Developing 21st Century Competencies In The Mathematics Classroom: Yearbook 2016, Association Of Mathematics Educators Yearbook 2016, Association of Mathematics Educators

"The aim of this book is to contribute towards literature in the field of mathematics education, specifically the development of 21st century competencies amongst learners of mathematics. The book comprising fourteen chapters, written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to foster skills and dispositions that will enable learners to thrive in the fast-changing and complex world that we live in today. The chapters in the book can be classified into three broad themes. The first is an examination of what is meant by 21st century competencies and how they can be developed within the context of the mathematics curriculum. The second is an in-depth discussion of evidence-based practices aimed at fostering specific competencies like metacognition and reflective thinking, critical thinking and communication skills. The last and third theme is about teaching approaches that are likely to feature increasingly in the 21st century classroom, for example flipped learning or the use of comics and storytelling."-- Provided by publisher Contents 6 Chapter 1 21st Century Competencies in Mathematics Classrooms 10 1 Introduction 10 2 Framework for 21st Century Competencies and Student Outcomes 12 3 The Mathematics Curriculum and 21st Century Competencies 14 4 Metacognition, Critical Thinking and Communications Skills 15 5 Pedagogical Approaches in the 21st Century Classroom 17 6 Concluding Thoughts 18 References 19 Chapter 2 Mathematics Education, Virtues and 21st Century Competencies 22 1 Introduction 22 2 21st Century Competencies and the Intellectual Virtues 24 3 Bounded Gaps Between Primes: The Polymath Project 29 4 Examples from School Mathematics 31 4.1 Tidal surges: Civic literacy 31 4.2 Mathematics through art: Critical and inventive thinking 33 4.3 Froebel and Scratch: Information and communication skills 35 5 Conclusion 38 Acknowledgements 39 References 39 Chapter 3 Enriching Secondary Mathematics Education with 21st Century Competencies 42 1 Introduction: Necessity for 21CC 42 2 21CC and the Singapore Mathematics Curriculum 43 3 Confident Person 45 4 Self-Directed Learner 48 5 Concerned Citizen 51 6 Active Contributor 54 7 21CC Mathematics Teachers 54 8 Concluding Remarks 56 References 57 Chapter 4 Mathematics in 21st Century Life 60 1 Introduction 60 2 The Productive Worker 61 3 The Careful Consumer 65 3.1 Shopping 65 3.2 Housing 67 3.3 Health 68 3.4 Gambling and intuition 71 3.5 Insurance 73 4 The Informed Citizen 73 5 The Balanced Person 79 6 Conclusion 81 References 82 Chapter 5 Mathematics Subject Mastery – A Must for Developing 21st Century Skills 86 1 Introduction 86 2 Mathematical Tasks 88 3 Teachers’ Perceptions about Metacognition 92 3.1 What does metacognition mean to you? What is your understanding of metacognition? 93 3.2 Do you engage your students in metacognition during mathematics lessons? Yes / No. If Yes, how do you engage your students in metacognition during mathematics lessons? Give an example of what you do. 96 4 Developing 21st Century Skills in Mathematics Classrooms 97 5 Conclusion 101 Acknowledgement 101 References 102 Chapter 6 Teaching in the 21st Century Mathematics Classroom: Metacognitive Questioning 104 1 Introduction 104 2 Metacognition in Problem Solving 106 3 Metacognitive Questioning in the Classroom 109 4 Conclusion 114 Acknowledgement 115 References 115 Chapter 7 Listening and Responding to Children’s Reflective Thinking: Two Case Studies on the Use of the 118 1 Introduction 118 2 Perspectives 120 2.1 Reflective thinking and the teacher’s mathematical knowledge 120 2.2 National Assessment of Academic Ability 121 3 Using the NAAA with Prospective Teachers 124 3.1 Prospective teachers’ anticipation of children’s responses 124 3.2 Prospective teachers’ lesson ideas using this problem item 126 3.3 Their reflections 127 3.4 Summary 128 4 Using the NAAA with Practicing Teachers 128 4.1 Teachers’ assessment of their children using the Park problem 129 4.2 Lesson study using item (3) of the Park problem 131 4.3 The three teachers’ reflections 135 4.4 Summary 136 5 Listening and Responding to Children’s Reflective Thinking 137 6 Conclusion 139 References 139 Chapter 8 Using Open-Ended Tasks to Foster 21st Century Learners at the Primary Level 142 1 Introduction 142 2 Review of Literature 144 2.1 Open-ended tasks 144 2.2 Research studies on open-ended tasks 146 3 Types of Open-Ended Tasks 147 3.1 Open-ended tasks that make assumptions on the missing information 148 3.2 Open-ended tasks to discuss a Concept, Algorithm or Error 150 4 Issues in Implementing Open-Ended Tasks in the Classroom 153 5 Concluding Remarks 155 References 155 Chapter 9 Productive Talk in the Primary Mathematics Classroom 158 1 Communication 158 2 Purpose of Mathematics Talk 160 3 Features of Effective Mathematics Talk 161 4 Getting Students to Talk in the Mathematics Classroom 164 5 Conclusion 171 References 172 Chapter 10 Justification in Singapore Secondary Mathematics 174 1 Introduction 174 2 What is Justification? 176 3 Importance of Justification 178 4 Justification Tasks 180 5 A Research Study on Mathematical Justification 183 5.1 Subjects 183 5.2 Test instrument 184 5.3 Procedures 185 5.4 Results and discussion 187 6 Strategies for Promoting Justification 193 7 Conclusion 195 References 195 Chapter 11 Examples in the Teaching of Mathematics: Teachers’ Perceptions 198 1 Introduction 198 2 Mathematical Examples 200 3 Teacher Knowledge 202 4 Teacher Knowledge and Mathematical Examples 204 5 Metholodogy 205 6 Results and Discussion 208 6.1 How do secondary mathematics teachers choose examples for introducing new mathematical ideas? 208 6.2 How do secondary mathematics teachers select homework task(s)? 211 6.3 What are the characteristics of a “good” mathematical example in secondary teachers’ perceptions? 213 6.4 Teacher knowledge 215 7 Conclusion 216 References 218 Chapter 12 On the Efficacy of Flipped Classroom: Motivation and Cognitive Load 222 1 Introduction 222 1.1 Definition of flipped classroom adopted in this chapter 223 1.2 Flipped classroom in Singapore schools 224 1.3 Critical analysis through Self-Determination Theory (SDT) and Cognitive Load Theory (CLT) 224 2 Theoretical Framework for Flipped Classroom Pedagogy 226 3 Constructing the Flipped Classroom Package 227 3.1 Flipped classroom for Mathematics at junior college 227 3.2 Description of the flipped classroom package 228 3.3 Design considerations of flipped classroom package 230 4 The Study 233 4.1 Intrinsic motivation versus extrinsic motivation 234 4.2 Autonomy, competence and relatedness 236 5 Method and Analysis 236 6 Findings 241 6.1 Autonomy 241 6.2 Competence 242 6.3 Relatedness 244 6.4 Cognitive load and its management 246 7 Implications and Conclusions 246 Acknowledgement 248 References 248 Chapter 13 Use of Comics and Storytelling in Teaching Mathematics 250 1 Introduction 250 2 Use of Cartoons and Comics in Mathematics Classrooms 251 2.1 What Research has shown about Cartoons and Comics 252 3 Storytelling in Mathematics Classroom 254 3.1 Principles in Selecting Appropriate Stories for Teaching 255 4 Combining Comics and Storytelling 256 4.1 Comics 256 4.2 Story associated with the Comic 260 4.3 Support for teaching 262 4.4 Trialling with the comics storytelling package 263 4.5 Lesson implementation 264 5 Conclusion 265 Acknowledgement 266 References 267 Chapter 14 Game Theory: An Alternative Mathematical Experience 270 1 Introduction 270 2 The Course 271 3 Mathematical Matching 272 4 Conclusion 279 References 280 Contributing Authors 282 "With this eighth volume, as part of the series of yearbooks by the Association of Mathematics Educators in Singapore, we aim to contribute towards literature in the field of mathematics education, specifically the development of 21st century competencies amongst learners of mathematics. The fourteen chapters are written by renowned researchers in mathematics education, provides readers with approaches and applicable classroom strategies to foster skills and dispositions that will enable learners to thrive in the fast-changing and complex world that we live in today. The chapters can be classified into three broad themes. The first is an examination of what is meant by 21st century competencies and how they can be developed within the context of the mathematics curriculum. The second is an in-depth discussion of evidence-based practices aimed at fostering specific competencies like metacognition and reflective thinking, critical thinking and communication skills. The last and third theme is about teaching approaches that are likely to feature increasingly in the 21st century classroom, for example flipped learning or the use of comics and storytelling."--Backcover