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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]

The increase in online education has implications for mathematics teacher educators who are tasked with teaching mathematics content and pedagogy to pre-service teachers (PSTs) who do not attend on-campus. Concerns about PSTs' content knowledge continues to be an ongoing issue, and ways to address this, especially in an online environment, require further investigation. While online courses offer accessibility and flexibility, it can be challenging to translate synchronous on campus teaching and experiences into the online environment. The importance of productive mathematical discourse has been identified as an appropriate pedagogy, yet the opportunity to engage in such discourse can be limited in the online environment. This paper provides the results from a case study of an online forum, which highlights how pre-service teachers can be engaged in productive online mathematical discussions, particularly when facilitated by the instructor's and other learners' interactions and presence. The findings indicated that social, cognitive, and teaching presence influenced the nature and frequency of online mathematical discourse. The study contributes to existing research through conceptualizing how productive mathematical conversations can occur outside of the classroom setting, with implications for mathematics teacher educators who are tasked with teaching content, pedagogy and practices to PSTs. [ABSTRACT FROM AUTHOR]

This cross-sectional study looks into how students' perceived teacher support is linked to achievement emotions in mathematics via academic control and value. The data was gathered from 602 secondary students (13-16-year-olds) in 16 mathematics classrooms from three public schools in Jiangsu province, China. Participants were asked to respond to the paper-pencil questionnaire assessing students' perceived teacher support, cognitive appraisals, and achievement emotions in mathematics. Findings showed that cognitive appraisals played complete mediation roles in teacher support and achievement emotions. Intrinsic value and mathematics self-concept were shown to serve a positive role in teacher support and achievement emotions, whereas extrinsic value was found to play a negative one. Besides, teacher support showed the greatest indirect effect on achievement emotions through mathematics self-concept. Lastly, findings indicated the great relevance of teacher support to students' anger, boredom, enjoyment and relaxation in mathematics classrooms. [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]

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]

Parents' and teachers' beliefs and evaluations of young people are important. Using a feminist institutionalist perspective, and drawing on rich data from one in seven nine-year-old children in Ireland, this paper examines mothers' (who make up the overwhelming majority of primary care-givers) and teachers' perceptions of boys' and girls' mathematics performance. The evidence shows that girls' mathematics performance is underestimated by both relative to boys'. Mother's gender bias was evident among high performing children, at all levels of children's academic self-concept, and among mothers with at least third level education. While the judgements reflect children's actual performance and engagement, a notable gender gap remains. It is suggested that the results reflect gender stereotypes: overestimating boys' and underestimating girls' mathematics achievements. The article indicates the importance of the informal dimension of institutions and the part played by women in the effective devaluation of girls by endorsing gendered stereotypes. Women teachers are less likely to rate children highly in mathematics, taking account of performance: arguably reflecting their own lack of confidence in mathematics assessment. The findings raise concerns for girls' futures since mathematics is seen as an indicator of intelligence. Given the move towards teacher-assessed grading during COVID-19, understanding, and challenging, gender-stereotyping is pressing. [ABSTRACT FROM AUTHOR]

This paper reports an action research study I conducted into the mathematical productive disposition of 29 tenth grade learners in the Philippines by analyzing their metaphorical conceptualizations of mathematics in a series of lessons following principles of Realistic Mathematics Education. Analysis of participants' pre-intervention metaphors of mathematics revealed four conceptualizations that capture learners' perceptions of mathematics reflective of their productive disposition: mathematics as a process, mathematics as a puzzle, mathematics as a problem, and mathematics as a difficulty. Insightful changes in the learners' metaphors of mathematics support the argument that making mathematics matter to students can be achieved if teachers make considerable and devoted attempts at making what matters to students mathematical. Several challenges in the implementation of realistic mathematics lessons on Permutation included developing and enabling students' awareness of their social and cultural environment and encouraging critical thinking. Reflecting on my experience, I argue that constant exposure to lessons that present mathematics as contextually and socially relevant can potentially improve students' mathematical productive disposition together with other strands of their mathematical proficiency. [ABSTRACT FROM AUTHOR]

In this paper, we approach modelling mathematics dispositions from a different methodological perspective in order to shed more light into the complex interplay between teaching practices and students' learning outcomes. We draw on survey data from around 5000 students from Year 7–11 (age 11–16) from 40 Secondary schools in England. Our methodological approach includes Rasch modelling to produce measures of attitudinal outcomes as well as students' perceptions of pedagogic practices. We then employ fuzzy-set Qualitative Comparative Analysis (fs/QCA) to explore the relationships between students' characteristics and the perceived type of teaching they receive in mathematics. We use two measures of 'transmissionist teaching' which aim to quantify the degree to which teaching practices are perceived as 'teacher-centred'. One measure gives the students' perceptions and the other gives the teacher's perspective. We find that different configurations of student and teacher perceptions of transmissionist teaching are associated with high and low mathematical dispositions for different year groups and for boys and girls. We discuss the methodological merits of this approach along with the substantive educational implications of these findings. [ABSTRACT FROM AUTHOR]

This paper shares findings from the study of a learning sequence designed to support prospective elementary teachers (PTs) in identifying evidence of conceptual understanding and procedural fluency. Conceptual understanding and procedural fluency are widely recognized as important to teaching and learning mathematics, and identifying evidence of each is emphasized on teacher candidates' high-stakes performance assessments. As PTs practiced selecting evidence from student work samples, our analysis revealed successes as well as associated challenges. Our findings suggest areas for supporting PTs' learning, as well as challenges stemming from the inherent overlap of these two knowledge types. This study raises important questions about the value of emphasizing PTs' ability to cite evidence of conceptual understanding and procedural fluency, given their integrated nature. [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]

Grouping by attainment is a relatively new and contested practice in Norway, where strong historical discourses of heterogeneous education are under pressure from international test comparisons, particularly in mathematics. At the same time, research indicates that Norwegian teachers have a high degree of autonomy in education policy enactment. Analysing thirteen Norwegian mathematics teachers' reflections on grouping practices, we seek to understand their decision-making processes within this context. Our findings indicate that teachers report a high degree of autonomy in grouping practices which is exercised through considerable diversity in practice and defended when necessary. Using an ecological model of teacher agency reveals how teachers explore and explain their highly situated practice and its tensions and contradictions. We find that teachers who are removed from the central locus of autonomy have less to draw on in making and justifying their pedagogic choices, while those who are more central are able to continually reassess in this highly sensitive arena. We note the implications for practice and research on attainment grouping, particularly the need for teacher autonomy and support for professionally-based local decision-making. [ABSTRACT FROM AUTHOR]

Teachers' perceptions of their teaching and learning activities are critical, especially given that the Malaysian preschool curriculum has undergone multiple revisions recently. The purpose of this study was to measure Malaysian teachers' perceptions on teaching early mathematics. The study aimed to assess teachers' perception of six constructs, namely, (1) knowledge about early mathematics, (2) readiness to involve in the early mathematics, (3) understanding of the importance of early mathematics, (4) past experience in mathematics, (5) attitudes towards early mathematics, and (6) importance of knowledge about teaching early mathematics. This study gauged the 76 Malaysian preschool teachers using a set of questionnaire. As this research discovered, the teachers in this study believed that they knew about early mathematics, were eager to get involved in early mathematics activities at preschool, understood the importance of Mathematics literacy, were positively disposed towards it, and considered mathematical knowledge regarding preschoolers to be critically valued. [ABSTRACT FROM AUTHOR]

With student-centered, hands-on approaches to real-world problems, integrated STEM (science, technology, engineering, mathematics) curricula have the potential to engage students more authentically in multi-disciplinary learning and to learn mathematics more deeply. However, researchers have shown concern that the "M" is often a silent partner and have called for increasing mathematics' visibility in STEM curricula. Taking into account this background, this paper investigated how teachers' and students' engagement with mathematics within a specific lesson in an integrated STEM unit evolved over four years in two elementary teachers' classrooms and the factors the teachers pointed to that may explain their adaptations. Using classroom observations and teacher interviews, the results showed that the time engaged with the mathematics and the depth of engagement with the mathematics decreased over the four years. Five themes emerged that may explain their adaptations: 1) limited time, 2) the need to address required school academic standards in limited time, 3) materials and preparation, 4) the teachers' comfort with the curriculum and, to a lesser extent, 5) their perceptions of their students' abilities. These findings have implications for those that are writing, studying, or potentially using integrated STEM curricula in elementary schools. [ABSTRACT FROM AUTHOR]

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]

The Moving Maths study was conducted to increase third grade pupils' physical activity and support their learning in Finland. Altogether 397 children (mean age 9.3 years) and 22 teachers took part in an intervention with two types of physically active maths lessons for five months. One group carried out lessons in which PA was integrated into maths learning goals, while another group implemented PA as short breaks. A control group was also allocated. The aim of the current study was to qualitatively examine classroom teachers' (n = 12) experiences and perceptions of student engagement during the intervention. The results indicated that pupils showed positive emotional and social engagement in both intervention groups. Positive cognitive engagement was indicated by concentration on seated work after the activities, but some teachers reported uncertainty about the learning results. It is concluded that in addition to reducing children's harmful sedentary behaviour, physically active lessons can positively affect student engagement and may thus enhance learning. [ABSTRACT FROM AUTHOR]

A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) nontraditional arithmetic practice, (3) concreteness fading exercises, and (4) comparison and explanation. In a large-scale randomized control trial in California public schools, 132 second grade teachers were randomly assigned to either use the ICUE intervention or an active control consisting of nontraditional arithmetic practice alone. Using data from 121 teachers in the analytic sample, the study found that students in the intervention group outperformed students in the active control on proximal and transfer measures of equivalence with no observable tradeoffs in computational fluency. The findings suggest that the ICUE intervention helps students construct a robust understanding of mathematical equivalence, a critical precursor to success in algebra. [ABSTRACT FROM AUTHOR]

Research shows that attention to pattern and structure is fundamental to mathematical learning and attainment yet early mathematics curricula in England underplay the importance of patterning. In a critical realist notion of powerful knowledge, pattern teaching has the potential to empower children to notice patterns, mathematise their everyday experiences and engage in mathematical sense-making. This study investigated how to harness this potential. It reports on participatory research with ten teachers of three to five-year-old children in England as they developed pattern teaching in their classrooms. Findings indicate that teacher knowledge, pedagogic interactions and pattern-rich environments (all underpinned by an appropriate developmental progression and extended to form a setting-wide shared approach) support the development of patterning praxis in early childhood classrooms. These offer potential priorities for ECE teachers in developing their patterning praxis in order to support children's mathematical learning. [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]

Teacher education institutions need to provide reflection opportunities for preservice teachers to develop their reflection level. This study investigated the impact of online reflection journals on the reflection level of preservice math teachers (PMTs) and their experiences. A mixed-method action research was utilised in the study. The twenty-four PMTs in a state university in the Philippines were the participants in the study. A rubric was used to evaluate their reflection level, while semi-structured interview and their reflection outputs were used to triangulate the results. Quantitative results revealed a significant increase in the reflection level of the PMTs, while the qualitative findings support the results. Hence, this study suggests the use of an online reflection journal to provide a venue for PMTs to reflect on their learning experiences in their mathematics courses. [ABSTRACT FROM AUTHOR]

This study aims at investigating inclusive pedagogical content knowledge (IPCK) of mathematics teachers who teaches in inclusive classes including learning disabilities (LD) students or hearing impairments (HI) students in the context of angle concept. The study is a cross-case study which facilitates the comparison as one of the multiple case designs. The participants of the study are six Turkish mathematics teachers, three of them have experience of teaching to students with LD, and three of them students with HI. The data of the study is collected via semi-structured clinical interviews, and analysed using cross-case analysis. According to the findings of the study that examines the IPCK of teachers regarding the concept of angle, it can be said that teachers' definitions of angle and their teaching strategies are insufficient. Additionally, it was found that HI teachers used much more multiple presentation such as speaking, writing, drawing shapes, and gestures than LD teachers. [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]