Wang

Role of Context in Social Creativity for the Design of Digital Resources

• Nataly Essonnier, Chronis Kynigos, Jana Trgalova, Maria Daskolia

Uses of Online Resources and Documentational Trajectories: The Case of Sésamath

• Katiane de Moraes Rocha

Teachers’ and Students’ Interactions Through Resources

Instructional activity and student interaction with digital resources.

• Kenneth Ruthven

Resourcing Teachers in Transition to Plan for Interactions with Students’ Ideas

• Jana Visnovska, Jose Luis Cortina

Prospective Teachers’ Interactions with Interactive Diagrams: Semiotic Tools, Challenges and Well-Trodden Paths

• Elena Naftaliev

Teacher Decisions on Lesson Sequence and Their Impact on Opportunities for Students to Learn

• Ok-Kyeong Kim

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. 

As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? 

As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? 

As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

• learning resources
• curricular resources
• e-textbooks
• learning materials
• mathematics teaching
• mathematics learning
• mathematics assessment
• teacher manuals
• assessment materials
• online resources
• Mathematics textbook
• Teaching mathematics
• Open educational resources
• Teacher interaction
• Pedagogical design capacity
• Digital educational resources
• Creative mathematical thinking
• Collaborative workspace for teachers
• Student interaction with digital resources

Lianghuo Fan

Luc Trouche

Sebastian Rezat

Jana Visnovska

Book Title : Research on Mathematics Textbooks and Teachers’ Resources

Book Subtitle : Advances and Issues

Editors : Lianghuo Fan, Luc Trouche, Chunxia Qi, Sebastian Rezat, Jana Visnovska

Series Title : ICME-13 Monographs

DOI : https://doi.org/10.1007/978-3-319-73253-4

Publisher : Springer Cham

eBook Packages : Education , Education (R0)

Copyright Information : Springer International Publishing AG 2018

Hardcover ISBN : 978-3-319-73252-7 Published: 27 February 2018

Softcover ISBN : 978-3-319-89245-0 Published: 04 June 2019

eBook ISBN : 978-3-319-73253-4 Published: 13 February 2018

Series ISSN : 2520-8322

Series E-ISSN : 2520-8330

Edition Number : 1

Number of Pages : XXIII, 377

Number of Illustrations : 50 b/w illustrations

Topics : Mathematics Education , Teaching and Teacher Education , Learning & Instruction , Study and Learning Skills , Educational Technology

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5 Ways Teachers Can Help Students Overcome ‘Math Trauma’

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Teaching math isn’t just about working through problems. Often, it’s about helping students work through baggage, too.

After years of historic declines in math performance nationwide and sharp post-pandemic spikes in general and math-specific anxiety , teachers may need to help students unpack negative emotions around math to help them gain traction in the subject.

“People are not OK with math; there’s so much trauma surrounding it,” Vanessa Vakharia, a K-12 math teacher and instructional coach in Ontario, Canada, said at the annual National Council of Teachers of Mathematics conference here this week.

Vakharia, who had crippling math anxiety until late high school, now chronicles her own and others’ traumatic experiences with math in the Math Therapy podcast. One in 4 K-12 educators reported being math-anxious in a 2019 survey by the EdWeek Research Center, and in a separate survey the center conducted last month, more than 40 percent of math teachers said they’d had at least some math anxiety.

“We’re talking about unpacking trauma, but none of us are therapists,” she said. “This is about how we can do this as educators with our expertise in a way that’s safe in our classroom and that we feel comfortable with.”

She highlighted five steps teachers can take to help students understand and let go of negative math experiences.

1. Create a myth-busting mindset.

Often small classroom practices—highlighting students’ wrong answers in front of the class, for example—can undermine students’ math identity, particularly for students from groups historically underrepresented in math, Vakharia said.

“It is a deeply embedded trauma being told what we need to look like, sound like, be like, perform like in order to be good at math, being told you have to shed your identity in order to be good at math,” Vakharia said.

She suggested teachers explicitly bust common misconceptions—such as that math ability is static or that creative or artistic students don’t need math—and quickly counter students’ negative talk about math.

“Let’s say something that’s more accurate,” Vakharia tells her students. “So instead of saying ‘I’m not a math person,’ how about, ‘I don’t feel as comfortable with math as I would like to, but I believe I could if I wanted to.’ That’s actually fair.”

2. Help students map out math trauma.

Vakharia encourages her students to identify and talk about experiences that made them feel bad about math.

These could include someone dismissing a student’s math struggles by saying they “ can be good at other things ,” media portrayals suggesting that “everybody hates math,” or parents who pressure or yell at their children during math homework (as student tweets like the one below can attest).

my dad explaining me trying to see a math problem the paper thru a for the 374th time blur of tears pic.twitter.com/EJSnfZehcb — Maruf (@m3aruf) September 10, 2019

“Your goal is to figure out what trauma exists in your classroom so that you can adjust your teaching style and your pedagogy, so you know what students will react to,” she said.

For example, Vakharia’s students discuss situations that trigger their anxiety—such as having another student yell “I’m done” while they are still working—and make student and teacher pacts to reduce class stressors.

3. Motivate students to persist.

Research suggests the vast majority of math-anxious students aren’t initially low-performers . Rather, the fear and stress they experience before starting math tasks takes up their mental bandwidth and leads them to avoid math-related tasks. Over time, students with severe math anxiety tend to progress more slowly in math, but even math-anxious students who objectively perform on average or even high in math often end up disengaging and avoiding math classes and fields they might otherwise thrive in.

Students with math anxiety tend to choose less-effective ways to study , too, like rereading already-solved problems instead of trying to solve new ones. That makes students less prepared come test time, which can create a cycle of stress, failure, and avoidance .

Some classes keep a “failure wall,” in which students regularly post cards describing mistakes or failures and what they learned from them. The process helps students both reflect on their own learning and realize they are not alone in struggling, Vakharia said.

4. Have ‘math identity makeovers.’

“If you ask any kid what being good at math is, they’ll say it means you’re really fast. It means you don’t make any mistakes. It means you always get the right answer. That kind of thing,” Vakharia said. “We have to myth-bust that for them.”

Vakharia advised teachers to use math journals and data reviews to help students analyze their own progress and think about what success means to them.

“When you have a track record of all the things in your class, you can prove that they can get better at a skill. And then you can go farther: Why did you [previously] think that you couldn’t do this? And why do you think you can do it now?’ And they’ll say things like, ‘I practiced,’ or ‘I got some help, I sought these resources.’ ... This is really helpful in bringing a growth mindset to life and myth-bust what it means to be good at math.”

Teachers should also help students to understand that having a disability that interferes with math, like dyscalculia or attention deficit disorders , doesn’t mean they can’t do math or succeed in a math field.

5. Measure and highlight progress.

Assessments can be particularly daunting for students with math anxiety. When possible, Vakharia advised teachers to avoid timed tests, and to allow students to talk through feelings of anxiety before assessments.

Second chances are also helpful. For example, when students ask to redo a test or assignment, she asks them to first list how they prepared the first time, and what they plan to do differently this time.

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202 Math Research Topics: List To Vary Your Ideas

Mathematics is an exceptional field of study dealing primarily with numbers. It also deals with structures, formulas, shapes, spaces, and quantities of where they are contained.

Maths encompasses different types of computations that are applied in the real world.

Math requires a lot of analysis. This is why there are different types of maths. They all encompass different subjects and deal with different things. What are the types of maths?

Arithmetic This is perhaps the commonest type or branch of maths. It is one of the oldest and it encompasses basic numbers operations. These are addition, subtraction, multiplication, and divisions; in some schools, the short word for it is BODMAS. This is known as the Bracket of Division, Multiplication, Addition, and Subtraction. Algebra This is where unknown quantities are represented by alphabets and used along with numbers. The letters these unknown quantities are represented by are usually A, B, X, and Y, and they could also be symbols. Geometry This is considered one of the practical branches of maths as it examines sizes, shapes, figures, and the features of these entities. The most common parts of geometry are lines, points, solids, surfaces, and angles.

There are many other types but the above are the most popular. Others are trigonometry, topology, mathematical analysis, calculus, probability, statistics, and a few others.

As many students find it hard to develop maths research topics on their own, this is a chance for you. It’s okay to be worked up when you can’t find undergraduate math research topics that fit your project, essay or paper choices. This article will provide custom maths education research topics for your use. Before that, how do you structure your math essay or paper?

How to Structure Your Math Essay or Paper

Structuring your essay or paper may require that you’ve been reading critical math journals. Reading them could have made it easy to understand how to structure your paper. However, you don’t have to worry if you haven’t. Structuring your paper as expected is an essential part of writing and you’ll know about it in this section. Before you learn that, how do you choose a topic?

Choosing a Topic to Discuss

One of the difficult yet significant parts of any math essay or paper is choosing your topic. This is because you need to solve a problem or engage in a subject that has got less attention. You also need to understand the background to the subject you want to discuss as you can’t write blindly.

You must also be able to articulate your thoughts well as you must show visible knowledge before you commence the research and writing. How do you go about this? You can consider reading existing research. You can even take notes during classes to see the areas you think more work needs to be done.

After choosing your topic, conduct your research to see if you can investigate the sphere. If you can, you need to structure your research thus:

The Background This includes the discussion on what the essay is about. Depending on what you’re writing about, you need to discuss the primary concepts, including the history of some terms, where essential, in this section. This section is more like general information about the subject you want to discuss with your paper. This helps your readers familiarize themselves with your intended discussion. The Introduction This is where the main ideas behind your essays (and the solutions you hope to proffer) are tended to the readers. This is where you also explain the symbols you’ll use and the principles which are required in your essay. Aside from this, you need to state the basic issues, the solutions you could offer, the laws which are essential to discuss to make your work comprehensible. The Main Body This is where you elaborate on your findings. You need to state the research problem, the formulas, the theories you’ll use in tackling the problem, and many other things. You also need to introduce different sections of maths into the main body which is divided by paragraphs and/or chapters as well as mathematical analysis where needed. Implications This is the last part of your essay or paper. This is where you share the insights of your research with your readers. You offer short explanations of the things you have discussed. If you have treated a subject in applied mathematics, this is where you give summaries of how math is connected to human life and the strategic importance of these to people.

By adhering to this structure, you would have crafted the best rated and high-quality maths paper. Furthermore, remember you always have an option to get help with dissertations and save your time. Since it is sometimes challenging to choose cool maths topics to research on your own, these are some for you:

Research Topics in Math

Math is a broad subject. There is a study of the history of math as well as its influence in education, amongst many other sub-sections. If you’d like to create stunning research, you may choose to discuss any of these research topics in math to fulfill one of your academic requirements:

• What are the distinctions between commutative and noncommutative algebra?
• Discuss the methods of factoring quadratics
• Types of sequences and your understanding of them
• Partial fractions: what are they and how do they work?
• Logarithms: what are they and how do they work?
• An overview of Gaussian elimination
• An overview of Brun’s constant relevant
• A description of the effect of dyscalculia on daily student lives
• Describe Descartes’s Dukes of Signs and their application
• Greeks and geometry: discuss
• Describe Euler’s formula
• The progression in the study of math
• Congruence meaning and methods
• Describe the correlation of CT scans to geometry
• Hypercubes and how they work
• The basis of Cramer’s rule
• The examination of Archimedean solids
• Projective geometry and why it’s studied
• Types of Transformations and the available types
• Picasso’s works and the application of geometry
• Difference between the conventional and unconventional approaches to teaching
• Math education and the process of Improvement in the US
• Rhombicosidodecahedron and how it operates in real life
• What are the STEM career fields and why are they important?
• Why women are needed in STEM
• The goals of teaching maths
• How to teach maths to special students
• The correlation between maths and accounting
• The distinction between computer programming and applied maths
• Applied maths and its dynamics
• Processes of solving Heesch’s problem
• Why should kids learn equations?
• History of calculus
• Why there is a need for math camps in schools
• The need for more maths competition in the US
• Methods of draining flight schedule for a country
• Why are some math problems unsolved?
• Discuss the consequences of the gender gap in math students
• Encryption and prime numbers: how do they apply?
• The significance of maths in day to day living.

Undergraduate Math Research Topics

As an undergraduate, you may also have a difficult time wrapping your head around math research topics. You may need to offer both practical and theoretical assessments while writing your paper or essay. The following are undergraduate math research topics:

• Show the proofs of what F-algebras are used
• Abstract algebra, what does it mean?
• Algebra and geometry: discuss
• Acute square triangulation: how it works
• Right triangles: discuss their importance
• Discuss number problems
• Why every math student should study non-Euclidean geometry
• Dirac manifolds and what it means
• Influence of geometry in physics, chemistry, and others
• The application of Riemannian manifolds in the Euclidean space
• How to improve your mathematical thinking ability
• Technology in maths: how is it used?
• Studies of maths in Europe
• Math anxiety and what it truly means
• Standardized testing and the goals of such
• Challenges of learning maths from public schools
• The significance of circles in maths
• The political and social significance of learning maths
• Research into how to increase student interest in maths
• How painting and drawing could help with maths
• Relationship of culture and maths
• History of algebra
• Role of maths in everyday life
• How math is used in Artificial intelligence
• The transferable belief model and its application
• An analysis of the Dempster-Shafer theory
• The role of continuous stochastic process in mathematics
• The major math theorems: discuss how they work
• Understanding the Gauss-Markov: The Evolution of maths
• Discrete random variable: an in-depth understanding of what it means in math and how to identify one.

Math Research Topics for High School Students

As a high school student writing a research paper, one way to get high grades is to write what you know. If you know any math research paper topics for high school, they are the topics you should pick. You can consider:

• Hyperbola: what it is and how it’s used in math
• When to use a calculator in class
• How to find solutions to linear equations
• The need for Pythagoras theorem in maths
• The role of art in maths and vice versa
• Role of philosophy in maths
• An overview of numerical data
• Egyptian mathematics explained
• Binomial theorem and its importance
• Probability, and how to solve a question on dice
• Why is math made compulsory in schools?
• Why do students hate maths?
• Why do students hate math teachers?
• How is math applied in the workplace?
• What are imaginary numbers and why are they needed
• How to calculate the interest rate and what is their importance in the banking sector?
• Discount factor: how is it achieved and why is it important for students?
• Types of techniques to be used while finding solutions to mathematical and finance gaps
• Solving a matrix: what are the important formulas and principles to embrace?
• How to create a chart on a company’s financial analysis for the past 5 years.

Interesting Math Research Topics

Writing a mathematical essay may seem complex to you if you can’t find simple topics to write about. There are many easy topics which are also general in maths. If you want to choose a relaxing topic for your math essay or paper, you can write about the following:

• The basic elements of Boolean algebra
• The life, time, and contribution of Isaac Newton to maths
• Sphericon and what it means
• Martingales and what they mean
• Hyperboloid and importance in geometry
• Describe the life, times, and contribution of Gauss to maths
• The most famous work of Jakob Bernoulli
• The most famous work of Jean d’Alembert
• Meaning and application of calculus in the banking field
• The meaning of congruence in math
• Analysis of De Finetti theorem in probability and statistics
• Describe Egyptian pyramids in concert with calculus
• Describe the enclosing sphere technique as used in combinatorics
• Tree automation meaning
• Pushdown automaton and Buchi automaton: differences and similarities
• What is the Markov algorithm?
• Describe what a Turing machine is
• What is the linear speedup theory in math?
• The Boolean satisfiability problem and what it means for students
• Why is the multiplication table important?
• Computational maths and its classes
• What does the post correspondence problem mean?
• What does the Scholz conjecture mean?
• How to calculate mean, median, and mode
• A study of the most difficult equations in math.

Cool Math Topics to Research

As a student of any level, you may love to create math topics that are not exactly complex. These are topics that lean on the history of maths, math education research topics, and others. Consider these math research topics for college students for your next essay or paper:

• Discuss what the Golden Ratio means in the paintings of the Renaissance period
• How to learn math
• An overview of the multiple ideas to probability
• How chess and checkers is essential in understanding mathematics
• How Pythagorean theorem is applied in real-life maths
• How to measure infinity
• The features of Mobius strip in geometry
• Describe what is meant by the Pascal’s Triangle
• Evaluate the Georg Cantor set theory
• What is the history of the number types?
• How does probability relate to card tricks?
• Compare and contrast abstract and universal algebra
• Describe Euclid’s role in the evolution of maths
• Evaluate the role of Indians in maths
• Explain the limits of calculus
• Discuss what predictive and prescriptive statistical analysis means
• What does chaos theory mean?
• Explain how to solve the Rubik’s Cube
• Why are some math equations so complex?
• How is geometry used in contemporary architectural designs?

Math Research Topics for Middle School

It’s okay to be worried about math topics for your research as a middle school student. There are still different unique topics that are rebranded from existing ones. You can find some of the right math research paper topics for you here:

• The role of statistics in business
• Definition of economic lot scheduling
• Why stock market crash
• The contribution of many traders in the New York Stock Exchange
• Revenue management and its history
• What are the financial indicators of a good investment?
• What are the odds of depreciation?
• How can any country benefit from the poor currency?
• Describe debt amortization and how math helps
• How to calculate net worth
• Distinctions in calculus, trigonometry, and algebra
• How did calculus start?
• How did trigonometry start?
• Why is Ito stochastic important in math?
• What do limits in math mean?
• How to know critical points in graphs
• What does nonstandard analysis in the probability theory mean?
• Describe continuous function
• The main principles of calculus
• The main principles of Pythagoras theorem
• Application of calculus in finance
• Value theorem in math
• Ratio and root test definition
• Linear approximations and how they work
• What is the Jacobson density theorem?
• Similarities and differences between epimorphisms and monopolists
• What does the Artin-Wedderburn theorem mean?
• Commutative ring and its meaning in algebra
• How difficult is it to teach maths?
• How standards examination curriculum affects math education.

Applied Math Research Topics

Applied math is a branch which deals with the application of mathematical methods in real life. These are manifested by applications in finance, physics, engineering, biology, medicine, and others. Through specialized knowledge, applied math is made possible. These are some topics for you in this area:

• How discovering genes can help determine healthy and unhealthy patients
• Role of algorithms in probabilistic modeling
• The need for mathematicians in developing robots
• The role of mathematicians in crime data analysis and prevention
• How did Isaac’s Laws of Motion help in real life?
• How math helped with energy conservation
• The role of math in quantum theory
• Analyze the features of the Lorentz symmetry
• Evaluate statistical signal processing in details
• Discuss how Galilean Transformation was achieved
• Examine nonlinear models
• Elucidate on the importance of data mining in banking
• The importance of step-stress modeling
• The significance of computer tomography
• What are the dimensions used in examining fingerprints?

Math Research Topics for College Students

As college students, you are at a critical level. You need maths topics for your essays and paper. You may also need them to prepare for your exams. These are some math research topics for you:

• Evolution of mathematics
• Explore the varieties of the Tower of Hanoi solutions
• Discuss how to use Napier’s bones
• Give examples of chaos theory and explain
• Discuss the important mathematical equations of all times
• Examine the nitty-gritty of barcodes
• What is the Traveling Salesman Problem?
• Natural selection and Fisher’s fundamental theorem of understanding it
• The Influence of math in biology
• The Influence of math in chemistry
• What is quantum computing?
• How to solve extremal problems in maths
• Analyze the meaning of fractals
• Discuss Einstein’s field equation theory
• Who created computer vision and object recognition?
• Five formulas and how they are applied
• Give three approaches to understanding maths
• Explain the origin and importance of algebra
• What do you know about the Fibonacci sequence?
• Trace the origin of math
• How does math help in geography?
• What does the operator spaces notion mean?

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