Mathematics Curriculum Reforms Around the World

Front matter

New ICMI Study Series

Yoshinori Shimizu Renuka Vithal Editors

Mathematics Curriculum Reforms Around the World

Foreword

The curriculum is central to schooling, and curriculum reform, including reform in the mathematics curriculum, is a phenomenon as old as schooling itself since it first existed. Every stakeholder seems to have an opinion on what should go into the curriculum, and on how the curriculum should be reformed. But curriculum reform in mathematics remains a much talked about and yet, as the editors of this Study Volume pointed out, under-researched topic. The aim of the book is therefore to take stock of the work that has been done in this area, and forge theoretical understanding and guide practice in curriculum reform in mathematics.

Curriculum reform entails at least three multi-faceted aspects: the development process of the reform, the content of the reformed curriculum, and implementation of the reformed measures. Each of these aspects involves a host of complex, interwoven elements. In addition, there are the important issues of the driving forces and barriers that shape the different aspects of curriculum reform. So it is hard to imagine that one book would be able to capture all these different aspects and elements of mathematics curriculum reform and their complexities. But this is exactly what this Study Volume intends to do. As such, this is perhaps one of the most ambitious studies within the series of ICMI Studies in terms of the scope and depth of the topic covered. And the authors of the book, under the leadership of the editors, have achieved this aim remarkably well.

To understand the development process, content and implementation of curriculum reform in mathematics, this book documents and critically examines major mathematics curriculum reforms in various countries from both historical and international perspectives. Major curriculum projects in the past from countries of a diversity of geographical and cultural backgrounds around the world are analyzed judiciously, and the impact of globalization on curriculum reform in selected countries is also examined. International perspectives have assumed particular importance in recent years in the wake of international studies of mathematics achievement such as TIMSS and PISA, which have a major impact on curriculum reforms in different countries. Learning from past reforms and from the impact of globalization on the curriculum does not only help us to understand the present curriculum better - how it has ended up in the state it is and why - and plan for the future vi Foreword curriculum better, it also contributes to theoretical understanding of the determinants of curriculum reform, issues on the underlying factors, causes, and agents of the curriculum.

As far as the content of curriculum reform is concerned, this book examines issues of coherence and relevance of the curriculum, illustrated with the curricula in different countries. Internal issues of coherence and relevance include relation with other disciplines (e.g., other STEM subjects), and external issues include the role of mathematics in society (e.g., mathematics citizenship). These eventually hinge on fundamental issues about the nature of mathematics and the purpose of mathematics education, such as: what is mathematics? what mathematical knowledge should students of this generation learn? what are mathematics and mathematics education for?

The above issues relating to the process and content of curriculum reform are extensive and complicated enough, but even more complex is the issue of curriculum implementation. The case studies on implementation of curriculum reforms in different countries provided in the book illustrate clearly the complexity of the issues involved in the implementation of the reformed curriculum in different contexts and traditions, and at the theoretical level, the authors put forward a generalization of the “laws” of curriculum implementation.

On the determinants of curriculum reform, a significant part of the book touches on cultural factors, an area that I am particularly interested in personally. Mutual influences of curriculum reforms in different countries and the impact of globalization on curriculum reform in individual countries result in a lot of similarities in both the reform processes and the reformed curricula among countries. Yet, mathematics curriculum reforms in different countries still differ in subtle and significant ways. Without resorting to explanations at the cultural level, sometimes it is hard to understand the deep-rooted reasons for the subtle differences. The development process of the reformed curriculum, how the content of the reformed curriculum is formulated and organized, and the way curriculum changes are implemented, are all profoundly influenced by cultural factors. These are important theoretical issues, both for researchers and for policy makers.

This informative book brings forth a rich and in-depth discussion of the various issues pertaining to curriculum reform in mathematics, offering valuable information and analysis for practitioners, policy makers and researchers in education. For front-line teachers, teacher educators and other practitioners, the book provides materials for a deeper understanding of the mathematics curriculum. For policy makers, it provides insights into what works and what doesn’t work in curriculum reforms, and why. For researchers, the book provides theoretical understanding on the various aspects of curriculum reform, and points to future research directions in the field.

Foreword vii

I congratulate the editors and authors on their remarkable efforts and achievement in putting together such an informative and insightful book. The book is an important addition to the series of ICMI Studies, and I am sure it will prove to be an invaluable reference in the area of mathematics curriculum reform, and in the field of curriculum reform at large.

Pokfulam, Hong Kong Frederick K. S. Leung March 2022

International Program Committee

Co-Chairs: Yoshinori Shimizu (Japan) Renuka Vithal (South Africa)

Members:

Ferdinando Arzarello (Italy, ICMI liaison member)

Marianna Bosch (Spain)

Will Morony (Australia)

Angel Ruiz (Costa Rica)

Al Cuoco (USA)

Yan Zhu (China)

Max Stephens (Australia, member since ICMI Study 24 Conference)

Jill Adler (South Africa, ex-officio member as ICMI President, during ICMI Study 24

Abraham Arcavi (Israel, ex-officio member as ICMI Secretary-General during ICMI Study 24)

Soheila Gholam Azad (Iran, member until ICMI Study 24 Conference)

Contents

PartI Introduction to ICMI Study 24

1 School Mathematics Curriculum Reforms: Widespread Practice But Under-Researched Yoshinori Shimizu and Renuka Vithal

Jeremy Kilpatrick

Part I Theme B - Analysing School Mathematics Curriculum Reforms for Coherence and Relevance

Coherence and Relevance Relating to Mathematics and Other Disciplines... 540450665 2) 4de pes seclasesbeoudiwe

Simon Modeste, Joaquin Giménez, José Luis Lupiáñez Gómez, Jaime Carvalho e Silva, and Thi Nga Nguyen

Coherence and Relevance of Materials and Technologies

Jennie Golding

What Theories and Methodologies Are Appropriate

for Studying Phenomena Related to Mathematics

Berta Barquero, Britta Eyrich Jessen, Juan Francisco Ruiz-Hidalgo, and Jennie Golding

Conclusion Achieving Coherence and Relevance in Mathematics

Part IV Theme C - Implementation of Reformed

Mathematics Curricula Within and Across Different Contexts and Traditions

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Angel Ruiz

A First Exploration to Understand Mathematics Curricula

Angel Ruiz, Mogens Niss, Michèle Artigue, Yiming Cao, and Enriqueta Reston

Towards a Model for Monitoring and Evaluating

Steve Thornton, Maitree Inprasitha, Angel Ruiz, Masami Isoda, Narumon Changsri, and Kristen Tripet

Contents

Contents xiii

18 Teachers, Resources, Assessment Practices: Alf Coles, Luis J. Rodríguez-Muñiz, Ida Ah Chee Mok, Angel Ruiz, Ronnie Karsenty, Francesca Martignone, Iman Osta, Federica Ferretti, and Thi Tan An Nguyen

19 Conclusion ‘Laws’ of Curriculum Implementation Angel Ruiz

Part V Theme D - Globalisation and Internationalisation and Their Impacts on Mathematics Curriculum Reforms

20 Introductöi 2. .142524675ecn i aa seraa rka 331 Max Stephens, Djordje M. Kadijevich, Mogens Niss, Nadia Azrou, and Yukihiko Namikawa

21 The Evolution and Uptake of Numeracy and Mathematical Merrilyn Goos and Kathy O’ Sullivan

22 Impacts of TIMSS and PISA on Mathematics Curriculum Reforms... .4.i5.4 6.0 oec seer eee eines eeseeann 359 Djordje M. Kadijevich, Max Stephens, Armando Solares-Rojas, and Raisa Guberman

23 Emergence of Computational/Algorithmic Thinking Djordje M. Kadijevich, Max Stephens, and Abolfazl Rafiepour

24 Conclusion: Future Visions of the Impact of Internationalisation Max Stephens, Merrilyn Goos, and Djordje M. Kadijevich

Part VI Theme E - Agents and Processes of Curriculum Design, Development and Reforms in School Mathematics

25 UMtROUUEUION: <6 6 6628-855 8h ace RRR eG LAL Oa eRe ORS RS 397 Ellen Jameson, Peter Sullivan, and Ferdinando Arzarello

26 Case Studies in Agents and Processes of Mathematics Iman Osta, Fidel Oteiza, Peter Sullivan, and John Volmink

27 Modelling Curriculum Reform: A System of Agents, Ellen Jameson and Janette Bobis

Alon Pinto and Jason Cooper

Xiv Contents

Stephen Quirke, Lorena Espinoza, and Gérard Sensevy

30 Conclusion Implications for Active Curriculum Ellen Jameson, Peter Sullivan, and Ferdinando Arzarello

Part VII International Perspectives and Influences on School Mathematics Curriculum Reforms

Yoshinori Shimizu and Renuka Vithal

32 OECD Learning Compass 2030: Miho Taguma, Kelly Makowiecki, and Florence Gabriel

33 Making Sense of Mathematics and Making Mathematics DRAG BENGE 230k E EEE there Beta eee eae 511 William McCallum

34 School Mathematics Curriculum Reforms: Berinderjeet Kaur

Part VIII Commentaries on ICMI Study 24

Renuka Vithal and Yoshinori Shimizu

36 Language of Teaching and Learning and School Mathematics

Anjum Halai

37 A Cultural—Political Reading of School Mathematics

Paola Valero

Part IX Conclusion to ICMI Study 24 38 Key Messages and Lessons from Mathematics Renuka Vithal and Yoshinori Shimizu ATOR WORE sorreran 64 cme a Saleh Ge Spee a oad toe oh eae: 565

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Contributors

Jill Adler University of Witwatersrand, Johannesburg, South Africa Thi Tan An Nguyen Hue University, Hue City, Vietnam

Michéle Artigue Université Paris Cité, Paris, France

Ferdinando Arzarello University of Turin, Turin, Italy

Nadia Azrou University of Yahia Fares, Blida, Algeria

Berta Barquero University of Barcelona, Barcelona, Spain

Maria G. Bartolini Bussi Universita di Modena e Reggio Emilia, Reggio Emilia, Italy

Janette Bobis University of Sydney, Sydney, Australia

Marianna Bosch University of Barecelona, Barcelona, Spain

Yiming Cao Beijing Normal University, Beijing, China

Narumon Changsri Khon Kaen University, Khon Kaen, Thailand

Alf Coles University of Bristol, Bristol, UK

Jason Cooper Weizmann Institute of Science, Even Yehudah, Israel

Lorena Espinoza Universidad de Santiago de Chile, Santiago de Chile, Chile Federica Ferretti Libera Universita di Bolzano-Bozen, Bologna, Italy

Florence Gabriel Directorate for Education and Skills, Organisation for Economic Co-operation and Development (OECD), Paris, France

Joaquin Giménez Barcelona University, Barcelona, Spain Jennie Golding University College London Institute of Education, Sidmouth, UK

José Luis Lupiáñez Gómez University of Granada, Granada, Spain

XV xvi Contributors

Merrilyn Goos University of Limerick, Limerick, Ireland Zahra Gooya Shahid Beheshti University, Tehran, Iran

Katalin Gosztonyi University Eötvös Loránd of Budapest, Budapest, Hungary Alfréd Rényi Institute of Mathematics, Budapest, Hungary

Raisa Guberman Achva Academic College, Teqoa, Israel

Anjum Halai The Aga Khan University, Karachi, Pakistan

Maitree Inprasitha Khon Kaen University, Khon Kaen, Thailand

Masami Isoda University of Tsukuba, Tokorozawa, Japan

Ellen Jameson University of Cambridge, Cambridge, UK

Britta Eyrich Jessen University of Copenhagen, Copenhagen, Denmark Djordje M. Kadijevich Institute for Educational Research, Belgrade, Serbia Ronnie Karsenty Weizmann Institute of Science, Rehovot, Israel

Berinderjeet Kaur National Institute of Education, Nanyang Technological University, Singapore, Singapore

Jeremy Kilpatrick University of Georgia, Athens, GA, USA Naomichi Makinae University of Tsukuba, Tsukuba, Japan

Kelly Makowiecki Directorate for Education and Skills, Organisation for Economic Co-operation and Development (OECD), Tsukuba, Japan

Francesca Martignone Universita del Piemonte Orientale, Alessandria, Italy William McCallum University of Arizona, Tucson, AZ, USA

Jasmina Milinkovic University of Belgrade, Belgrade, Serbia

Simon Modeste Université de Montpellier, Montpellier, France

Ida Ah. Chee Mok University of Hong Kong, Hong Kong, China

Will Morony The Australian Association of Mathematics Teachers, Inc., Adelaide, Australia

Yukihiko Namikawa Nagoya University, Nagoya, Japan

Thi Nga Nguyen Ho Chi Minh city University of Education, Ho Chi Minh, Vietnam Mogens Niss Roskilde University, Roskilde, Denmark

Niamh O’Meara EPI-STEM, University of Limerick, Limerick, Ireland

Kathy O’Sullivan University of Limerick, Limerick, Ireland

Iman Osta Lebanese American University, Beirut, Lebanon

Contributors xvii

Fidel Oteiza Ministry of Education, Santiago, Chile

Alon Pinto Weizmann Institute of Science, Rehovot, Israel

Stephen Quirke EPI-STEM, University of Limerick, Offaly, Ireland Abolfazl Rafiepour Shahid Bahonar University of Kerman, Kerman, Iran Enriqueta Reston University of San Carlos, Cebu, Philippines

Luis J. Rodríguez-Muñiz Universidad de Oviedo, Oviedo, Spain

Angel Ruiz University of Costa Rica, Concepcion/La Union, Costa Rica Juan Francisco Ruiz-Hidalgo University of Granada, Granada, Spain Gérard Sensevy University of Western Brittany, La chapelle des Fougeretz, France Shizumi Shimizu Teikyo University, Hachioji, Japan

Yoshinori Shimizu University of Tsukuba, Ibaraki, Japan

Jaime Carvalho e Silva University of Coimbra, Coimbra, Portugal

Armando Solares-Rojas Centre of Research and Advanced Studies, Cinvestav, IPN, Mexico City, México

Max Stephens The University of Melbourne, Melbourne, Australia Peter Sullivan Monash University, Monash, Australia

Miho Taguma Directorate for Education and Skills, Organisation for Economic Co-operation and Development (OECD), Paris, France

Steve Thornton Australian Academy of Science, Canberra, Australia Kristen Tripet Australian Academy of Science, Canberra, Australia

Marja van den Heuvel-Panhuizen Utrecht University, Utrecht, the Netherlands Nord University, Bodø, Norway

Marc van Zanten Utrecht University, Utrecht, the Netherlands Netherlands Institute for Curriculum Development, Amersfoort, the Netherlands

Paola Valero Stockholm University, Stockholm, Sweden Renuka Vithal University of Fort Hare, Alice, South Africa John Volmink Cape Peninsula University of Technology, Cape Town, South Africa

Thu-Huong Vu-Nhu Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam

Part I Introduction to ICMI Study 24

Chapter 1 A School Mathematics Curriculum Reforms: 3° Widespread Practice But Under-Researched in Mathematics

Education

Yoshinori Shimizu and Renuka Vithal ©

Introduction

The International Commission on Mathematical Instruction (ICMI) studies are unique in that they create opportunities to bring together large numbers and a diversity of scholars across countries and all kinds of practitioners to discuss a particular topic and generate publications deemed important and useful for different communities. An international study on school mathematics curriculum reforms, some might argue, is overdue given its long history and given that it is a practice engaged by a large number of countries, states or regions around the world.

Typically, ICMI Studies are commissioned when there is a considerable scholarship in particular area and the studies serve to pull these together in providing a “state of the art’ discourse on a particular topic and to shape the direction going forward. This ICMI Study 24 is especially singular in that while school mathematics curriculum reforms are a widespread and enduring practice internationally and globally, as the Study Conference (Shimizu & Vithal, 2018) revealed, its in-depth study is arguably less so in comparison with, say, ICMI Study 23 on primary mathematics study on whole numbers or ICMI Study 22 on mathematics task design.

This became particularly evident to the International Program Committee (IPC) as a search was undertaken for leading mathematics education scholars in the broad area of school mathematics curriculum reforms to provide keynotes and plenary lectures for the conference. That is to say, there are a number of leading mathematics educators participating in or even leading major school mathematics curriculum

Y. Shimizu (È) Faculty of Human Sciences, University of Tsukuba, Tsukuba, Ibaraki, Japan e-mail: yshimizu@human.tsukuba.ac.jp

R. Vithal Faculty of Education, University of Fort Hare, Alice, South Africa e-mail: rvithal @ufh.ac.za

© The Author(s) 2023 3 Y. Shimizu, R. Vithal (eds.), Mathematics Curriculum Reforms Around the World, New ICMI Study Series, https://doi.org/10.1007/978-3-03 1-13548-4_1 reforms in their countries, (many of whom participated in the study conference), but arguably a dearth of scholars or researchers in school mathematics curriculum reforms in the traditional sense of expert scholars with a wealth of publications about mathematical reforms. In fact, it would appear that those mathematics educators involved in, say, national school mathematical curriculum reforms seldom seem to develop an extensive and deep scholarship of the intense practice of the curriculum reform itself that they engaged in driving, leading or participating.

Not only are those who may be considered insiders to mathematics curriculum reforms not generating scholarship in this critical area, but there is also a general lack of in-depth study of those very reform processes, which are often highly contested within governing structures that are tasked with making curriculum reforms. Even for those considered to be outsiders to these processes, such as independent researchers, clearly one challenge would be the issue of access to government curriculum policy review and development environment to study all aspects of how, what and who makes and shapes curriculum reforms. This is alluded to and long recognised as a gap in mathematics education research in the broad area of policy studies (Lerman et al., 2002; Vithal & Volmink, 2005).

This suggests that, while there are considerable scholarly developments in general education on curriculum reform studies, these have not crossed boundaries to the same extent into mathematics education as other areas or have not been developed by mathematics educators themselves to the same extent. One consequence of this lack of in-depth research in school mathematics curriculum reforms, especially at macro levels, is that there is equally a lack of theories to explain the many different aspects and consequences of school mathematics curriculum reforms as well as limited writings about appropriate research methodologies for studying this topic in all its manifestations, dimensions, levels and components.

This ICMI Study is, therefore, a part of a process of taking stock of the work that has been done and forging an un- or under-explored area of research in which there is diverse and considerable practices, but not as much scholarly work to understand and guide these practices. Furthermore, literature reviews show that, while there are rich descriptions and analyses of individual cases of mathematics curriculum reforms at macro levels (e.g. Li & Lappan, 2014; Thompson et al., 2018), drawing out key messages or learning points from across these is less common. Therefore, while school mathematics curriculum reform is a well-established and entrenched practice in countries, districts or regions around the world, it begs questions about research — methodologies and theories — informing those diverse practices that eventually impact schools, teachers and learners on the ground. Many reasons may be advanced for this state of affairs.

This study volume seeks to contribute to such gaps (among others) and open up for new directions in research, theory, policy and practice. It points to an emergent but very necessary area of deeper study requiring re-conceptualisation of research questions, and the development of appropriate theories and methodologies that are able to take account of the enormous contextual variation within which school mathematics reforms take place around the world.

1 School Mathematics Curriculum Reforms: Widespread Practice... 5 Background and Rationale of the Study!

School mathematical reforms have taken place in many countries around the world in contexts that vary significantly on many different dimensions - culturally, politically, geographically, economically, historically — to name but a few. It is evident that much could be learnt from deeper and more substantial reflections and research about all different aspects of these reforms. Reforms have been large-scale involving an education system as a whole, at a national, state, district or regional level in which mathematical curricula, standards or frameworks have been developed and implemented. Changes have taken place at all levels of mathematics in the school educational system from pre-primary through senior secondary.

School mathematics reforms are often conducted with changes in all different aspects of the curriculum: mathematics content, teaching and learning methodologies and resources (e.g. texts and technologies), as well as assessment and examinations. It is possible to observe different influences on school mathematics curriculum reforms over time. During the mid-twentieth century, school mathematics curriculum reforms were shaped by developments within the discipline of mathematics and by the ideas of some mathematicians. This is captured in an address by the French mathematician Jean Dieudonné, one of the proponents of what was then termed the “New Math’ in 1959:

In the last fifty years, mathematicians have been led to introduce not only new concepts but a new language, a language which grew empirically from the needs of mathematical research and whose ability to express mathematical statements concisely and precisely has repeatedly been tested and has won universal approval.

But until now the introduction of this terminology has been steadfastly resisted by secondary schools, which desperately cling to an obsolete and inadequate language. And so, when a student enters the university, he will most probably never have heard such common mathematical words as set, mapping, group, vector space, etc. (cited in Howson et al., 1981, p. 102)

The New-Math reform, took place in a particular historical context of the ‘cold war’ and colonialism. It became a mathematical movement that spread to many countries around the world with different influences on national curricula and practical implementations in schools. The character of this reform and its challenges was a departing point for many developments and discussions in the teaching of mathematics. Since then, with the lessons from the New-Math reform movements, the field of mathematics education has progressed immensely.

Another major influence on school mathematics curriculum reforms in the second half of the twentieth century has been from outside mathematics, that is, developments in other disciplines, most notably, psychology. Studies and theories in behaviourism, the rise and development of cognitive science and constructivism, to

'This introductory chapter integrates the text from the ICMI Study 24 Discussion Document, which called for the Study Conference entitled School Mathematics Curriculum Reforms: Challenges, Changes and Opportunities authored by the International Programme Committee (2017) for the study.

name a few, have especially impacted content and approaches advocated in mathematics curriculum reforms. Other trends in mathematics curriculum reforms included problem solving and back-to-basics (among others).

More recent influences on mathematics curriculum reforms, in this twenty-first century, have come from other areas, such as large international studies, especially those focusing on student achievements. These studies have enabled comparisons of mathematics curricula (such as intended and attained curricula) across many countries and generated particular conceptions (such as mathematics literacy), which have found their way into mathematics curriculum reforms. Nowadays international comparative studies like the Trends in International Mathematics and Science Study (TIMSS) (Mullis et al., 2016) and the Organisation for Economic Co-operation and Development Programme for International Student Assessment (PISA) (OECD, 2016), which attract a great deal of public attention and media focusing on student and teacher performance in mathematics education (and to which politicians and policy makers are especially responsive), are impacting and shaping school mathematics curriculum reforms as countries or regions both compete and share curriculum policies, materials and approaches.

These studies have raised the stakes significantly, and arguably, entrenched a focus on student performance and better test scores as opposed to better student learning within mathematics curriculum reforms. There are a diversity of studies and findings from international experience and research that can and does influence the nature of curriculum changes, and the possibilities of educational reform and its implementation: curricular design results; a revised role for components in the teaching of mathematics (e.g. mathematics content, pedagogy and assessment); the role of technology; new cognitive, socio-cultural and socio-political perspectives.

In recent years, the internationalisation and globalisation of the economy, universality of technological development and related needs for new skills and knowledge play the role of strong motivations for curriculum reforms that have brought calls for unified standards for mathematics in school. In the international debate, many scholars, teachers and policy-makers speak of the “twenty-first-century competencies” and consider important items like: “critical and inventive thinking; communication, collaboration and information skills; and civic literacy, global awareness and cross-cultural skills”.? In many countries, the so-called ‘‘21st-century competencies framework”? is being worked on, in order to guide the development of the national curriculum and to design school-based programmes to nurture these competencies.

In relation to this, new mathematics curriculum discourses have emerged and taken hold. Notions of mathematical ‘competences’ and that of mathematical ‘literacy’ are important examples that have been raised, from different perspectives around the world (Niss, 2015). In particular, from the approach of OECD’s PISA, several notions (and their underpinning theoretical framework) have become very

? See, for example, the Singapore Ministry of Education website: https://www.moe.gov.sg/education/education-system/2 | st-century-competencies

3See, for example, Towards Defining 21st-Century Competencies for Ontario, Canada: http:// www.edugains.ca/resources2 1CL/About21stCentury/21CL_21stCenturyCompetencies.pdf influential in many countries in the changes being made in local curricula and standards: for example, in Denmark, Germany, Japan, South Korea, Costa Rica, Spain, Norway, Mexico, Sweden. PISA stresses the role of mathematical literacy as a central goal in school mathematics education, because it improves the life chances of most students, and justifies why mathematics is essential to describe, explain and predict the world. According to the PISA 2015 Mathematics Framework:

Mathematical literacy is an individual’s capacity to formulate, employ, and interpret mathematics in a variety of contexts. It includes reasoning mathematically and using mathematical concepts, procedures, facts, and tools to describe, explain, and predict phenomena. It assists individuals to recognize the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective citizens. (OECD, 2016, p. 65)

However, the word literacy itself is ambiguous with multiple meanings, and trying to translate it into different languages and cultures has proved to be a difficult, if not sometimes impossible, task. In the literature, one finds different names and definitions; and many changes over the years showing the notion of literacy to be:

a socially and culturally embedded practice, and [... its] conceptions [... vary] with respect to the culture and values of the stakeholders who promote it. (Niss & Jablonka, 2014, p. 395)

The differences in approach are directly linked to the goals that are pursued in mathematics education in individual countries. Its inclusion in curriculum reforms identifies new demands about what citizens are obliged to know (or not allowed to ignore). Hence, a careful analysis of this notion is relevant in order to focus its rationale in a curriculum.

International studies that examine the successes and failures in achieving the promised aims from different reforms, across countries need to be undertaken. The aftermath of the New-Math reform alludes to the importance of reflecting on the requirements for a new curriculum, suitable to escape the causes of the complete, or partial, rejection of this reform in so many countries.

The challenges of this particular reform and others that followed opens a discussion about different aspects of curriculum reforms, which go beyond content, such as:

e the existence of different epistemological and cultural positions concerning mathematics and its relevance in different societies;

e the distance of the proposed reform from the mathematical, educational and material conditions and possibilities in different countries, including teacher quality, their preparation, knowledge, beliefs and expectations;

e the relationships with the social, cultural and personal contributions brought by the students in the classroom, so relevant to avoid students’ alienation from their social and cultural environment and to allow students to engage in learning in a productive way;

e the influence of political and institutional scenarios within educational systems, that can promote, discourage or weaken curricular reforms.

A consequence of these reflections is that the communities of researchers, teachers and policy-makers need to become more aware that considerations of curriculum reforms from various perspectives and constructs (mathematical literacy or competences, for instance) raises many issues, from a scientific, political and cultural point of view.

This ICMI study topic invokes not only questions about changes in curriculum design but — with force — questions about the implementation of these changes across an educational system. A curriculum reform will be influential or have impact in so far as it can be implemented. What has functioned (or not) at the time of implementing a curricular change? What are the limitations? How have resources (e.g. textbooks and technology) influenced the reforms and their enactment? How must large-scale teacher preparation be conducted to achieve the reform goals? How do diverse social, economic, cultural and national contexts condition the nature and extent of curricular reforms — especially teacher expectation, attitudes and beliefs — as well as the social and cultural background of students? How are assessments of students’ learning influential in curriculum reforms? An ICMI Study offered an opportunity to provide a synthesis and meta-analysis of different aspects of school mathematics reforms historically, geographically and globally.

There are many studies conducted in different parts of the world about these issues of mathematics curriculum reforms and their implementation with findings that can be systematised, compared and studied. The way curricula are elaborated, proposed, changed and reorganised is, however, still a rather under-explored area in mathematics education. This ICMI Study allows for a more informed and comprehensive analysis of the roles of different actors and of the many aspects influencing and shaping mathematics curriculum reforms that are taking (or have taken) place; and of the possibilities and means to tackle a curricular reform in the current scenario we live in and unfolding future developments.

It is as crucial an issue for developing countries as it is for developed ones, given by the global changes taking place in societies, as they confront different challenges of growing inequality, unemployment, poverty, mass migration, environmental disasters, various form of discrimination and conflicts (to name but a few), and within which school mathematics reforms must take place. However, the processes of curriculum reform may differ in developed versus developing countries, due to different protocols followed, different intentions and agendas, resources and conditions as well as policy and political rhythms. Other comparative fault lines are, for example, East-West differences in mathematics curricula and reforms which have gained much interest, largely from the results of international studies and the migration of students. New global phenomena such as the spread and actions against infectious diseases (for example, COVID-19), and the massive shift to on-line teaching and learning creates new urgent imperatives related to all aspects of technology in mathematics curricula.

A further rationale for this study is to stimulate further research and publications that explore mathematics curriculum reforms, especially at a policy level and across multiple and diverse contexts. Some recent volumes, such as by Thompson et al. (2018) and Li and Lappan (2014), point to the growing need for further research in this area and its potential for more evidence-based mathematics curriculum policy generation and implementation.

An ICMI Study offers a unique opportunity to examine past and present mathematics curriculum reforms in different parts of the world, from a macro- perspective and meta-level and to investigate larger questions of who or what in a society drive and most influence curriculum reforms, what reforms precisely are taking place, how are these being implemented and, whether they are deemed successful (or not), what counts as success. Hence, this study has the potential to build understanding of the implications — current and future — of these larger questions for school mathematics, for different aspects of teaching and learning mathematics, and for its role in the broader society. By studying curriculum reforms across multiple contexts, key messages and lessons may be derived to inform, improve and better conduct future mathematics curriculum reforms.