The Mathematics Teacher in the Digital Era: International Research on Professional Learning and Practice

Description

This book brings together international research on school teachers’, and university lecturers’ uses of digital technology to enhance teaching and learning in mathematics. It includes contributions that address theoretical, methodological, and practical challenges for the field with the research lens trained on the perspectives of teachers and teaching. As countries around the world move to integrate digital technologies in classrooms, this book collates research perspectives and experiences that offer valuable insights, in particular concerning the trajectories of development of teachers’ digital skills, knowledge and classroom practices. Via app: download the SN More Media app for free, scan a link with play button and access the videos directly on your smartphone or tablet. Introduction A Journey Through the Text References Contents Contributors About the Editors Professional Development for Teaching Mathematics with Technology: Fostering Teacher and Facilitator Noticing 1 Introduction 2 Theory 2.1 Teaching Mathematics with Multi-representational Tools 2.2 Facilitators 2.3 The Three-Tetrahedron Model for Design and Research on PD 2.4 Teacher Noticing and Video-Case-Based-Learning 3 Research Questions and Methodology 4 Research-Based Design of the Video-Case-Based Activity and Related Findings 4.1 Classroom Level 4.2 Teacher PD Level 4.3 Facilitator PD Level 5 Discussion 6 Conclusion References Using the Instrumental Orchestration Model for Planning and Teaching Technology-Based Mathematical Tasks as Part of a Restructured Practicum Course 1 Introduction 2 Instrumental Orchestration 3 Methods 3.1 Research Context 3.2 Participants 3.3 Procedure 3.4 Data Collection 3.5 Data Analysis 4 Results 4.1 General Perspective of the PMTs’ Orchestrations in Micro-teaching and Classroom Practices 4.2 Extended Results of PMT2 4.2.1 What Did He Plan? 4.2.2 Micro-teaching 1 4.2.3 Micro-teaching 2 4.2.4 Actual Classroom Teaching 5 Conclusions and Discussion References An Ensemble Approach to Studying the Teaching of Multiplication Using TouchTimes 1 Introduction 2 Multiplication 3 Situating the Theoretical Foundation 3.1 The Instrumental Approach 3.2 The Construct of Instrumental Orchestration 4 On Method 4.1 TouchTimes as a Multiplying Machine 4.2 Study Context and Participants 4.3 Data Analysis 5 Case Studies of Instrumental Orchestrations 5.1 Sequences of Orchestrations 5.2 New Orchestrations 5.3 Exploring the Tool–Teacher Relation 5.4 The Order Matters, So Language Matters Too 6 Discussion 6.1 The Mathematics, the Teacher and the Tool 6.2 Types of Orchestrations in Primary Classrooms 7 Conclusion References Using First- and Second-Order Models to Characterise In-Service Teachers’ Video-Aided Reflection on Teaching and Learning with 3D Pens 1 Introduction 2 Theoretical Framework 2.1 Decentering 2.2 First- and Second-Order Models 2.3 Pedagogical Consequences of Second-Order Modeling 3 Methods 3.1 Participants and Study Context 3.2 The Video 3.3 Video-Based Semi-structured Interviews 3.4 Method of Analysis 4 Results 4.1 Vignette 1: 3D Pen Constructions with Varying Sizes 4.2 Vignette 2: Straightening the Edges with 3D Pens 4.3 Vignette 3: Two Ways of Constructing and Perceiving a Triangular Prism 4.3.1 “Originally I Thought He Was Drawing Something Wrong” 4.3.2 “Why Did He Do That, and What Was He Thinking?” 4.3.3 “They Might Struggle to Understand.” “The Instructor Could Have…” 5 Discussion and Conclusion 5.1 Video-Aided Reflections of Teaching and Learning with 3D Pens 5.2 Researching Teachers’ Second-Order Modeling Associated with Technology-Rich Teaching References Opportunities and Challenges That Silent Video Tasks Bring to the Mathematics Classroom 1 Introduction 2 Background: Silent Video Clips for Mathematics Teaching and Learning 3 Silent Video Tasks 4 Icelandic Context 5 Teaching for Robust Understanding in Mathematics 6 Formative Assessment 7 Method 7.1 Participants 7.2 Silent Videos Used in This Study 7.3 Collected Data 7.4 Challenges in Data Collection 7.5 Ethical Considerations 7.6 Research Design and Data Analysis 8 Findings 8.1 Teachers’ Existing Assessment Practices and their Influence on SVTs Instructional Sequence 8.2 Description of Perceived Classroom Norms 8.3 Description of How SVT2 Was Used by Teachers 8.4 In Theory: Opportunities and Challenges that SVTs Might Bring 8.5 In Practice: Opportunities and Challenges That SVTs Brought 8.5.1 Challenge: It Is Hard to Change a Prevailing Socio-Mathematical Norm (For Example, That There Is a Single Correct Answer) 8.5.2 Opportunity: Previously Inaccessible Information Revealed by Students’ Task Responses 8.5.3 Challenge: It Can Be Tempting to Return to Teacher-Centred Transmission of Knowledge 8.5.4 Challenge: It Is Challenging to Lead Group Discussions Based on Students’ Ideas 8.5.5 Opportunity: SVT Practices Might Support Teachers to Institutionalise Knowledge 8.5.6 Challenge: It Is Hard to Change Prevailing Social Norms on the Motivation Role of the Final Grade 8.5.7 Opportunity/Challenge: Providing Access to the Classroom Discussion 9 Discussion Along the Five TRU Dimensions 10 Conclusion References Teaching Linear Equations with Technology: A Flipped Perspective 1 Introduction 1.1 Flipped Classroom: Overview of Components & Implementation 1.2 Technology, Pedagogy and Flipped Implementation 1.3 Teacher Experiences in Flipped Implementation 2 Methodology 2.1 Methodological Basis 2.2 Setting of the Study 2.3 Teacher Participant 2.4 Research Design 2.5 Flipped and Non-flipped Lesson Content and Structure 2.6 Semi-Structured Interviews 2.7 Data Analysis 3 Results and Discussion 3.1 Requirements for the Flipped Classroom – Theme 1 3.1.1 Clear Expectations of Students’ Participation in the Flipped Classroom 3.1.2 Teacher Technology Competence 3.2 Understanding the Process of Flipping a Classroom – Theme 2 3.2.1 Flipping Lessons Is a Time-Consuming Process 3.2.2 Video Quality Does Not Need to Be Perfect 3.2.3 Formative Assessment in the Flipped Classroom Assists Planning and Preparation 3.3 Key Perceived Outcomes: Resources – Theme 3 3.3.1 Flipped Tutorials Are Reusable 3.4 Key Perceived Outcomes: Student Classroom Engagement – Theme 4 3.4.1 More Engagement and Less Behavioural Issues After Flipping 3.4.2 Increased Collaboration Opportunities in a Flipped Classroom 3.5 Key Perceived Outcomes: Teacher Specific – Theme 5 3.5.1 Increased Opportunities to Observe and Support Student Progress 3.5.2 Reduced Teacher Stress in a Flipped Classroom 3.6 Key Perceived Outcomes: Learner Specific – Theme 6 3.6.1 More Time for Student Work in the Face-to-Face Classroom 3.6.2 The Flipped Classroom Supports Lower Achieving Students 3.6.3 The Flipped Classroom Enables Flexible and Individualised Learning 4 Implications and Conclusions 4.1 Advantages for Teachers 4.2 Technology Considerations 4.3 Student Expectations 4.4 Future Directions for the Flipped Classroom in Secondary School Mathematics 4.5 Capitalising on Lessons from the COVID-19 Pandemic Appendix: Semi-structured Interview Questions and Rationale First Interview: Before Starting the Flipped Classroom with Students Second Interview: During (Mid-way) Implementation of the Flipped Classroom Third Interview: After Completion of the Flipped Classroom References Tensions and Proximities in Teaching and Learning Activities: A Case Study of a Teacher’s Implementation of Tablet-Based Lessons 1 Introduction 2 Theoretical Background and Analytical Tools 2.1 Defining Tensions 2.2 Defining Proximities 3 A Case Study 3.1 Context and Data 3.2 Introducing Roger 3.3 Task Analysis 3.4 Tensions and Proximities in Teaching and Learning Activities 4 Findings 5 Conclusion References Digital Resources in Kindergarten Teachers’ Documents and Resource Systems: A Case Study in France 1 Introduction 2 Mathematics at Kindergarten in the Digital Era and Teachers’ Practices 3 Teachers’ Documents, Teachers’ Resource Systems: A Theoretical Framework 4 The Case Study Design 4.1 Methodological Principles 4.2 The Case of Mia: Profile and Working Environment 4.3 Analysing the Data Collected 5 Analysis of Mia’s Case 5.1 Selected Digital Resources Used by Mia 5.2 Focus on the Development of a Document by Mia 5.3 Mia’s Resource System and Its Evolutions 6 Discussion and Conclusion References Analysis of Primary School Teachers’ Roles in the Dynamics of Mathematics Lessons That Integrate Technology Resources in Challenging Socio-economic Contexts 1 Introduction 2 Literature Review and Background 3 Theoretical Framework 4 Research Questions 5 Methodology 5.1 The Teachers, Students and Schools 5.2 Research Tools 6 Results 6.1 Carla’s Case 6.1.1 Proportionality and Movement with the Cycle Track Program 6.1.2 Carla’s Case: First Session 6.1.3 Carla’s Case: Second Session 6.2 Yasmin’s Case 6.2.1 Developing Spatial Reasoning and Collaborative Skills with Lego: 2D–3D Dimensional Change 7 Discussion 7.1 On the Emergence of Mathematical Activity 7.2 Creation of a Classroom Culture That Introduces Students in Socio-Economically Disadvantaged Context to Important Mathematical Ideas 8 Conclusions References Characterising Features of Secondary Teachers’ Curriculum Scripts for Geometric Similarity with Dynamic Mathematical Technology 1 Introduction 2 Specifying the SFCP Framework for Mathematics: The Case of GS 2.1 Operationalising Curriculum Script in the Context of GS with DMT 3 Research Context 3.1 Setting the Scene 3.1.1 Introducing the CM Project 3.1.2 Defining the CM Software as DMT 3.2 Design for the Study 3.3 Participants 3.4 Methods of Data Collection 3.4.1 Classroom Observation 3.4.2 Teacher Interview 3.4.3 Lesson Resources 3.5 Data Analysis 4 Results 4.1 The Diversity of GS-Related Teaching Goals Enacted in the Lessons with the DMT 4.2 The Range of Mathematical and Technological Discourse in the Classroom 4.3 The Depth and Variety of Questioning Referencing the DMT 4.4 The Variety of Students’ Misconceptions About GS Anticipated, Identified, and Addressed in the Lessons Using the DMT 5 Conclusion References Instrumental Orchestration of the Use of Programming Technology for Authentic Mathematics Investigation Projects 1 Introduction 2 Programming Integration and Teaching in the Mathematics Classroom: An Overview 2.1 Programming for Authentic Mathematics Investigation Projects: An Example 3 Theoretical Framework 3.1 Instrumental Genesis, Schemes, and Instrumental Orchestration 3.2 Instrumental Genesis of Using Programming for Mathematics Investigation Projects 3.3 Research Question and Link with Our Previous Work 4 Methods 4.1 Participant 4.2 Data Collection 4.3 Data Analysis 5 Instrumental Orchestration of Using Programming for Math Investigation Projects: A Case Study 5.1 Bill’s Overall Instrumental Orchestration 5.1.1 Didactical Configuration 5.1.2 Exploitation Mode 5.1.3 Didactical Performance 5.2 Bill’s Orchestration of Two Selected Student Schemes 5.2.1 Student Scheme of Articulating a Mathematics Process in the Programming Language 5.2.2 Student Scheme of Validating the Programmed Mathematics 6 Model of Instructor’s Instrumental Orchestration and Students’ Instrumental Genesis Alignment 7 Discussion 8 Recommendations and Perspectives Appendix: Bill’s MICA II Assignment 1 Guidelines, Winter 2019 References Researching Professional Trajectories Regarding the Integration of Digital Technologies: The Case of Vera, a Novice Mathematics Teacher 1 Introduction 2 Teacher Education and Digital Technologies 3 Theoretical Framework 4 The Contextual Frame of the Study 4.1 Vera’s Educational Context as a Preservice Teacher 4.2 The Context of Vera’s Current School 5 Methodological Procedures 5.1 Vera as a Student 5.2 Vera Acting as a Mathematics Teacher 6 Results 6.1 Vera’s Relationship with DTs in Different Educational Contexts 6.2 Vera’s First Teaching Practice: DTs as Media to Teach and Facilitate Mathematical Production 6.3 The Integration of DTs into Current Vera’s Daily Work 7 Discussion and Conclusions References The Abrupt Transition to Online Mathematics Teaching Due to the COVID-19 Pandemic: Listening to Latin American Teachers’ Voices 1 Introduction 2 On the Notion of Teachers’ Voice 3 Previous Research on Obstacles and Constraints to Digital Technology Integration 4 Method 4.1 Context of the Study 4.2 Study Participants 4.3 The Questionnaire 4.4 Implementation of the Questionnaire 4.5 Analysis of the Teachers’ Responses 5 Results 5.1 Implementation Obstacles 5.2 Time Needed to Adapt Mathematics Lessons 5.3 Teachers’ Lessons Descriptions 5.4 Implementation of Digital Tools 5.5 Teachers’ Emotions 5.6 Teachers’ Suggestions and Recommendations 6 Discussion Appendix: Questionnaire Given to the Mathematics Teachers Who Participated in the Study References Meta-Didactical Transposition.2: The Evolution of a Framework to Analyse Teachers’ Collaborative Work with Researchers in Technological Settings 1 Introduction: The Meta-Didactical Transposition Framework 2 Three Examples to Chart the Evolution from MDT.1 to MDT.2 2.1 Example 1: A Focus on the Where of Internalisation 2.1.1 Aim of the Research Regarding MDT and Focus of the Analysis 2.1.2 Actors Involved and Initial State of the Praxeologies 2.1.3 What is the Theoretical Gap in the MDT.1 Framework? 2.1.4 What Do We Add and Why? 2.1.5 Data 2.1.6 Analysis 2.1.7 Final State of the Praxeologies 2.1.8 Conclusion of This Example 2.2 Example 2: A Focus on the Why of Internalisation 2.2.1 Aim of the Research Regarding MDT and Focus of the Analysis 2.2.2 Actors Involved and Initial State of the Praxeologies 2.2.3 Data: Two Contrasting Cases 2.2.4 What is the Theoretical Gap in the MDT.1 Framework? 2.2.5 What Do We Add and Why? 2.2.6 Analysis 2.2.7 Final State of Praxeologies 2.2.8 Conclusion of This Example 2.3 Example 3: A Focus on the How of Internalisation 2.3.1 Aim of the Research Regarding MDT and Focus of the Analysis 2.3.2 Actors Involved and Initial State of the Praxeologies 2.3.3 The Data 2.3.4 What is the Theoretical Gap in the MDT.1 Framework? 2.3.5 What Do We Add and Why? 2.3.6 Analysis 2.3.7 Final State of the Praxeologies of Teachers and Researchers 2.3.8 Conclusion of This Example 3 The Evolution of the MDT Framework from MDT.1 to MDT.2 References Revisiting Theories That Frame Research on Teaching Mathematics with Digital Technology 1 Introduction 2 Evolutions of Theories Related to Teaching with Technology 3 An Example of a Theory and its Evolution: The ‘Instrumental Approach’ 3.1 An Overview of the Instrumental Approach 3.2 Towards a Focus on the Teacher: Instrumental Orchestration, Teachers’ Instrumental Geneses and the Documentational Approach 4 Reflections on Theory Development in Mathematics Education 4.1 Some Philosophical Reflections on Theories Relation to Technology 4.2 An Exploration of Technology Related Theories from the Work of Simondon 5 Looking Forward Appendix: List of the Journals Reviewed References Index