Search

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

The paper addresses the potential relationships between shared authority in mathematics classrooms and students' mathematical reasoning. Even though tensions and challenges related to shared authority are explicated in the literature, there are few examples of how these issues play out in mathematics teaching. We investigate the case of a mathematics teacher attempting to share authority as well as applying several moves recognized as supporting meaningful student learning. Data has been collected in a fourth-grade Norwegian classroom and is analyzed by means of open coding, inspired by literature. We identify the moves used by the teacher, and we rank these moves along two dimensions: (1) their potential to support mathematical reasoning and (2) their potential for sharing authority. From this, we uncover how a teacher's work of orchestrating mathematical discussions involves moves in all four quadrants, and we discuss how the interplay of moves affects the authority structures and the collaborative reasoning in the classroom. [ABSTRACT FROM AUTHOR]

Teacher quality in primary schools in South Africa is a serious concern, and how best to prepare teachers in initial teacher education—with regard to mathematics—remains an open and vexing question. There is a confluence of challenges facing the mathematics education community in South Africa: poor conceptual understanding of mathematics amongst teachers; poor attainment in Primary Teacher Education mathematics tests at both first and fourth year levels; and few initial teacher education programmes having evidence of improving knowledge for teaching mathematics. In addition, few lecturers in initial teacher education make explicit the theoretical tenets informing their course design for mathematics. In response to the latter challenge, this paper makes explicit the design choices made in the Emergent Number Sense first year mathematics module in Bachelor of Education degrees, used across six universities in South Africa. It then theorises the choice to commence the B.Ed mathematics programmes with two pathways into number knowledge: (1) a counting pathway, making use of discrete objects or events which can be quantified by counting in ones; and (2) a measurement pathway, making use of continuous extents which can be quantified by introducing a unit of measurement. Each has a distinct metaphor, strategy for the reification of the 10 and supporting representation. This offers the lecturers using the course in their own design trials, and initial teacher educators beyond the Maths4Primary Teachers collective, a conceptual framework for this design choice, which can now be critiqued and further improved. [ABSTRACT FROM AUTHOR]

Classroom management is an emotionally demanding task for mathematics teachers, especially if students exhibit frequent discipline problems. Intense classroom conflicts can result in persistent latent emotional dispositions, such as fear or anger, that teachers are not directly aware of but that have a strong influence on their classroom management. However, little is known about the relationship between mathematics teachers' latent emotions and their classroom management strategies. This paper reports on findings from an exploratory, video-based single case study in an urban secondary school in Germany. One mathematics double lesson (95 minutes in total) was videotaped to conduct a depth-hermeneutical analysis of identified classroom management strategies and the corresponding latent teacher emotions. The results suggest that mathematics teachers use classroom management strategies not only to establish orderly lessons but also to regulate intense latent emotions that arise during classroom teaching. [ABSTRACT FROM AUTHOR]

In this paper, we report an enquiry into elementary preservice teachers' learning, as they engage in doing mathematics for themselves. As a group of researchers working in elementary Initial Teacher Education in English universities, we co-planned and taught sessions on growing pattern generalisation. Following the sessions, interviews of fifteen preservice teachers at two universities focused on their expressed awareness of their approach to the mathematical activity. Preservice teachers' prospective planning and post-teaching evaluations of similar activities in their classrooms were also examined. We draw on aspects of enactivism and the notion of reflective "spection" in the context of teacher learning, tracing threads between preservice teachers' retro-spection of learning and pro-spection of teaching. Our analysis indicates that increasing sensitivity to their own embodied processes of generalisation offers opportunities for novice teachers to respond deliberately, rather than to react impulsively, to different pedagogical possibilities. The paper contributes a new dimension to the discussion about the focus of novice elementary school teachers' retrospective reflection by examining how deliberate retrospective analysis of doing mathematics, and not only of teaching actions, can develop awarenesses that underlie the growth of expertise in mathematics teaching. We argue that engaging preservice teachers in mathematics to support deliberate retrospective analysis of their mathematics learning and prospective consideration of the implications for teaching can enable more critical pedagogical choices. [ABSTRACT FROM AUTHOR]

Improving mathematical skills is a priority in England, and a series of policy levers and government change projects have focused on improving mathematical outcomes in further education (FE) in recent years. Yet little is known about the mathematics teacher workforce that supports these students on vocational and technical programmes. This paper addresses this knowledge gap by examining important features of the mathematics teacher workforce in colleges and the implications for recruitment, initial training and ongoing professional development. We report findings from a national survey targeted at all mathematics teachers in around one-sixth (N = 31) of England's general FE colleges. Teachers have transitioned into FE from three main areas: another career, curriculum area, or educational context. We discuss the varied assets and training needs of these three subgroups and argue that the mathematics teacher cohort in FE should be seen as distinct from that in either primary or secondary education. We highlight the bimodal distribution of mathematics qualifications amongst this workforce; those having level 2 mathematics qualifications being more likely to be teaching functional skills mathematics courses than GCSEs. The rapid expansion of the mathematics teacher workforce that followed the changes to the condition of funding in 2014 has come disproportionately from teachers who were previously working in schools. This, together with a trend of funnelling increasing numbers of FE students into academic mathematics rather than functional skills courses, raises important questions about the nature of mathematical education for learners on vocational and technical programmes, and the teachers thereof. [ABSTRACT FROM AUTHOR]

Mathematical structure is central to the interconnectedness of numerical, spatial or logical relationships, but it is not known how well teachers understand this concept or implement it in pedagogical practice. In this paper, we examine three junior secondary mathematics teachers' understanding of mathematical structure and observe whether they apply it in their teaching. Case study data comprised teacher interviews and mathematics lesson observations. Analysis of interviews and teacher-directed communication (utterances) in lessons utilised an emergent framework for categorising mathematical structure: connections to other learning (C), recognising patterns (R), identifying similarities and differences (I) and generalising and reasoning (G). Findings from the interviews indicated that teachers supported the development of mathematical structure, but the interview responses were not generally reinforced by their utterances in mathematics lesson observations. Analysis of teacher utterances revealed superficial understanding and use of mathematical structure although there was some evidence of CRIG components in the teacher-directed communication for individual cases. [ABSTRACT FROM AUTHOR]

Professional noticing of children's mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169–202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children's mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics teachers' (PTs') responses to a pedagogical activity designed to engage them in an approximation (Grossman et al. in Teach Coll Rec 111(9): 2055–2100, 2009) of professional noticing of children's mathematical thinking in the moment of teaching, with a focus on developing responses which extend the student's thinking. PTs were provided two different examples of student work and a series of questions designed to elicit information about their ability to professionally notice student work. We present data and analysis of 73 PTs' abilities to engage in the individual skills associated with noticing as well as their abilities to use the skills cohesively in concert. Our results demonstrate the type of representation used determined PTs' success in all three facets of noticing, with a particular effect on interpreting. Further, our focus on a specific type of response move, along with the introduction of a scaffold for that response move, made a difference in PTs' ability to successfully respond to student work when compared to a prior study with the same PTs (Tyminski et al. 2014). We unpack these results along with suggestions for pedagogical practice as well as directions for future research. [ABSTRACT FROM AUTHOR]

Researchers have been paying attention to the convergence of technologies for it can result in improving human behaviour, including student's learning and teacher's instruction. The present paper intends to describe the different types of convergence of technologies in the classroom in general and the mathematics classroom in particular, focusing on the convergence of two types of them: convergence of the learner with the technological tools and convergence of the teacher with those tools. This focus is concerned with two instrumental frameworks: the instrumental genesis and the instrumental orchestration. The paper discusses the foundations of these two theoretical frameworks, the components of the frameworks and their educational uses as tools for analysing learners' and teachers' convergences with technological tools. Researchers assert that the two frameworks have contributed to the understanding of convergence of the learner and the teacher with technological tools, pointing, at the same time, at the need to extend these frameworks or combine them with other frameworks in order to understand the different aspects of this convergence. [ABSTRACT FROM AUTHOR]

Inquiry into the teaching and learning of mathematics is a central aspect of the work of both the mathematics teacher and the mathematics education researcher, yet there are profound differences between the practices and processes underlying educational inquiries within each community. These differences are known to hinder implementation of research, yet they can also become a valuable resource. This paper explores a particular model of implementation of research: mathematics teachers adopt and adapt practices and processes of disciplined educational inquiry in a co-learning partnership with mathematics education researchers. We present a narrative inquiry of a teacher–researcher community that designed and studied classroom activities aimed at encouraging students to ask meaningful mathematical questions. The data analysis, informed by the literature on boundary objects and boundary crossing, highlights how the teachers and researchers leveraged their different processes and practices of educational inquiry as a resource in their collaborative inquiry. We conclude by suggesting that informed and thoughtful attention to the differences between teacher inquiry and disciplined inquiry may support and enhance mathematics education research implementation. [ABSTRACT FROM AUTHOR]

Learning to name and notice students' mathematical strengths is a challenging process requiring time and multiple iterations of practice for prospective teachers (PTs) to adopt. Mathematics teacher educators (MTEs) can approximate and decompose the complex practice of naming and noticing students' mathematical strengths so PTs learn to teach mathematics while emphasizing what students know and can do. This study uses two tools MTEs can use to support PTs as they learn to name and notice students' mathematical strengths: A LessonSketch experience, a digital platform with comic-based storyboards showing children engaged in a mathematics task, and a strengths-based sentence frame. Our study presents the findings from the 111 noticing statements from 18 PTs as they engaged in the LessonSketch digital experience and practiced making noticing statements about what children know about mathematics. The study found that after a sentence-frame intervention, the PTs are more likely to use strengths-based language and more likely to identify mathematical evidence in their noticing statements. Uncommitted language (statements that do not align with a strength- or deficit-based coding scheme), suggests a fruitful, yet complex space for supporting more PTs as they learn to name and notice students' mathematical strengths. The paper concludes with implications for future research in teacher education. [ABSTRACT FROM AUTHOR]

This paper focuses, empirically, on the developments seen in a group of South African early grades' mathematics teacher educators in the course of a university-provincial education department partnership project. This project sought to support the district Mathematics Subject Advisers to support, in turn, teachers to implement an intervention consisting of a sequence of four lessons focused on multiplicative reasoning. Outcomes based on pre- and post-tests administered by the Subject Advisers suggested substantial pre- to post-test improvement at the student level. Subject Adviser observations and reflections pointed to successes in engendering more dialogic conversations between mathematics teachers and mathematics teacher educators focused on mathematics and its teaching and learning. The 'double move' of increasing overlap between the subject adviser and teacher communities, coupled with evidence that implementing the intervention had enabled the Subject Advisers to develop their mathematical and pedagogical understandings, provides a useful way of considering development in the capacity of mathematics teacher educators to support mathematics teaching and learning. [ABSTRACT FROM AUTHOR]

The study investigated the effects of condonation on the promotion of senior phase mathematics learners into the FET phase in a high school in KwaZulu-Natal. Condoned learners were assisted to progress, despite not meeting the pass requirements. The study suggests learning support strategies teachers could use to improve condoned FET mathematics learners' performance. An exploratory case study investigated the condonation policy and its effects thereof. Interviews were conducted with two mathematics teachers, and open-ended questions were posed. The data analysis entailed collating the data, followed by a thematic data analysis approach. The literature study was done on pertinent theories, prior studies, and pragmatic research. The findings suggest that condoned learners did not master the foundational knowledge and accumulated knowledge gaps. Consequently, learners struggle to achieve good performance in FET mathematics. This may lead to condoned learners failing FET mathematics, dropping mathematics in favour of more uncomplicated mathematical literacy, or dropping out of school rather than completing Grade 12. The study recommends that condoned senior phase mathematics learners struggling to perform well in FET mathematics need to undergo an individualised learning support programme. Teachers will then employ various academic teaching and learning support strategies to help improve learners' FET mathematics performance. The success of learning support depends on a collaborative relationship between nurturing teachers and parents and positive discipline in group teaching within supplemental classes. [ABSTRACT FROM AUTHOR]

Copyright of Tecné, Episteme y Didaxis is the property of Universidad Pedaggica Nacional and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of REICE. Ibero-American Journal on Quality, Effectiveness & Change in Education / REICE. Revista Iberoamericana Sobre Calidad, Eficacia y Cambio en Educación is the property of Red Iberoamericana de Investigacion sobre Cambio y Eficacia en Educacion and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Background: Key elements of instructional quality include the teacher's ability to immediately react in domain‐specific classroom situations. Such skills – defined as action‐related skills – can only be validly assessed using authentic representations of real‐life teaching practice. However, research has not yet explained how teachers apply domain‐specific knowledge for teaching and to what extent action‐related skills are transferable from one domain to another. Aims: Our study aims to examine (1) the relationship between action‐related skills, content knowledge, and pedagogical content knowledge, and (2) the domain specificity of action‐related skills of (prospective) teachers in the two domains of mathematics and economics. Sample(s): We examined German pre‐service and in‐service teachers of mathematics (N = 239) and economics (N = 321), including n = 96 (prospective) teachers who teach both subjects. Methods: Action‐related skills in mathematics and economics were measured using video‐based performance assessments. Content knowledge and pedagogical content knowledge were assessed using established paper–pencil tests. Correlation analyses, linear regressions, and a path model were applied. Results: In mathematics and economics, we find a similar pattern of moderate correlations between action‐related skills, content knowledge, and pedagogical content knowledge. Moreover, a significant correlation between action‐related skills in mathematics and economics can be explained almost entirely by underlying relations between content knowledge and pedagogical content knowledge in both domains. Conclusions: Our findings suggest that action‐related skills empirically differ from domain‐specific knowledge and should be considered as domain‐specific constructs. This indicates that teacher education should not only focus on domain‐specific teacher knowledge, but may also provide learning opportunities for action‐related skills in each domain. [ABSTRACT FROM AUTHOR]

This article presents the results of a small-scale, comparative study on the perceived impact that having students enter Mathematics competitions has on Mathematics teachers in Puerto Rico, Switzerland and the UK and on their classroom practice. The study surveyed a small number of Mathematics teachers in the three countries who teach in both public and private schools and in both rural and urban regions. The perceived advantages and disadvantages to students from taking part in competitions and to teachers who have students taking part in competitions are discussed and the findings compared across the three countries. The effect that Mathematics competitions have on the identification and development of the mathematical talent of students is considered together with the contribution of these activities to the academic environment of the classroom. For the teachers who did have students taking Mathematics competitions, the limitations of entry and the different methods in which teachers prepare or assist students to prepare for the competitions are compared between countries. Since the study is small in scale, no firm conclusions are drawn but suggestions are made as to where future, larger scale, studies might be carried out to see if the classroom experiences of all could be positively influenced by exposure to Mathematics competitions. [ABSTRACT FROM AUTHOR]

We give an unconventional, mythopoetic response to the question of Why teach mathematics to all learners in school? In our work with pre-service teachers, we attempt to teach how to value the vulnerability of the multispecies world in a relational, anti-colonial way through passionate immersion, and to use mathematics education towards the ends of promoting its and our own (human) flourishing through taking on relationships of curatorial care. Our contribution includes the novel theoretical assemblage and elaboration of the metaphors of plot and curating as "medicine" [Doolittle, E. (2007). Mathematics as medicine – plenary lecture. In P. Liljedahl (Ed.), Proceedings of the 2006 CMESG Annual Meeting (17–25), Burnaby, BC, Canada.] for addressing challenging ethical questions for mathematics education [Karrow, D., Khan, S., & Fleener, Y. (2017). Mathematics education's ethical relation with and response to climate change. Philosophy of Mathematics Education Journal, 32 (Special Issues on Mathematics Education and the Living World: Responses to Ecological Crisis). ISBN: 1465-2978.] of its ongoing relationship with the precarity produced by unexamined plantation commitments. [ABSTRACT FROM AUTHOR]

The development of mathematical reasoning skills has increasingly been of focus for the teaching and learning of mathematics. This research utilizes a teaching simulation using the methodology of scriptwriting, in which prospective teachers are asked to complete a script of a dialogue from a classroom simulation involving fraction multiplication and division with justification, assisting fictional students to work through their difficulties and helping them to justify their reasoning. Such tasks allow for the examination of the prospective teacher moves to support student reasoning through their imagined action and choice of words. Scripts from forty-one prospective primary teachers were examined for the study, and five clusters based on the type of teacher move for supporting student reasoning were found. Overall, the prospective teachers emphasized the elicitation and facilitation of students' ideas. The cluster analysis, however, provided a nuanced examination of the cohort's teacher moves. While cluster one saw the highest incident of eliciting teacher moves, albeit only in the low potential category, clusters two and three mostly used facilitating teacher moves, but varied in their use of high and low potential moves. Cluster four concentrated moves on facilitating, eliciting, and responding to student reasoning. Cluster five employed teacher moves from all main categories, with some instances of high potential moves in all categories except extending student reasoning, which can better support reasoning. The prospective mathematics teachers' scripts and the five clusters that were found during analysis are discussed with implications for future teacher education and the support of building mathematical reasoning. [ABSTRACT FROM AUTHOR]

Teacher identity has become important in mathematics education research, but mainly in relation to programmes for teacher education (TE) and professional development (PD). Less attention has been paid to understanding the role and development of identities in the majority of cases in which teachers are not involved in long-term TE or PD. This paper presents a study that seeks to develop such understandings. The study defines teacher identities as their shifting experiences of being, becoming and belonging related to the profession. It is a longitudinal case study of a novice teacher, Anna, and it asks how Anna's identities change over the first 4 years of her career at her school, Northgate. To address the question I use a framework called Patterns of Participation (PoP) in combination with a range of methods, including interviews with Anna, her closest colleagues and the leadership at her school, and observations of Anna's classrooms and of team meetings. I argue that this combination invites new understandings of identity development, because it does not prioritise teacher engagement in one particular practice (e.g., as promoted by PD), but allows interpretations of how Anna's engagement with a multitude of different practices play a role for her professional experiences. The results suggest that in general terms, Anna's identity changes from being 'a mathematics teacher at Northgate' to becoming 'a mathematics teacher at Northgate'. [ABSTRACT FROM AUTHOR]

Mathematics teachers across the Western world are faced with an expectation that they make significant change to their teaching, but repeated attempts have shown little embedded success. This paper draws on a longitudinal study of two apparently well-placed English mathematics departments attempting to make change aligned with both policy and internationally-valued ‘good practice’. It suggests deep teacher change draws on a wide range of both social and affective characteristics, as well as sophisticated professional skills and knowledge. The study supports a construct of ‘(mathematics) teacher capacity for change’ at both individual and group levels within teachers’ ‘personal domains’, synthesising the range of characteristics apparently needed by teachers in times of change. In particular, it argues for the development of dispositions for collaborative learning and of other learning-supportive affects. Such an approach has the potential to place teachers in a better position to respond to demanding aspirations. [ABSTRACT FROM PUBLISHER]

Australian students' attitudes to mathematics are in decline relative to other countries. Their participation in senior secondary mathematics that provide pathways to further study is also falling. Pedagogical approaches that improve students' attitudes to mathematics and knowledge of mathematics are required. This paper reports on preservice secondary mathematics teachers' objectives for their students' learning and their anticipated teaching and learning activities. The study was conducted over one year using quantitative analysis of paired responses to items in pre and post questionnaires. At the end of the year, the preservice teachers emphasised objectives for understanding and positive disposition but anticipated using fluency activities almost daily. Investigations involving problem solving and reasoning were anticipated to occur at least weekly. However, a significant decline in their anticipated use of activities that link mathematics to other disciplines or applying mathematics to real world problems occurred. Other data suggest a lowering of emphasis on developing students' disposition and interest in mathematics. The findings suggest that more attention needs to be given to raising preservice teachers' awareness of the importance of students' disposition. Further research on the impact of teaching experience and opportunities to develop all proficiencies and to link mathematics to other disciplines and real-world problems during preservice teacher education is recommended. [ABSTRACT FROM AUTHOR]

Teacher dashboards in mathematics classrooms tend to provide teachers with information on student performance that are often linked to classroom management systems, online course systems, or peer-tutoring software. Teacher dashboards also tend to emphasize features that support teachers using a "transition" or "direct instruction" model. In our approach, we iteratively designed, developed, tested, and refined a teacher dashboard that is linked to a student digital collaborative environment with an embedded problem-based mathematics curriculum. In this study, we investigate teacher dashboard features that support teacher enactment of problem-based mathematics curriculum embedded in a digital collaborative platform. We report on design principles that guided the development of three teacher dashboard features: (1) monitoring evidence of student thinking in real-time or after class, (2) accessing workspace for whole-class discussions of the problem, and (3) creating and sending "just-in-time" supports. The pedagogical advantages and challenges teachers face throughout the iterative development process are also discussed. Evidence from observational data and teacher interviews suggests that the organic synergism generated from the student and teacher digital platform offers several ways that teachers are provided with new and timely information from teacher dashboards that supports problem-based mathematics teaching. [ABSTRACT FROM AUTHOR]

Copyright of Bartin University Journal of Faculty of Education is the property of Bartin University Journal of Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Participating in classroom mathematics conversations, particularly engaging with the opinions of others, can improve learners' mathematical comprehension. Teachers can use a variety of invitation and follow-up moves to encourage student engagement. The study aimed to explore teacher follow-up on learners' initial responses to teacher questions and building on learner ideas in Grade 9 mathematics classrooms. A qualitative approach and descriptive case study design were utilised. Data were collected from three schools in the same circuit in South Africa through classroom lesson observations, face-to-face teacher interviews and researchers' field notes. Three Grade 9 mathematics teachers, one from each school, were purposively selected, and the selected teachers' already established Grade 9 classes, with a maximum of 30 learners each (owing to the COVID-19 health protocol), were automatically involved. Cognitively guided instruction, a learner-centred approach that uses social constructivism as a research paradigm, guided this study. The exploration was supplemented by Brodie's conceptual framework on teacher follow-up moves. The findings revealed that the three teachers followed up on learner contributions and used different follow-up moves, namely insert, elicit, press, maintain and confirm. The study showed hybrid teacher moves. Although more teacher moves were skewed towards elicit and insert, which are closer to traditional practices, there is an indication of moving towards the press, maintain and confirm, which are reform-oriented moves. In addition to these moves identified by Brodie, acknowledging or praising the learner for responding was another move that emerged in this study. [ABSTRACT FROM AUTHOR]

This study analyses school mathematics teachers' attitudes towards using provocative mathematics questions in teaching and assessment as a potential pedagogic innovation. By a provocative mathematics question, we mean here a question designed to deliberately mislead the solver. It normally calls for an impossible task. For example, the question might ask for a proof of something that is not provable or show the existence of a solution of an equation that does not have a solution. Often a catch is based on a restricted domain or indirectly prompts the use of a rule, formula, or theorem that is inapplicable due to their conditions/constraints. Five groups of school mathematics teachers did a mini-test consisting of provocative questions. A post-test questionnaire was given to the teachers to obtain their feedback on the possible use of provocative questions in their teaching practice to enhance students' critical thinking skills. Teachers' responses are discussed and analysed in the paper. [ABSTRACT FROM AUTHOR]

Definitions are an integral aspect of mathematics. In particular, they form the backbone of deductive reasoning and facilitate precision in mathematical communication. However, when multiple non-equivalent definitions for the same term exist, their ability to serve these purposes can be called into question. While ambiguity can be productive, the lack of an agreed upon definition can make the truth value of certain mathematical statements unclear. In this study, we presented pre-service and in-service mathematics teachers with three mathematical claims in which definitional ambiguity was a consideration; then, we asked them to determine the correctness of each claim, justify their positions, and anticipate what reasoning might lead to a possible counterargument. Based on their responses, we identified several factors that influenced the participants' approaches in each situation as well as cross-cutting themes that describe their considerations. Finally, we consider the pedagogical implications of employing such a task in teacher preparation programs and in-service teacher education. [ABSTRACT FROM AUTHOR]

Inclusive education strives to support all students, regardless of their differences, so no child is left behind. However, some teachers, especially those in high schools, may oppose inclusive education. This study aimed to examine the experiences and actions of high school mathematics teachers as they taught students with visual impairments to understand the challenges they faced and how these affected their willingness to embrace the inclusion of these students. Researchers conducted semi-structured interviews with eight mathematics teachers experienced in teaching students with visual impairments. The findings were organized into five themes: mathematics teaching practices, curriculum, material preparation, assessment practices, and beliefs about inclusive education and students with visual impairments. The results revealed that while mathematics teachers were conscious of not being adequately equipped to implement inclusive education, those with strong teaching efficacy beliefs were more inclined to teach rigorous mathematics to students with visual impairments. [ABSTRACT FROM AUTHOR]

This study examined the mathematical learning opportunities provided to emergent bilinguals (EBs) through their participation in whole class discussions in an elementary classroom. Positioning theory (Harré & van Langenhove, 1999) was used to examine a third-grade monolingual teacher's positioning acts and related storylines across two years. An examination of the data revealed the teacher utilized three prevalent positioning acts with EBs (i.e., inviting EBs to share mathematical thinking, valuing EBs' mathematical contributions, and inviting peers to consider EBs' mathematical contributions) that provided multiple and varied opportunities to participate in whole class mathematical discussions while circulating two storylines: EBs are mathematically competent and EBs can explain their mathematical reasoning to others. Findings suggest that positioning acts can be used in similar ways by other teachers across contexts to strive for equitable mathematics education. [ABSTRACT FROM AUTHOR]

Anyone involved in mathematics education will at some point encounter a classroom situation in which a student's statement provides an opportunity for the teacher to enhance students' mathematical understanding. This paper aims to characterize such classroom situations, known as critical events, as noticed by pre-service mathematics teachers during classroom observations and teaching. Analysis of 80 critical events reported by 20 pre-service mathematics teachers during a field-based teaching preparation program yielded a model that enables teacher-educators and researchers to characterize critical events while reflecting on the wide variations within these events. The model comprises three axes: the participants in the event, the focus of the event, and the dimensions in learning and teaching mathematics (i.e., cognitive, affective and social). The paper discusses the theoretical and empirical construction of the model and demonstrates its potential contribution using examples taken from our research. • Pre-service teachers identified critical events during classroom observations. • A model for characterizing critical events was constructed theoretically and empirically. • The model affords eliciting the multidimensional nature and complexity of critical events. • The model's potential contribution is presented using examples from our research. [ABSTRACT FROM AUTHOR]

Copyright of Revista Electrónica Interuniversitaria De Formación del Profesorado is the property of Asociacion Universitaria de Formacion del Profesorado (AUFOP) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In 1908, Felix Klein suggested that to mend the discontinuity that prospective secondary teachers face, university instruction must account for teachers' needs. More than a century later, problems of discontinuity remain. Our project addresses the dilemma of discontinuity in university mathematics courses through simulating core teaching practices in mathematically intensive ways. In other words, we interpret teachers' needs to include integrating content and pedagogy. We argue that doing so has the potential to impact teachers' competence. To make this argument, we report findings from the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools (MODULE(S2)) project. The results are based on data from 324 prospective secondary mathematics teachers (PSMTs) enrolled in courses using curricular materials developed by the project in four content areas (algebra, geometry, modeling, and statistics). We operationalized competence in terms of PSMTs' content knowledge for teaching and their motivation for enacting core teaching practices. We examined pre- and post-term data addressing these constructs. We found mean increases in PSMTs' outcomes in content knowledge for teaching and aspects of motivation. [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]

Issues about poor achievement in mathematics (angles and polygons topics) among Palestinian students has led to the need for developing new effective strategies that can be used to improve mathematics achievement among Palestinian 7th grade students. The aim of study is to reveal the effect of employing the mantle of the expert on the achievement of angles and polygons topics among seventh grade students in Palestine. A quasi-experimental non-equivalent control group design using experimental and control groups with a pre and post-test was conducted. Data were collected using achievement test. The sample of study consisted of (76) students in the seventh grade that were divided into two groups, the experimental group (37) students and the control group (39) students. Data collected from the pre-test and post-test was analyzed using descriptive and inferential statistics. One-way MANOVA test was used to verify the differences of achievement between experimental and control groups. The research found that there is a significant impact of employing the mantle of the expert in increasing the achievement in geometry among seventh grade students. Students who are studied using mantle of the expert had better achievement than those who did not. This study recommended employing the mantle of the expert in teaching other topics in mathematics and in different study stages. This study too showed the necessity of paying attention to the use of classroom and extra-curricular activities in different academic subjects, particularly in mathematics, as well as indicated the necessity of holding courses and workshops to train teachers to use the mantle of the expert in the educational process. [ABSTRACT FROM AUTHOR]

Copyright of Cumhuriyet International Journal of Education is the property of Cumhuriyet University, Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of this study is to examine the effect of the intervention with teaching applications of mathematics in other disciplines on teachers' attitudes towards teaching applications of mathematics. The research was conducted in the 2021-2022 school year in Israel and a two-groups pretest- posttest quasi-experimental research design was used. The participants were four classes (two of them are 11th grades and two are 12th grades) with four teachers at Al-Bukhari High School in Arraba city in northern Israel. The research instruments were three interview guides. The first interview was conducted before the intervention with all the 4 teachers and it contained 16 questions about their attitudes toward teaching mathematics and applications of mathematics. The second and third interview was similar and it was conducted during respectively after the intervention with the teachers in the experimental group. These interviews contained 5 questions related to teaching applications of mathematics in other disciplines. The results of the study showed that teaching applications of mathematics in other disciplines has a positive effect on teachers. Before the intervention, the teachers taught using the standard method, and they rarely taught applications. The teachers were not qualified enough to teach applications of mathematics and were not aware of the advantages of teaching applications of mathematics. By the intervention teachers were exposed to the inclusion of applications in teaching mathematics, and their attitudes towards teaching applications of mathematics improved and their level of confidence to teach applications increased significantly (increased from 7 to 9 on a scale from 1 to 10). That means, the intervention helped the teachers to teach the applications of mathematics successfully and with self-confidence. Furthermore, despite the difficulties and the obstacles in teaching applications of mathematics in other disciplines, teachers liked to teach the applications of mathematics and were satisfied with the results and the change among the students. They reported that they would implement the teaching applications of mathematics in other disciplines in all classes that they teach and would recommend it to their fellow teachers. [ABSTRACT FROM AUTHOR]

This qualitative study explores the implementation and adoption process of the use of digital devices and tools in teaching and learning before, during, and after the COVID-19 pandemic in Nepal. Using Rogers' diffusion of innovation theory as a framework, the study examines the adoption and adaptation of digital devices by in-service secondary mathematics teachers (n = 62) and the teachers' perceptions of and preferences for instructional modalities. The findings suggest that, despite the increased reliance on digital devices during the pandemic, there is a lower likelihood of them being used in face-to-face classrooms in developing countries, such as Nepal. The adoption of online learning had not yet reached the adoption stage, even after the onset of the COVID-19 pandemic. Prior to the pandemic, online learning was not widely adopted by teachers in developing countries societies. The study also provides important insights into the challenges of and opportunities provided by using digital devices in post-COVID-19 classrooms, and its implications for policymakers and educators in Nepal. [ABSTRACT FROM AUTHOR]

This study investigates the viewpoints of 20 preservice post-primary mathematics teachers taking a module of Group Theory in the final semester of their university teacher education programme. The purpose of the study was to investigate preservice mathematics teachers' perception of the value of studying a module in Group Theory and their perception of its relevance to the content they will teach at post primary school. The sample were surveyed again 12 months later, having taught at post primary level for almost a full academic year to see if their perspectives had changed. The findings are discussed in this paper. [ABSTRACT FROM AUTHOR]

Well-written curriculum materials are known to support teacher learning. Less discussion has focused on whether teachers' guides, curriculum materials written specifically for teachers by textbook publishers, provide sufficient support. In this study, I analyse four US-based mathematics teachers' guides to understand the opportunities within them for teacher learning. Drawing on positioning theory, I conceptualised teacher learning opportunities as teacher positionings observable from teachers' guides. With this conceptualisation, I explored teacher positionings that were regularly or idiosyncratically observable from the selected teachers' guides. The results revealed only a small number of regularly observable positionings existed, indicating limited opportunities for teacher learning from the guides. Irregularly, or idiosyncratically observed positionings provided limited opportunities, as well. Based on the findings, I suggest the necessity of presenting diverse positionings to best utilise the potential from teachers' guides as materials for teacher learning. [ABSTRACT FROM AUTHOR]

In this study, we aimed to determine Cypriot primary mathematics teachers' perspectives and lived experiences during the transition to emergency remote teaching (ERT) in the early stage of the COVID-19 pandemic. An in-depth online survey combining closed-ended and open-ended questions was administered to sixty-two (n = 62) educators teaching mathematics in public primary schools during the first lockdown in spring, 2020. The data from closed-ended questions were analyzed using descriptive and inferential statistics, whereas, for the open-ended questions, a thematic analysis approach was employed. Our findings provide useful insights regarding teachers' self-reported technology backgrounds and levels of instruction regarding the use of technology in mathematics prior to the pandemic, as well their level of preparedness for ERT and the main challenges they faced in implementing ERT of mathematics. Our findings also indicate teachers' levels of satisfaction with their ERT practices and their beliefs concerning the extent of achievement of the curriculum learning objectives through ERT, and how these varied based on teachers' self-reported levels of familiarity with technology, their self-reported levels of preparedness for teaching at a distance, and their engagement (or non-engagement) in synchronous instruction during ERT. Teachers' suggestions, based on their experiences from the lockdown period, regarding how to transform mathematics teaching and learning in the post-COVID-19 era are also presented. [ABSTRACT FROM AUTHOR]

Often, mathematics teachers do not incorporate whole-class discourse of students' various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students' thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students' various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers' in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers' decision-making was shaped by the teachers' own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals. [ABSTRACT FROM AUTHOR]

This article reports on a second national survey of higher education institutions in the USA to answer the question "Who teaches mathematics content courses for prospective elementary teachers, and what are these instructors' academic and teaching backgrounds?" and addresses valuable information not collected with the first survey conducted in 2010. We surveyed 1740 institutions and a faculty member from each of 413 institutions (23.7%) participated in the survey. The survey results demonstrate that the majority of these institutions are not meeting the recommendations of the Conference Board of Mathematical Sciences (2012) and the Association of Mathematics Teacher Educators (2017) for prospective elementary teachers to take at least 12 semester-hour credits of mathematics content designed specifically for them. The data do indicate that there is movement toward more activity-based approaches for these courses as compared to the 2010 survey. Additionally, there is an increase in these courses having instructors with doctorates in mathematics education as well as an increase in instructors having grades 7–12 teaching experience. Most instructors for these courses do not have elementary teaching experience and have likely not had opportunities to think deeply about the important ideas in elementary mathematics. While most institutions still do not provide training and/or support for these instructors, formalized support and training appear to be increasing since the 2010 survey. [ABSTRACT FROM AUTHOR]

The Trends in International Mathematics and Science Study (TIMSS) is an influential mathematics and science assessment administered at fourth and eighth grades in around 60 countries across the world. Under current practices, TIMSS does not support claims about teachers unless the inference is drawn as a student characteristic ("Half of the eighth graders in the country have mathematics teachers with Master's degrees."). With this in mind, this paper proposes and tests through a simulation study two methods that would allow for teacher-centric inferences ("More than half of the eighth-grade mathematics teachers have Master's degrees.") if links between sampled teachers and the unsampled yet eligible classes were known. The first method posits that with such links inverse-probability weights could be calculated, and the second method, the Multiplicity-Adjusted Indirect Sampling (MAIS) approach, posits that teacher estimates could be obtained by adjusting downward the classroom weights based on these links. • Discusses teacher reporting in Trends in International Mathematics and Science Study. • One method creates and implements inverse-probability weights for teachers. • Another method reweights the class weights for each teacher. • A simulation study shows that both methods produce unbiased results. • Both methods would require collecting data on teachers' links to unsampled classes. [ABSTRACT FROM AUTHOR]

This article approaches the relationship between mathematics education and field education, based on the academic production of the research group on mathematics education in field education contexts (Gpemce) created in 2008 at the Federal University of Pernambuco. After presenting the repercussions and lines of research of the group, we reflect on the roots and principles of field education and some approximations of this domain with mathematics education. Then, we present a documentary study, whose corpus consists of 20 articles published in journals by researchers from Gpemce from 2009 to 2020. These articles are organised around four thematic categories that are associated with the research lines of the group: teaching and learning mathematics in field education contexts; relationships between curriculum contents, mathematical practices and productive field activities; resources in the teaching of mathematics in field schools and qualification of mathematics teachers of schools in field areas. The study highlights the diversity of educational subjects, themes, and sociocultural contexts contemplated in the research, and points out ways to conduct new investigations that contribute to deepen our understanding of the teaching and learning of mathematics in field schools and initial and continuing teacher education in field education contexts. [ABSTRACT FROM AUTHOR]

This article draws on the notion of epistemic agency to illustrate how the enactment of shared epistemic agency is enabled or hindered in a mathematics classroom for student teachers. I used data from an ethnographic study that was conducted in a third-year class of mathematics for educators. Data was drawn from verbal interactions that took place between mathematics student teachers, and between student teachers and myself as their lecturer, as they worked on class tasks. A narrative mode of analysing data was employed to synthesise data from critical incidents, while excerpts of these incidents represented data. From this analysis, I argue that, with extended wait time by a facilitator, students' disposition of epistemic virtues and vices may enable or hinder enactment to epistemic agency, respectively. In article, those vices presented themselves as epistemic stinginess, prejudices against answers by peers and epistemic disclaimer. The epistemic virtues were presented as impartiality and intellectual courage. I further suggest that the recommended wait time of 1–3 during classroom questioning and answering should be extended for classes where epistemic practices are encouraged. [ABSTRACT FROM AUTHOR]