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.

We report on a group theory activity in which learners explored dihedral symmetries through a tangible geometric model. This approach has historical roots in the work of Felix Klein's Erlangen Program and his . We situate our study with respect to this history as well as current educational research in spatial visual reasoning, abstract algebra, and teacher knowledge. Our findings highlight opportunities that tangible geometric models can provide for fostering structural and interconnected understanding characteristic of teachers' .

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.

This article proposes an interconnected framework, , which addresses cognitive processes that facilitate learning, problem solving, and interdisciplinary concept development. The framework comprises critical thinking, incorporating critical mathematical modelling and philosophical inquiry, systems thinking, and design-based thinking, which collectively contribute to adaptive and innovative thinking. It is argued that the pinnacle of this framework is learning innovation, involving the generation of powerful disciplinary knowledge and thinking processes that can be applied to subsequent problem challenges. Consideration is first given to STEM-based problem solving with a focus on mathematics. Mathematical and STEM-based problems are viewed here as goal-directed, multifaceted experiences that (1) demand core, facilitative ways of thinking, (2) require the development of productive and adaptive ways to navigate complexity, (3) enable multiple approaches and practices, (4) recruit interdisciplinary solution processes, and (5) facilitate the growth of learning innovation. The nature, role, and contributions of each way of thinking in STEM-based problem solving and learning are then explored, with their interactions highlighted. Examples from classroom-based research are presented, together with teaching implications.

Much of the mathematics that children experience in school neglect the skills increasingly needed for citizenship, particularly the power of complex data to investigate and make sense of the world. We draw on the relatively new field of data science as a multi-disciplinary approach to investigate problems through analysis of massive, non-standard, incongruous and/or messy data. Our exploratory qualitative study had as its research question: What can children learn about citizenship when they engage with data science? The case study in this paper illustrated ways that children's learning about citizenship were enriched through an age-appropriate data science investigation. The study analysed classroom video from a Year 4 classroom (aged 9-10) over six lessons that integrated curricula in digital technologies, health, and mathematics. In these lessons, the children generated and analysed non-standard data and debated social, well-being and privacy issues as they considered their activities in cyberspace. The video data were analysed using a framework based on critical citizenship education literature that examined dimensions of power, collective engagement, individual responsibility and action. Three key findings emerged. First, the case study highlighted skills in citizenship education developed through data science, positioning children as agents and advocates. Second, the study showed how a complex data investigation in citizenship education was achievable with primary children through meaningful curriculum integration. This is important given that problems that citizens address are typically interdisciplinary. Finally, the findings revealed a gap between data science skills and those developed in the mathematics curriculum, and recommend ways that the maths curriculum could be updated.

Assessments, in particular high stakes assessments, impact the nature of teaching and learning. Given this, the goal of citizenship if seen as important needs to feature within high stakes school exit assessments rather than only as part of curriculum and assessment policy rhetoric. South Africa's Mathematical Literacy (ML) curriculum foregrounds critical democratic citizenship. We analyse the ML Grade 12 exit assessments from their start in 2008 to 2020 to understand the emphasis placed on critical citizenship and how this emphasis has shifted over time. The literature base links critical citizenship orientations with reasoning and reflecting questions, so we focused on examination questions in this category. Our findings show shifts away from critical citizenship related agendas towards foregrounding a life preparation orientation for the self-managing person. Linked with this shift, we note a move away from general societal contexts towards more personal/individual contexts and moves from almost entirely national contexts to inclusion of global contexts. We noted movement from more open-phrased questions towards closed 'check figure calculated is valid'-type questions. Assessment memoranda suggest assessors view these questions as reasoning items, eroding the critical citizenship agenda. While increasing numbers of students are taking ML rather than Mathematics, average performance stands at around 40%. This points to limited and diminishing access to mathematical reasoning and reflecting for critical democratic citizenship. The paper highlights ways in which analysis of examinations over time can provide a window into the presence or absence of the citizenship agenda in mathematics education.

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary decisions and policies which do, in fact, affect society as a whole. The mathematical tools that are used derive from nonlinear systems of difference equations (possibly viable at a high school level, using spreadsheets or adequate software) as well as nonlinear systems of ordinary differential equations (therefore using mathematical tools and software well within the reach of undergraduate students of many courses). This purpose is accomplished by motivating students and learners to study existing SIR-type models and modifying them in order to have a fully understandable translation of dynamics for infectious diseases such as COVID-19 in several different realistic scenarios, that is to say, situations that consider social distancing policies, widespread vaccination programmes, as well as possible and even probable results when in the presence of negationist postures and attitudes. Several modelling choices referring to real-life situations are shown and explored. These models are analysed and discussed, implicitly proposing similar attitudes and evaluations in learning environments. Conclusions are drawn, stimulating further work using the described mathematical tools and resources.

The mathematical medium of data visualization and other data representations (DV) has served as a primary means of communicating about the COVID-19 crisis. DVs about the pandemic are highly visible across news journalism and include an increasingly innovative and diverse set of representational forms. These representational forms employ multimodal, interactive, and narrative elements, among others, that create new possibilities for data storytelling. Building on current efforts to expand the teaching and learning of data practices in K-12 mathematics education, we argue that innovative DVs create new opportunities for teaching and learning mathematics, particularly during times of crisis. We illustrate our argument using three examples of innovative DVs from news journalism. We discuss how these DVs could serve as complementary resources alongside conventional graphs to support students as they use mathematics and mathematical representations to make sense of crises such as the COVID-19 pandemic. Our commentary seeks to bring current trends in data representation to bear in mathematics education. Leveraging such trends offers artifacts useful for teaching and opens up space for elevating emotion and experience as important aspects of mathematics curricula.

[This corrects the article DOI: 10.1007/s11858-022-01447-2.].

Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Our contribution has the aim of showing that basic mental models about exponential growth are important for understanding media reports of Covid-19. Furthermore, we highlight how the coronavirus pandemic can be used as a context in mathematics classrooms to help students understand that they can and should question media reports on their own, using their mathematical knowledge. Therefore, we first present the role of mathematical modelling in achieving these goals in general. The same relevance applies to the necessary basic mental models of exponential growth. Following this description, based on three topics, namely, investigating the type of growth, questioning given course models, and determining exponential factors at different times, we show how the presented theoretical aspects manifest themselves in teaching examples when students are given the task of reflecting critically on existing media reports. Finally, the value of the three topics regarding the intended goals is discussed and conclusions concerning the possibilities and limits of their use in schools are drawn.

In this paper, we discuss the theoretical background of mathematical modelling and its connection to citizenship education. Citizenship education in this context means that young people are equipped with competencies to respond as responsible citizens in situations relevant for society. To outline the connection between mathematical modelling and citizenship education in theory, we discuss the aims of mathematical modelling, modelling competences and the connection between numeracy and modelling. Based on these reflections we present an extended modelling cycle that specifically highlights modelling steps relevant to citizenship education. To show how the theoretical connection between mathematical modelling and citizenship education can be used in teaching practice, we describe three different examples of modelling tasks and analyse them with the help of the extended modelling cycle. We argue that the three tasks support different learning aims in relation to citizenship education and require modellers to carry out different steps of the extended modelling cycle. As an example of context, we used the pandemic caused by COVID-19, as it affected the quality of human life greatly, as all students in the Western world experienced.

Emotions and motivation are important for learning and achievement in mathematics. In this paper, we present an overview of research on students' emotions and motivation in mathematics. First, we briefly review how early research has developed into the current state-of-the-art and outline the following key characteristics of emotions and motivation: objects, valence, temporal stability (vs. variability), and situational specificity (vs. generality). Second, we summarize major theories in the field (the control-value theory of achievement emotions, expectancy-value theory of achievement-related motivation, self-determination theory of human motivation, and social-cognitive theory of self-efficacy). Third, we present an overview of instructional characteristics that have been shown to foster emotions and motivation. Fourth, we provide an overview of the contributions to the special issue on "Emotions and Motivation in Mathematics Education and Educational Psychology." Finally, we suggest directions for future research in the field with respect to advancing theory, improving measurement, and considering diversity and inclusion.

The research on which we report in this paper was framed within the socioepistemological theory and dealt with the fundamental role of variational practices in the understanding of COVID-19 pandemic graphs. Given the proliferation of mathematical graphs related to the pandemic in the media, we proposed to analyse the variational practices in use in the interpretation of graphs of exponential behaviour that a Chilean newscast of high rating used to inform the population about the pandemic in Chile. For this purpose, a thematic analysis intertwined with documentary analysis techniques was carried out, in order to describe the types of graphs shown in the newscast, and a variational reference system was studied to analyse the use of variational practices. To obtain our results, the types of graphs most frequently shown in the newscast at the beginning of the pandemic were identified and the use of the variational practices of and in such graphs was analysed. In conclusion, the need is discussed for the conceptual evolution of the exponential function to be accompanied by a pragmatic evolution in school that favours the use and development of variational practices in the student body.

This paper introduces this special issue aiming to deepen and extend research on mathematics teachers' work, from a resource perspective, by taking language and culture into account, and exploring two questions: How are teachers' interactions with resources interpreted and modeled across contexts? And, What challenges and insights emerge through recent efforts to engage these models in cross-cultural (and linguistic) research? The fields of resources, language and culture in mathematics education are each extensive, and we do not attempt to survey comprehensively across them. We have chosen instead to propose three approaches on resources in mathematics teachers' work that developed somewhat contemporaneously from three different countries with differing linguistic, curricular, and social contexts, corresponding to the work of the three guest editors. The models developed through these approaches are driven by the educational, and so cultural and material conditions of the time and the location of each author, and allow us to propose preliminary answers to our two guiding questions. We then move to pull the threads from these models together, and discuss the contributions to this Special Issue. This results in more robust and nuanced responses to our questions, and in identifying two themes that emerge from research that sit at the convergence of studies of teachers' interactions with resources, languages, and cultures: an invisibility-visibility dialectic and a local-global tension. Finally, this study leads us to consider a new region of mathematics education research.

Understanding the structure, antecedents, and outcomes of students' emotions has become a topic of major interest in research on mathematics education. Much of this work is based on the Achievement Emotions Questionnaire-Mathematics (AEQ-M), a self-report instrument assessing students' mathematics-related emotions. The AEQ-M measures seven emotions (enjoyment, pride, anger, anxiety, shame, hopelessness, boredom) across class, learning, and test contexts (internal structure). Based on control-value theory, it is assumed that these emotions are evoked by control and value appraisals, and that they influence students' motivation, learning strategies, and performance (external relations). Despite the popularity and frequent use of the AEQ-M, the research leading to its development has never been published, creating uncertainty about the validity of the proposed internal structure and external relations. We close this gap in Study 1 ( = 781 students, Grades 5-10, mean age 14.1 years, 53.5% female) by demonstrating that emotions are organized across contexts and linked to their proposed antecedents and outcomes. Study 2 ( = 699 students, Grade 7 and 9, mean age 14.0 years, 56.9% female) addresses another deficit in research on the AEQ-M, the lack of evidence regarding the assumption that emotions represent sets of interrelated affective, cognitive, motivational, and physiological/expressive components. We close this gap by evaluating extended AEQ-M scales, systematically assessing these components for five core mathematics emotions (enjoyment, anger, anxiety, hopelessness, boredom). Our work provides solid grounds for future research using the AEQ-M to assess emotions and their components in the domain of mathematics.

When the COVID-19 pandemic began, many universities switched to fully online teaching. This unexpected switching to online teaching was challenging for both teachers and students, and restrictions that were put in place because of pandemic made this challenge even greater. However, new ways of teaching might also open new opportunities for students' learning. The research question driving our study was as follows: how do students regulate their learning and specifically their choice of resources and peer learning in university mathematics classes that are fully taught online as offered during the COVID-19 pandemic? We report on a longitudinal, qualitative study in which students recorded a brief audio diary twice a week over one whole semester (14 weeks). We focused on three students who completed 70 interviews in total and finished the semester with varying degrees of success. The results show how the students structured their studying (e.g., the roles that deadlines or synchronous teaching events played). They illustrate the strengths and limitations of digital materials provided by the lecturer and the use of complementary media. Further, the pandemic uncovered the double-edged role of simple, often anonymous exchanges (e.g., via Discord servers), with few binding forces for either side, and the significance of stable learning partnerships for students' success. Our research highlights aspects that should be focal points when comparing traditional instruction and online instruction during the pandemic from a self-regulatory perspective. Practical implications refer to how these aspects can be combined sensibly in fully online courses, but also in blended learning contexts.

After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) . 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.

While classical studies have highlighted the many potential benefits of using original historical sources in the classroom, few studies have documented actual classroom practices outside of research contexts. In this case study, I aim to describe and explain how five French high school teachers autonomously designed and implemented classroom sessions starting from the same document, namely an excerpt from Euler's presenting an algorithm for square root approximation. From a methodological viewpoint, it enables me show how two general frameworks for the study of teachers' professional practices-the Documentational Approach to Didactics and the Didactic and Ergonomic Double Approach-can be tailored to fit the specific challenges of using historical sources. The empirical results provide fresh insights into the conditions for a mathematically rich use of historical sources in the classroom, and on the connections between this use and the integration of a historical perspective in the teaching of mathematics.

Due to the COVID-19 pandemic, educational institutions at all levels closed their doors and began to operate remotely. In this paper, we analyze the educational experiences of preservice mathematics teachers (PMTs) enrolled in mathematics teacher education programs from three South American universities, as the pandemic was unfolding. An exploratory study was conducted, based on an inductive and thematic qualitative text analysis of narratives written by 24 PMTs. Based on the study, we report on the following aspects: (1) experiences of PMTs in the passage to remote education (RE) mode (considering characteristics of remote classes-interactions, the rhythm of the class, teaching work-time management, home-classroom fusion, and physical and psychological discomfort), and (2) opportunities and limitation experienced by PMTs in relation to the use of technologies. The results of the study suggest the need to rethink teacher education programs regarding the integration of technologies in mathematics classes, the opportunities offered by hybrid education, and teacher education for distance teaching.

In March 2020, many schools worldwide were closed due to the COVID-19 pandemic. This closure confronted mathematics teachers with the challenging transition to emergency remote teaching (ERT). How did students experience ERT, and how did these experiences relate to context variables and to their teachers' beliefs and practices? In particular, what didactic approaches and formative assessment practices did secondary mathematics students experience, and which beliefs did they hold concerning digital mathematics education? How were these student experiences and beliefs related to student context variables (gender, need to support family, personal home equipment), teacher beliefs, delivery modes, and student appreciation of mathematics? To investigate these issues, we set out online questionnaires for mathematics teachers and their students in Flanders-the Dutch-speaking part of Belgium-, Germany, and the Netherlands. Data consisted of completed questionnaires by 323 mathematics teachers and 2126 of their students. Results show that even though students preferred regular face-to-face teaching, they were content with the quality of their teachers' distance mathematics teaching. Students reported that they were taught new topics often, but did not experience teachers initiating peer feedback. High student appreciation of mathematics, good home environment, and more synchronous delivery of ERT were related to ERT experiences and more positive beliefs concerning digital mathematics education. These findings have implications for ERT teaching strategies in future, as well as for hybrid teaching practices.

Based on an opportunity-use model of instructional quality, this study investigates the extent to which subject-specific instructional quality rated by experts is reflected in students' assessments of their own learning and understanding, and how students' perceptions predict their achievement. The analyses used data from a German-Swiss sample of 36 classes with around 900 lower secondary students, obtained as part of the so-called "Pythagoras study" in the school year 2002/2003. The teachers were instructed to introduce the Pythagorean theorem in three lessons, which were videotaped. Using the videos, the experts assessed the instruction quality with respect to the goal of promoting a deep understanding of the theorem. The students completed the questionnaires assessing their understanding of the content, their learning process, and the general comprehension orientation of the teacher. The results showed significant and moderate correlations on the class level between expert-rated subject-specific teaching quality and students' perceptions of their own learning and understanding, as well as of the teacher's general comprehension orientation. Multilevel models revealed that subject-specific expert ratings are reflected in individual students' perceptions of their own learning and understanding. Student perceptions were also associated with achievement gains. The results suggest that the assessment of quality by students and experts is more closely linked if a distinction is made between the quality of the learning opportunities offered and their use and if subject-specific criteria are used instead of generic criteria. This study contributes to a more nuanced understanding of the validity of student perspective in assessing instructional quality.