Changing Contexts of ICMI Study 24

In this concluding chapter, the key messages from the themes represented in the different parts and their contributing chapters are pulled together to distil some major learning points for understanding and informing school mathematics curriculum reforms. The five themes that were identified and formed the basis for the organisation of the ICMI Study conference have been retained in the structure of this volume (see Shimizu & Vithal, 2018). These themes are represented in Parts II to VI of this volume – a historical perspective, a focus on coherence and relevance of curriculum reforms, on implementation aspects across contexts, on the impact of internationalisation and globalisation and on agents and processes of school mathematics curriculum reforms.

Each of the five themes were explored by addressing a number of key questions (see Chap. 1). Just as the conference attracted more papers in some themes than others, some questions were addressed in greater detail and others much less. This is reflected in this volume as authors in each part engage on the questions addressed in the respective chapters. In addition, these concluding remarks also draw on the chapters from keynotes and the plenary panels, which sought to focus on more macro perspectives in school mathematics curriculum reforms.

This study volume seeks to build on and extend earlier works in this area. When Howson, Keitel and Kilpatrick released their seminal book Curriculum Development in Mathematics in 1981, which captured the state of the art of mathematics curriculum reforms in the preceding decades, the world was a very different place. Four decades later this ICMI Study 24, attempts to similarly, provide an understanding of school mathematics reforms taking place around the world. The last ICMI Study that focused on mathematics curricular was ICMI Study 2 on School Mathematics in the 1990s, edited by Howson and Wilson and published in 1986, shows how much this area has grown and how complex it has become (ICMI Studies may be accessed from the ICMI website). 

This ICMI Study 24 was initiated in 2016 and conceptualised in a Discussion Document which was disseminated internationally in 2017. The Study Conference took place in November 2018 in Japan, and work on developing the volume was underway in 2019, well before the major global catastrophic event in 2020 in the form of the COVID-19 pandemic. This means that the volume has been finalised while major changes in the functioning of all levels of education systems and societies have been taking place, which were not part of the study and were not deliberated on in the study conference. This significant unpredicted COVID-19 pandemic, has impacted schooling fundamentally and changed life for learners and teachers in the vast majority of societies generally, and specifically, in mathematics education. Hence, all authors were requested to consider including their reflections on the impact of the pandemic on school mathematics curriculum reforms in their respective chapters and themes; and these will be similarly drawn on in this concluding chapter.

This study itself offers an approach to the study of mathematics curriculum reforms across multiple countries or regions of the world. The methodology adopted in the themes of the study has been to present rich descriptions of school mathematics curriculum reforms in diverse contexts and to cluster these in a variety of ways for analysis and to learn lessons about what happened, what worked or did not work, in a variety of different aspects of curriculum reforms.

The volume as a whole draws on curriculum reforms from some thirty-two countries and regions, including: the Netherlands, Hungary, France, Brazil, Japan, Ireland, Italy, Serbia, South Africa, Iran, Vietnam, Portugal, Denmark, Unites States of America, Costa Rica, Israel, China/Hong Kong, Mexico, England, Spain, Andorra, Australia, Lebanon, Luxembourg, Philippines, Canada, Tunisia, Wallonia-Brussels Federation, Chile, Peoples’ Democratic Republic Lithuania and Singapore. However, many more countries or regions are referred to in the chapters, which draw on the related literature in this area.

It also includes discussion on curriculum frameworks that have had more global or international impacts in the mathematics curricula of many countries beyond what may have been intended. For example, implications for mathematics curricula of recent curriculum frameworks developed by OECD (Organisation for Economic Co-operation and Development) for their member countries (Taguma et al. Chap. 32); as well as the Pan-Asian curriculum efforts to develop a mathematics curriculum shared by countries in ASEAN (Association of Southeast Asia Nations) (Pinto and Cooper, Chap. 28). Despite this wide diversity, what is also acknowledged, is the lack of representation from several parts of the world in this volume, such as Africa, especially sub-Saharan countries (excluding South Africa). Nevertheless, this broad inclusion of such diverse countries and regions is a unique strength of this ICMI Study upon which many more studies have the potential to build.

The approach in this concluding chapter to distilling key messages or lessons from the chapters and the themes, is not to summarise what has been set out in the conclusions of the various sections and chapters, but rather to step back and review these from across the volume and to extract elements that have stood out by virtue of being repeated or significantly emphasised and that may be of relevance and value to school mathematics curriculum policy makers, analysts, practitioners and researchers. Authors of chapters were encouraged to draw out key conclusions from their respective chapters and similarly theme leaders extracted the main learning points from their theme. The aspects discussed below are therefore a selection of the key messages and main conclusions from those identified by authors and theme leaders. Readers are referred to the main texts for the extensive rich detailed and varied deeper nuances of the points highlighted below.

Challenges in Defining School Mathematics Curriculum Reforms

What is meant by curriculum, by reform or even by school mathematics within curriculum reforms? These were abiding questions throughout the study.

Chapter 1 describes the challenges of defining the key concepts of the study and how the study drew on different definitions of ‘curriculum’. An evolution can be observed from the definitions of ‘intended’, ‘implemented’ and ‘attained’ curriculum as set out in the Discussion Document; to the definition presented by Niss (2016) comprising six curriculum ‘vectors’ in the study conference that was taken up across a number of themes and chapters; to further definitions drawn on by authors in their chapters in this volume.

It is possible to observe that the difficulty of defining the key concepts increases with greater diversity in the cases being considered in the analysis. While international studies have developed definitions that are applicable across contexts, two major driving forces identified as significant, that of cultural values and political movements (Bosch et al., Chap. 8), point to how sensitive definitions need to be to particular contexts in order to adequately grasp the working of a particular reform effort in any analysis.

Difficulties in defining school mathematics curriculum reforms also come from its complex and multi-facetted nature as an endeavour with a wide variety of stakeholders and a general public (parents and students) who receive and experience the impact of reforms. As was discussed in theme E on agents and processes of curriculum design, development, and reforms in school mathematics, curriculum reforms are shaped by actors from a wide variety of sectors - business, industry, media, teacher unions, and parents and so on.

The very use of the word ‘reform’ in school mathematics curriculum reforms has also come under critique especially in cases were the intention is to completely overhaul a curriculum – where a ‘transformation’ or ‘reimagined’ curriculum is being argued. With new areas being introduced in mathematics curriculum reforms (e.g. statistics, modelling, computational/ algorithmic thinking, mathematical literacy) foundational questions about what constitutes mathematics in the school mathematics curriculum have equally been raised. The challenges and difficulties of defining mathematics curriculum reforms may therefore be linked to the sheer complexity and magnitude of school mathematics curriculum reforms as well as their deep context boundedness. We will return to this point.

Lack of Research, Gaps in Theories and Methodologies in the Study of Reforms

It became evident early in the study, as Kilpatrick points out in Chap. 2,

Despite enormous amount of curriculum development, we do not have an enormous amount of curriculum development research. (p. 29)

Across the themes of this volume, authors raise this lack of scholarly work in mathematics curriculum reforms as a major challenge and give different explanations. It is identified as one of the barriers that have hindered reform efforts historically because as Bosch and O’Meara(Chap. 8) point out research in mathematics education “tend to focus on smaller units of analysis like the teaching of a given topic or recurrent student difficulties in learning. Analysing a whole curriculum and its evolution over time […] requires specific research tools” (p. 114) and those which will allow a more neutral stance by researchers who are variously involved in the reform.

Authors focusing on the agents and processes in curriculums reforms expand the research challenge, pointing to the long time-scale of reforms, the political sensitivity of reform processes at each level, and difficulties of obtaining data on the inner workings and dynamics of curriculum committees which could contribute to greater understanding of reforms and hence to improving different reform processes and communication (Ellen et al., Chap. 30). Hence, it appears that there is wide-spread practice of mathematics curriculum reforms nationally and regionally across the world but with limited in-depth studies at macro or policy levels to inform and drive evidence-based improvements over time and across contexts.

While there is research published on mathematics curriculum reforms, especially of pilots conducted before a reform is rolled out or on smaller aspects of a reform, and especially on the outcomes of a reform in the form of students’ achievements, the point being made is that much less is known, for example, about the inside workings at a curriculum policy level, and on how particular decisions get made, implemented and resourced. Furthermore, much more research is needed about the broad scaling up of the implementation after the piloting stage of a mathematics curriculum reform (where piloting does take place). It is evident that developing, implementing and evaluating a mathematics curriculum reform, say, at a country, state or district level, constitute different domains of practice and, therefore, of research.

Another significant related point is the dearth in the development and use of theories. A direct question was posed in the theme on curriculum reform coherence and relevance regarding this issue. Morony (Chap. 14, p. 219) concludes that “there is a lack of conscious and careful application of theory to analyses of mathematics curriculum reforms.” This is not to discount development and applications of some theories (e.g. on didactic transposition – see Bosch et al., Chap. 7; Artigue, in Chap. 16; Barquero et al., Chap. 13) or models for curriculum reforms (e.g. Jameson and Bobis, Chap. 27; Thornton et al., Chap. 17 ). Barquero et al. (Chap. 13) provide a useful exposition on this situation in mathematics curriculum reform research and state that the most striking finding from their work to identify theoretical approaches in analyses of curriculum reforms is that such examples are in a distinct minority and many reviews of curriculum reforms are not supported by a clear theoretical basis that guides the methodology used. As a relatively under-developed area of research in mathematics education, it is evident that “Choices of research questions, research designs and interpretation of results all depend on the development of a research community sharing some common theoretical foundations and employing compatible methodological approaches.” (Jameson et al., Chap. 30, p. 471).

A main conclusion is that mathematics curriculum reforms, currently, therefore do not appear in the main, to be strongly evidence-based or guided by research. The challenge is double-edged in that, on the one hand, curriculum policy makers may not use research or use only research that supports the stance they seek to promote, while on the other hand, mathematics education researchers are not engaging the kind of research that can appropriately speak to and inform large-scale curriculum reform efforts. Morony (Chap. 14) highlights the need for a commitment from all stakeholders to consider evidence from relevant scientific studies of curriculum reforms, and to initiate such studies to guide reforms. In addition, several themes acknowledge the importance of continuous monitoring and evaluation of curriculum reforms. It is hoped, therefore, that this study will galvanise such efforts in the mathematics education community.

With the lack of theory and theorising, there appears to be a concomitant lack of development of appropriate methodologies in mathematics education literature for studying large reforms. The primary methodology in this volume, across themes, is one that draws on selected groups of national or regional case studies of mathematics curriculum reforms to extract key messages and learning points. Although the volume is driven by authors who were delegates (whose papers were accepted) in the ICMI Study 24 conference, the selected invited keynotes and plenary panellists as well as members of the International Programme Committee (IPC), who were variously leading or involved in major reforms of their countries or regions, provided a unique rich data source and reflections on the inner working and challenges of macro curriculum reforms across a wide variety of diverse contexts. These include: Angel Ruiz (Costa Rica); Peter Sullivan and Will Morony (Australia); Bill McCallum and Jeremy Kilpatrick (USA); Yoshinori Shimizu (Japan); Mogens Niss (Denmark); Fidel J. Oteiza (Chile); John Volmink and Renuka Vithal (South Africa); Berinderjeet Kaur (Singapore) and Miho Taguma (OECD, for member countries), among others. This, in itself, represents a significant strength of this study volume as it brings together the reflections of key figures in school mathematics curriculum reforms from diverse countries and contexts.

This ICMI Study volume itself therefore, offers a methodology for studying curriculum reforms while presenting an emergent approach to international reviews and collaborations, to jointly learn about and from each other about school mathematics curriculum reforms.

Shifts in the Content of School Mathematics Curriculum Reforms

A central and major element in all school mathematics curriculum reforms is the concern about mathematical content. What is the appropriate content in school mathematics, how is it represented at all levels and for different groups of students, what is its purpose, how does it compare with other countries, and so on, which take centre stage in any mathematics curriculum reform effort. A few key messages are highlighted on this aspect from a complex, multi-faceted and substantive discussion in the volume.

From a historical perspective, Kilpatrick (Chap. 2) points to a major movement from a pure mathematics focus, especially in the secondary grades in the period before the eighties, to a much more applied mathematics focus since the nineties, which is explained, in part, by the advancements and ubiquitous availability of technology and shifts in student interests. The evidence for this is in the introduction of new areas such as mathematical modelling, statistics, financial mathematics and programming in curriculum reforms observed across many countries. Mathematics curriculum reform content and pedagogies are also being influenced by particular mathematics education movements such as Realistic Mathematics Education, Critical Mathematics Education and Ethnomathematics as well as discourses on social justice and equity, which have become established in the past few decades and may be observed explicitly or implicitly in some reforms.

Another major shift has been in the introduction of mathematical literacy or numeracy or similar content in multiple ways. This shift may be explained, in part, from the wide media coverage and public interest in international studies like PISA which focus on mathematics literacy but also from concerns about ensuring student learning outcomes impart necessary mathematics knowledge and skills appropriate for functioning in contemporary society. It is underpinned by wider concerns about how economic and social inequalities may be entrenched through mathematics education provisions. This debate is also extended into how mathematics curriculum reforms build in different pathways for different groups of learners which serve as gateway or gatekeeping functions into further study of mathematics and ultimately into different career opportunities. This aspect is arguably under-explored in this volume.

The very question of the relevance of content matters in mathematics curriculum reforms is raised with contemporary and future curriculum reforms pointing to a major shift from content-based to a competency-based curriculum. The OECD frameworks, as presented in the chapter by Taguma et al. (Chap. 32) shows how these frameworks are taken up across countries and the shape of possible future curriculum reforms. The widespread adoption of the USA Common Core State Standards in Mathematics to inform content and pedagogical choices in mathematics curriculum reforms across many other countries, is another case in point.

The chapters in the theme on globalisation and internationalisation describe and analyse in detail how these curriculum reform processes are unfolding and their impacts. In particular, this theme explores how TIMSS and PISA are serving as vehicles for curriculum reforms across countries, how numeracy and mathematical literacy are evolving and finding representation in curriculum reforms in multiples ways; and the most recent emergence, that of computational thinking or algorithmic thinking is finding expression in some of the most recent national curriculum reforms. The inclusion of some aspects of computational thinking in the PISA 2021 Mathematics Literacy Framework will no doubt, open questions about the relation between the disciplines of computer science and mathematics in future curriculum reforms.

From a coherence perspective, Morony (Chap. 14) points out that a key principle underpinning the design and rollout of a mathematics curriculum is the careful consideration of the subject of the curriculum reform – the mathematics - its structure and ways of knowing and doing, not only within mathematics but also in relation to other disciplines. Arguably, an area not adequately addressed in the volume is that of mathematics curriculum content and its relation to curriculum pathways that open or close for student progression in schooling and beyond (see Kilpatrick, Chap. 2).

Key Role of Teachers, Teacher Education and Professional Development

There is no doubt that there is wide recognition of the role of multiple agents in school mathematics curriculum reforms. However, the critically important role of teachers stands out across themes in this ICMI Study. Even in themes that did not specifically pose research questions related to teachers, it is evident that teachers have the potential to make or break a mathematics curriculum reform.

This lesson was learnt very early as one key explanation for the failure of “New Maths” reforms of the mid twentieth century. There is a recognition of the importance of teacher education and professional development and of different models of professional development that can be scaled up so that they reach a great majority of teachers in any system of mathematics curriculum reform. From a historical perspective O’Meara and Milinkovic (Chap. 5) conclude that in any reform movement, teachers are key agents in the effective delivery of the new curriculum, and so the potential success of the reform is heavily dependent on them. Respect for the existing knowledge of teachers, building their capacity to adopt new ways of working with their students when provided with appropriate and sustained support in the form of materials, induction, initial and continuing professional development and acknowledgement of their work is spelt out as a key principle in the focus on coherence and relevance of curriculum reforms (Morony, Chap. 14).

Teacher involvement, ownership and commitment to the reform are regarded as important for successful implementation of a curriculum reform, and both bottom up and top-down strategies are needed (Ruiz, Chap. 19). Several themes emphasise that appropriate forms of resources need to be provided to teachers that are coherent with the curriculum and main objectives of the reform. Central to this is developing and testing practical models of teacher preparation that align with their responsibilities in the intended curriculum (Stephens et al., Chap. 24). Stakeholder communication and negotiation (Pinto and Cooper, Chap. 28) are important at all stages of a curriculum reform. However, finding ways to meaningfully involve all teachers who will eventually have to implement a reform is difficult but also critical in a mathematics curriculum reform.

The Rise of the Importance of Resources and Technology

The question of the role of resources, including teaching and learning materials and technology in mathematics curriculum reforms was expressly asked in all themes except for the one focusing on agents and processes of curriculum reforms. With the emergence of the Covid-19 pandemic and the resultant shift to online, blended or hybrid teaching and learning, this issue of resources and technology has been brought into much sharper relief. However, the study identified the importance of adequate and appropriate resources before the pandemic struck.

One of the key principles identified for the design and rollout of a curriculum reform that is coherent and relevant is that resources developed to support the implementation need to be “adaptable to different contexts and changing circumstances, accessible and sustainable” (Morony, Chap. 14, p. 220), and Golding (Chap. 12) describes the conditions and some of the pitfalls for this in large scale reforms. Success in implementation of mathematics curriculum reforms requires not only the existence of appropriate resources for teachers and learners but a close relation between the school and any pedagogical materials, in a bi-directional process that is both top-down and bottom-up, noting that the way this is done varies significantly (Ruiz, Chap. 19).

The range of issues related to the development and use of a broad range of resources including digital technologies and the diversity across countries and regions as well as invariant aspects in curriculum reform implementation processes is explored in detail by Coles et al. (Chap. 18). In school mathematics curriculum reforms, as they point out, “textbooks arise as an important resource to promote good alignment with the curricular reform, considering not only their content but also their methodological approaches. They are strongly influenced by external high stakes assessments, which can be coherent or not with curricular reforms” (p. 291).

While warning of the dangers of inadequate resourcing or rushed design of resources in school mathematics curriculum reforms and how these can create tensions within the curriculum system, Golding (Chap. 12) concludes, that textual, manipulative and digital resources can be harnessed to support increased relevance for students and promote enactment of a curriculum reform by teachers; and notes the lack of research about the affordances and constraints of digital materials, and on student use of resources in relation to curriculum reform intentions. The need for research assumes much more significance in the Covid-19 and most likely post-Covid era where new digital technologies as well as digital and digitalised books and other teaching and learning resources will gain considerable traction within education systems.

Alignment as a Key Feature Within School Mathematics Curriculum Reforms

While the theme on coherence and relevance in mathematics curriculum reforms is defined and explored in detail, the issue of alignment has arisen consistently alongside it. Morony (Chap. 14) concludes that their analyses demonstrate “the importance of alignment between the curriculum and the curriculum system in which it is enacted, and […] the negative impacts of the mis-alignment between the two. This mis-alignment limits the effective and coherent enactment of a curriculum and the reform it embodies” (p. 220). Alignment is, in fact, identified as one of the ‘laws’ for successful implementation of reforms in that “all the educational means (and) the reforming efforts” must be aligned (Ruiz, Chap. 19, p. 326).

Within any curriculum reform, a central key message for its success is the alignment of the aspects and components of the curriculum, however, it is defined. That is, any curriculum reform effort must seek to work towards and sustain the alignment of the intended, implemented and attained curriculum as well as the alignment of curriculum vectors as defined by Niss (see Chap. 1) – goals, content, materials, teaching, student activities and assessment.

Given that a curriculum reform by its nature involves multiple stakeholders, each with different vested interests, roles and responsibilities at different levels of an educational system, sustaining alignment will always be a challenge. To this end the ‘law’ of alignment may be associated with the ‘law’ of two directions in that “implementation strategies must be considered allowing for both top-down and bottom-up developments. What is essential is to create a good synergy between these two processes” (Ruiz, Chap. 19, p. 325).

In addition, to maintain this alignment would require recognising the importance of communication across boundaries of different communities (Pinto and Cooper, Chap. 28). Attention is drawn to the range of stakeholders in any curriculum reform and “the significance of interaction between different professional communities, within and across levels by direct dialogue and mediated by documents and materials” (Jameson et al., Chap. 30, p. 471–2), pointing to how the design and implementation of reforms can benefit from multiple forms of professional expertise, practice and engagement. In particular, the involvement of key agents who are members of multiple communities can serve as brokers mediating different discourses to facilitate alignment in its different forms and facets.

School Mathematics Curriculum Reforms as Context-Bounded and Invariant

The notion that school mathematics reforms are deeply bounded to their context and yet also demonstrate invariant aspects across contexts, is well captured in the final comment by Kilpatrick (Chap. 2)

I think the idea of curriculum as a process, and one that needs to be shaped by the situation in the school, the situation in the country, the situation in the classroom – all of that has changed from what it was in the 1980s. Today, I would say we are moving much more toward recognising that the goals for school mathematics may be different across different school systems, countries, and situations. Each country has to figure out what its goals are, and in what directions it wants to go. (…)

The bipolar nature of school mathematics (pure and applied mathematics), in contrast, shines through regardless of the curricular context or level. We have learned since the new math era that school mathematics is complicated, contextualized, not easily changed, and not easily studied. (p. 33–4)

In all the themes, there is a recognition of how context-bound mathematics curriculum reforms are by virtue of different cultural values, social, political and economic systems and living conditions. In the implementation of curriculum reforms, this is a key message presented as one of the ‘laws’ of the enormous diversity in different dimensions observed in experiences of a variety of countries and regions. This diversity can refer to: the many different agents involved in the various levels of intervention in reforms, the cycles or timing of reforms which may be linked to social, cultural and political stability or some change event or condition; or to the scale and breadth of a reform which could involve some or all of the curriculum vectors identified in the definition by Niss. A consequence of this diversity is that a curriculum reform that may be successful in one country may not be so in another country and the importing/exporting of mathematics curriculum reforms from one context to another cannot therefore, be translated in a mechanical or an instrumental approach.

Despite this diversity, there are aspects and components of mathematics curriculum reforms that are invariant across contexts, given in part, by the internationalisation and globalisation processes. The impact of international studies like TIMSS and PISA on mathematics curriculum reforms being undertaken in individual countries or regions has been recognised across the themes. Stephens et al. (Chap. 24) in the theme on internationalisation and globalisation, document in detail the influence of TIMSS and PISA in diverse countries on intended curricula, support for teacher professional development, coverage of content knowledge and skills, and inclusion of concepts of mathematical literacy or numeracy in mathematics curriculum reforms. They caution however, on the importance of evaluating these when adapting components of international studies in national curriculum reforms.

It is noted that the activities of ICMI itself may influence and impact on particular globalisation and internationalisation processes in mathematics curriculum reforms. A wide range of ICMI activities bring diverse participants from many different countries together and this sharing leads to similar aspects being taken up across very different contexts. The point however, is not against such activities but rather that great consideration should be given to the unique features of a particular context in adopting any aspect of a curriculum reform from it into another context.

The role and impact of technology in mathematics curriculum reforms is already observed and has been highlighted as likely to increase in future, which will take different forms and emphasis in different contexts but is invariant in that it will influence school mathematics curriculum reforms in multiple ways across the world. Some reasons advance are the increased reliance on digital technology by their application to all facets of life in contemporary society, the expectations of parents and students for a better technology-assisted education that combines the peculiarities of local contexts with the global in opportunities for further education and jobs, the increasing use of algorithmic techniques including artificial intelligence and the general unfolding of what is being referred to as the fourth industrial revolution (4IR) across diverse societies. These have been accelerated by the impact of the Covid-19 pandemic.

In the theme on agents and processes of curriculum design, development and reforms, curriculum reform contexts are considered as systems that can make important choices stand out. That is, within a particular country or region, Jameson et al. (Chap. 30) conclude that curriculum reform is, “always situated in a particular context at the jurisdictional level, and further instantiated within multiple contexts like schools and training programmes” (p. 469) in which agents may make different choices in what is focused on and emphasised in a curriculum reform. Hence, the lessons learned from importing curricula at a global level to a national context also apply within countries in recognising diversity within a country or region in the design and implementation of any curriculum reform and its impacts and outcomes.

School Mathematics Curriculum Reforms as Long-Term and Unpredictable Endeavours

Large macro-level mathematics curriculum reforms are typically conceived of as long-term. These type of curriculum reforms are often conducted in cycles of five to ten years or when there is a change event, which triggers a mathematics curriculum reform. Depending on the extent of the reform in terms of its departure from the status quo, the actual curriculum redesign and development might take place over a shorter period of a year or more but the implementation could be rolled out over many years through an education system (e.g. primary and/or secondary grades). This long-term timeframe has also been identified as one of the ‘laws’ for successful implementation with experience showing “inappropriate reduction of time and resources needed for a reform inevitably conspires against its success” (Ruiz, Chap. 19, p. 326).

The long-term timeframe together with diverse agents and stakeholders at multiple levels in any reform contributes to several unknowns that are invariably part of any curriculum reform design and implementation plan. Those involved in or leading large-scale mathematics curriculum reforms point to how unpredictable the implementation of a reform can be and hence, the ‘law’ of uncertainty has been proposed to recognise that reforms are not linear processes as debates and challenges arises in diverse contexts (Ruiz, Chap. 19). The theme exploring agents and process of curriculum reforms refer in their concluding key message to unexpected events and circumstances that may arise since a reform is by its nature a disruption and some degree of shock to the system. Jameson et al. (Chap. 30) connect this with the notion of resilience in the design and implementation of a curriculum reform and outline characteristics that contribute to resilient systems.

The impact of the COVID-19 pandemic has demonstrated in very real terms how curriculum reform design, implementation and outcomes will need to account for the unexpected, the uncertain and the unpredictable by being open to continual “rethinking, reforming and reprogramming” (Ruiz, Chap. 19, p. 327). This difficulty is exponentially increased in education systems already characterised by deep inequities, instability and disruption. In this context, Jameson et al. (Chap. 30) similarly cite “the importance of ‘resilience’ as a property that allows a system to experience some degree of shock and disruption while fulfilling its basic characteristics and functions” (p. 473) and argue for how a mathematics curriculum reform may be designed to withstand unexpected changes.

Further Issues in the Study of School Mathematics Curriculum Reforms

This ICMI Study demonstrates the magnitude and complexity of school mathematics curriculum reforms as well as the challenges of studying these. This complexity and difficulty increases many-fold when school mathematics reforms are but one part of a broader curriculum reform that involves many other school subjects and involves one or several levels of an education system. In this ICMI Study, the unit of analysis has been school mathematics curriculum reforms and to that extent the study has not focussed on these reforms as part of a broader school curriculum reform.

The challenges of studying mathematics curriculum reforms are many-fold. Not only are there theoretical and methodological challenges requiring particular knowledge and skill sets, large scale studies require large funding grants which may be difficult to obtain. Nevertheless, the need for undertaking these studies is abundantly demonstrated in this study and it is hoped it will be a catalyst for this area of research and development within mathematics education.

As it is observed in the study, and for which there is a long tradition in mathematics education research and practice, boundary crossings and borrowings from other disciplines such as from general education studies, policy studies and curriculum studies may greatly advance and benefit studies in mathematics curriculum reforms (Halai, Chap. 36; Valero, Chap. 37). Furthermore, while it may be difficult to mount large studies in mathematics curriculum reforms, approaches adopted in other disciplines (such as the medical sciences) that actively undertake synthesis studies, meta-analysis and reviews across different countries or contexts need to be more deliberately planned and conducted so that what is context specific and what is invariant becomes better understood and able to be implemented with greater confidence in and through mathematics curriculum reforms.

One of the areas which did not generate papers to the study conference and remains under-explored is the role of media in macro school mathematics curriculum reforms. Experience across countries show that major changes in school mathematics curriculum generate sharp interest across many different sectors and stakeholders. This is explained, in part, by the role of school mathematics curriculum outcomes as either, an obstacle to or facilitating of further educational and job opportunities for students. Yet this area on the role of media is not understood even though it can and does directly impact the eventual curriculum reforms that get accepted and implemented in real terms in any given context. Carefully crafted and co-ordinated media releases across many countries simultaneously by major international studies like TIMSS and PISA provide lessons in demonstrating their influence in curriculum reforms and which need to be studied.

Curriculum reform processes are as much an educational matter as they are political. They involve a broad range of stakeholders and agents with vested interests. Actors from outside education such as politicians, business, industry, various professional associations and trade unions together with and through the traditional and newer forms of (social) media influence and shape curriculum reforms as much as (if not more than) those with different expertise such as curriculum policy makers, educators, mathematicians, and researchers.

An area that requires further exploration and study is the relation between mathematics education/educators in the broadest sense and other stakeholders, especially those in government with the power to initiate, develop, implement, review and evaluate school mathematics curriculum reforms. School mathematics curriculum reforms are no longer the preserve of mathematicians primarily driving such processes as they once were such as in the “New Math” era. In countries around the world the processes by which curriculum reforms are undertaken are as complex as the reforms themselves. In today’s world mathematics educators, are but one (among many) of the key agents in any reform, hence, their understanding and ability to communicate and negotiate with multiple stakeholders, agents and the general public is critically important for their expertise to find expression in the reform itself.

In conclusion, this ICMI Study 24 points to an emerging scholarship in school mathematics curriculum reforms (especially large macro-reforms) that is still in its infancy and requires much more deliberate and focused attention to develop it into a fully-fledged area of study in mathematics education. This is critically important if mathematics education researchers and practitioners seek to significantly impact the day to day functioning and outcomes of the vast majority of mathematics classrooms on the ground, in whichever context they find themselves. It is by influencing school mathematics curriculum policy at a macro level that will create the necessary openings for the inclusion of the considerable research and knowledge that exists about mathematics education to find expression and impact the largest numbers of mathematics learners and teachers, and eventually any society as a whole.