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This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.'s triadic conceptualization of instruction, which draws attention not only to the main actors of the didactical process (i.e., the Teacher and Students) and the Content around which the actors' work is organized (herein, content related to proof and proving), but also to the relationships among the actors and the content. Out of the 103 papers we reviewed, almost half fell in the Student-Content category, which is consistent with the existence of a substantial number of frameworks, methods, and research findings related to students' engagement with proof and proving. About a quarter of the papers fell in the Student–Teacher-Content category, which reflects an emphasis on viewing instructional practice in proof and proving in a holistic, systemic way. Only few papers fell in the categories that did not include Content in them, namely, the categories of Student, Teacher, and Student–Teacher; this suggests mathematics education research on proof and proving has a strong disciplinary identity, which potentially differentiates it from other mathematics education research strands. About a fifth of the papers were oriented towards 'breaking ground' through making an explicit theoretical and/or methodological contribution (Student–Teacher-Content and Content were the main categories where such contributions appeared), whilst the majority of the papers were focused on 'building ground' through elaborating or employing existing methodological and/or theoretical approaches. [ABSTRACT FROM AUTHOR]

The paper responds to the need for understanding trends and gaps in extant research related to adult education in mathematics and numeracy, given changing skill demands and skill gaps regarding adults, and related policy, theorizing, and practice trends. This paper presents the results of a scoping review of recent empirical research related to adult education in mathematics and numeracy, published in 22 selected journals from 2019 to 2022, including 15 journals in adult education and seven in mathematics education. The results show that only 39 relevant empirical studies were found among over 2300 research papers reviewed, and that few of those focus on practice-related of adult education in mathematics and numeracy. The results provide quantitative evidence suggesting that the field of adult numeracy education is under-researched, and help to identify gaps in empirical research involving adult numeracy, including on emerging topics such as on modeling and critical interpretation. The results also point to research opportunities that can strengthen theorizing and practice in both mathematics education and adult numeracy education. [ABSTRACT FROM AUTHOR]

The interrogation of often unintended practices of marginalisation has gained focus in research on mathematics teaching and mathematics teacher education throughout the last decades. In this introductory survey paper, work against marginalisation in these contexts of mathematics education is viewed in terms of work towards equity, diversity and inclusion. Based on this interpretation, we present a framework on awareness and practice of equity, diversity and inclusion in mathematics teaching and mathematics teacher education research. We then use this framework and a survey method of mapping review to identify and comment on a selection of studies. As a result, we illustrate three research moves towards equity, diversity and inclusion, in the form of interconnected themes: (1) Widening the understanding of the mathematics and the mathematics education curricula (2) Improving the practice and discussion of mathematics teaching (3) Unpacking ideologies in mathematics teaching and mathematics teacher education. We finally examine the themes and the special issue papers together to foreground commonalities regarding awareness of discriminatory discourses and practices of creating and distributing opportunities for all groups, including those historically and currently marginalised. Despite the important increase of equity-driven principles of awareness, we conclude that mathematics education research on teaching and on teacher education needs more examples of practices whose development has been proved to challenge marginalisation. [ABSTRACT FROM AUTHOR]

In this survey paper, we describe the state of the field of research on teaching mathematics with technology with an emphasis on the secondary school phase. We synthesize themes, questions, results and perspectives emphasized in the articles that appear in this issue alongside the relevant foundations of these ideas within the key journal articles, handbooks and conference papers. Our aim is to give an overview of the field that provides opportunities for readers to gain deeper insights into theoretical, methodological, practical and societal challenges that concern teaching mathematics with technology in its broadest sense. Although this collection of articles was developed prior to the global coronavirus pandemic, we have taken the opportunity to survey the contributing authors to provide some country perspectives on the impact the pandemic has had on mathematics teaching with technology in the period January–July 2020. We conclude the survey paper by identifying some areas for future research in this increasingly relevant topic. [ABSTRACT FROM AUTHOR]

This survey describes the structure of the field of research on curriculum resources in mathematics education in the period from 2018 till 2023. Based on the procedures of a systematic review relevant literature was identified using Web of Science as a database. The included literature was analyzed and categorized according to the type of curriculum resource and the area of study. Seven areas of studies were identified: studies on the role of curriculum resources, content analysis, user studies, studies on the effects of curriculum resources, studies on curriculum resource design, curriculum resources as data, and reviews. The areas were further subdivided into different subcategories based on the research questions of the included papers. The findings show that research on mathematics textbooks is still predominant in the field. The most popular areas of research are content analysis, user studies, studies on design, and studies on effects. Emerging areas are research on students' use of curriculum resources and the employment of user data from digital curriculum resources as data basis in mathematics education research. [ABSTRACT FROM AUTHOR]

In this paper we review selected significant developments in the use of digital technology in the teaching and learning of mathematics over the last five years. We focus on a number of important topics in this field, including the evolvement of STEAM and critical making as well as the process of redefining learning spaces in the transformation of the mathematics classroom. We also address the increasing use of computer algebra systems and dynamic geometry packages; and the issue of student collaboration online, especially using learning environments and social media. We briefly touch on artificial intelligence systems, including hyper-personalisation of learning, multimodality and videos. We include a brief discussion on the impact of COVID-19 on mathematics education, and lastly on the more theoretical perspective of the epistemology of digital technology and the construct of humans-with-media. We conclude the discussion with some possible concerns and mentioning some possible new topics for research in the field. [ABSTRACT FROM AUTHOR]

The teacher noticing construct is widely recognized in teacher competence and education research, particularly in the field of mathematics education. This paper surveys recent research on mathematics teacher noticing published between July 2019 and 2022, following an earlier literature review on teacher noticing across different disciplines. The study presented here analyzed 118 English-language articles published in peer-reviewed journals, focusing on conceptualizations, research methods, and relationships with other constructs, including teacher knowledge and beliefs. The findings suggest that the cognitive-psychological perspective on noticing, which emphasizes a set of cognitive processes, remains the predominant conceptualization. Recent research on noticing is characterized by a high proportion of studies based on small samples and qualitative research methods. While several studies have demonstrated the interrelatedness of noticing and professional knowledge, the relationship between noticing and beliefs and between noticing and instructional quality has rarely been addressed. Based on these findings, we highlight noteworthy contributions and critical shortcomings, and suggest directions for future research. [ABSTRACT FROM AUTHOR]

In this paper, I report the results of a study of a large-scale implementation of an evidence-based, objective-oriented approach to teaching via digital platforms among mathematics teachers in Denmark. The aim of the study was to investigate how these platforms affect the work of mathematics teachers and how emergent problems in this process can be addressed from an implementation perspective. This objective was achieved by applying concepts from the theory of instrumental genesis to analyze ethnographical data of teachers' platform usage and data from participatory workshops. The results of the study indicate that the design of platforms is likely to conflict with the needs of mathematics teachers and thus I argue for the need of addressing such issues by supporting teachers in enacting innovations rather than by redesigning them. Furthermore, in the paper I suggest that future workshop is an adequate format to support such enactments. [ABSTRACT FROM AUTHOR]

This paper reviews research on equity in mathematics education (excluding gender equity) for the period 2017–2022. From the publications identified, five themes were distilled: conceptualizations and framing of equity in mathematics education; research methodologies and researcher positionalities; equity-focused practices, pedagogies and teacher education; equitable mathematics curriculum content, access and pathways; and equity in mathematics education at system levels, nationally and internationally. The review concludes by engaging some of the critique and suggests future directions for research. The research demonstrates that there is growing voice and visibility of equity-focused studies in mathematics education and that conceptualizations of equity have broadened and deepened through an increasing diversity of studies in this area. At the same time, the review also shows the dominance of the Global North in shaping equity discourses and the paucity of research on equity in mathematics education from the Global South. [ABSTRACT FROM AUTHOR]

Implementation has always been a paramount concern of mathematics education, but only recently has the conceptualizing and theorizing work on implementation as a phenomenon begun in our field. In this survey paper, we conduct a hermeneutic review of mathematics education research identified as related to the implementation problematics. The first cycle of the review is based on examples of studies published in mathematics education journals during the last 40 years. It is organized according to five reasons for developing implementation research. The second cycle concerns 15 papers included in this special issue and is organized by four themes, as follows: objects of implementation, stakeholders in implementation, implementation vs. scaling up, and implementability of mathematics education research. The paper is concluded with a refined glossary of implementation-related terms and suggestions for future research. [ABSTRACT FROM AUTHOR]

It is the intention of this special issue to provide an opportunity for mathematics education researchers from all around the world to offer their complementary accounts and to engage in reflective scholarly exchange regarding research into the complexity of classroom practice. Other major international projects informed by the LPS, and led by Clarke, cohered around a desire to understand, model and ultimately optimise the practices of the mathematics classroom. For most of his career Clarke's research activity centred on capturing the complexity of classroom practice through a programme of international video-based classroom research in more than 20 countries. The work of David Clarke The work of David Clarke profoundly influenced the field of mathematics education. [Extracted from the article]

In this special issue we introduce the state of the art of empirical studies on creativity in mathematics and mathematics education. To do so we conducted a retrospective analysis of empirical studies on mathematical creativity with special attention to the studies conducted during the last decade. In the paper we present a brief survey of research on mathematical creativity up to 2009 and then a detailed review of empirical studies performed during the past decade. We note an optimistic development of attention paid to mathematical creativity in schools. A systematic search conducted to examine research on creativity in mathematics education journals and research in the field of mathematics in creativity-related journals, yielded 49 papers that described empirical studies on creativity in mathematics education. The retrospective analysis examined the following: (a) the main goals of the studies; (b) conceptual frameworks used by the researchers; (c) research methodologies; and (d) tools and tasks. Of these, 18 studies examined the relationships between creativity in mathematics and other characteristics, 25 were on creativity related to instructional practices and mathematical tasks, and 6 studies investigated teachers' creativity-related conceptions and competencies. Of these studies, 29 used quantitative methodologies, 10 of which integrated analysis for problem solving or problem posing strategies or outcomes. Ten additional studies employed qualitative methodology (mainly content analysis of lesson observations). We conclude the paper with a short review of papers in this special issue, and outline directions for future research on creativity in mathematics (education). [ABSTRACT FROM AUTHOR]

This paper is a survey paper for the special issue on changes in Eastern European mathematics education in recent decades. In it I attempt to describe briefly the development of Eastern European mathematics education during the years that preceded the changes of the late 1980s and early 1990s, and to indicate certain questions for research pertaining to the subsequent period. Existing scientific literature about these topics is also discussed. One of the key problems that must inevitably be addressed is the problem of influence in mathematics education, which may be linked to quite varied political and organizational circumstances. The questions raised in the paper may be posed with respect to other countries as well, but in the countries of Eastern Europe, with their tumultuous and complex political history, the social aspect may be observed in greater relief than anywhere else. It is assumed that the analysis of general tendencies and patterns of development will be of interest even to a readership whose pursuits are otherwise far from Eastern Europe. [ABSTRACT FROM AUTHOR]

Mathematics education in Serbia in the New Millennium has drawn on various traditions—Yugoslavian and post-Yugoslavian—and there has also been an acute awareness of the historical roots of mathematics education in Serbia before the founding of Yugoslavia in the twentieth century. In this paper I report on a comparative study of its two main journals in mathematics education since the break-up of Yugoslavia at the beginning of the new millennium. From this analysis, the focus of mathematics education is shown to be on talented students, which produces some excellent results in international competitions. However, new emerging trends are becoming more visible. First, the work of international colleagues is beginning to be published in Serbia, and second, a new community of scholars, who base their research on mathematics education rather than the mathematical content itself, is beginning to appear in some more recent publications. Nonetheless, the latter development is taking place only outside of the two journals at the center of this paper. [ABSTRACT FROM AUTHOR]

Calculus continues to be an important topic of discussion among mathematics education researchers given how it often acts as a gatekeeper for students in STEM. In their extensive 2017 review of calculus literature, Larsen and colleagues identified two main areas of applied research that had largely been neglected: research related (1) to efforts to improve calculus teaching and learning and (2) to equity and social justice. In this review we investigate how scholars have answered this call by reviewing recent literature related to these two themes. First we identified some promising intervention studies that investigated changes at the course level (e.g., calculus courses intended for engineering students) and at the level of specific calculus topics (e.g. using digital tools to help students understand the Fundamental Theorem). Second, we identified several studies on diversity, equity, and inclusion. We found that some studies in this collection still approached this research through traditional methods (e.g., so called achievement gaps) but we also identified promising new directions for research in which scholars utilize critical theories and provide counter-narratives that highlight the strengths of calculus students from historically marginalized groups. We conclude our review by discussing future directions we hope to see in the field that we argue will strengthen current work. [ABSTRACT FROM AUTHOR]

In this paper, we turn to the notion of networking theories with the aim of contrasting two theoretical mathematics education perspectives inspired by Vygotsky's work, namely, the Theory of Objectification and the Documentational Approach to Didactics. We are interested in comparing/contrasting these theories in accordance with the following three main questions: (a) the role that the theories ascribe to language and resources; (b) the conceptions that the theories bring forward concerning the teacher, and (c) the understandings they offer of the mathematics classroom. In the first part of the paper, some basic concepts of each perspective are presented. The second part includes some episodes from a lesson on the teaching and learning of algebra in a Grade 1 class (6–7-year-old students). The episodes serve as background to carry out, in the third part of the paper, a dialogue between proponents of the theoretical perspectives around the identified main questions. The dialogue shows some theoretical complementarities and differences and reveals, in particular, different conceptions of the teacher and the limits and possibilities that language affords in teaching–learning mathematics. [ABSTRACT FROM AUTHOR]

This narrative review of current research on gender and mathematics covers the years 2020 to 2022. The number of exemplary publications within these 3 years and the diversity of topics, theoretical frameworks, subjects, and authors are indications of gender and mathematics remaining a robust and evolving area of study. Of particular interest are studies of lived experiences of students in secondary school and university programs, many of which featured continuing and troubling discriminatory incidents. In addition, the focus in several studies on the intersectionality of gender with race and other identity features is a commendable trend that should be continued. Similar to the transition from sex differences to gender differences that emerged in the 1990s and 2000s, in the papers examined, some authors have reconceptualized gender as a fluid, non-binary construct, although most gender data are reported in binary ways. Gender remains a focus of research in mathematics education because of persistent inequities in achievement, attitudes, representation, and lived experiences. [ABSTRACT FROM AUTHOR]

Lesson planning is of central importance to the teaching of all subjects in school. However, despite its high relevance, there is still a substantial need for a comprehensive review of factors affecting lesson planning. Empirical evidence on how teachers' competence in lesson planning can be developed, what challenges may be encountered during the lesson planning process, and successful lesson planning designs and practices should come to light on. To close this gap the current paper presents the results of a systematic review of 20 empirical research studies on teacher competence in mathematics lesson planning. For detailed insight into the most recent contributions of the reviewed studies on mathematics lesson planning, we analyzed studies conducted during the past decade, adapting the "process model of lesson planning" and the model of "competence as continuum" as a heuristic for approaching lesson planning. We present key results of the studies related to four major themes: (1) dispositions and their influence on developing and implementing lesson plans, (2) quality aspects of lesson plans and the development of lesson planning skills, (3) difficulties in lesson planning, and (4) the relationship between lesson planning skills and performance in implementation of lesson plans. The results of our literature review reveal that teachers (especially novice teachers) face difficulties in lesson planning and their overall competence (and knowledge) are not at an expert level. However, as the results of the examined studies pointed out, teachers can acquire such competence and knowledge through training within initial teacher education and professional development. Overall, teachers need support in planning mathematics lessons by delineating their lesson plan to improve their awareness of students' thinking, possible learning trajectories, effective usage of the curriculum and teaching resources, and the potential of innovative pedagogies that incorporate new technology. [ABSTRACT FROM AUTHOR]

Advocacy of STEM curricular approaches is based on a concern to engage students in authentic disciplinary and interdisciplinary practices in the STEM (science, technology, engineering, mathematics) disciplines, and the need to promote participation in STEM pathways. The STEM Academy professional learning program was developed to support teachers to engage and motivate students by creating real-world, challenging problems. The initiative involved interdisciplinary teams of secondary STEM teachers attending workshops and working with university experts to design, implement and evaluate STEM curricular experiences. This paper focuses on case studies undertaken in two of the twelve schools involved in the initiative, using interview data from teachers and students, to explore the nature of their programs and their experiences. We investigate key features of these two schools' approaches, using a conceptual framework for integrated STEM, and explore the challenges and benefits of different features of integrated STEM that promote different dimensions of engagement in learning mathematics. We explore how the framework characteristics can be reframed into four dimensions that promote mathematics engagement in integrated STEM education - design thinking in authentic contexts, content integration, STEM practices and 21st Century skills, and exposure to professional practice. [ABSTRACT FROM AUTHOR]

Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer science in intriguing ways. Behind programming practices is computational thinking (CT), a mode of thinking involved in formulating and solving problems so that the solutions could be represented and carried out by computing means. In this paper, CT is seen as a boundary object connecting mathematics and computer science in a school problem-solving context. In particular, we examine and analyse middle school students' work upon engaging in mathematical problem solving-in a programming environment, taking CT as a boundary object embedded in the block-based programming environment, Scratch. The analysis is guided by observing boundary crossing features of CT in the students' artefacts produced in Scratch while solving mathematical problems related to symmetry and arithmetic sequence. The findings of this study open up new dimensions to explore CT as a boundary object in integrated STEM pedagogy. [ABSTRACT FROM AUTHOR]

In the research reported in this paper, using a modified version of the interconnected model of teacher professional growth (IMTPG) proposed by Clarke and Hollingsworth (Teaching Teacher Educ 18:947–967, 2002), we aimed to understand the learning dynamics in a lesson study of a group of five teachers of grades 5–6, during their work around mathematical tasks and in the elaboration and analysis of a diagnostic test of students' knowledge. We draw on examples from a lesson study that took place in a school in Lisbon, involving five teachers that constituted the whole mathematics group of the school. The main feature of our adaptation is the consideration of a Group Domain instead of the Personal Domain of the original model. In the original model, the Domain of Practice had a broad definition but usually it was restricted to classroom experimentation. In the research reported in this paper, the lesson study sessions were taken as part of the Domain of Practice. For data collection, there was audio and video recording of the lesson study sessions and of the research lesson and the writing of a research journal. Data analysis was done using the modified IMTPG. The results suggest that this model is helpful in understanding the processes that make lesson study a valuable professional development setting, contributing to responding to the question of 'how lesson study works' (Lewis et al., Theory and practices of lesson study in mathematics: an international perspective, Springer, New York, 2019). In addition, the use of this model showed that the lesson study promoted the teachers' development regarding knowledge of didactics, especially knowledge of students and their learning processes and of teaching practice. [ABSTRACT FROM AUTHOR]

In this paper a part of the data from a larger study, the Enactment Project, is explored. The exploration is guided by two research questions. The first is specific to the instructional core of teacher practice while the second is related to student perceptions of how they learn mathematics. The project adopted the Complementary Accounts Methodology. Micro-analysis of how three teachers enacted their instructional objectives, using qualitative data analysis methods, led to the identification of three components of an instructional core, namely, Development of concepts and skills [D], Student work [S] and Review of student work [R] that pervade the lessons of the three teachers. They enacted their instructional objectives through instructional cycles comprising combinations of D, S, and R. A lesson was found to comprise one or more instructional cycles. The post-lesson video-stimulated student interview data, showed that teachers helped their students learn mathematics in their lessons specifically in the S and R activity segments. This paper also dispels the myth about stereotypical mathematics instruction in Asian classrooms whilst contributing to this issue of ZDM in memory of David Clarke. It was his work related to the Complementary Accounts Methodology that provided colleagues in Singapore with a tool to illuminate mathematics instruction in their schools. [ABSTRACT FROM AUTHOR]

Promoting engagement is crucial for encouraging student participation, interest, and learning in mathematics. Student engagement has been conceptualized as interrelated types comprising behavioural, emotional, and cognitive characteristics. Cognitive engagement, our focus in this paper, relates to students' psychological investment in learning and practices used to enhance learning, such as self-regulatory strategies and metacognitive processes. Although crucial for students' learning, research suggests that teachers' practices for promoting students' cognitive engagement are not well understood. In this qualitative study, we investigated the beliefs of 40 secondary mathematics teachers across eight English schools concerning promoting cognitive engagement in mathematics classrooms, and whether teachers with different cognitive engagement beliefs differ in the features of classroom practice they attend to in relation to promoting student self-regulation and metacognition. We developed a Cognitive Engagement Framework (CEF) for the following purposes: (1) to develop vignettes that described the practices of two contrasting teachers (Teacher A and Teacher B), who differed in their use of specific self-regulation and metacognitive processes; and (2) to use as a tool for analysis. 17 participants identified with Teacher A who favoured a controlling style towards student strategy use such as activating knowledge, planning, and enacting and regulating strategies, and a passive approach towards students' use of self-reflection. 14 participants identified with Teacher B who favoured promoting student autonomy for planning and enacting and regulating strategies, self-reflection, and acknowledged affective elements. In addition to its findings, the paper makes a methodological contribution by using 'vignettes' as a new way of investigating teachers' beliefs, and a theoretical contribution through the development of the CEF. [ABSTRACT FROM AUTHOR]

Growing use of the internet in educational contexts has been prominent in recent years. In this survey paper, we describe how the internet is transforming the mathematics classroom and mathematics teacher education. We use as references several reviews of use of the internet in mathematics education settings made in recent years to determine how the field has evolved. We identify three domains in which new approaches are being generated by mathematic educators: principles of design of new settings; social interaction and construction knowledge; and tools and resources. The papers in this issue reflect different perspectives developed in the last decade in these three domains, providing evidence of the advances in theoretical frameworks and support in the generation of new meanings for old constructs such as 'tool', 'resources' or 'learning setting'. We firstly highlight the different ways in which the use of digital technologies generates new ways of thinking about mathematics and the settings in which it is learnt, and how mathematics teacher educators frame the new initiatives of initial training and professional development. In this survey paper, we identify trends for future research regarding theoretical and methodological aspects, and recognise new opportunities requiring further engagement. [ABSTRACT FROM AUTHOR]

This paper belongs to a field of research that has appeared comparatively recently, namely, the study of mathematics competitions. The paper utilizes historical-theoretical methodology and is devoted to changes in the way in which mathematics competitions have been conducted in Russia in recent decades. Mathematics competitions, like mathematics education as a whole, are seen as part of a social process, and changes in them are seen as expressions of new social needs and possibilities. The analysis of the system of competitions, as it evolved in the USSR, and the literature devoted to them, makes it possible to identify certain challenges recognized by the mathematics community. In this paper I discuss examples of new competitions that have emerged to address these challenges. It is noted that new types of competitions have emerged, including team competitions and competitions involving mass participation by students. Also discussed is the emergence of new competitions with subject matter closer to that of ordinary school mathematics than that of old, traditional competitions. An analysis of the situation in Russia reveals the existence of a significant group of mathematics educators, parents, and children interested in the development of mathematics competitions. Also, in the paper I call attention to certain questions that I consider worthy of further study. [ABSTRACT FROM AUTHOR]

After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) normal. However, after the period of mostly teaching online, there is uncertainty about the extent to which we will return to the way we were teaching before. In this survey paper we attempt to give some background to the impact that emergency remote teaching may have had on teaching mathematics. We examine the possible social implications and then focus on the changing mathematics classroom, focusing on the actual mathematics curriculum, learning design and assessment, the role of collaborative activities and social media, educational videos, and the role of family and parents in future. There are indicators from the literature that educators may not return to the traditional way of teaching entirely, especially in secondary and higher education. We conclude with describing some possible new research areas that have developed through emergency remote teaching, including online education for younger learners, local learning ecosystems, the role of family and parents, instructional design, and the mathematics content of curricula. [ABSTRACT FROM AUTHOR]

It is commonly known that the letter M in the two acronyms HPM and STEM stands for mathematics, and it is natural to regard mathematics as playing a significant role in science education. However, it seems that appropriate attention is not usually accorded to the role of M in the area of STEM where mathematics tends to be marginalized. In fact, throughout history one witnesses STEM at work so that the discussion of HPM and STEM in parallel will be beneficial to both. In both the historical and pedagogical aspects, it may be worthwhile to note that history of mathematics affords some means to mirror several different mathematical worlds in the context of HPM in a pluralistic way in order to offer a fuller view of the subject. In this paper I examine this issue through sampling many examples gleaned from the history of mathematics, particularly the role of M in the world of science and technology. [ABSTRACT FROM AUTHOR]

This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020–4) of ZDM Mathematics Education. The research covers the broad spectrum of educational research focusing on different content and methods in teaching and learning mathematics among the youngest children in the educational systems. Particular focus in this paper is directed to what lessons can be drawn from teaching interventions in early childhood, what facilitates children's mathematical learning and development, and what mathematical key concepts can be observed in children. Together, these themes offer a coherent view of the complexity of researching mathematical teaching and learning in early childhood, but the research also brings this field forward by adding new knowledge that extends our understanding of aspects of mathematics education and research in this area, in the dynamic context of early childhood. This knowledge is important for future research and for the development of educational practices. [ABSTRACT FROM AUTHOR]

Engaging students in processes of mathematizing and active knowledge organization (instead of telling and rehearsing ready-made mathematics) is a key demand for high quality mathematics instruction. Although many mathematically rich context problems have been designed and published in textbooks, their impact on regular mathematics classrooms remains limited, as teachers face challenges in shaping and enacting the important phase of knowledge organization. The 15-year project KOSIMA presented in this paper was aimed at supporting teachers in really enhancing these processes by means of a textbook for Grades 5–10. The paper provides an overview of different studies conducted during the project in order to show how the project developed a research base for the support of teachers. The paper also shows that different research approaches need to be combined to establish an appropriate research base: In iterative design research cycles of topic-specific didactical design research, learning environments were designed and investigated with the aim of understanding the obstacles encountered in implementing the desired processes. In this paper, we focus on an example of one particular obstacle, namely, teachers' need of support in engaging students in processes of active knowledge organization. This obstacle was overcome by developing new types of tasks for active knowledge organization. The theoretical outcome of the design research resulted in two hypotheses for improving relevant features of the design of these tasks, which were tested in two controlled trials. Finally, a longitudinal field study of 312 students gave first indications that the classes that worked with the textbook had significantly higher learning gains than classes using other textbooks. In sum, we can show that textbooks can support changes in classroom practices when the obstacles that occur for both teachers and students are carefully investigated and treated. [ABSTRACT FROM AUTHOR]

This paper concerns the relationship between research and governance policy in three Swedish major development projects in mathematics education: the New Math project (1960–1975), the PUMP project (1970–1980), and the Boost for Mathematics project in (2012–2016). All three projects were driven or financed by the Swedish central school authorities. Using a historical comparative method, this study deepens the understanding of how research co-exists with governance policy when preparing innovations in mathematics education. The main historical sources are official reports and governmental decisions concerning the three projects. The analysis is focused on the nature of the innovations of each project and the role of researchers in the process of creating the innovations. The analysis highlights the theories and the methods involved in those processes. The three projects are also positioned in a context of school governance policy. In Sweden, the prevailing school governing policy changed from a highly centralised governance in the 1960s to a highly decentralised governance in the 2010s. The paper concludes by discussing to what degree the researchers adhered to principles of research or school governance; in particular, the Boost for Mathematics project is considered in this regard. The relevance of the paper in relation to the emerging field of implementation research in mathematics education concerns how historical studies can give new insights about contemporary development projects in mathematics education. [ABSTRACT FROM AUTHOR]

Language is a source of power that preserves the status quo in its relationships with learners and mathematics. However, there is a dearth of research that examines how multiple systems of power (e.g., racism, cisheteropatriarchy, colonialism) shape variation in structural inequality and experiences of oppression for language learners. This conceptual paper argues that intersectionality is a promising analytical lens to advance interdisciplinary research on language in mathematics education that nuances knowledge about linguistic justice for racially minoritized and Indigenous learners. To develop this argument, we present insights from a scoping review of research in language education and mathematics education. Our review shows how intersectional analyses can interrogate inequities of language in mathematics education contexts, which are entrenched in ideologies of neutrality that leave exclusionary practices of teaching and learning unchecked. The review also depicts how uptake of intersectionality extends sociopolitical research on language in mathematics education that left interplay between racism, colonialism, linguicism, and other power systems unexamined for nuanced insights on linguistic justice. Following the review, we look across three cases of research studies from our review that vary in terms of their designs and methodologies to illustrate the analytical possibilities of intersectionality in future research on language in mathematics education. We conclude with a discussion of how adopting the lens of intersectionality is necessary to advance interdisciplinary scholarship for linguistic justice. [ABSTRACT FROM AUTHOR]

In this paper we consider implications of the current world-wide inclusion of computational thinking in relation to children's development of algebraic thinking. Little is known about how newly developed visual programming environments such as Scratch could enhance early algebra learning. The study is based on examples of programming activities used by mathematics teachers in Sweden, teaching students aged 10–12 years during the first two years of implementing programming in the mathematics curriculum. Informed by Chevallard's praxeology in terms of praxis and logos, we describe, unpack, discuss and expand these activities. Core issues related to algebra found in the three activities are as follows: making implicit variables explicit; using a counter variable; and identifying parameters as a specific type of variable. Our findings show that, in addition to already identified uses of variables in early algebra, programming activities in the early years bring in new aspects and new ways of treating variables that could, potentially, enhance students' understanding of variables and generalization, provided that programming praxis is embedded in an appropriate algebra logos. [ABSTRACT FROM AUTHOR]

In this paper, we consider mathematical competitions for pre-university students, such as the International Mathematical Olympiad (IMO) and many national and regional Olympiads following a similar model. The problems proposed in these contests must be solvable by 'elementary' methods (i.e., without using calculus) and belong traditionally to four areas, namely, algebra, combinatorics, geometry, and number theory. Usually there is no explicit curriculum prescribing what parts of these subjects may be involved in the problems, however there is a hidden curriculum (HC) that may be deduced from the problems proposed and from what is considered a complete solution. In this paper, we try to characterize this HC showing typical problems, subjects, solutions, and strategies for each of the main areas. We also make a comparison of the HC with the traditional secondary school curriculum (SSC), with the following two goals: (1) to identify the main points that should be addressed in the preparation of students aspiring to participate in mathematical competitions, and (2) to suggest possible changes to it and diminish the gap between school and contemporary mathematics. [ABSTRACT FROM AUTHOR]

Mathematical competitions feature in most developed countries as a part of the secondary school experience, but to a lesser extent in developing countries. In this paper we investigate how widespread these competitions are in Africa, both historically as well as currently, focussing both on national Olympiads and on the participation of African countries in competitions beyond their borders, such as the continent-wide Pan African Mathematical Olympiad and the global International Mathematical Olympiad. Since we could not find a consolidated source of information on African competitions, we include many details and links, hoping that this paper will serve as a valuable starting point for future investigators. Next, we present some survey findings on the attitudes towards and experiences of mathematical competitions, both from the perspective of teachers in secondary schools as well as from secondary school students, and whether these experiences have served to improve or degrade their perceptions of mathematics in general. Among other results, we find that teachers view their students' participation in mathematics competitions as being important, with the biggest barrier to participation being that there are not enough competitions at appropriate levels available, and that students enjoy mathematics competitions and are more likely to pursue a STEM career because of them. Finally, we present some suggestions on how this research may be taken further, and on how the state of mathematical competition culture in Africa may be improved. [ABSTRACT FROM AUTHOR]

This paper conceptualizes children's mathematical thinking from a materialist perspective on language and mathematics. This perspective considers human and non-human bodies as ontologically equivalent; that is, as both being agentive, vibrant, and animated, thus resisting static representations. This conceptualization is an alternative to the interactionist and language-based models that have dominated research in language and mathematics. This conceptual approach informs the paper's non-hierarchical analysis of a bilingual classroom studying the concept of equivalent fractions. The non-hierarchical nature of this analysis permits a dynamic shift of focus from learners to materials to mathematical concepts. This non-traditional analysis informs the paper's final discussion regarding the nature of children's mathematical thinking. The discussion highlights how working outside language-based interactionist models provides an alternative view of children and artefacts as equal partners working within and as part of the vibrant boundaries between matter and meaning. [ABSTRACT FROM AUTHOR]

Teacher noticing has become increasingly acknowledged as a fundamental aspect of teacher professional competence. Teacher education scholars have examined how the development of noticing might be supported both in initial teacher education and in professional development. In mathematics teacher education, several studies have explored the use of video as a supporting tool for teacher noticing. It remains unclear how this body of work builds on the various theoretical perspectives of noticing prevalent in the literature, thus broadening our understanding of noticing. Furthermore, the field has not examined systematically the extent to which research has leveraged the affordances of digital video technologies, and whether scholars have employed different research methods to answer questions that are critical to teacher educators. This survey paper reviews studies published in the last two decades on programs centered on mathematics teacher noticing that used video as a supporting tool for teacher learning. Thirty-five peer-reviewed papers written in English were identified and coded along three dimensions: (1) theoretical perspectives; (2) use of video technologies; and (3) research questions and methods. This review summarizes important findings and highlights several directions for future research. Most studies involved pre-service teachers, and only a few centered on in-service teachers. Developers of the large majority of programs took a cognitive psychological perspective and focused on the attending/perceiving and interpreting/reasoning facets of noticing. Few studies used video-based software and few studies used grouping, and even fewer used randomized grouping. Evidence of program effects on responding and decision making, and on instructional practice, is limited and should be extended in the future. [ABSTRACT FROM AUTHOR]

Properties of arithmetic operations are important in mathematics and play a significant role in elementary school students' learning of mathematics. At the same time, it is quite challenging to help students learn arithmetic operational properties beyond memorization, so that they know when and how to use a specific arithmetic property. This paper reports a study containing two parts to explore students' learning of the Commutative Property of Addition (CPA) as related to the content presentation in textbooks. Part one is to assess selected students' performance on CPA at the end of Grade two, and part two is to explore possible contributions of textbooks to students' performance in Shanghai. Firstly, we evaluated the performance of 41 second-graders on CPA by collecting data through a paper-and-pencil test, which was followed up with individual interviews. Through analyzing how textbooks present and organize this topic, we sought to better understand from a curriculum standpoint how students' performance on CPA is impacted by textbooks. Results revealed that Shanghai textbooks make a positive contribution to students' learning performance. The findings from this study help to shed light on how those textbooks aid student learning, and provide an example for further reflection on student learning of arithmetic operational properties in different curricula. [ABSTRACT FROM AUTHOR]

Identity research in mathematics education has become increasingly prominent over the past two decades. In the last few years, there have been several reviews of identity literature in the field of mathematics education generally, or specifically focused on mathematics learner identities or mathematics teacher identity. We begin our paper by summarizing the key findings of these reviews, pointing to various categorizations proposed by their authors, and the key critiques raised therein. We then report on our more recent review of identity literature in mathematics education published in the top twenty mathematics education journals over the past 5 years (47 articles in total). This review enables us firstly to speak descriptively about the extent to which the field is evolving (or not) in relation to earlier findings (dominant regions, focus of research, methods and perspectives used). Secondly, following deeper analysis of the papers, we speak to the way in which the field is addressing (or not) key critiques raised by reviews. Our analysis points to several theoretical, methodological and empirical absences and challenges requiring further engagement. We further highlight key absences in the research, particularly a lack of cross-national comparative studies and studies that connect learner and teacher identities. We then provide a summary discussion and analysis of the contributions of the present special issue papers and engage with how these take the field forward. Finally, we engage with the implications of our analysis and recommendations for future directions for research. [ABSTRACT FROM AUTHOR]

This paper examines how different approaches in mathematics education conceptualise the relationship between school mathematics and university mathematics. The approaches considered here include: (a) Klein's elementary mathematics from a higher standpoint; (b) Shulman's transformation of disciplinary subject matter into subject matter for teaching; and (c) Chevallard's didactic transposition of scholarly knowledge into knowledge to be taught. Similarities and contrasts between these three approaches are discussed in terms of how they frame the relationship between the academic discipline and the school subject, and to what extent they problematise the reliance and bias towards the academic discipline. The institutional position implicit in the three approaches is then examined in order to open up new ways of thinking about the relationship between school mathematics and university mathematics. [ABSTRACT FROM AUTHOR]

Internationally, questions about the perceived utility of university mathematics for teaching school mathematics pose an ongoing challenge for secondary mathematics teacher education. This special issue is dedicated to exploring this topic and related issues in the preparation of secondary mathematics teachers—by which we mean teachers of students with ages, approximately, of 12–18 years. This article introduces this theme and provides a semi-systematic survey of recent related literature, which we use to elaborate and situate important theoretical distinctions around the problems, challenges, and solutions of university mathematics in relation to teacher education. As part of the special issue, we have gathered articles from different countries that elaborate theoretical and empirical approaches, which, collectively, describe different ways to strengthen university mathematics with respect to the aims of secondary teacher education. This survey paper serves to lay out the theoretical groundwork for the collection of articles in the issue. [ABSTRACT FROM AUTHOR]

In the Hungarian "Guided Discovery" approach to teaching mathematics, teachers' planning work plays a crucial role. Teachers following the approach develop teaching trajectories based on "series of problems". This work includes the choice, creation, transformation, organization and networking of problems with regard to various teaching objectives. However, most of this planning work remains implicit; the structure and rationale of the teaching trajectories are often inaccessible for an external observer (including, for example, student teachers). An ongoing project based on teacher–researcher collaboration aims to reveal the hidden characteristics and principles of teachers' work with series of problems through the creation of innovative resources for teachers. In this paper, we present the design of this collaborative work, a process we designate "reverse engineering", and analyse the development process of resources, focusing particularly on the emergence of new vocabulary and representation tools serving as mediators in the communication between teachers and researchers. [ABSTRACT FROM AUTHOR]

This paper introduces two central questions (1) what are available methodologies for making claims about mathematical practice and (2) when and how do claims about mathematical practice influence mathematics instruction. To motivate these questions, we critically analyze the relationship between research into mathematicians' practice and the design of mathematics instruction in three ways. First, we describe three influential research programs in mathematics education and illustrate how each research program uses claims about mathematical practice to inform their instructional goals. Second, by examining these important works, we highlight intrinsic difficulties in investigating mathematical practice. Our conclusion is that every research methodology for investigating mathematical practice is fundamentally limited and we require triangulation from multiple methods and theoretical lenses to fully understand mathematical practice. Third, we highlight reasons for why mathematical practice sometimes should not inform mathematics instruction. We conclude this paper by discussing how the articles in this special issue address our two central questions. [ABSTRACT FROM AUTHOR]

Attempts to better conceptualize and measure teacher knowledge, and through that examine its association to instructional quality have been intensified over the past decades. Despite the progress made, a review of pertinent literature points to four challenges related to studying this association: proximity (i.e., the extent to which the measures of teacher knowledge and instructional quality are proximal to the actual work of teaching); alignment (i.e., the degree to which these measures are aligned to each other); comparability (i.e., the extent to which the instructional interactions and milieu are comparable across the lessons investigated and the degree to which the conceptualization, operationalization, and measurement of teacher knowledge are comparable across studies); and occurrence (i.e., the degree to which instructional settings provide the possibility for certain events to occur to study how teacher knowledge plays out in instruction). Teaching simulations that allow for the investigation of teacher action-related competence—a construct occupying the intermediate space in between static aspects of teacher knowledge and instructional quality—can partly address these challenges. In this paper, I present such a teaching simulation and explain how it can support the capture of teacher action-related competence, by manipulating instructional complexity and providing a productive platform for performing the work of teaching in controlled environments. I partly illustrate the potential of this approach for disentangling and unpacking the focal association, by presenting results from an exploratory study examining the association between preservice teachers' paper-and-pencil mathematical knowledge for teaching (MKT) and their action-related competence yielded by studying their performance in the simulation. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the following question: How do students use mathematics in modeling activities? With this purpose, the paper reports on mathematization and use of mathematics, and deals with empirical data with focus on modeling activities performed by students in the first year and in the fourth year of a degree in mathematics. After the description of a theoretical framework of modelling, what can be seen by means of a qualitative analysis is that the perception of messy world situations leads to idealization, and the idealized situation acts as the basis for mathematization in each activity. The mathematization in turn leads to different mathematics concepts, tools and procedures. The use of mathematics that students perform is anchored in their previous experiences, be it in their experiences with the concepts and tools of mathematics, or in their experiences with mathematical modeling practices. Besides that, after this process students have advanced and have expanded their knowledge and made significant progress by means of a balance between teacher guidance and students’ independence. Moreover, beyond mathematical knowledge, the research indicated that success in performing modeling activities also requires knowledge-based mathematical modeling anticipation. [ABSTRACT FROM AUTHOR]

The political changes in the USSR and Russia almost coincided with the beginning of an unprecedented leap in the development of information technologies in the country (and to a certain extent spurred it). Gradually, many different initiatives emerged to apply these technologies in education in general, and in mathematics education. In the paper, we discuss several examples of didactical innovations in teaching and learning mathematics with technology, namely, LOGO-based microworlds, dynamic geometry and computer algebra systems, as well as verifiers. The examples we provide, along with the theoretical perspective of productive learning and thinking, seem to demonstrate the innovative potential of new tools to make learning more visual, dynamic, and interactive. However, the issues of aligning with curriculum and standard examinations, teacher professional development, and rapid changes in technologies, require more attention by mathematics educators. The presence of such opposite trends makes the task of analyzing the history of the development of mathematics teaching technologies and underlying pedagogies relevant and important for predicting the development of this field in the near (and far-extended) future, and eventually preventing the repetition of errors in this new direction for mathematics education. In the paper we focus primarily on problems and processes in Russia, but they are investigated in connection with and against the backdrop of global trends. [ABSTRACT FROM AUTHOR]

Over the last decades, digital technologies (DTs) have become ubiquitous in mathematics education. Still, their integration into classroom teaching and learning varies enormously. In this narrative overview, we focus on the different purposes for which DTs are used in mathematics education in order to study how the effectiveness of DTs depends on researchers' underlying goals and perspectives. We set up an experience- and literature-based framework including five different purposes. Applying this framework gave rise to the following results: (1) there is evidence for the benefit of using DTs for mathematics learning; (2) research on DTs leads to new theoretical developments and (3) to new design paradigms; (4) issues of equity with respect to access to and use of DTs are important but under-researched; and (5) DTs challenge curricula and teaching and assessment practices. While early research on the use of DTs focused on questions such as "does it work?" or "does it work better?", the maturing of the field has shifted to more nuanced questions. As a future research agenda, we recommend further study of how the use of DTs in mathematics education impacts the time required for learning as well as the temporality of teaching and learning, how it changes the nature of doing mathematics and the relation to basic skills and higher-order skills in particular, how curricula, teaching practices, and assessment might change due to the availability of sophisticated mathematical tools, how DTs and other resources might be combined in teaching and learning, and how they may help to address equity issues in education. These questions will prompt the development of new theoretical constructs and approaches. [ABSTRACT FROM AUTHOR]

In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers' influence on the implementation of change through curriculum resources; (4) Students' influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers' teaching nor students' learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs. [ABSTRACT FROM AUTHOR]

In this paper we report on a survey study of teachers' perceptions of how mathematics textbooks, including broadly student books, teacher manuals, and exercise books, facilitate or hinder teachers' teaching in Shanghai educational settings. For the study we established a conceptual framework about teachers' teaching, partly drawing on Shulman's model of pedagogical reasoning and action of teachers. The data were collected from a stratified random sample of 133 mathematics teachers in 13 secondary schools through a questionnaire, and follow-up interviews with 24 of them. The results revealed the following: the textbooks were highly regarded and used by the Shanghai mathematics teachers as facilitators rather than barriers for their teaching and instructional change, and the facilitation was most evident in the process of transformation and comprehension, and least evident in evaluation in teachers' pedagogical reasoning and action; compared with student books and exercise books, teacher manuals played a larger facilitating role in teachers' teaching; and finally, compared with teacher characteristics, school characteristics had a greater influence on the extent to which textbooks played a role of facilitation or hindrance for teachers' instructional practice. Implications and suggestions are given at the end of the paper. [ABSTRACT FROM AUTHOR]