Mathematics Curriculum Reforms Around the World: The 24th ICMI Study

Foreword
International Program Committee
Contents
Contributors
Part I: Introduction to ICMI Study 24
Chapter 1: School Mathematics Curriculum Reforms: Widespread Practice But Under-Researched in Mathematics Education
Introduction
Background and Rationale of the Study
Themes and Questions
The ICMI Study 24 Conference
Defining Key Concepts Related to School Mathematics Curriculum Reforms
Structure of the ICMI Study 24 Volume
References
Chapter 2: School Mathematics: A Bipolar Subject
The New Math Era
Critique
Bipolarity
Subsequent Changes
An Applications Turn
A Social and Cultural Turn
The Context of the United States of America
International Comparisons in Mathematics Performance
Final Comments
References
Part II: Theme A – Learning from the Past: Driving Forces and Barriers Shaping Mathematics Curriculum Reforms
Chapter 3: Introduction
International Co-operation and Influential Reforms
Case Studies of Past ‘Local’ Curriculum Reforms in Mathematics
The Role of Values and Culture in Past Mathematics Curriculum Reforms
The Effects of Past Reforms on the Construction of the Knowledge to Be Taught
Driving Forces and Barriers
References
Chapter 4: International Co-operation and Influential Reforms
International Reform Movements in the Twentieth Century
The ‘Mathématiques Modernes’ Reform in France
A Reform Movement from the Eastern Bloc: Varga’s ‘Complex Mathematics Education’ Reform
Realistic Mathematics Education in the Netherlands
Mathematics Curriculum Reform in Japan
Conclusions
References
Chapter 5: Learning from the Past: Case Studies of Past ‘Local’ Curriculum Reforms
Introduction
Case Study A: Ireland
Case Study B: Serbia
Case Study C: South Africa
Conclusion
Lesson 1: The Influence of International Assessments
Lesson 2: The Influence of RME and Importance of Consultation
Lesson 3: Time
Lesson 4: Teacher Professional Development
Lesson 5: The Need for Continuous Research
References
Chapter 6: The Role of Values and Culture in Past Mathematics Curriculum Reforms
Italy: The Most Recent Global Curriculum Reform
Serbia: Changing the Perspective of Mathematics as a Subject
Iran: Two Aspects of the Educational Systems Affected by Curriculum Reforms
The Driving Forces Behind Various Mathematics Curriculum Changes
Considering Values and Goals
Concluding Remarks
References
Chapter 7: Curriculum Reforms and the Construction of the Knowledge to Be Taught
The Evolution of the Knowledge to Be Taught: The Case of Proportionality
Classical Mathematics
The Effects of the New Math Reform
Proportionality in Today’s School Mathematical Organisations
Didactic Transposition Constraints
Didactic Transposition Phenomena in Curriculum Reforms in Vietnam
Is It Time or Content? Lessons Learnt from an Irish Curriculum Reform
Conclusions
References
Chapter 8: Conclusion Final Considerations: Driving Forces and Barriers Affecting Curriculum Reforms
References
Part III: Theme B – Analysing School Mathematics Curriculum Reforms for Coherence and Relevance
Chapter 9: Introduction
Definitions for Coherence and Relevance
Components of Mathematics Curricula
Theme B Analyses
Curriculum to Meet Needs (of Students, the Workplace, Higher Education, Society etc.)
‘Top-Down’ as Opposed to ‘Bottom-Up’ Curriculum Development and Reforms
Theme B Chapters
References
Chapter 10: Coherence in a Range of Mathematics Curriculum Reforms
Coherence Between Components of the Niss Framework
Portugal
Brazil
Vietnam
Coherence Within Components of the Niss Framework
Costa Rica
Vietnam
Japan
Coherence with Mathematics as the ‘Parent Discipline’
Israel
Japan
An Alternative
Coherence of the Curriculum with the Curriculum System
China
Mexico
Portugal
England
Other Examples
Some Possible Responses to Achieve This Coherence
Conclusion and Key Messages
References
Chapter 11: Coherence and Relevance Relating to Mathematics and Other Disciplines
Emergence of Interdisciplinary Approaches
In Education and Curricula
The Case of STEM
The Case of Mathematics and Citizenship
Issues
Examples of Reforms That Lead to Interdisciplinary Approaches
Vietnam
Spain
Andorra
Issues and Questions
Modelling as Central
Coherence and Relevance at Different Levels
Examples of Ways to Make Mathematics Interact with Other Disciplines
The Example of Mathematics and Computer Science Interaction in France
Tensions and Synergies
Conclusion and Key Messages
References
Chapter 12: Coherence and Relevance of Materials and Technologies to Support Mathematics Curriculum Reforms
Background: Curriculum Resources Supporting Reform
Non-textual Resources
The Role of Resources in Recent Curriculum Reforms
Case Study 1: England’s National Curriculum and Related Post-16 mathematics Provision from 2014 (Top-Down, Time-Pressured Reform with Initial Attempted Coherence)
Case Study 2: Curriculum reforms in Mexico, 1993 to 2011 (Top-Down, Variably Coherent Curriculum System Reform)
Case Study 3: University Entrance Curriculum reform in Vietnam (Top-Down, Not Yet Coherent with Supporting School Curriculum Materials)
Case Study 4: Bottom-Up Italian Development of a Radical Approach to the Fraction-Related Curriculum (Focus on Use of Naïve Concrete Materials to Build Relevance, But with Exposed Tensions for Coherence)
Case Study 5: Reform of the Israeli Intermediate Geometry Curriculum (Negotiated, Measured Building of Systemic Coherence and Relevance)
Case Study 6: Harnessing Technology to Improve Intended/Enacted Curricular Coherence Across Domains and Levels of Teaching, in Bottom-Up Curriculum Development
Curriculum Materials: Affordances for Supporting Curriculum Reform Coherence and Relevance
Digital Tools Supporting Coherence and Relevance of Enacted Curricula
Curriculum Materials: Constraints for Supporting Curriculum Reform Coherence and Relevance
Conclusion and Key Messages
References
Chapter 13: What Theories and Methodologies Are Appropriate for Studying Phenomena Related to Mathematics Curriculum Reforms?
Overview of Theoretical Approaches for Analysing Phenomena Related to Mathematics Curriculum Reforms
Approaches Focusing on Curriculum Conceptualisation
Approaches Focusing on the Didactic Process of Creation and Dissemination of Curriculum Reforms
Socio-Cultural Approaches Focusing on the Conditions for Communities in Curriculum Reforms
Summary of Theoretical Frameworks Used to Address Curriculum Reforms
Research Questions About Curriculum Reforms, Unit of Analysis and Methodologies for Curricular Analysis
Research Questioning the Intended Curriculum Through the Interaction Between the Scholarly Knowledge and the Knowledge to Be Taught
Research Questioning the Selection and Elaboration of the Knowledge to Be Taught and of the Resulting Intended Curriculum Transposed to School Systems
Research Questioning the Conditions Under Which Curriculum Reforms Are Implemented, Through What Means, Under Which Constraints
Research Questioning Teachers’ Actions and Engagement with How the Implementation of Curriculum Is Planned and Works in Classrooms
Research Questioning Communities Involved in Curriculum Reforms
Conclusion and Key Messages
References
Chapter 14: Conclusion Achieving Coherence and Relevance in Mathematics Curriculum Reforms: Some Guiding Principles
Part IV: Theme C – Implementation of Reformed Mathematics Curricula Within and Across Different Contexts and Traditions
Chapter 15: Introduction
Diversity
The ‘Process’ Dimension and the Wider Perspective
Structure
Chapter 16: A First Exploration to Understand Mathematics Curricula Implementation: Results, Limitations and Successes
National and International Curricular Use of the Competency-Based Danish “KOM” Project – Mogens Niss
Terminological Clarification of Key Concepts
Competency-Based Mathematics Curricula: The Case of Denmark
KOM-Referenced Curriculum Reforms in Denmark in the Twenty-First Century
The Competency Approach in Other Countries
Implementing Curricular Reforms: A Systemic Challenge – Michèle Artigue
Introduction
Elements for an Ecological Approach Supported by the ATD
Didactic Transposition
Anthropological Theory of the Didactic (ATD)
A First Case Study: The High School 2000 Reform in France
Main Characteristics of the 2000 Reform
The Implementation of the Reform
A Second Case Study: Recent Curriculum Reforms in the Francophone Space
Concluding Comments
Chinese Mathematics Curriculum Reform in the Twenty-First Century – Yiming Cao
The Background of New Century Chinese Mathematics Curriculum Reform
Mathematics Curriculum for Compulsory Education (Grades 1–9)
The Development of a New Standard for Compulsory Education
The Implementation of Standards for Compulsory Education
Epilogue
Implementing the K to 12 Mathematics Curriculum in the Philippines: Models and Processes of Teacher Development – Enriqueta Reston
The Philippine Educational System and the Contextual Realities of Curriculum Reform
The K to 12 Mathematics Curriculum Reform Mathematics Curriculum Reforms in the Philippines
Professional Development Models and Processes for K to 12 Mathematics Teachers
A Needs-Based Professional Development Model for K to 12 Mathematics Teachers
Implications and Future Directions
Implementations of Reforms Are Diverse, Multifactorial and Non-linear – Angel Ruiz
The Nature of the Reforms Studied
Some Particular Aspects
The Dichotomy Between Top-Down or Bottom-Up Strategies, and Other Factors
Struggle and Uncertainty
Final Comments
References
Chapter 17: Towards a Model for Monitoring and Evaluating Curricula Reforms
Values, Vision, and Goals Within Curriculum-Reform Implementation
Curriculum Development and Reform in Japan
The Early Years of Curriculum Centralisation and the Beginnings of Lesson Study
Curriculum Development by Teachers and the Evolution of Lesson Study
Values, Vision and Goals in Japanese Mathematics
Mathematics Education Reform in Thailand
Mathematics Curriculum Reform in Costa Rica
What Factors Intervene in the Implementation of Reformed Curricula?
Description of General Factors
External Factors
Internal Factors
Realisation Factors
How These Factors Intervene in Implementation of the Reform
External Factors
Internal Factors
Realisation Factors
The Assessment of Curricular Reform Success
Relationship and Alignment Between Curriculum Reform Factors
External Cohesion
Internal Coherence
Realisation Fidelity
A Proposed Model Describing the Relationships Between Factors in Mathematics Curriculum Reform Implementation
Conclusion
References
Chapter 18: Teachers, Resources, Assessment Practices: Role and Impact on the Curricular Implementation Process
Teachers in the Curricular Implementation
Aims and General Contexts for Teacher Participation in Curriculum Reform Implementation
Preparation of Prospective Teachers
Professional Development and Implementation of Curriculum Reforms
Aims of Reform-Oriented Teacher Professional Development
Models Suggested for Reform-Oriented Professional Development
Types of On-Going Support Provided to Teachers
Empowering Teachers’ Voices in Reform-Oriented PD Programmes
Evaluating the Work with Teachers in Reform-Oriented PD Programmes
Resources in the Curriculum Reforms Implementation
Textbooks, Tasks, Teaching Resources
Digital Technology
Support Agents for the Use of Resources
Final Remarks on the Use of Resources
Role of Assessment in Curriculum Reform Implementation
International, National and Classroom Assessment
Conclusion
References
Chapter 19: Conclusion ‘Laws’ of Curriculum Implementation and the Future in Which We Are Living
The ‘Law’ of Diversity
The ‘Law’ of Two Directions
The ‘Law’ of Alignment
The ‘Laws’ of the Long-Term and Uncertainty
A final ‘Law’ (Within the Scenario of the Pandemic)
The Place of Implementation
Reference
Part V: Theme D – Globalisation and Internationalisation and Their Impacts on Mathematics Curriculum Reforms
Chapter 20: Introduction
Theme Globalisation and Internationalisation and Their Impacts on Mathematics Curriculum Reforms: Specific Foci and Questions From the Discussion Document (ICMI, 2017)
Introducing the Major Theme: Globalisation and Internationalisation
Definitions and Distinctions
Retrospective on New Math – What Has Been Learned?
ICMI Studies as Exemplars of Internationalisation
Is There an Emerging International Curriculum or Curricula?
Internationalisation or Uniformity? Local Factors, Cultures and Beliefs
Looking Ahead
References
Chapter 21: The Evolution and Uptake of Numeracy and Mathematical Literacy as Drivers for Curriculum Reform
Conceptualising Numeracy and Mathematical Literacy
Conceptualising Curriculum
Numeracy as a Cross-Cutting Competency in Australia and Ireland
Rationale for Numeracy in Australia and Ireland
Representation of Numeracy in the Official Curriculum of Australia and Ireland
Mathematical Literacy as a Stand-Alone Subject in South Africa
Rationale for Mathematical Literacy in South Africa
Representation of Mathematical Literacy in the Official Curriculum of South Africa
Infusing Mathematical Literacy into the Mathematics Curriculum in Japan
Rationale for Mathematical Literacy in Japan
Representation of Mathematical Literacy in the Official Curriculum in Japan
Conclusion
References
Chapter 22: Impacts of TIMSS and PISA on Mathematics Curriculum Reforms
Global Influences of TIMSS and PISA
TIMSS Influences
PISA Influences
Particular Influences of TIMSS and PISA
Australia
Israel
Mexico
Serbia
Conclusion
References
Chapter 23: Emergence of Computational/Algorithmic Thinking and Its Impact on the Mathematics Curriculum
Professional and Societal Perspectives: Connections Between Internationalisation and Globalisation
Using Technology in Mathematics Education: Computational and Algorithmic Thinking
Chapter Outline
Computational Thinking
Cultivating and Assessing CT
Implications for Algorithmic Thinking (AT)
Computational/Algorithmic Thinking
Relevance to Mathematics Education
Emerging Implications for Mathematics Education
Conclusion
References
Chapter 24: Conclusion: Future Visions of the Impact of Internationalisation and Globalisation on School Mathematics Curriculum
Influence of TIMSS and PISA
Evolving Understandings About Numeracy and Mathematical Literacy
References
Part VI: Theme E – Agents and Processes of Curriculum Design, Development and Reforms in School Mathematics
Chapter 25: Introduction
Chapter 26: Panel Discussions
Chapter 27: Agents, Objects and Processes in Curriculum Reform
Chapter 28: Boundary Crossing in Curriculum Reform
Chapter 29: Teacher Professional Identity and Curriculum Reform
Conclusion
Reference
Chapter 26: Case Studies in Agents and Processes of Mathematics Curriculum Development and Reform
Introduction
The Math Curriculum Reform in Lebanon: Achievements, Problems and Challenges – Iman Osta
Reflection on the Lebanese Math Curriculum
Foundational Documentation
Textbooks
Teachers and the Reform
National Exams
In Summary: From Design to Implementation
Processes and Agents of Curriculum Design, Development and Reforms in Three Decades of School Mathematics in Chile – Fidel Oteiza
Some Milestones
Tendencies in the Process of Reform of the National Mathematics Curricula
Agents, Institutions and Driving Forces
The Consultation Process, Its Major Contributors and the Role of the National Education Commission
Main Social, Cultural and Technical Factors Shaping School Mathematics Curricula, New Questions and Pending Issues
The Aspirations of the Australian Curriculum in Prompting Reform of School Mathematics – Peter Sullivan
The Process of Development
Dichotomy 1: Teacher Proofing or Teachers as Learners
Dichotomy 2: Documenting Everything Possible vs. Including Just Enough Information
Dichotomy 3: Practitioner vs. Specialist Writers
Dichotomy 4: Mathematics as Preparation for Later Study or Mathematics as Experience
Dichotomy 5: General vs. Specific Descriptions of Expected Mathematical Actions
Dichotomy 6: Mathematics for Elite or Mathematics for All
School Mathematics Reform in South Africa: A Curriculum for All and By All? – John Volmink
Challenges Facing Curriculum Reform in South Africa
Mathematics Curriculum Pre-1994
Mathematics Curriculum Reform Post-1994
Mathematics for All
Mathematics By All
Final Conclusions
References
Chapter 27: Modelling Curriculum Reform: A System of Agents, Processes and Objects
Definitions of Curriculum
A Model of Curriculum Reform
Agents, Objects and Arenas
Processes
Maintaining Stability (Fig. 27.2a)
Agreeing and Communicating Preferred Practices for Reform (Fig. 27.2b)
Mapping Curriculum Content to Aid Decision-Making (Fig. 27.2c)
Distilling Curriculum Content by Negotiation (Fig. 27.2d)
Validating Curriculum Changes (Fig. 27.2e)
Designing and Implementing Learning sequences (Fig. 27.2f)
Co-ordinating Perspectives (Fig. 27.2g)
Other Processes
Summary
References
Chapter 28: Boundary Crossing in Curriculum Reform
Cases of Stakeholders in Interaction
Curricular Reform in France
Developing a Pan-Asian Curriculum
Curriculum Documentation in Australia
Teacher Identity as Designated in Curriculum Documents in Ireland
Boundary Crossing in Israel
Coherence in Curriculum Design in the UK
Agents and Tensions
Boundary Crossing in Curriculum Reform: Challenges and Opportunities
References
Chapter 29: Teacher Professional Identity and Curriculum Reform
Identity
Discourse and Identity
Socially Situated and Recognisable Identities
Identity and Learning
Teacher Agency and Curriculum Reform
The Teacher’s Trajectory Through Curriculum Reform
Theories and Concepts Which Help to Frame the Transformation of Teachers’ Identities
Mathematics Curriculum Reform Materials
Designated Curriculum and Instructional Materials
Teacher Professionalism
Teacher Professionalism and Teacher Professional Identity
Summary
References
Chapter 30: Conclusion Implications for Active Curriculum Reform Work and Future Research
Considering Curriculum Reform Contexts as Systems Can Make Important Choices Stand Out
The Integration of Teachers Into Reform Efforts Is a Key Factor in the Success of Those Efforts
Enhancing Communication Across Community Boundaries Benefits Reform
Some Challenges to Applied Curriculum Reform Research
Outstanding Questions
Curriculum Reform, Resilience and the Unexpected
Reference
Part VII: International Perspectives and Influences on School Mathematics Curriculum Reforms
Chapter 31: Introduction
Chapter 32: OECD Learning Compass 2030: Implications for Mathematics Curricula
OECD Future of Education and Skills 2030 Project and the OECD Learning Compass 2030
What Is the OECD Learning Compass 2030?
How Was This Framework Developed?
Student Agency and Co-agency at the Centre of the Learning Framework
Competences: Importance of Knowledge, Skills, Attitudes and Values
How Can the OECD Learning Compass 2030 Influence Mathematics Learning and Teaching?
Student Agency
Core Foundations and Knowledge
Skills, Attitudes and Values
Transformative Competences
Anticipation–Action–Reflection (AAR) Cycle
How Can the OECD Education 2030 Project Influence Mathematics Curriculum?
Curriculum Overload2
Managing the Time Lag Between Future Needs and Current Curriculum3
Equity Through Curriculum Innovations4
Curriculum Flexibility and Autonomy
Embedding Values in Curriculum5
Ecosystem Approach to Curriculum Redesign and Implementation
Implications for Action
Learning Trajectories in Mathematics
Twelve Design Principles in Curriculum Redesign
References
Chapter 33: Making Sense of Mathematics and Making Mathematics Make Sense
Views of Mathematics
The Making-Sense Stance
Coherence
Fidelity
Concluding Thoughts
References
Chapter 34: School Mathematics Curriculum Reforms: Insights and Reflections
School Mathematics Reforms
The Era of “New Math”
Realistic Mathematics Education (RME)
The ‘Model’ Method: A Pedagogical Reform in Primary School Mathematics
Era of Problem Solving
‘Looking Forward’ and ‘Looking Back
Concluding Remarks
References
Part VIII: Commentaries on ICMI Study 24
Chapter 35: Introduction
Chapter 36: Language of Teaching and Learning and School Mathematics Curriculum Reform: Tensions in Equity and Access
References
Chapter 37: A Cultural–Political Reading of School Mathematics Curriculum Reform
References
Part IX: Conclusion to ICMI Study 24
Chapter 38: Key Messages and Lessons from Mathematics Curriculum Reforms Around the World
Changing Contexts of ICMI Study 24
Challenges in Defining School Mathematics Curriculum Reforms
Lack of Research, Gaps in Theories and Methodologies in the Study of Reforms
Shifts in the Content of School Mathematics Curriculum Reforms
Key Role of Teachers, Teacher Education and Professional Development
The Rise of the Importance of Resources and Technology
Alignment as a Key Feature Within School Mathematics Curriculum Reforms
School Mathematics Curriculum Reforms as Context-Bounded and Invariant
School Mathematics Curriculum Reforms as Long-Term and Unpredictable Endeavours
Further Issues in the Study of School Mathematics Curriculum Reforms
Reference
Afterword
Author Index
Subject Index