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The paper describes a case study of mentoring support provided to a novice mathematics teacher in using Guided Discovery in her classroom. The study used qualitative methods: thematic analysis of interviews and discussions. A central theme that emerged in the results was agency, and we observed that the high level of student and teacher agency in Guided Discovery results in the importance of teacher agency within and over the mentoring framework. We conclude that when supporting teachers in using Guided Discovery in their mathematics classrooms, teacher educators need to put an increased focus on teacher agency within and over the mentoring process. [ABSTRACT FROM AUTHOR]

Since teachers have the greatest impact on student learning, it is crucial to consider how professional development programs (PDP) for teachers can enhance their contribution, especially in designing mathematical tasks for teaching. This paper focuses on identifying patterns of practices of mathematics teacher educators related to crucial aspects of two teacher PDPs: one conducted face-to-face and the other using a Massive Open Online Course (MOOC). The Meta-Didactical Transposition is employed as the theoretical framework for comparing the two PDPs and for identifying patterns of practices. The findings suggest that educators, both in face-to-face and online settings, consider certain practices to guide teachers in designing mathematical tasks. This paper aims to share experiences of good practices that can be implemented by other researchers seeking to guide teachers in task design, either alone or in small groups. [ABSTRACT FROM AUTHOR]

The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is called in the paper) computational triangulation in the context of four digital tools. Computational problem solving and problem formulating are presented as two sides of the same coin. By revealing the hidden mathematics of Fibonacci numbers included in the Brain Teaser, the paper discusses the role of computational thinking in the use of the well-ordering principle, the generating function method, digital fabrication, difference equations, and continued fractions in the development of computational algorithms. These algorithms eventually lead to a generalized Golden Ratio in the form of a string of numbers independently generated by digital tools used in the paper. [ABSTRACT FROM AUTHOR]

This paper extends earlier research on prospective and practicing teachers' (PPTs') developing understandings of culturally responsive pedagogy (CRP) while enrolled in a teacher education course for CRP and mathematics. Here, we take as our starting point a framework we refer to as COFRI, which describes five integral components of PPTs' perspectives on CRP: Challenges, Opportunities, Fears, Resistance, and Insights. Viewing PPTs' reflective journal entries through the lens of this framework, we noticed interesting relationships between the five components that had not been evident in our initial analysis. Specifically, we observed that, as we coded participants' reflections according to C, O, F, R, and I, each I (insight) appeared to be related to one (or more) of the other components in quite different ways. Additionally, careful study of the insights expressed by PPTs lead to our categorization of insights according to one of three types: mathematical, pedagogical, or ideological. As a result, this paper offers a new way to interpret the five components, specifically their relationships to new insights into CRP and the corresponding types of insights that PPTs produce over the course of one semester. In closing, this paper discusses implications for mathematics teacher educators in understanding and processing PPTs' evolving understandings of CRP. [ABSTRACT FROM AUTHOR]

This paper clarifies and expands the definition of teacher professional practice, grounded in the commonplaces of professionalism outlined by Lee Shulman. We present the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework as a lens for transforming professional development into a practice that engages teachers as professionals. This discussion explores teachers' roles in both their classrooms and the profession. The inclusion of PrimeD evaluation and research in the development and practice of mathematics teachers addresses Shulman's professionalism commonplaces. PrimeD was tested as a lens for professionalism in mathematics teacher education programs at four universities. In the study, teachers collaborated as professionals on developing and testing novel ways to approach mathematics lessons. In general, teachers' efforts to conduct structured experimentation in their lessons were disconnected from traditional views of the role of a teacher. As a result, teachers who did develop and test lesson trials in this PD program did not frequently continue experimentation. Typically, teachers wanted to collaborate on testing classroom activities but did not have resources to do so (e.g., time, collaborative planning). Systemic changes are needed to promote sustainable change, allowing teachers to collaborate and share the results of classroom research. [ABSTRACT FROM AUTHOR]

A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers, teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed. [ABSTRACT FROM AUTHOR]

In this paper, we discuss how critical mathematics education (CME) and actor–network theory (ANT) come together in a mathematics teacher education course that focuses on the thematic context of climate change to study statistics. Acknowledging the complexity that student teachers encounter when asked to move from a mainly instrumental treatment of statistics toward a critical foreground of data in society, we turn to explore the actant networks, as theorized by ANT, utilized by student teachers when asked to imagine teaching from a CME perspective. For this, our study is based on a series of interviews with student teachers who participated in a statistics course where pollution data graphs were discussed, inquiring about their role as future critical mathematics teachers. The transcribed interviews, analyzed through ANT, inform us as to how student teachers' foregrounds are being shaped by actants such as the curriculum, social justice, democracy, and source critique, among others. Based on the above, we recommend that teacher education should invite active discussion of the complexity created when a CME perspective is required. This move would allow for a critical approach to critical mathematics education itself that could prepare student teachers to navigate, instead of ignoring or opposing, such complexity. [ABSTRACT FROM AUTHOR]

Learning styles is the idea that there are unique ways in which individuals approach learning and process information. Though refuted, the idea of learning styles has not declined in peer-reviewed reports of empirical studies or teacher/practitioner resources. Some reports have also used learning styles as a tool for improving the mathematics education of students with learning disabilities—an area of interest for mathematics education and special education communities alike. In this paper, we review articles published by the National Council of Teachers of Mathematics to investigate the perspectives of learning styles at the intersection of mathematics education and learning disabilities. Analyses highlight the relationship between mathematics education, learning disabilities, and learning styles, and the varied meanings and perspectives of the articles' authors. Of note is both the perpetuation of unfounded concepts and the lackluster response to explicit contests of the idea of learning styles. [ABSTRACT FROM AUTHOR]

We have interviewed becoming mathematics teachers, in the last semester of their education, asking how they experience their time as teacher students with the focus on inclusive teaching. In their forthcoming daily work, they will be responsible for arranging for inclusive teaching that addresses all the learners' needs in mathematics. We believe the voices of future teachers are important to include in conversations about how programs prepare future mathematics teachers for the work of teaching in today's schools and classrooms. We used storylines as a theoretical construct to discuss the socio-political aspects of mathematics teacher education through the lens of two research questions: What storylines emerged in interviews with becoming mathematics teachers in their last semester of teacher education when they talked about teaching in diverse classrooms? What implications might these storylines have on mathematics teacher education? Our analysis made us aware of three important storylines: (1) storylines about the importance of language in mathematics education; (2) storylines about the importance of accepting diverse methods when doing mathematics; and (3) storylines about issues of invisibility at play in mathematics classrooms. In this paper, we discuss the importance of creating space for discussions in teacher education about issues that may challenge inclusive practices in mathematics classrooms. [ABSTRACT FROM AUTHOR]

This article draws from a longitudinal case study of trainee (the term used in official documentation related to Initial Teacher Training (ITT) in England and with some reservations throughout this paper) and early-career teachers (ECT) of mathematics. The sample represents migrant teachers that the Immigration Act of 2020 seeks to attract to the UK to address national shortages identified by the Migration Advisory Committee (MAC). The analysis examines how multimodal semiotic repertoires of language, bodies and pedagogical practices are entangled in classroom encounters. It shows how the ideology of Standard English can create an uncomfortable sense of different deficits amongst multilingual professionals and evidences how these can be addressed through a model of authority in which teachers get the right mix of mathematical subject knowledge (epistemic authority), the use of school practices and expectations (practical authority), and individual biography (personal authority). It uses translanguaging spaces to examine how teachers use communicative repertoires to orchestrate semiotic resources and manage their identity positions in ways that promote intercultural competencies during the daily encounters of teachers and their pupils. [ABSTRACT FROM AUTHOR]

This paper aims to provide an understanding of effective professional development (PD) for mathematics teachers according to the context of South Sudan schools. Hunsicker's (2011) checklist of effective PD was taken as a framework. The framework has five characteristics—supportive, job-embedded, instructional focused, collaborative, and ongoing—and these five characteristics have been used for shaping the study. Interviews were designed and administered to educational officials, principals of two schools, and six sampled mathematics teachers, patterning their understanding about effective PD of mathematics teachers in the South Sudan school context. The analysis showed that the types of PD that exist in the South Sudan school context include the preparation of a lesson plan and the scheme of work for novice teachers, a weekly professional participation of teachers within their working hours, and informal dialog and guidance among peers. In addition, some unqualified teachers are sent to teacher training institutions during holiday times, which can be regarded as a kind of in-service and continuous PD. Our findings are that most of the participants do not have a clear view of what effective PD means. The participants mentioned aspects that can be seen as parts of effective PD according to the literature, but none of them had a holistic or explicit understanding. There is a need to engage those stakeholders to work deeply on aspects of effective PD if a meaningful improvement in student learning is to happen in classrooms. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the images of mathematics and its teaching, as expressed by mathematics teachers, in reaction to educational programs broadcasted by Polish public television channels during the first lockdown in 2020. For our analysis, we deployed a theoretical framework mostly drawn from the work of Paul Ernest. Our data came from a variety of sources such as educational fora, social networks, websites and email exchanges. Our results, based on an interpretative analysis, revealed four overarching images of mathematics and its teaching which, although related to the specificities of television, resembled images found by other relevant studies. The first image of mathematics views it as an unambiguous discipline in which there is no room for more than one point of view. The second image refers to the teacher as a presenter who is expected to possess particular verbal and non-verbal skills, especially given the fact that the television programs did not involve any live audiences. The third image refers to the unappealing nature of the broadcasted lessons, while the fourth image refers to the underlying approach of crude memorization associated with 'traditional' mathematics teaching. Our study's contribution is twofold: in the improvement of televised educational programs (and possibly online courses) and in the improvement of the public's image of mathematics. [ABSTRACT FROM AUTHOR]

Existing initiatives in mathematics education demand establishing a continuous professional development program for teachers in Ethiopian schools. However, implementing such programs first requires an understanding of the school and district environment in which the participating teachers work, as mathematics instruction is in part a function of the environment. In many cases, school and district settings are dynamic, and it is difficult to incorporate unplanned and intervening factors into the change process. This case study attempts to investigate the influences of the school and district settings in promoting reform visions in mathematics education. This study applies the theory of communities of practice as a framework and qualitative coding of data to understand the dynamic school setting and its implications for the teaching practices of mathematics teachers. The findings reveal that the school setting does not adequately promote reform visions, but rather it maintains the practice that is supposed to be changed. The current situation includes an accountability system loosely connected to reform visions, the absence of reform-oriented school leaders and expertise to guide the teachers, and a lack of instructional materials that the teachers can refer to regarding the new reforms. This paper suggests a possible configuration of the school situation to promote an environment that fosters the teaching of mathematics toward reform objectives. [ABSTRACT FROM AUTHOR]

In this paper, we describe an educational experience in the context of the Master's degree that is compulsory in Spain to become a secondary education mathematics teacher. Master's students from two universities in Madrid (Spain) attended lectures that addressed—emphasizing the concourse of a dynamic geometry software package—some historical, didactic and mathematical issues related to linkage mechanisms, such as those arising in the 18th and 19th centuries during the development of the steam engine. Afterwards, participants were asked to provide three different kinds of feedback: (i) working on an assigned group task, (ii) individually answering a questionnaire, and (iii) proposing some classroom activity, imagining it would be addressed to their prospective pupils. All three issues focused on the specific topic of the attended lectures. In the framework of Mason's reflective discourse analysis, the information supplied by the participants has been analyzed. The objective was to explore what they have learned from the experience and what their perception is of the potential interest in linkages as a methodological instrument for their future professional activity as teachers. This analysis is then the basis upon which to reflect on the opportunities (and problems) that this particular bar-joint linkages methodological approach could bring towards providing future mathematics teachers with attractive tools that would contribute to enhancing a STEAM-oriented education. Finally, the students' answers allow us to conclude that the experience was beneficial for these pre-service teachers, both in improving their knowledge on linkages history, mathematics, industrial, technological and artistic applications, and in enhancing the use in the classroom of this very suitable STEAM context. [ABSTRACT FROM AUTHOR]

In recent years, the inclusion of computational thinking in education has become very important. This is a response to the needs of the evolution of our society and the skills demanded in students to obtain practical and integrated training. For this reason, the educational inclusion of these types of practices, strategies, and skills has been the subject of study in recent years. However, it is equally important to prepare and analyse the initial training of future teachers in this area. This research paper presents an empirical experience in which the degree of development of skills associated with computational thinking in preservice primary teachers is examined. For this purpose, programming practices with Scratch were carried out with a total of 149 students of primary education university degrees as part of their training in mathematics education. An experiment was designed for a control group and an experimental group with initial and final measurements using a validated diagnostic instrument consisting of 30 questions associated with computational concepts and their application: a computational thinking test. The result of the experience is positive, as a more significant improvement was observed in the experimental group, which was also accompanied by the impressions, provided by participants, that point in a positive, useful, and practical direction in terms of the development of this type of educational practice being relevant enough to introduce to the teaching and learning process of mathematics. [ABSTRACT FROM AUTHOR]

Educational data classification has become an effective tool for exploring the hidden pattern or relationship in educational data and predicting students' performance or teachers' competency. This study proposes a new method based on machine learning algorithms to predict the technology-integrated competency of pre-service mathematics teachers. In this paper, we modified the inertial subgradient extragradient algorithm for pseudomonotone equilibrium and proved the weak convergence theorem under some suitable conditions in Hilbert spaces. We then applied to solve data classification by extreme learning machine using the dataset comprised of the technology-integrated competency of 954 pre-service mathematics teachers in a university in northern Thailand, longitudinally collected for five years. The flexibility of our algorithm was shown by comparisons of the choice of different parameters. The performance was calculated and compared with the existing algorithms to be implemented for prediction. The results show that the proposed method achieved a classification accuracy of 81.06%. The predictions were implemented using ten attributes, including demographic information, skills, and knowledge relating to technology developed throughout the teacher education program. Such data driven studies are significant for establishing a prospective teacher competency analysis framework in teacher education and contributing to decision-making for policy design. [ABSTRACT FROM AUTHOR]

Science, technology, engineering and mathematics (STEM) fields occupy a significant role in human prosperity and advancement. This study explores the factors affecting student STEM outcomes. Traditionally, the associations of students' own motivational or cognitive inputs to their STEM career outcomes have been investigated before. Similarly, association of teacher quality to student achievement outcomes have been made before. This paper presents a novel approach by introducing teacher quality as the contextual factor within the social cognitive career theoretical (SCCT) model using a comprehensive and robust model for teacher quality including teachers' motivation, qualifications, and self-reported practices. This study examines the extent to which high school students' mathematics and science teachers' beliefs, professional background, and instructional practices relate to students' motivation, achievement, and future career plans in STEM using a nationally representative, large dataset: High School Longitudinal Study 2009. The results indicate that science and mathematics teachers' professional background, motivational beliefs, and self-reported instructional practices have significant impact on students' motivation, persistence, and achievement outcomes in science and mathematics. No direct impact of teacher factors on STEM career plans are found; however, students motivational and achievement outcomes (impacted by teacher factors) do have significant impact on students' career plans in STEM. [ABSTRACT FROM AUTHOR]

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada. He is currently the Director of the Centre for Mathematical and Statistical Sciences India. His research contributions cover a wide spectrum of topics in mathematics, statistics, physics, astronomy, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, and a member of the International Statistical Institute. He is a founder of the Canadian Journal of Statistics and the Statistical Society of Canada. He was instrumental in the implementation of the United Nations Basic Space Science Initiative (1991-2012). This paper highlights research results of A.M. Mathai in the period of time from 1962 to 2015. He published over 300 research papers and over 25 books. [ABSTRACT FROM AUTHOR]

This paper addresses two critical issues in mathematics education, the need: (a) to understand the nature of educator's subject matter knowledge and pedagogical content knowledge; and (b) to find ways to measure them. It stems from a mixed-methods study designed to inspect the secondary mathematics teachers' pedagogical content knowledge (PCK) related to the area of a trapezoid, a common topic in intermediate/secondary school classes. Based on the provided exemplars of student work, in-service teachers were invited to propose possible ways for addressing perceived difficulties of students and provide extensions. Using a Grounded Theory approach, we identified themes in our data and incorporated them with existing conceptualizations of knowledge for teaching secondary level mathematics, and developed rubrics that allow discriminating different levels of teachers' PCK. In this paper, we describe the process of developing the rubrics, and propose ways to: (a) extend the existing frameworks for PCK in/for teaching mathematics at the secondary level; and (b) measure multiple facets of PCK in order to design technology-based professional development for mathematics teachers. [ABSTRACT FROM AUTHOR]

This paper reports on how 10 middle and high school preservice teachers (PSTs) designed a social justice focused lesson using the culturally responsive mathematics teaching (CRMT) tool. Results from our analysis indicate that most of the PSTs were able to select appropriate social justice topics, though not all the PSTs integrated mathematics and social justice throughout their lessons. The results show that most of the PSTs need more experience with mathematization, handling controversial discussions, and developing transformative student action. Our work also led to a modification of the tool (CRMT-M). We discuss the implications of the study for mathematics teacher preparation. [ABSTRACT FROM AUTHOR]

A time of crisis is a time of uncertainty, when many decisions need to be made. This study combines self-reflection, along with community inquiry, as three mathematics teacher educators recount a lesson that they taught in the past and how it was changed due to the COVID-19 crisis. Decisions were analyzed in terms of goals, orientations, and resources. The findings showed that the key issue was the immediate requirement to change one's regular routine. For some, resources were replaced. For others, dominant orientations receded to the background, and new goals were set. A final reflection conducted after returning to the classroom revealed how challenges during the crisis led to change and the adoption of new goals both during and after the crisis, clarifying our values and leading to the use of additional resources today. [ABSTRACT FROM AUTHOR]

In this paper we propose STEAM practices that would foster mathematics learning through modelling architecture while connecting to culture and history. The architectural modelling process is applied by the teachers as participants of these practices from different countries allowing a broad cultural and historical connection to mathematics education. The modelling is implemented in GeoGebra platform as it is an open-source platform to allow teachers to model on a mathematics basis. The architectural modelling process does not provide participants with steps to follow but rather allows them to explore the architectural models' components and construct them with various approaches which may foster problem solving techniques. We aim to investigate how different phases of this approach (such as motivation, modeling, and printing process) reflect on opportunities of learning in STEAM education, with a particular lens in mathematical development from open tasks. This paper will show two use cases that took place in Upper Austria and the MENA region. [ABSTRACT FROM AUTHOR]

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher's professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra. [ABSTRACT FROM AUTHOR]

Drawing on Martin's Multilevel Framework for Analyzing Mathematics Socialization and Identity Among African Americans this study explores the mechanisms that influence Black students' decision-making processes related to math course taking in high school. Three years of student transcript data for 1561 Black seniors in a Southern California school district were analyzed using descriptive statistics and logistic regression analyses in STATA. The findings reveal factors that impact students' ability and desire to complete a fourth year of math in high school, interconnected with institutional, structural, identity, and parental factors. One such finding is that accelerated 8th-grade math placement significantly increases the likelihood that a student would enroll in upper-level math coursework, such as "Beyond IM3" courses in high school. The researcher also investigated the influence of the concentration of Black math teachers in a school on the likelihood of a Black student enrolling in a Beyond IM3 math course. The results of this study contribute to an understanding of the limited racial diversity in STEM fields, highlighting the role of math as a major deterrent for Black students' interest and persistence in STEM. The findings suggest the need for policy and curriculum changes to promote equitable access to advanced math coursework for Black students, especially in the 8th grade. This study also emphasizes the need to address the structural and institutional factors that influence Black students' decision-making processes related to math course taking in high school. [ABSTRACT FROM AUTHOR]

While the pre-service teacher education (PSTE) programme holds global significance, there is a lack of evidence regarding its impact on the teaching practices of mathematics student teachers. Therefore, this study examines the impact of PSTE programmes on mathematics student teachers' teaching practices during school experiences. Grounded in a post-positivist paradigm, the study employs a mixed-methods research approach and a sequential explanatory mixed-methods design to gather data through questionnaires and semi-structured interviews. The research findings indicate that PSTE programmes have a significant impact on mathematics student teachers' ability to teach mathematical content that aligns with curriculum standards, enhances their subject knowledge, and increases their confidence. However, the programmes have minimal influence on their ability to implement differentiated instruction during their teaching practices. Based on these findings, the study concludes that although mathematics student teachers may lack the necessary skills to implement differentiated instruction, high-quality teacher education programmes can build their confidence and enable them to effectively manage their classrooms and adapt teaching practices to meet diverse learner needs. Therefore, the study suggests that stakeholders involved in PSTE programmes should provide continuous guidance and constructive feedback to help student teachers overcome challenges and improve their teaching practices. This support system is crucial for the success of the PSTE programme and has a direct impact on the quality of mathematics instruction in schools. [ABSTRACT FROM AUTHOR]

This quantitative, non-experimental study explored the relationship between the features of math and science teachers' preparation programs and their graduates' instructional rigor and persistence in teaching. Five math and science teacher preparation programs from across the United States were examined. Six sets of instructional tasks were collected from forty-six recent graduates of these programs to provide insights into novices' instructional rigor, and employment data were collected for thirty-seven of these graduates three to eight years after graduation. Regardless of the program's features, all teachers could design and implement instruction with moderate to high rigor. However, this ability was not the norm. Mixed-effect models suggest the strongest evidence between degree types (bachelor versus post-bachelor) was related to teachers' persistence: novices from graduate programs were more likely to persist in the work. However, no program feature was strongly associated with instructional rigor. Further research is needed to determine if the differences we found in teacher persistence are due to the nature of applicants drawn to particular programs (undergraduate versus graduate) or the program's structure. Future research is also needed to explore the influence of instructional context (i.e., district, school, and department norms for instruction) on math and science teachers' instructional rigor. [ABSTRACT FROM AUTHOR]

Research around mathematics teachers' professional noticing has been largely contextualised by the formal setting of the classroom. In addressing the lack of relevant studies in non-formal learning environments, this paper draws on student teachers' observations within a Mathematics Fair, which was part of a mathematics methods module of a primary education undergraduate programme. Working in pairs, 64 student teachers designed interactive mathematical games which upper primary school pupils had the opportunity to play in an event having taken place at our university. In this study, we analyse student teachers' individual reflective essays written after the Fair, where they discussed important, in their view, incidents and observations. Employing a thematic analysis approach, we identified four themes discussed by students: the task; learning; teaching; non-formal environment. We conclude with the implications for teacher education and suggestions for future research. [ABSTRACT FROM AUTHOR]

In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers' professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished using MOOCs. By taking into account the MOOC "Task Design for Math Trails", with 93 finalists, we analyze the learning progress of 19 selected case studies from different nations and learning levels by taking into account their answers in a pre- and post-questionnaire and their posts on a specific communication message board, with a special focus on the MOOC's topics' task design for outdoor mathematics and the digital tool MathCityMap. The analysis is performed using different quantitative and qualitative approaches. The results show that the teachers studied have benefited from professional development, which is evident in the expansion/evolution of their knowledge from a content, pedagogical, and technological perspective. Finally, we formulate consequences for professional development in STEM education, and conclude the paper with limitations to be drawn and a perspective for further research. [ABSTRACT FROM AUTHOR]

This paper reports an investigation of mathematical resources available on the social media site Pinterest. Pinterest is an online bulletin board where users create visual bookmarks called pins in order to share digital content (e.g., webpages, images, videos). Although recent surveys have shown that Pinterest is a popular reference for teachers, understanding of the mathematical resources available on the site is lacking. To take initial steps in investigating the curriculum resources provided by Pinterest, we used keyword searches to gather a database of pins related to the topic of negative integers. A content analysis was conducted on the pins with a focus on several characteristics including mathematical operations, mathematical models, use of real-world context, and whether mathematical errors were present in source material. Results show a dominance of addition and subtraction over other operations, use of mathematical models in half of pins, infrequent use of real-world context, and mathematical errors in roughly one-third of pins. We provide a breakdown of these results and discuss implications of the findings for mathematics teacher education and professional development. [ABSTRACT FROM AUTHOR]

This article is a self-narrative of our 18-year research into the Technological Pedagogical Content Knowledge (TPACK)-guided professional development of teachers in ICT-enhanced mathematics learning. Using autoethnography as the methodology to elucidate our transformative personal evolution in implementing the TPACK model, we describe how we conceptualized and enacted the TPACK framework across three distinct phases of our research trajectory. In the first phase, our efforts focused on offering afternoon seminars and workshops on using educational software. Mathematics teachers attended the seminars and workshops voluntarily. In the second phase, we concentrated on designing programs guided by the principles of adult education, which emphasize the importance of learner autonomy and relevance, and socio-constructivist views of teacher professional growth, which stress the role of collaboration and reflection in learning. In the final phase, we adopted a systemic, school-based approach to investigating and expanding TPACK for mathematics and other STEM/STEAM teachers. At the end of each phase's description, we delve into the profound lessons learned and how these led to a paradigm shift, expanding our perspective on TPACK as practitioners and researchers. Finally, we present a set of recommendations for future research and practice aimed at facilitating the sustainability of STEM/STEAM teacher professional learning initiatives. [ABSTRACT FROM AUTHOR]

Assessment for learning (AFL) has been associated with curriculum and teaching reform for the past three decades. However, studies on undergraduate students' perceptions of their mathematics teachers' AFL practices are still very limited in the Chinese higher education context. This quantitative study investigated three independent variables—teacher formal feedback and support, interactive dialog and peer collaboration, and learning-oriented assessment—that influence undergraduate students' ability to take responsibility for their learning through the mediation of the factor of active engagement with subject matter in first-year mathematics courses. One hundred and sixty-eight students from a Chinese "double-first-class" university were recruited to provide valid questionnaire data using the convenience sampling method. Partial least-squares structural equation modeling (PLS-SEM) was used to analyze the data. The results showed that interactive dialog and peer collaboration, as well as learning-oriented assessment, have a direct effect on students' active engagement with the subject matter and an indirect effect on undergraduate students taking responsibility for their learning in first-year mathematics courses. In addition, learning-oriented assessment was the biggest factor influencing undergraduate students' ability to take responsibility for their learning in first-year mathematics courses. This study contributes by developing a conceptual model and providing new insights into Chinese higher education sectors on factors that can improve undergraduate students' ability to take responsibility for their learning. [ABSTRACT FROM AUTHOR]

This document is the introduction to a special issue of the journal Education Sciences focused on critical perspectives in mathematics teacher education. The authors argue that mathematics education research should encompass not only cognitive but also cultural, social, and political issues. They use the term "critical" to address these issues from a Freirean perspective, aiming to inspire learners and educators to understand and critique power structures and patterns of inequality. The special issue covers a range of critical perspectives in mathematics teacher education, including coursework with prospective teachers, professional development for practicing teachers, and theoretical reflections on research and practices. [Extracted from the article]

This research investigates how minority students demonstrate their math self-efficacy and performance, shaped by factors such as class preparation and math teacher support. Leveraging a comprehensive US national dataset, this study aims to provide broadly applicable insights and suggestions for students from diverse racial and linguistic backgrounds. The findings underscore the substantial influence of high school students' class preparation on teacher support, math self-efficacy, and math performance. Notably, teacher support exhibits a positive impact solely on math self-efficacy but does not extend to their math performance. Upon examination of various demographic groups, this research identifies noteworthy disparities in the effects experienced by different racial and linguistic groups. This study's results carry practical implications for educators and practitioners, shedding light on strategies to enhance various minority students' math self-efficacy and outcomes. [ABSTRACT FROM AUTHOR]

Although the field of mathematics education has made gains in centering the need for justice-oriented approaches and antiracist teaching practices in teacher education, much of this work remains in its infancy. Moreover, research focused on this area highlights teacher candidates' knowledge and dispositions and often ignores the role of the mathematics teacher educators facilitating the process. We contend that mathematics teacher educators must pay more attention to how intersectional identities, contexts, Mirror Tests, and principles of Rehumanizing Mathematics manifest in teacher education to better understand how teacher candidates develop political knowledge in teaching mathematics. To this end, we introduce a framework of considerations, which we call a compass, that identifies four dimensions (or strands) and offers guiding questions for mathematics teacher educators to consider. We offer examples from a multi-site research study to illuminate each dimension and build the case for the necessity of braiding the four strands together as we engage in this line of work. Implications for practice and future research are discussed. [ABSTRACT FROM AUTHOR]

This paper examines how 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face to face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, TCs, classroom mentor teachers, field experience supervisors, and university faculty formed a Networked Improvement Community (NIC) to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the NIC at the subsequent monthly meeting. The Technology Pedagogical Content Knowledge framework (TPACK) and the TPACK levels rubric were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP2) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs. MCOP2 results indicated that TCs increased their use of effective mathematics teaching practices. However, growth in TPACK was not significant. A relationship between TPACK and MCOP2 was not evident, indicating a potential need for explicit focus on using technology for mathematics conceptual understanding. [ABSTRACT FROM AUTHOR]

After providing a brief summary of what has already been said about pedagogical imagination, data are presented showing how prospective mathematics teachers can become engaged in such imaginations. With reference to this data, the notion of pedagogical imagination is explored further by relating it to dialogue, social justice, mathematics, hope, and sociological imagination. To illustrate these relationships, different episodes from the data are highlighted. Finally, the central role that pedagogical imagination can play in mathematics teacher education is discussed. [ABSTRACT FROM AUTHOR]

Teacher preparation to address the needs of disabled learners in mainstream mathematics classrooms is quintessential for the implementation of the inclusive educational policies that governments are often committed to. To identify teacher preparation needs, we draw on data and analyses from the doctoral study of the first author, who endorsed sociocultural and embodied perspectives in an investigation—first exploratory, then interventional—of visually impaired (VI) learners' experiences and their teachers' inclusion discourses. Here, we focus on the intertwined contributions of physical and digital resources in the mathematical learning experiences of VI pupils, as these resources co-existed simultaneously in the observed mathematics lessons. We first summarise findings from the exploratory phase that highlighted inclusion issues related to resource use in the mathematics classroom. We then offer a critical account of the circumstantial and systemic obstacles that impeded the successful intertwinement of digital and physical resources and discuss teacher–researcher collaborative design and implementation of classroom tasks (auditory, tactile) in the intervention phase. We conclude by making the case that well-meaning individual teacher–researcher collaboration is a necessary condition for such interventions to succeed but not a sufficient condition for these interventions to be scaled up and have longevity. [ABSTRACT FROM AUTHOR]

U.S. educational reform is often the harbinger of global demands on mathematics education practices globally. It behooves teacher education to 'catch up' on current trends, hopefully, to stave off the worst of the fascist tendencies of contemporary politics of education. Past foci on research-based 'best practices' and 'mathematics for all', grounded in liberal multiculturalism (confirming expectations from critical mathematics education scholarship), have become the targets of activists and politicians, turning once-exemplary teachers and their students into casualties. The four phases of currere are employed to study this phenomenon and to identify strategies and tactics for teacher education programs. The currere methodology indicates that the content of such programs must reduce time devoted to evidence and research-based practice in order to accommodate techniques and knowledge bases for the recognition of right-wing tactics, clowning, slogan parody, and political organizing. Teacher education must further place mathematics teachers' embrace of expertise, authority, and neutrality within broader perspectives on the politics of education, organizational infrastructure strategies and tactics, resource curation, and personal safety planning. Teacher educators themselves must prepare responses to threats on their careers, lives, and families, and proactive 'game plans' for the development of new program curricula. [ABSTRACT FROM AUTHOR]

Over the past 30 years, teacher education has changed to incorporate a larger emphasis on understanding students' sociocultural backgrounds, knowing that these influence their learning. However, in terms of mathematics and mathematics education in teacher education, less has been done to recognise the sociocultural mathematics backgrounds of students. An example is provided to show how entrenched colonial attitudes to mathematics have developed into neocolonial policies that influence mathematics education. This example is based on a large historic research project in Papua New Guinea (PNG) that aimed to document and analyse the nature of mathematics education from tens of thousands of years ago to the present. Data sources varied from records of first contact and later records, archaeology, oral histories, language analyses, lived experiences, memoirs, government documents, field studies, and previous research especially doctoral studies. The impacts of colonisation, post-colonial aid and globalisation on mathematics education have been analysed, establishing an understanding of the current status of mathematics education as neocolonial. Neocolonial education policies diminish cultural ways of thinking. Thus, teacher education has an important role in sensitizing preservice and inservice teachers to the impact of neocolonial approaches as well as in developing with students some ways of reducing this impact and encouraging more holistic, culturally relevant mathematics education. [ABSTRACT FROM AUTHOR]

Inquiry, an approach that departs from traditional mathematics teaching, empowers students through active participation and increased accountability in exploration, argumentation, evaluation, and communication of mathematical ideas. There is broad research consensus on the benefits of inquiry-based approaches to teaching and learning mathematics, including their potential to support equitable mathematics classrooms. While research has separately explored teachers' conceptions of inquiry and their efforts to enact the practice, little is known about the interplay between mathematics teachers' conceptions and enactment, and how it could be harnessed in professional development. In this study, we follow Alex, an experienced upper secondary mathematics teacher unfamiliar with inquiry, as he participates in a one-semester professional development course that draws on inquiry in multiple ways. His trajectory towards learning to teach through inquiry is revealed through patterns and shifts in his reflections and classroom actions. Our findings reveal significant developments in Alex's conception of inquiry and in how he realizes it in his classroom, identifying three paths that illuminate his inquiry trajectory: the teacher's role in inquiry interactions, a growing idea of inquiry, and orchestrating whole-class situations. In the interplay between enacting and reflecting, he moves from distributing authority separately between himself and 'the students' (as one unit) to fostering shared authority, a key aspect of empowerment, between himself and his students (as multiple voices) in both groupwork and whole-class episodes. [ABSTRACT FROM AUTHOR]

The discussion about first-year engineering students' difficulties in mathematics is continuous in the fields of engineering, mathematics and higher education. The present study aimed to examine the initial barriers academic math teachers need to have in mind if they want to improve students' performance in engineering math courses through appropriate teaching practices in order to face their initial interindividual differences. During the first phase of the study, we examined first year engineering students' initial beliefs about the nature of mathematics, their self-efficacy beliefs about mathematics and their basic mathematical knowledge. The math school grade was used for their previous mathematical performance. Results indicated the predominant role of the previous mathematical knowledge and the important role of the formalistic disposition toward mathematics. The lack of experience of using mathematics for problem-solving situations within an engineering framework prevented students from recognizing and appreciating the value of mathematical courses during the engineering studies. The second phase of the study examined, through an interview with a group of students, their perceptions of the teaching practices which were introduced after their teacher attended a training program. The discussion concentrates on how academics can use teaching processes for equity and not equality in order to motivate their students. [ABSTRACT FROM AUTHOR]

In the paper, we present a study devoted to the utilization of multiple-solution tasks (MSTs) in combinatorics as a part of a pre-service teachers course on didactics of mathematics from the view of the mathematics teachers' specialized knowledge (MTSK) theoretical framework. The study was carried out over the standard course of a summer semester in 2021. The course was attended by 13 pre-service teachers (PSTs). It was carried out online, due to COVID-19 restrictions. Ten combinatorial multiple-solution tasks were assigned to the PSTs. Analyzing pre-service teachers solutions to these tasks, we sought the description and better understanding of the combinatorial knowledge of the topic from the perspective of MSTK. The results revealed some critical aspects of mathematical knowledge in combinatorics that pre-service teachers education should focus on. [ABSTRACT FROM AUTHOR]

This paper aims to illustrate how a teacher instilled norms that regulate the theorem construction process in a three-dimensional geometry course. The course was part of a preservice mathematics teacher program, and it was characterized by promoting inquiry and argumentation. We analyze class excerpts in which students address tasks that require formulating conjectures, that emerge as a solution to a problem and proving such conjectures, and the teacher leads whole-class activities where students' productions are exposed. For this, we used elements of the didactical analysis proposed by the onto-semiotic approach and Toulmin's model for argumentation. The teacher's professional actions that promoted reiterative actions in students' mathematical practices were identified; we illustrate how these professional actions impelled students' actions to become norms concerning issues about the legitimacy of different types of arguments (e.g., analogical and abductive) in the theorem construction process. [ABSTRACT FROM AUTHOR]

The paper is a reflection on the author's work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the diversity of mathematical ideas behind a contextual question asked by a second-grade pupil allowing for multiple solution strategies to be used in addressing the question. The second issue deals with the use of Wolfram Alpha in aiding different mathematical features of this demonstration. The paper is congruous with mathematics teaching standards used across six continents and illustrated by reflective comments of the author's students regarding their mathematics teacher education experiences. Teaching ideas shared in the paper may be of interest to instructors who want to explore elementary mathematics in depth with teacher candidates. [ABSTRACT FROM AUTHOR]

Research on mathematics teachers' knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student' learning of PS. [ABSTRACT FROM AUTHOR]

In 2020, Germany and Spain experienced lockdowns of their school systems. This resulted in a new challenge for learners and teachers: lessons moved from the classroom to the children's homes. Therefore, teachers had to set rules, implement procedures and make didactical–methodical decisions regarding how to handle this new situation. In this paper, we focus on the roles of mathematics teachers in Germany and Spain. The article first describes how mathematics lessons were conducted using distance learning. Second, problems encountered throughout this process were examined. Third, teachers drew conclusions from their mathematics teaching experiences during distance learning. To address these research interests, a questionnaire was answered by N = 248 teachers (N1 = 171 German teachers; N2 = 77 Spanish teachers). Resulting from a mixed methods approach, differences between the countries can be observed, e.g., German teachers conducted more lessons asynchronously. In contrast, Spanish teachers used synchronous teaching more frequently, but still regard the lack of personal contact as a main challenge. Finally, for both countries, the digitization of mathematics lessons seems to have been normalized by the pandemic. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic generated a new scenario in education, where technological resources mediate teaching and learning processes. This paper presents the development of a virtual teacher training experience aimed at promoting inferential reasoning in practicing and prospective mathematics teachers using inference problems on the Chi-square statistic. The objective of this article is to assess the implemented or intended institutional meanings and the degree of availability and adequacy of the material and temporal resources necessary for the development of the training experience. For this purpose, we use theoretical and methodological notions introduced by the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA), among which are the notions of practice and suitability criteria. The participants of this experience were divided into three groups; one of them was comprised of practicing teachers and the other two of prospective teachers. The intervention used different virtual modalities that enabled the development of the participants' inferential reasoning in a similar way. [ABSTRACT FROM AUTHOR]

This paper discusses a model of a mathematics teacher professional development implemented in Italy and Hungary with in-service and pre-service mathematics teachers. The model focuses on comparative geometry, and it develops with the use of an artifact: the Lénárt spheres. The teacher training model is the result of several years of experience of the two authors both as regards the activities in the classroom with the Lénárt spheres and as regards the training of teachers in this field. The proposed teachers' professional development, in addition to providing ideas for activities to be implemented in the classroom, has the objective of proposing reflective activities from a community of inquiry perspective; during the activities, mediated by the artifact, both the Pedagogical Content Knowledge and the Mathematical Content Knowledge are taken into consideration (Ball et al., 2008). The model has been implemented in Italy in more than 15 training courses taught in the last 5 years, both with primary school teachers and with secondary school teachers. In Hungary, the model is at the basis of elective courses under the title 'Ball Geometry' at ELTE University, Budapest, for decades. These courses have been aimed at prospective preschool and elementary school teachers at the Faculty of Primary and Preschool Education, as well as future secondary teachers at the Faculty of Natural Sciences. The subject of the teachers' professional development paths corresponds to the comparative geometry between the plane and the sphere. After the presentation of the model, some examples of activities implemented in Hungary during the pandemic period will be illustrated and commented from a didactic point of view, which will serve to exemplify the path described. The described path was carried out remotely in online mode through synchronous and asynchronous activities. The distance obviously changed the way we interacted with the artifact, but it did not prevent the achievement of the courses' objectives. [ABSTRACT FROM AUTHOR]

This paper presents a long-term study of Preservice Mathematics Teachers (PMTs) at the Faculty of mathematics, physics and informatics, Comenius University in Bratislava (FMFI UK), focusing on the implementation of digital technologies (DT) into the teaching of theoretical and practical (or applied) subjects. We conducted parallel research into two aspects, one on Calculus lessons as a theoretical subject, another on the Financial Mathematics module as an applied subject. The implementation of DT and the way this was measured varied from year to year and also in the method of implementation into the aforementioned subjects. The methods of implementation and the results are briefly described, and a comparison of these two subjects in the PMTs' preparation is also discussed. [ABSTRACT FROM AUTHOR]

Although the knowledge required by mathematics teacher educators is a relatively recent area of research, there has been significant progress in the field over the last few years. The classic distinction of a teacher's knowledge into content knowledge and pedagogical content knowledge prompts us to reflect in this regard on what should constitute the content of primary teacher education programmes, and how the educator might mediate this content to make it accessible to their prospective teachers. This paper aims to contribute to this progress through a study into the work of Lucas, a teacher educator, during the course of a training session with prospective primary teachers. Critical observation of the video recording brought to the fore salient teaching situations on the topic of symmetry, which led us to explore the pedagogical content knowledge deployed in the session through a guided interview with the educator. Analysis of extracts from this interview enabled us to identify three main categories of this PCK: knowledge about how to teach programme content; knowledge about the characteristics of prospective primary teachers' learning; and knowledge about the standards and norms of primary teacher education programmes. [ABSTRACT FROM AUTHOR]