Teacher Education Professional Development Research Articles

Signature pedagogies of teacher education in physical education: a scoping review

ABSTRACT Introduction and purpose There is a need for contemporary studies which establish a shared language to further analyze and develop pedagogies in the field of teacher education in physical education (PE). This includes both initial teacher education (PE-ITE) and continuous professional development (PE-CPD), holding the responsibility for preparing pre-service teachers (PSTs) and teacher educators, as well as facilitating the ongoing professional learning of in-service teachers (ISTs) and teacher educators. This study entails a comprehensive scoping review covering the period from 2015 to 2023, encompassing studies within the broad field of teacher education in PE across international contexts, all examined through the perspective of Shulman’s, L. S. (2005. “Signature Pedagogies in the Professions.” Daedalus 134 (3): 52–59) concept of signature pedagogies. The purpose was two-fold: (1): to map the current literature on teacher education in PE (including PE-ITE and PE-CPD for both ISTs and teacher educators), and (2) to propose a preliminary shared language of signature pedagogies of teacher education in PE. Theoretical lens Signature pedagogies refer to the forms of teaching-learning that leap to mind when thinking about the preparation and ongoing learning and development of teachers (i.e. pre-service teachers, in-service teachers and teacher educators; Shulman, L. S. 2005. “Signature Pedagogies in the Professions.” Daedalus 134 (3): 52–59). Signature pedagogies are both pervasive and routine, cutting across topics and courses, programs, and institutions, and are described through three layers of structure – the surface, deep, and implicit. Method The research process was guided by a five-stage framework for conducting a scoping review. In line with the specific purposes articulated above, the research question guiding the review was: What is known from the literature on signature pedagogies of teacher education in PE? The search was restricted to articles published between 2015–2023. Both empirical and conceptual articles (i.e. those with data collection and those without) were included, provided the inclusion criteria were met. A total of 465 articles were included in the review, and the pedagogies identified from each article were co-constructed into themes/categories. Findings and discussion Three signature pedagogies of teacher education in PE across international contexts are identified and presented in terms of their surface, deep and implicit structure, including: (auto)biographical pedagogies, experiential pedagogies, and pedagogies of professional learning. Subsequently, we explore the similarities and differences between each of the three groups of pedagogies and what makes a pedagogy of teacher education in PE distinct from a pedagogy of teacher education more broadly. Conclusion and further research This study offers a preliminary shared language of teacher education pedagogies in the field of PE and is intended to open a dialogue around preparing and supporting pre-service teachers, in-service teachers, and teacher educators in the context of PE. While this review represents an initial step in addressing a gap in the literature by exploring and articulating teacher education pedagogies in PE, there remains a need to analyse their use across teacher education contexts and to consider how this shared language might inform a more intentional practice of these pedagogies within and across teacher education contexts in ways that might ensure more authentic, transformative and equitable teacher education practices in PE.

Identifying Teaching and Laboratory Instruction Concerns of Illinois Agriculture Teachers

Concerns of teachers must be identified to provide quality teacher education programs and professional development. The theoretical framework of this study was the Teacher Career Cycle (Fessler & Christensen, 1992). The theory explains that as teachers move through the cycle, their characteristics and professional needs change. The purpose of this study was to identify the concerns of Illinois agriculture teachers of different experience levels. A multi-part instrument of demographic information, two teacher concern statements, and a Likert-type scale of concerns was administered. The sample was divided into three experience groups: early career, mid-career, and late career. The results indicate that certain concerns do change with the level of experience and that mid-career teachers in this sample have the most concerns. We recommend that these results be shared with the Illinois Association of Vocational Agriculture Teachers, universities, state agricultural education staff, and other stakeholders. Those leading professional development should consider years of experience when planning for workshops. Professional development topics on student motivation, funding for supplies, and student safety should be explored.

Content teachers’ beliefs and attitudes toward working with multilingual learners through integrative approaches

IntroductionThe fast-growing population of multilingual learners (MLs) in U.S. schools calls for ML-focused instructional support from content classroom teachers to acquire content knowledge and language proficiency simultaneously. However, teachers in general lack competency in content-language integrative pedagogy that builds on MLs’ transliterate capabilities, placing MLs at a greater disadvantage in the content classroom. Given that teachers’ classroom practices are shaped by their underlying language ideologies, it is important to examine what ideological beliefs and attitudes teachers are operating with for their day-to-day work with MLs. Framed by scholarship on content-language integrated instruction, language ideologies, and transliteracies approaches, this study examined the relations between content teachers’ ideological beliefs and attitudes toward teaching MLs in the content classroom and several teacher-related variables.MethodsThis study employed a sequential mixed-methods design for a more comprehensive understanding of teachers’ ideologies about working with MLs. Quantitative data analysis was conducted by confirmatory factor analysis and multiple regressions using survey responses of in-service content teachers (N=100) followed by focus group interviews (N=24).ResultsResults of a confirmatory factor analysis using a survey suggested that teachers who were more likely to endorse English-only monolingual pedagogy did not necessarily view themselves as having lesser sensitivity to MLs’ backgrounds in their classroom. Results of regression analyses showed that teachers using pull-out or push-in instruction were more inclined to support language-integrated content teaching and considered themselves more sensitive to MLs’ backgrounds than teachers who instruct specialized content. Interestingly, the specialized content teachers having a greater percentage of MLs in their classroom were more supportive of the language-integrated content teaching pedagogy than other teachers using the teaching role. Analysis of focus groups provided contextualized rationales for teachers’ chosen stances toward the English-only monolingual, separatist pedagogy or the transliterate, integrative pedagogy for MLs.DiscussionThe findings demonstrated that teachers’ ideologies were not merely individual beliefs but also intertwined with the hegemonic language ideologies of the larger education system. The complexity of the shifting ideologies points to the pressing need for integrating ML-specific attention into teacher education and ongoing professional development programs.

The Power of Visuals: The Significance of Higher Education Teacher Professional Development in Visual Literacy in Kuwait

This study explores the role of higher education professional development in the integration of visual literacy instruction at the university level. Visual literacy is a crucial skill that empowers students to comprehend and generate visual content across diverse domains. However, many instructors lack necessary training and support to effectively incorporate visual literacy into their teaching practices. The research survey investigates the significance of teacher professional development in visual literacy implementation, encompassing the status of training, effective professional development programs for teachers, suitable teaching methods, education technologies, attitudes of higher education instructors towards visual literacy, and the influence of student engagement with visual materials on visual literacy advancement in Kuwait. The questionnaire was administered to a sample of higher education teachers. That data was analyzed employing descriptive and inferential statistical techniques, with SPSS v.26 software. Regression analysis and other multivariate analyses were conducted to test the research hypothesis and model. The outcomes should provide insights into the effectiveness of collaborative, experiential, and technology-enhanced teacher professional development programs in fostering visual literacy development within higher education, the significance of student engagement with visual materials, and the necessity for further research on effective teaching methods and educational technologies for promoting visual literacy. The findings can inform policy and practice by highlighting the importance of equipping higher education instructors with necessary skills and resources to effectively incorporate visual literacy into their teaching approaches, enhancing the quality of higher education by fostering competencies among students and facilitating their engagement with visual materials across various disciplines.

Is meaningful physical education and social justice a complimentary combination? A physical education teacher educator collaborative self-study

ABSTRACT Background Physical Education Teacher Education (PETE) programmes are expected to support future teacher learning about contemporary innovations and big ideas for teaching physical education. Teacher educators are challenged to learn about and incorporate contemporary innovations while maintaining programme cohesion. Exploring how teacher educators make sense of and teach about innovations, such as ideas related to meaningfulness, alongside foundational ideas, such as social justice, can provide insight on teacher educator pedagogies and their professional development journeys. Purpose This study explored the concepts of and relationship between Meaningful PE and social justice in our teacher education pedagogies when implemented in combination. We pay particular attention to when ideas of Meaningful PE and social justice were complementary, overlapping and when they were distinctive. Method A self-study of teacher education practices methodology supported four teacher educators to collectively and individually interrogate our evolving understanding, decisions and practices across a 13-month period. [Loughran, J. 2014. “Professionally Developing as a Teacher Educator.” Journal of Teacher Education 65 (4): 271–283] signposts for teacher educator professional development provided theoretical guidance to make sense of our experiences combining the two pedagogies. This paper focuses on the recordings of collective meetings (n = 9, over 12 h) where we shared and analysed experiences, raised questions and formulated developing understandings of the relationship between teaching for meaningfulness and social justice approaches. Data analysis involved thematic analysis methods to review all data and collective identification and refinement of themes through back-and-forth discussion. Findings From the thematic analysis, the following themes were co-created: (a) Meaningful PE can act as social justice but is not social justice per se; and (b) the combination of Meaningful PE and social justice facilitates a dance between ‘the individual’ and ‘the social’ with democratic and reflective practices as the choreography. These features of the relationship provide direction and encouragement to combining Meaningful PE and social justice ideas in teacher education pedagogies. Conclusions Through cycles of experiencing and articulating, we made sense of the relationship between Meaningful PE and social justice. Our story highlights the value of teacher educators engaging with knowledge and practice of teaching about teaching and learning about teaching in the context of innovation.

Towards practice-based professional development by teacher educators

Teacher education reform has advocated the implementation of widely espoused pedagogic changes in many contexts, particularly in Sub-Saharan African countries. This paper focused on the central agents in the reform process, i.e., teacher educators. Framed within the emerging conceptualizations of practice-based professional development of teacher educators, the study explores perspectives for improving educators’ teaching based on the self-study experiences of the first author while supporting the reflective practices of a group of student teachers in Eritrea. Self-study methods and tools including interactive discussions among colleague educators and critical friends, journaling, and course artifacts were used while developing the findings. The findings identified the dynamics of how researching situated concerns of teaching and learning frames problems of practice and also invokes sources and situations for developing motivations of educators in maintaining inquiry and improvement stances. We argue that such a dynamic is critical in productively engaging with teacher educators' professional learning in practice in similar contexts.

Teacher education effectiveness as an emerging research paradigm: a synthesis of reviews of empirical studies published over three decades (1993–2023)

ABSTRACT Numerous reviews have synthesized the empirical research on the effectiveness of teacher education, highlighting teacher education effectiveness research (TEER) as an emerging research paradigm. Our systematic search identified 27 reviews related to TEER, wherein teacher education is broadly understood as comprising all stages of teacher professionalization—namely, initial teacher education, teacher induction, and teacher professional development. In reviewing these reviews, we carry out a synthesis of existing research on TEER. Guided by four research questions (RQ), we focused major frameworks (RQ1), outcome measures (RQ2), processes (RQ3), and central research gaps (RQ4). Highlights: Only few reviews provide a background or macro framing, whereas most reviews apply TEER for examining a specific topic (RQ1); outcome measures often relate to the notion of teacher competence, making increased competence the true outcome of TEER (RQ2); coursework is the most dominant category of characteristics-forming processes (RQ3); the frameworks underlying the outcome measures appear to be an object of criticism on a theoretical but even more on a methodological level. Building on these findings, we suggest a processes-and-criteria classification (PCC) grounded in basic distinctions of the various studies synthesized by the reviews. We discuss perspectives on how this classification may provide an orientation for future TEER studies.

Technology Integration in Christian Religious Education Teacher Professional Development to Produce Scientific Writing

Scientific writing is one of the tasks in the professional development of teachers and the requirements for promotion outlined by the Ministry of Education in Indonesia. Producing scientific writing requires skills, and this is a trending issue among Christian religious education subject teachers in Indonesia today, how they struggle to develop effective scientific writing. At present, in private and other public schools, it is common for teachers to produce writing using digital technology. However, this has not happened for teachers of Christian religious education subjects. Integrating technology in schools by Christian religious education subject teachers can help improve writing initiatives and skills that focus on writing pedagogy. This initiative will provide technical support to teachers of Christian religious education so they can focus on writing scientific papers. Professional development of teachers in the subject of continuing Christian religious education based on scholarly writing will emphasize how to utilize digital tools to deliver evidence-based writing instructions. Christian Religious Education subject teachers gain the most when given systematic and explicit instruction in science-based strategies for writing and the writing process, and how to make effective use of digital tools as part of the scientific paper writing process

FOREIGN LANGUAGE LEARNING USING A COMMUNICATIVE APPROACH WITH NEW LITERACY THEORY

This study discusses a number of influences related to teachers' understanding of the application of new literature theory and communicative learning, such as teacher trust, teacher education, and teacher professional development. The research is literature-based, with documentary data collection and analysis methods using content analysis. This research focuses on important issues that can help in the development of foreign language teaching curriculum. The focus of discussion in this article includes the lack of understanding of new literacy theories and communicative language teaching methods, curriculum understanding, teacher professional development through new literacy theories, and ideological tensions arising from the foreign language teaching gap in Indonesia. Implementation of the contemporary curriculum may differ between cities and villages. The lack of language activities, especially listening and speaking skills, in the old curriculum is what causes apathy and boredom among students and prevents them from interacting with their communities.

Professional Development Progress of Rural Aesthetic Education Teachers in China —Visual Analysis Based on CiteSpace

Rural teachers are a crucial driving force behind the development of China's rural education, and their professional development has a direct impact on its progress. However, there exist significant challenges that hinder the development of rural aesthetic education, including a shortage of qualified teachers and low-quality instruction. This paper analyzes the current state of rural aesthetic education teacher professional development in China based on papers published in CNKI database core journals from 2012 to 2022. The results indicate that while research on rural teachers' professional development has shown steady growth in terms of volume, it has yet to develop into a comprehensive research system. Moving forward, future studies should focus on addressing the deep-seated issues facing rural teachers' professional development using innovative technological tools, as well as exploring new methods for conducting research on this topic.

Science Teaching in Culturally Diverse Classrooms: Application of Sociocultural Knowledge at a School System in Nepal

ABSTRACT This study focuses on teaching and learning science in three secondary public school classrooms with mostly culturally marginalized students from Gurung and Magar communities in a semirural district in Nepal. The study aims to understand how three science teachers in different schools engage students in culturally relevant transformative science learning. I use a constructivist case study design. Data were collected through 18 classroom observations, three interviews with science teachers, and a student focus group interview. Analysis of the data showed that culturally marginalized students are experts in the cultural knowledge they bring into the classroom, science teachers felt ambivalence between culturally relevant science and success in tests, and science teachers showed a need for greater pedagogical skills in cultural relevancy. The study suggests a need for focused and intentional culturally relevant courses in science teacher education programs and professional development. Educating teachers for more transformative and relational science teaching will support embedding cultural knowledge and values in classroom teaching and curriculum.

Changing teacher educator cognition within a collaborative teacher education programme for CLIL: A case study in China

This study reports on a six-month collaborative teacher education programme designed to support the implementation of Content and Language Integrated Learning (CLIL) in the Chinese primary education context. ‘Activity theory’ was used as an analytical framework to investigate the changes in cognition regarding CLIL experienced by two teacher educators – one at district level and the other at school level – and the factors that contributed to shifts in their cognition. Thematic analysis was conducted on data consisting of semi-structured interviews, field notes, a reflective report, and project meeting minutes. Results indicate that for both teacher educators, the programme functioned as an activity system that facilitated the emergence of advanced cognition of CLIL over the six months of the project, and did so along two distinct trajectories, one focusing on pedagogical applications of CLIL tenets and the other centring on implementing CLIL as an educational policy. The results also show how the collaborative nature of the teacher education programme fostered the expression of diverse views as well as shared motives through frequent interaction and co-construction of knowledge. As such, it offers a viable alternative to more traditional top-down approaches that are used to foster the professional development of teacher educators.

The pedagogy of teacher education in Ethiopia: Reconstructing understandings and practices on teaching about teaching and learning to teach

There is an argument that Marshal McLuhan’s ‘the medium is the message’ adage is more likely to be underpinned in the context of teacher education since pedagogy is not only a means of delivering content in teacher education but also the content (what) in teachers’ professional preparation (Grossman, 2009). The quality of teacher education depends heavily on the practice of teacher educators and the learning experiences of student teachers: Pedagogy of teacher education. The pedagogy of teacher education is conceptualized as teaching about teaching and learning to teach. Using primary data from teacher educators and student teachers and secondary data sources (documents and research studies), the paper examined and reflected on Ethiopian teacher education pedagogy. Questionnaire, interview and observation were used to collect primary data. The findings revealed ingrained assumptions that student teachers learn to teach by learning theories and facts of different courses through lectures, discussions, and group work. Teacher educators in the study characterized their typical classroom as a combination of ‘reviewing of the previous lesson, explanation, discussion, and lesson summary’ which inherently reflects features of a typical classroom in Ethiopian schools. When asked which pedagogies help student teachers to learn to teach, teacher educators mentioned group work, discussion, lecturing, oral questioning and classwork, quiz, and practicum (ordered in terms of frequencies). It is argued that teaching about teaching and learning to teach are customarily reduced to the delivery and learning of course contents rather than the ‘how’ of teaching through teacher educators’ modeling and reflection, student teachers’ school experiences, or other pedagogies that develop learning to teach among student teachers. Teacher educators’ practices, however, in some cases demonstrated elements of active learning techniques aimed at improving mastery of content and practicing teaching skills. However, their interview responses on preparing teachers largely lack pedagogies relevant to learning to teach. Efforts to improve the quality of education in general and teacher education, in particular, should prioritize the critical examination and reform of teacher educators’ preparation, professional development of teacher educators, and pedagogical practices at teacher education colleges and universities.

How early career teachers overcome everyday work-related challenges: an analysis from the perspective of teacher buoyancy

ABSTRACT Drawing on the concept of teacher buoyancy which is teachers’ capacity to deal with the everyday challenges that most teachers face in their teaching, this qualitative study investigates the capacity of ten early career teachers to derive sustenance from overcoming minor and frequent challenges in their everyday work. A semi-structured interview was used to investigate early career teachers’ adaptive and proactive experiences dealing with frequent challenges at work. Findings indicated that early career teachers utilised problem-focused strategies, cognitive-related strategies, and well-being and emotion-related strategies, and mobilised different personal and contextual resources to sustain themselves in the realities of their professional work and life. This study advocates the enhancement of teacher buoyancy as a capacity among early career teachers to empower them to stay on top of recurrent problems, and suggests potential implications for teacher education programmes and professional development for early career teachers.

Creating a Free Space for Professional Development through Collaborative Self-Study

ABSTRACT This article explores how collaborative self-study, initiated by experienced challenges and insecurity in new roles, contributes to the professional development of teacher educators. We document how four vocational teacher educators created a free space for self-development in a self-study process of dialogue and collective reflective inquiry. This study was initiated during the 2019/2020 academic year as we facilitated a school-based mentor course for vocational high school teachers. We analyze personal reflective journals written during and after mentoring sessions, group meetings, and throughout the process. Drawing on the self-study tradition within educational research, we examine the dilemmas, challenges, and opportunities this experience presented for our roles as teacher educators. The results indicate that investing time in group meetings established an atmosphere of mutual trust and developed the self-study group as a free space. Furthermore, we show the value of collaborative self-study as a tool for individual and collective self-understanding and professional development for teacher educators. Our experiences indicate that a self-study group must be self-selected to achieve an open and trusting process. Furthermore, the study shows that creating free space in academia is possible but highlights a need for academia to recognize free space and self-study as integral parts of the work culture.

Competences for promoting mental health in primary school

Background: The mental health od school-age children is of growing concern in many countries. School professionals require the competences and methods to intervene effectively to promote mental health in schools. Objective: The objective of this study was to describe school professionals’ perceptions of the competences needed and effective methods to promote mental health in primary schools. Design and setting: Qualitative study conducted in five European countries. Method: Multidisciplinary focus group interviews were conducted with teachers, school nurses, psychologists and social workers in Greece ( n = 2), Lithuania ( n = 3), Slovenia ( n = 2), Bulgaria ( n = 2) and Finland ( n = 2). Data were analysed using qualitative content analysis. Results: Competences perceived as required for mental health promotion in primary schools were related to (1) knowledge of child development and mental health among primary school age children, (2) skills such as communication and empathy and (3) teachers’ self perception as health promoters. Insufficient attention is currently given to the development of these competences in basic teacher education and ongoing professional development. Providing a safe and inclusive school environment for children and families, early intervention and the use of structured models of support were viewed as effective approaches to use. Digital tools, online materials, and online support were seen as having a valuable role to play in children’s mental health promotion. Conclusion: School professionals require multiple competences to undertake mental health promotion in primary schools. The development of these competences is best supported by basic and ongoing education. Teachers, school nurses, psychologists and social workers see mixed methods as likely to be most effective in promoting mental health in primary schools.

An Investigation into the Attitude Toward Special Education Curriculum and Teaching of Special Education Teachers: The Data from China’s Guangdong Province

To further understand the curriculum and teaching attitude of teachers in special education schools in Guangdong Province, this study adopted a stratified whole-group unequal probability sampling method and selected 768 teachers from special education schools in Guangdong Province’s 21 cities for a questionnaire survey. The data on special education teachers’ attitudes towards special education curriculum and teaching were selected. Descriptive statistics, one-sample t-test, independent sample t-test, and one-way analysis of variance (ANOVA) were used to analyze the data and compared with the data of special education teachers’ attitudes towards special education curriculum and teaching in the National Survey of Special Education Teacher Professional Development (NSETPDS). The results indicated that the cognitive response of special education teachers in Guangdong Province to the special education curriculum and teaching attitude is positive (M=1.81, SD=0.51), significantly higher than that of the national special education teachers. The emotional response and general attitude were positive but significantly lower than that of the national special education teachers. The attitude of male special education teachers toward the special education curriculum and teaching was significantly higher than that of female special education teachers. Special education teachers with more than 20 years of teaching experience had a more positive attitude towards special education curriculum and teaching than those with 1-5 years of teaching experience. Based on the analysis of the research results, some suggestions are put forward to provide a basis for the professional development of teachers in Guangdong Province.

Introducing Assistive Technology (AT) to Pre-Service Teachers: Observations and Experiences

Assistive technology (AT) can help students with special needs with their learning, and the importance of AT is on the rise with the development of new technologies and the diversification of student body. However, it is observed that pre-service teachers need to be better prepared for the use of AT in their teaching, including awareness, creative and innovative ways of problem solving, and pedagogical use of “low-tech” “mid-tech” and “high-tech” AT. Based on the observation and experience of the author in his teaching of an ICT (Information and Communication Technologies) course in a teacher education program at a middle-sized university in Ontario, Canada, this paper intends to broaden educators’ understanding of AT including hardware and software, emphasize the necessity of the introduction of AT in teacher education programs, and discuss the pedagogical uses of various types of AT tools. By sharing our observations and experiences, it is hoped that educators can be inspired to use various methods to expand the understanding of AT in pre-service teacher education and in-service teacher professional development programs.

An examination of teachers’ beliefs about critical thinking in New Zealand high schools

With new directives from the New Zealand government (2022) to increase the use of critical thinking (CT) within curriculum, this study set out to find out New Zealand high school teachers current beliefs about the teaching and learning of critical thinking (CT), in what ways these beliefs aligned or misaligned with international high school teachers beliefs about CT and if there are any beliefs that are surprising or concerning. The study used a mixed methods designs with an anonymous online Qualtrics questionnaire posted on teachers curriculum webpages that contained both quantitative and qualitative questions. The quantitative results were analysed in Qualtrics. 353 teachers completed the entire survey, with 141 males and 212 females. The results of the quantitative and qualitative Qualtrics questionnaire demonstrated that most teachers agreed critical thinking (CT) should be taught within curriculum; that the biggest barriers to the teaching and learning of critical thinking (CT) were the lack of training in CT and time. The teachers recognised that to achieve the highest grades in the national current assessments in New Zealand students required CT. The teachers held low expectations of students’ abilities to use dialogue online to incorporate CT and believed students were most likely to use CT in whole class discussions, suggesting a teacher-led approach was preferable. The teachers held diverse views of the relevance of the teachers and students cultural background to CT. The implication of this study is that there needs to be much greater emphasis on CT within teacher education programmes and professional development with teachers, with a focus on culturally diverse definitions of CT, addressing teacher beliefs about the importance of cultural backgrounds of both teachers and students, and instruction in student-led discussions to foster CT.

What About Early Childhood Mathematics Education in Early Childhood Teacher Education?

From existing research, it is known that early childhood teacher education provides few opportunities to learn mathematical content or mathematics pedagogical content knowledge. Furthermore, little is known about the extent to which teacher educators are qualified to teach early childhood mathematics within teacher education programs. This study investigates the frequency of opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge. Additionally, we investigate some characteristics of teacher educators, namely the sources they use for professional development with respect to early mathematics education. We report descriptive results as well as correlations. The results indicate that opportunities to learn mathematical content knowledge and mathematics pedagogical content knowledge have increased over time. Moreover, the results indicate that teacher educator professional development formats that encourage professional exchange among teacher educators, experts in early mathematics education and in-service teachers may increase teacher educators’ competence in early childhood mathematics and thereby the frequency with which this topic is addressed in teacher education.