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This paper describes a Lesson Study in which in-service mathematics secondary-school teachers, collaborating with researchers, involve grade 10 students in tessellation problems. The data are collected by an experiment carried out in the context of the "Liceo Matematico" project, with three volunteer teachers. The experiment goal was to craft a collaborative design of the research lesson between teachers and researchers. The research aim of the paper is to examine the use of Lesson Study in the institutional and cultural context of Italian secondary school with the use of Cultural Transposition as a theoretical framework. The research is qualitative with idiographic aims, based on video research. The educational aim of the research is to provide a solid basis for a revamped in-service teacher education first in the context of the project, then in curricular context. Semiotic mediation is used to provide, within Lesson Study, the conceptual framework for teachers and researchers collaborative design of the research lesson. The results show that Lesson Study, as a foreign practice, is an opportunity for teachers to confront their teaching practices, to enrich their professional development, resulting in more awareness on their didactical action in and outside the classroom.

Catering for the mathematical needs of disabled learners equitably and productively requires the anti-ableist preparation and professional development of teachers. In CAPTeaM (Challenging Ableist Perspectives on the Teaching of Mathematics), we design tasks that emulate inclusion-related challenges from the mathematics classroom, and we engage teachers with these tasks in workshop settings. In this paper, we focus on evidence from one type of task in which participants engage in small groups with solving a mathematical problem while at least one of them is temporarily and artificially deprived of access to a sensory field or familiar channel of communication. In this paper, we focus on evidence of emerging resignification -- discursive and affective shifts in the participating teachers' sense-making about what makes the construction of mathematical meaning possible and valuably different -- as they work on the tasks. By linking Vygotsky's vision about the educational changes required to empower and include disabled learners with more contemporary ideas from embodied cognition and disability studies, our analyses show how engagement with the tasks affects participants' realisation and appreciation of interdependencies between learners, teacher, resources, and emotions, highlights alternative forms of mathematical agency and gives opportunities to turn initial sense of impasse and despair into joy.

This paper draws from a broad study that explored mathematics teachers' engagement with textbooks within the Lesson Study context. In the current paper, we report on teachers' use of mathematics textbook activities to inform their instructional decisions during collaborative lesson planning of numeric and geometric patterns. The study took place within the Lesson Study (LS) context -- a teacher development practice that emphasises, inter alia, collaborative lesson planning. Data was collected by observing teachers during collaborative lesson planning and through interviews. Data analysis was informed by the Mathematics Knowledge for Teaching (MKT) framework and Modes of teacher engagement with the textbook. Findings suggest that teachers' instructional decisions are mainly stimulated by the textbooks, teachers use textbook activities with fidelity, and they seldom adapt the activities drawn from the textbooks. However, where adaptation occurs teachers do it superficially. We contend that the capacity to conduct in-depth interrogation of the text is a derivative of mathematics subject matter knowledge (SMK) as well as pedagogical content knowledge (PCK). Therefore, the widespread adoption of text without interrogation could be indicative of the lack of requisite content knowledge and pedagogical skills.

Two-year college mathematics teaching has interesting challenges, and it helps to have a national organization representing the profession that provides professional development, issues position statements on relevant topics, and cultivates leaders. This chapter illustrates how the AMATYC organization provides these services.

It is widely accepted that the classroom teaching practices of in-service secondary mathematics teachers can benefit from the advanced mathematics they learned during their university education. However, pinpointing explicit instances of how this advanced knowledge informs teaching practices has proven challenging for both teachers and mathematicians alike. This paper aims to address this challenge by examining three statements related to Calculus and demonstrating how advanced mathematical knowledge can be utilized to generate counterexamples. By using results encountered in university-level courses, we construct functions that counter these statements. In conclusion, we identify a thought process that can be generally followed in assessing whether a given statement is true, highlighting the explicit connections of advanced mathematics in generating counterexamples via these statements. Similar endeavors of carefully generating counterexamples using advanced mathematics in other areas of mathematics can contribute to the designing of courses for teacher development that aim at explicitly highlighting connections between university mathematics and school mathematics.

While numerous studies have investigated teachers' professional learning through their interaction with resources, the question of how teachers' knowledge evolves at different stages of the instructional process remains underexplored. To address this gap, this article builds on the documentational approach to didactics (DAD) and the theory of instrumental orchestration to investigate teachers' professional learning in terms of document development through their interaction with resources in and out of class. To this end, the paper proposes a theoretical and methodological model to analyze the evolution of a document, focusing on the joint evolution of utilization schemes and professional situations. This model provides analytical tools to track the development of teachers' professional knowledge. The theoretical and methodological model was applied to a case study involving a Tunisian primary school teacher who used the technological resource GeoGebra for the first time to introduce the properties of parallelograms to 6th grade students (aged 11-12). Findings suggest the relevance and operationality of the proposed model, through a short-term analysis of documentational genesis, to track the evolution of the teacher's professional knowledge related to the use of GeoGebra in class. This model can be considered as a theoretical and methodological contribution, deepening the understanding of teachers' professional learning when using technological resources and providing insights into the dynamic nature of teachers' professional knowledge development.

This paper describes and analyzes three cases to show the impact that curiosity-driven (CD) discourse based on self-video can have on the professional awareness and noticing skills of mathematics teachers and instructors of mathematics teachers. The findings indicate that CD discourse raises awareness of heretofore unnoticed events in the lesson, and improves the mathematical and pedagogical knowledge, teaching skills, and efficacy of teachers and instructors. This study combines pedagogical content knowledge (PCK) of teachers with Mason's "levels of awareness" model in studying, from an epistemological point of view, the contribution that CD discourse makes to growth of professional awareness in mathematics teachers and instructors. Thus, this study contributes to the theoretical and practical understanding of the growth of mathematics teachers as teachers and as teacher instructors, in their professional awareness, noticing skills, and attention shifting.

Mathematical modeling (MM) -- a cyclical process that involves using mathematics to make-sense of and analyze relevant, real-world situations -- has the potential to advance equity and challenge spaces of marginalization in the elementary mathematics classroom. When informed by culturally responsive teaching practices, MM creates opportunities to center the knowledge and experiences that students from diverse racial, cultural, and linguistic backgrounds bring to the classroom as valuable resources to support learning and inform action. It can disrupt power and status hierarchies in the classroom that contribute to structural and ideological marginalization. This paper describes ways teachers connected their teaching of MM with key components of a culturally responsive mathematics teaching framework. Analysis synthesizes data from an innovative, research-based professional development for elementary teachers to support teacher learning of equity-centered, culturally responsive MM instruction. Data sources include end of year teacher interviews, and professional development discussions from 19 teachers at four geographically, racially, and culturally diverse sites. Findings focus on how teachers connected their teaching of MM with key dimensions of culturally responsive mathematics teaching, and affordances and challenges related to resisting ideological and structural forms of marginalization.

Globally, there is considerable investment in education technologies leading to increased attention from stakeholders (Trucano, 2017). For a deeper understanding about the implementation of various technologies, research is needed to examine how teachers are incorporating them in teaching and learning. This study focused on eight countries to examine how teachers used ICT in mathematics instruction and factors that contributed to ICT use. Results show that teachers' education levels and cooperation amongst educators are associated with ICT use in instruction. The paper includes recommendations and implications for practice and future research.

This paper is based on an argument that the disruption of school spaces can demerit the myth that Mathematics is difficult and a struggle for learners in some contexts. Combining spatial theories and the phenomenon of disruption, the paper reports from a qualitative research project that analyzed the dynamics of space and place in South African schools. From a sample of two secondary schools and three primary schools in Tshwane South, the paper reports on the data from one school where the theme of disruption of school spaces for the teaching of mathematics was drawn. Two Mathematics teachers and one Head of Department (HoD) were interviewed in the school and one classroom was observed. The findings indicate that the disruption of school spaces leads to collaboration across post levels in terms of teaching, management, and personal professional development. Such collaboration disrupts the representations of space and improves teachers' spatial practices and a potential for better learning. The paper concludes by recommending research that will explore the applicability of the conclusions it makes to the enhancement of Mathematics learners' results.

Mathematics teaching is viewed as an inquiry process and a powerful context and practice for professional development with the goal of providing greater access, challenge, and support for every learner. This paper stems from a larger research project that investigates the research productivity and processes of integrating research in the curriculum delivery of high school mathematics. This descriptive work through survey, interview and documentary analysis involved 211 high school mathematics teachers in the quantitative component and four purposively selected in the qualitative section. Findings show that mathematics teachers demonstrate suboptimal level of research productivity but have shown promising potential for growth. Research is employed in various layers but typically as a mean to revisit teaching practices, as a basis of a teaching strategy, as a source of another research, and as a motivation for a research-oriented mindset. Research is strongly linked to the mathematics teaching and learning process and thus, have policy implications on nurturing and sustaining mathematics teacher-researchers. It is recommended to develop professional development plans that enhances the productivity and incorporation of research in the teaching-learning process.

Lockdowns imposed by many countries on their populations at the beginning of the COVID-19 crisis forced teachers to adapt quickly and without adequate preparation to distance teaching. In this paper, we focus on one of the most formidable challenges that teachers faced during the lockdowns and even in the post-lockdown emergency period, namely, developing assessment that maintains the pedagogical continuity that educational institutions typically require. Based on the results of a previous study, focused on the analysis of answers to an open-ended questionnaire administered to a population of 700 teachers from France, Germany, Israel and Italy, a semi-structured interview series was designed and implemented by the authors of this paper with a small group of teachers. The transcripts of these interviews were analysed according to the interpretative phenomenological analysis methodology, with the aim of investigating teachers' own perspectives on the following: (a) the difficulties with which they had to contend, with respect to the question of assessment; (b) the techniques adopted to deal with these difficulties; and (c) the ways in which the lockdown experience could affect the future evolution of teachers' assessment practices. This analysis supported us in formulating hypotheses concerning the possible long-term effects of lockdown on modes of assessment in mathematics.

In this paper, I examine deficit talk, utterances that depict students and/or families based on their perceived deficits, in an equity-oriented professional development (PD) setting. Researchers often attribute deficit talk by mathematics teachers (MTs) to their biased beliefs and perceptions. From an interactional approach, namely conversation analysis and discursive psychology, I offer an alternative perspective on how deficit talk is produced in PD interactions. The analysis shows the rhetorical functions of deficit talk, which are designed for MTs to manage their accountability with a range of potential issues and to portray themselves as competent teachers. The analysis also reveals the action-performing nature of deficit talk (e.g., refusing a request) situated in the social interaction. To conclude, this paper suggests that mathematics teacher educators need to attend to the micropolitical nature of deficit talk and their co-participation in the production of deficit talk as they formulate ways to respond to deficit talk in PD interactions.

A comprehensive graduate teaching assistant (GTA) training program in mathematical sciences designed at one institution is being adapted and replicated at two peer institutions. Using a case study approach, this paper outlines the development of the program components, which include a first-year teaching seminar, peer mentoring and support from a peer TA Coach, a Critical Issues in STEM Education seminar, and K-12 outreach to inform understanding of the pipeline. Additionally, adaptations due to institutional context and the impact of the COVID-19 pandemic are described. Implications for components of the comprehensive program, based on GTA-provided feedback, are discussed.

Purpose: The purpose of this paper is to explore students' mathematization through a flow of lessons using the Thailand Lesson Study Incorporated Open Approach (TLSOA) to improve the excellence of instruction. Design/methodology/approach: A total of 16 Grade 4 students were selected because they have been taught using the TLSOA model for four years. Six Lesson Study (LS) team members participated, and two instruments were utilized, namely student worksheets, and field notes. An ethnographic research design was employed. Findings: The results revealed that the students' mathematical ideas were developed from the real world to the mathematical world through a flow of lessons based on the four phases of the Open Approach (OA). Practical implications: Firstly, the students demonstrated their ability to represent the real world independently when the teacher posed an open-ended problem. Secondly, the students demonstrated their ability to use semi-concrete aids to develop their ideas while self-learning. Thirdly, the students showed how they developed their ideas to solve the open-ended problem using relevant objects or related concepts as part of a whole-class discussion and comparison exercise. Finally, the students demonstrated their abilities to represent the mathematical world using numbers and symbols to communicate their ideas when they were required to make a summary by connecting their mathematical ideas. Originality/value: This study adds new insight to the literature on students' mathematization using the TLSOA model.

The paper evaluates math performance at four high-need middle schools during a four-year intervention, which was designed to help math teachers diagnose students' areas of need and to design lesson plans responsive to those needs. Before the intervention began, the researchers pre-selected four comparison schools by matching based on achievement and also on demographics. A difference-in-difference analysis finds a significant increase of about 0.11 standard deviation in test scores per year for students in the program schools. Supplementary event study and synthetic control analyses to detect year-by-year effects lack precision but are weakly suggestive of a smaller impact in year 1 than later years. A cost analysis considers the affordability of extending similar programs.

In this collaborative, multi-voice paper we tell the story of our design collaboration. By describing the process of one design team of teacher educators, we offer a template of what it means to center teachers' lives and experiences as we design professional development with and for them.

Background: South African schooling is caught in a vicious cycle, characterised by weak initial teacher education (ITE) and weaker-than-average learning outcomes, resulting in low teacher status and attempts to reform schooling by means of continuous professional development (CPD). Aim: The paper attempts to understand the reasons for poor performance in mathematics and to explore avenues for improvement. Setting: Teaching in South African schools. Method: Three mechanisms for improving teaching and learning are identified: ITE, CPD and the management of and support to teachers. Drawing on the research literature, the paper examines the potential of each for reforming the system. Results: Tests based on the school curriculum indicate that final-year BEd students are quite unprepared to teach mathematics in primary schools, revealing very significant shortcomings in ITE curricula. CPD, where it is well designed and rigorously evaluated, has been shown to have small effects on both teacher knowledge and learner performance. However, unless ITE is reformed at the same time, CPD becomes a never ending task of making marginal differences to the shortcomings of each successive cohort of qualified but incompetent teachers emerging from the universities. Conclusion: While the weak state of governance in the civil service remains a major obstacle to improved schooling, and while every effort must be made to raise the capacity of inservice teachers, maximal leverage in boosting teacher capacity sits firmly with the universities. While CPD has, at most a few hours a month to bridge huge gaps in teacher knowledge, ITE has at its disposal four years of full-time study with young, plastic minds.

Teacher professional learning occurs across various contexts. Previous studies on teacher learning and changes in practice have focused on either classroom contexts or learning communities outside of school, but have rarely investigated teacher learning across multiple contexts. Investigating teacher learning across the double contexts of classroom and learning community has presented methodological challenges. In response, this paper proposes the suitability of adopting a socio-cultural development framework to further the analytical approach to such challenges. Using the framework, this paper considers the case study of a middle school mathematics teacher who resolved a problem of teaching practice through interacting with other members of the community of practice where they build shared goals and knowledge. This paper contributes to the field by expanding the scope of research on teacher learning across these two contexts, in which problem of practice becomes conceptual resources that the teacher uses in her teaching practice.

Purpose: The aim is the introduction of lesson study (LS) in geometry in Malawi secondary schools supported by a teaching framework that includes a focus on language responsive teaching. Design/methodology/approach: The study reports an LS on geometry for professional development (PD) of secondary teachers. Data analysed includes lesson plans, transcripts of lessons, reflective discussions. The analytical approach is qualitative content analysis. Findings: Teachers' lexicalisation of an exterior angle of a triangle evolved as a function of a teaching framework that guided their participation in planning, teaching and reflecting through LS cycle, and that was derived from networking between theories. Research limitations/implications: This is both a small-scale study, and a limited content focus in the lesson, a function of LS being a new practice, and teachers simultaneously learning ideas about geometry teaching, those embedded in the framework and doing LS. Practical implications: The paper includes a description of how LS might contribute to teachers' learning of language responsive teaching, and so is useful for others working on LS and language practices. Originality/value: This paper fulfils an identified need to learn more about how networking theories to inform and support LS can create learning opportunities for teachers, particularly about language responsive teaching, an interest and concern worldwide.

Noticing is often dependent on time-sensitivity and uses video or live observations. This paper explores loosening the time-sensitivity component and implementing self-narrative and inquiry approaches by having teachers write to explore noticing. This study explores narrative writing of beginning mathematics teachers using a noticing framework as opposed to data from video, discussion, or prompted writing as most noticing studies have implemented. This study analyzed narrative writing, termed written teaching replays, by early career secondary mathematics teachers to understand what these teachers attended to when writing about a classroom situation. Written teaching replay analysis results were similar to other mathematics noticing research studies, including earlier teacher development work on beginning teachers' focus on self. Differing from this literature, the majority of teaching replays did not focus on managing student behavior. The narrative inquiry work also revealed teachers connecting the professional development experience to their classrooms and vice versa. The paper suggests noticing may not need to be captured in the moment and highlights potential applications for teacher education and professional development as well as implications for research.

Just as students experience productive struggle or spend time in the 'zone of confusion' when engaging with challenging tasks, teachers also experience similar difficulties and periods of confusion when engaging with new pedagogical approaches. Prior to a 19-week lockdown due to Coronavirus (COVID-19) during 2020, two Foundation teachers implemented a student-centred pedagogical approach when teaching with challenging tasks. While they had some initial success implementing the pedagogical approach and a three-phase lesson structure, they struggled to do so online during the lockdown. It is the experiences of these teachers, in particular their experience of confusion relating to aspects of the pedagogical approach, and how this confusion was overcome, that is reported in this paper. Central to our findings is the importance of teachers reflecting on their own experiences of struggle and the impact this had on their professional learning, as well as the notion that adversity can be a catalyst for change.

The EU-funded project "Supporting Mathematics and Science Teachers in Addressing Diversity and Promoting Fundamental Values" (MaSDiV) (2017-2020) promoted inquiry-based learning as a pedagogy that supports diverse and multicultural classrooms. This project included the design of a professional development (PD) programme for teachers. This paper explores the mismatches between acts of promotion and offering in this PD programme when it was implemented in Malta with mathematics teachers. Findings suggest that a promotion-offering mismatch, especially when a PD programme forms part of an international project, is: (1) inevitable in view of the personal interpretations that participants construe from the texts that promote the programme; and (2) costly for everyone involved and for the quality of the PD experience itself. These results position mismatches as unwelcome occurrences. While it appears impossible to eliminate mismatches completely, the argument is made that the costs of mismatches could be mitigated by developing PD content and adopting a PD model that would increase the possibilities that the implementation of a PD programme maintains fidelity to the programme's principles. This calls for an approach to PD programme development and implementation that recognizes mismatches as a reality to be factored in from the design stage onwards.

Active learning is becoming more widely accepted in mathematics as a superior teaching method for student learning and, as a result, faculty are increasingly convinced of the benefits. Our study was designed to close a research gap by determining how to support mathematics faculty in transforming their instruction to active learning. We investigated actual challenges of faculty during the transition to more active pedagogy, then researched and tested solutions to reported challenges. To do so, we executed a participant observation study of six diverse faculty members from a mathematics department and followed typological analysis techniques of focus group and interview transcripts. Participants' challenges include overcoming a dominant culture of teaching through lecture in the mathematics community, combatting a tendency to default to lecture, and acquiring specific skills and confidence to implement active learning. We suggest that specific characteristics of a robust department-wide professional development program could provide solutions to many challenges faced by faculty. This paper reports on the challenges for faculty, alongside proposed solutions through purposefully defined faculty professional development.

The M@t.abel2020 project supported Italian teachers during the COVID-19 pandemic period, proposing activities based on the mathematics laboratory teaching method which are suitable for distance learning situations. The project resulted in the establishment of an online community of 1,500 teachers. In this paper we present an exploratory study based on an open-ended questionnaire assigned to teachers involved in the project, with the aim of analyzing the results of this training project in terms of mathematics teacher's specialized knowledge. Results show that the project enriched teachers' knowledge not only in terms of pedagogical content knowledge but also in mathematical knowledge.

Adaptive teaching on the micro-level of teacher-student interaction has often been investigated, but rarely with respect to students' content-specific learning pathways. In this paper, we present an analytic approach to disentangle the learning content into its components and to capture the content-specific adaptivity in teaching practices with respect to teachers' student focus and goal focus. For this, adaptive teaching is conceptualized as teachers' targeted steering trajectories navigating from students' initial ideas towards the content goals. In a case study with video data from 19 middle school small-group sessions on comparing fractions in context problems, we show how the adaptivity of the teaching practices can differ with respect to student focus and goal focus even when the same teacher moves are used. This calls for extending professional development programs that combine working on teacher moves with unpacking content goals.

In this survey paper we focus on mathematics learning in Chinese contexts, as a way to contribute to broader discussions about mathematical learning. We first review the features of Chinese students' mathematical learning depicted in the literature, followed by a review of student mathematical learning in recent Chinese research journals. This leads to an introduction of the papers on Chinese students' learning in this issue. For Chinese students' learning contexts, we discuss four aspects, namely, classroom instruction, teachers' professional learning, curriculum materials, and learning outside of school. For each context, we review the literature findings on the identified features, introduce emerged practices and most recent policies under the reformed era, and discuss the relevant papers in this special issue. Whenever possible, we connect findings on Chinese students' learning with the associated contexts and relate these findings in the Chinese contexts to findings in the broader world context. We conclude this survey paper with possible lessons learned from Chinese students' learning features and from the varied Chinese contexts. In particular, we discuss these aspects from culturally contextualized and semantically decontextualized dimensions, which is expected to facilitate broad international discourse centering on the three questions proposed at the end of this paper.

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.

This paper contends that, although there is much to commend in the remediation reform movement, it is unlikely to attain its goals. These goals include the Lumina Foundation's target of having 60% of Americans attain a degree or certificate, the Bill and Melinda Gates Foundation's goal of doubling the number of low income students who earn a post-secondary degree, and President Obama's goal of the U.S. having the world's highest percentage of degree holders by 2020. This is due to several factors including (a) the failure to distinguish between remedial and developmental education, (b) the limited focus of reform on remedial and gateway courses, (c) the mistaken assumption that there is a causal relationship between remediation and attrition, (d) the failure to address students' reading problems, (e) the non- systematic nature of most reform efforts, (f) and the subsequent failure to address other causes of student attrition and the difficulties of many community college students' lives. There are, of course, many commendable efforts to improve student performance in the community college. This paper describes the most popular of these efforts. It also discusses data on their effectiveness. In spite of their success, community colleges will need to do more if they are to dramatically enhance degree and certificate completion, particularly among minority, low income, and first-generation students. The authors suggest that there are three phases involved in attaining the dramatic increase in college completion desired by foundations and government. The first phase is to improve the quality of teaching and learning in community college classrooms. This will require a substantial faculty development effort, particularly for adjunct instructors. The second phase is to fully integrate courses and student support services. At present, the academic and the student affairs divisions of community colleges usually operate randomly and independently of each other. Their full impact cannot be obtained unless support services are more directly linked to course goals and objectives and courses are more directly connected to the services designed to support them. The third phase is expanding the connections between community colleges, public schools, and community services. High schools and colleges need to collaborate more closely to insure that the exit standards of secondary education are more consistent with the entry standards of post-secondary education. In addition, community colleges need to establish closer ties and better relationships with services available in the local community to address the varying nonacademic needs of our least advantaged students. The authors then provide concrete examples of how community colleges might implement all three phases of student completion. Some of these examples represent new thinking about how community college courses and services might be organized and delivered. Many, however, represent things we already know but have, for a variety of reasons, failed to implement.

To facilitate the professional learning of teachers and bring about changes in pedagogical practices, it is necessary to understand the process by which teachers grow professionally. Professional growth can be achieved when teachers work together to engage in professional experimentation and see results in terms of salient outcomes for their students. This paper reports on a study of teachers' pedagogical practices as they introduced adaptations to focus on personalising students' learning in mathematics. Two cases are presented to demonstrate how teachers in two schools used student mathematics test data to determine students' strengths and needs, in order to personalise learning experiences. The findings highlight how shared responsibility and purposeful use of student data can lead to positive professional growth for teachers and improved learning outcomes for students.

Over the past decade, teaching mathematics ambitiously has received increased attention. In this paper, we argue that to materialize this vision in contemporary classes we need to understand how practicing teachers experiment with certain aspects of this teaching and what challenges they encounter. Toward this end, we focus on an aspect of teaching ambitiously--designing and using enablers and extenders--and examine how four elementary schoolteachers experimented with it in their practice while also participating in a video-club setting. Drawing on a corpus of data including lesson plans, videotaped lessons, pre- and post-lesson interviews, end-of-program interviews, and videotaped video-club sessions, and looking across the four cases, we sketch how these teachers worked with enablers and extenders and the challenges they faced. Our analysis helped identify certain components entailed in working with enablers and extenders during the phases of lesson planning and enactment; it also yielded a classification of observed and reported challenges encountered as teachers engage with this work. This mapping of work associated with designing and using enablers and extenders, along with the classification of challenges generated, can inform professional learning development attempts aiming to support teachers enact ambitious teaching by identifying and naming separate components of practice that merit consideration and by providing insights into the types of scaffolds needed to support teachers in teaching ambitiously.

This paper argues that the practice of teaching and learning is being re-defined as technology enables a re-imagining of what can be taught, and how it could be taught. In Namibia, demands on mathematics teachers to incorporate technology use into their teaching practice are often mismatched with the curriculum. This theoretical paper proposes meaningful mathematics teaching via technology, instead of a mere response to societal adoption of digital tools. The concept of meaningful teaching is viewed through a Vygotskian lens. Kilpatrick et al.'s five Strands of Mathematical Proficiency inform the interpretation of goals for teaching mathematics with technology. We discuss the gaps in current models for professional development for teaching with technology when we take the Namibian cultural historical context into consideration. Activity Theory is used to conceptualise a two-triangle embedded activity system of teachers and professional developers, and to reflect on nodal interactions. We conclude by proposing some principles for the design of professional development programmes that aim to support mathematics teachers in using technology in their teaching. The principles may be useful for professional development in other developing countries with uneven access to both technology and reformed mathematics curricula.

Purpose: The aim of the study is to better understand how lesson study (LS) contributes to challenging teachers' views of mathematics teaching and learning. Design/methodology/approach: This study is part of a wider ongoing project aiming at improving primary mathematics teaching in Malawi through professional development (PD) of teachers using a LS model. The units being analyzed are teachers' written reflections and lesson plans. The analytical approach is qualitative content analysis. Findings: Initially, the participating Malawian primary teachers report traditional views of mathematics teaching and learning. After having participated in a LS cycle, they reported on the need to work on how to involve and create space for learners' participation in mathematic lessons and highlight the importance for learners to discover mathematics on their own. Research limitations/implications: This is a small-scale study due to LS being quite new in the Malawian context and the need to test before possible upscaling. Practical implications The paper includes a description on how LS might contribute to challenging Malawian teachers' views of mathematics teaching and learning; this can be valuable information for others who are attempting to use LS in a similar context. Originality/value: This paper fulfills an identified need to learn more about how LS might contribute to challenging teachers' views of mathematics teaching and learning worldwide.

The aim of the study reported in this paper was to explore and enhance experienced school mathematics teachers' knowledge of students'thinking, as it is manifested in practice. Data were collected from records of classroom observations, interviews with participating teachers, and weekly teacher-researcher meetings organized in the school. In this paper, we discuss the mathematical challenges faced by a primary school teacher as she attempts to unpack the structure of the division algorithm, while teaching in a Grade 4 classroom. Through this case study, we exemplify how a focus on mathematical knowledge for teaching 'in situ' helped in triggering a change in the teacher's well-formed knowledge and beliefs about the teaching and learning of the division algorithm, and related students' capabilities. We argue that in the context of educational reform, an analysis of knowledge demands placed on the teacher helps in understanding and supporting teachers' work.

Professional development (PD) courses are the main context for mathematics teachers' lifelong learning. Leaders with expertise are needed to facilitate these courses; thus, there is a growing interest in understanding the nature of this profession, its core practices, and the challenges it entails. This paper focuses on a specific group of facilitators: experienced mathematics teachers who have just begun facilitating PD courses in addition to their classroom teaching. To better understand these novice facilitators' practices, a commognitive approach was implemented to examine how they draw on their mathematics teaching experience when leading PD courses. In commognitive terms, these practitioners draw on multiple professional discourses, but mostly on the discourses of teaching and facilitation. The analysis of the challenges and affordances associated with participating in these two professional discourses showed that novice facilitators bring into play their teaching practices in four distinct ways: enacting a familiar practice, negating a familiar practice, questioning the relevance of a familiar practice, and generating a new practice based on their teaching experience. We claim that novice facilitators' well-established identity as teachers is both a challenge and an asset in grounding successful facilitation practices. Overall, facilitators modify their teaching experience through the adoption, adaptation, and retraction of their teaching practices. Implications for the preparation and support of facilitators, within processes of upscaling PD programs, are discussed.

This paper describes a professional development (PD) programme design integrating just-in-time learning (JITL) to support teachers to learn about and enact inquiry teaching. Through JITL, teachers are provided with support that is responsive and applicable to their needs. This case study reports on the professional journeys of three teachers who received JITL via online resources, face-to-face meetings, opportunities for community building within and across schools, and reflections on pupils' reactions to learning mathematics through inquiry. Findings indicate that JITL embedded within PD facilitated teacher learning about inquiry enactment, since the PD was responsive to teachers' immediate and contextual needs. We suggest that explicit attention to JITL is given in the design of teacher PD, providing support that is made readily available for teachers to access and utilise.

Tasks play a central role in the mathematics classroom. Especially when teaching in a heterogeneous mathematics class, teachers should be able to find, select, modify, and assign tasks adequately. The focus in this paper is on adaptivity to cognitively activate all learners at the individual level, and on teachers' abilities to allow for such adaptivity by means of selecting appropriate tasks. More specifically, when planning lesson phases for practice and consolidation, teachers may consider which tasks have differentiation potential and can thus be completed by all students at the same time but at different levels. In order to analyse teachers' strategies in this regard, we investigated the task features that teachers may consider when assessing the differentiation potential of exercise tasks. We first deductively constructed rating categories based on the literature on instructionally relevant features of adaptive tasks. Then, we inductively extended and refined the constructed categories by analysing teachers' reasoning based on a sample of 78 in-service teachers at secondary schools. We validated the resulting 22 categories by determining interrater reliability. Our findings indicate that teachers consider a broad spectrum of task features when analysing the differentiation potential of tasks. However, only some of these features are directly relevant with regard to using adaptive tasks as a differentiation strategy. Our results also show that many teachers arrived at conclusions about the differentiation potential of tasks that were different from task-design experts. Based on our findings regarding teachers' perspectives on the differentiation potential of tasks and on certain task features, we discuss how these findings may have arisen and how important the knowledge about the deep structure of adaptive tasks is for teachers' professional development.

In this work, we discuss the development of descriptive actions that facilitators take in semester-long online professional development geared at supporting instructional change at the undergraduate level. Current work in undergraduate mathematics education includes various large-scale projects aimed to support individuals or departments in reforming their instruction to align with recommendations from professional organizations and existing mathematics education research standards. One research area that has recently grown is the use of online synchronous environments to form collaborations to support the inclusion of student-centered instruction in mathematics. This paper discusses the actions that facilitators take in these collaborative environments and highlights how these actions supported the overall goal of the semester-long online faculty development.

In this paper, we investigate the learning experiences, beliefs and motivations of students in classes where the mathematics teachers have received support for using inquiry-based learning activities. Data were collected from 248 students in the age-range 11-16 using electronic questionnaires. Our results show that key features of inquiry-based mathematics were only moderately reflected in these students' beliefs about the subject, their dispositions towards mathematics were less positive across the transition from primary to secondary school, and with respect to motivation this decline was stronger for girls than for boys. Furthermore, medium to strong correlations between belief- and motivation subdomains were found, for instance, students who view mathematics as a creative subject and/or have a growth mindset of mathematics also tend to find this subject enjoyable and perceive it as useful. Finally, our results indicate that inquiry-based teaching has a potential for fostering positive dispositions towards mathematics, as students who often experience inquiry-related activities in class also tend to see mathematics as a creative and interesting subject that will be useful for them in the future.

Out-of-field teaching refers to the practice of assigning teachers to teach subjects that do not match their training or education. This paper reports on a study evaluating the impact of a national professional development programme for out-of-field teachers of post-primary school mathematics in Ireland -- the Professional Diploma in Mathematics for Teaching. Evidence of impact was collected from three surveys. Two surveys evaluated changes in the prevalence of out-of-field teaching before and six years after the introduction of the programme. The third survey investigated programme graduates' beliefs about mathematics, mathematics teaching and mathematics learning, and reported changes in teaching practices. Outcomes of the programme included a reduction in out-of-field teaching of mathematics and increased opportunities for graduates to teach higher level mathematics in the senior post-primary years. These teachers also endorsed child-centred beliefs and reported teaching practices consistent with the problem-solving orientation of the new mathematics curriculum. The findings go some way towards testing a theory of teacher change in order to enhance our understanding of how professional development works to upskill out-of-field teachers.

Purpose: This paper seeks to understand how teachers' mathematical knowledge for teaching (MKT) is developed during a lesson study regarded as a professional development process that places particular emphasis on teachers' knowledge of tasks, representations and students' learning. Design/methodology/approach: This study is based on the networking of two theories, namely the Interconnected Model of Teacher Professional Growth (IMTPG) and MKT. The methodology is qualitative and interpretative. The participants are three primary school teachers and team members involved in a lesson study. Data collection was conducted by means of participant observation, with audio recordings of the sessions and a final individual interview. Findings: The participant teachers developed their knowledge of tasks and representations, which are essential elements of content and teaching knowledge, as well as knowledge of the curriculum, content and students. Additionally, they developed specialized knowledge of mathematics, the meaning of fraction as a measure and its representation on the number line. This development arose from activities conducted in the Domain of Practice, in many cases prompted by the External Domain, and was particularly important when these activities gave rise to unforeseen consequences. Connections among the various domains were established through enactment and reflection processes. Originality/value: The study shows how the networking of two different theories, in this case the IMTPG and MKT, may enhance further understanding of educational phenomena. This networking involved the coordination of these two theories, which were superimposed in the Group Domain.

Purpose: The authors investigate the use and potential of a theoretical combination of Realistic Mathematics Education (RME) and the Theory of Didactic Situation (TDS) to support Lesson Study (LS) in upper secondary mathematics. Design/methodology/approach: Case study performed by university researchers, based on theoretical analysis and case studies based on documents and observation from lesson studies. Findings: Even within a project lasting just about three years, teachers (with no preliminary experience of lesson study) engaged in lesson design based on the combination of theoretical perspectives from TDS and RME in ways that confirm the potential of that combination to enrich and focus teachers' professional development within the framework of LS . It is not clear to what extent the intensive and continued engagement of university researchers has been or would be essential for similar and longitudinal realizations of these potentials. Practical implications: As current European frameworks seek to engage researchers and teachers in collaboration and exchange across countries, networking of major paradigms of research (like TDS and RME) and uses of them as supports for teachers' inquiry (like demonstrated in this paper) is of considerable institutional interest and potential impact on schools. Social implications: Teachers' Inquiry in Mathematics Education (TIME) is a prerequisite for the development of Inquiry Based Mathematics Education, which in turn is required in many countries across the world, with the aim of fostering critical and competent citizens. Originality/value: This combination of (major) mathematics education theories to support and enrich LS has not previously been investigated. While several aspects of adapting to LS Western contexts have been investigated in the past, including the inclusion of perspectives and tools from academic research, the role of university researchers is also quite open. While authors do not offer a systematic study of this role, authors examine how this role may involve development of new practical combinations of different, complementary theoretical tools, which indeed hold potential to support lesson study in a European context.

Following the seminal work of Gloria Ladson-Billings, research on culturally responsive pedagogy (CRP) has, in recent years, expanded significantly. Ladson-Billings proposes three elements of CRP: academic achievement, cultural competence, and sociopolitical consciousness. Nevertheless, in mathematics education research on CRP, the sociopolitical consciousness element is often under-explored or even absent. This paper began as an investigation of how Ladson-Billings' three elements could be used to examine prospective and practicing teachers' (PPTs') perspectives on CRP, prior to their participation in a professional development course on CRP in the mathematics classroom. Thirty-one participants from three separate offerings of the course responded in writing to a set of open questions about CRP (in general and in mathematics). Thematic data analysis pointed to the complexities of categorising the data based primarily on Ladson-Billings' three elements. In addition, our analysis indicated five components underpinning participants' responses: challenges; opportunities; fears; resistance; insights. We conclude with a revised conceptualisation of CRP for mathematics teacher education programmes aimed at supporting PPTs' development of their CRP-related knowledge, skills, and dispositions.

Purpose: This paper examines how mathematics teacher educators (MTEs) learn to enact equitable mathematics instruction using technology through lesson study (LS). Design/methodology/approach: A LS team with three MTEs conducted three iterations of LS on teaching the Pythagorean Theorem in an in-person, technology-mediated environment. Many forms of data were collected: Desmos activities, videos of research lessons (RLs), videos of MTE RL debriefings, artifacts of student learning in the Desmos Dashboard, and MTEs' written self-reflection. The authors investigate the teacher educators' learning through LS by analyzing the MTE debriefings of the RLs using Bannister's (2015) framework for teacher learning in communities of practice. Findings: The MTEs learned to enact equitable mathematics instruction using technology through addressing emerging issues related to intellectual authority and use of student thinking. Throughout the LS, the MTEs sought ways of promoting students' mathematical authority and using student thinking through features of the Desmos platform. Research limitations/implications; This study focuses on MTEs' learning without examining participating preservice teachers' learning. It demonstrates the benefits of LS for MTEs' professional learning. Practical implications; This study showcases how a research-based Desmos activity is used and refined to promote MTE learning how to implement equitable mathematics instruction. Originality/value: The study contributes to better understanding of how LS could be used to develop MTEs' professional learning. Moreover, the dual process of participation and reification was concretized through diagnostic and prognostic frames in the LS context, which enriches the concept of community of practice.

Traditional teacher andragogy models oversimplify teaching multilingual students, overlooking both the complexity of identity and the contexts in which this work occurs. In this paper, we describe our intersectional approach to research, highlighting its affordances for research on teachers' learning to support multilingual students. This intersectional lens opens urgent new research questions, invites different types of data, and offers informative analytic approaches to improve both research and practice.

Given the importance of mathematics performance of learners and the challenges in South Africa, it is important that the expertise of all role-players, including the subject advisors who visit the teachers to guide and support them, is used to its full potential. While some studies have explored the experiences of teachers in this regard, literature on the experiences of mathematics subject advisors is scant. Furthermore, little has been published on the experiences of subject advisors within the context of rural areas with a low population, such as the Northern Cape Province. This article addresses the gap by exploring the deeper understanding of mathematics subject advisors' experiences when conducting school support visits. Taking a qualitative research approach, I conducted semi-structured interviews with six mathematics subject advisors from the four phases (foundation, intermediate, senior, and further education and training) in all five of the education districts of the Northern Cape Department of Education (Frances Baard; Z.F. Mgcwawu; Pixley Ka Seme; Namakwa; and J.T. Gaetsewe). Through Husserl's phenomenological theoretical framework, complemented with Gibbs' reflective cycle and Colaizzi's seven steps of data analysis, participants were found to have had both good and bad experiences when conducting school support visits. Experiences included positive attitudes from educators and schools in general, and good curriculum implementation and teaching and learning practices. However, participants were sometimes received with hostility, and observed poor curriculum implementation and teaching and learning practices. Noteworthy is some negative union influence, lack of specialisation in mathematics by foundation phase departmental heads, lack of coherence in communication, and lack of cooperation and collaboration amongst district officials. If the concerns raised by mathematics subject advisors in this paper are not addressed, these may have a negative impact on the experiences of subject advisors and, by implication, on learner performance as well as education in general.

Professional learning communities can be important sites for teacher learning depending on the quality of the conversations in these communities. This paper investigates how different activities in teacher communities support different content and depth in teacher conversations, through examining the conversations of four professional learning communities of mathematics teachers over two years. Our analysis suggests three key findings. First, there were strong relationships between different activities and the content of the conversations in the communities. Second, the depth of the conversation in the communities was constant across activities and over time. Third, conversations about learner thinking, a key goal of the project, did not increase over time, but there were increases in talk about mathematics and practice. We explore the implications of these findings for teacher learning.

The interplay between mathematics teachers' beliefs and practices has been widely investigated and research has examined how teachers' beliefs about mathematics, teaching and learning change when participating in continuing professional development (CPD). In this paper, I track teachers' self-reported beliefs and practice changes as they participate in a 1-year CPD programme intended to support them in "learning to teach mathematics through inquiry" (LTMI). LTMI is a blended programme that integrates two phases: summer workshops and monthly follow-up meetings held during the scholastic year. Using a case-study design, data focusing on self-reported beliefs and practices were collected, using questionnaires and interviews, from three teachers at different stages: before, during and at the end of the CPD. Results show that, following teachers' participation in summer workshops, they reported stronger connectionist beliefs. However, by the end of the CPD, while their connectionist beliefs remained strong, teachers reported increased discovery beliefs. Discovery beliefs were consistent with their reported changes in teaching practices. It appears that, in changing from transmission to inquiry teaching, these teachers adopted a non-interventionist and non-interactionist discovery teaching approach. This finding has implications for the design of CPD and, hence, the need to offer a supportive structure that helps teachers to recognise and address the limitations of their practices, along their journey to change towards more inquiry teaching.

The present paper studies the effects of lesson study as a sample of participative researches in classroom as well as Behrangi Education Management Model in courses by aiming at exploring and allowing students to use the indexes of course concepts as an effective model in learning. The research plan is pre-test, posttest with control group type. In this research, first the characteristics of lesson study in professional development of teachers through participative research and improving students' learning have been studied, followed by discussing the ten commands or ten steps of implementing education management model in teaching curriculum as well as using modern and suitable teaching models. The subjects were selected at random from five lesson study pilot schools in district 3 and were taught and tested accordingly. The measurement tools which are used in this research included teacher-developed education progress test underwent contents validity and reliability examination and their reliability was examined by reliability method which was agreed by assessor. That is, the papers were given to a number of paper correctors for scoring. The scoring scale was 1 to 14. The teaching was carried out in two methods of lesson study and education management for teaching mathematics to second grade boy students at public elementary schools in district 2 of Tehran and the effects were measured on three groups of students in pre-test and posttest methods. The results from analyzing research data showed the average mathematics score in education management model in pretest was 9.85 and in posttest, it was 11.26; while, the average mathematics scores in lesson study group in pre-test was 9.19 and in posttest, it was 9.04. In the control group, those scores were 9.75 in pre-test and 9.65 in posttest. The average score in mathematics lesson in education management group showed considerable increase compared to the lesson study method group. The research hypothesis of the research showed education management model led to increase in mathematics learning of students; while, lesson study did not show tangible effects on mathematics learning of students. This research can be carried out in higher school grades and in other courses in Tehran for providing more complementary studies.

A non-specialist teacher of mathematics is a school teacher who qualified to teach in a subject other than mathematics yet teaches mathematics to students in secondary school. There is an emerging interest internationally in this population, a brief report of which is given in the paper. Because of concerns about the quality of non-specialists' mathematics teaching, in-service courses for these teachers have been provided by some educational jurisdictions, including within the United Kingdom (UK). This paper reports on a research project based on designing and teaching such courses in London. The paper operationalises "Mathematics Teacher Identity" by adapting Wenger's (1998) social ecology of identity to give a framework of "Modes of Belonging" for a teacher of mathematics, which is then used to analyse qualitative data of different types. Analysis of the data identifies (1) aspects of non-specialists' mathematics teacher identity in terms of indicators and (2) through two case studies, "trajectories" towards development of a mathematics teacher identity.