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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]

Inclusive teaching practices can be characterized as recurrent ways how teachers work with their students' diverse abilities, but how exactly are they enacted in subject matter classrooms? The paper proposes a conceptual framework to unpack inclusive practices according to the student ability to which they refer, in five typical jobs for teachers: (a) identifying the demands for the ability, (b) differentiating learning goals, (c) compensating for low abilities, (d) enhancing abilities, and (e) addressing the abilities in joint learning. The proposed job-ability framework for inclusive teaching practices is substantiated in a video study of 25 mathematics lessons on percentages with the same curriculum material. In total, rather than 50, 133 different inclusive teaching practices were identified in 3862 sequences and structured into 20 cells. They address four abilities (from most often to least often): (1) selective attention/working memory, (2) mathematical pre-knowledge, (3) language proficiency, and (4) metacognitive regulation. The large variance of enacted practices identified within and between lessons calls for professional development that elicits, leverages, and extends the repertoire of practices. While the reported frequencies are specific to the chosen teaching unit, the job-ability framework can be transferred to other subject-matter classrooms and used in professional development programs. [ABSTRACT FROM AUTHOR]

Approximately one in three people worldwide suffers from mathematics anxiety, with scholarly literature demonstrating that it has significant consequences for both individuals and wider society. While underlying related concepts, such as self-efficacy and emotional regulation, have been studied, there has been less research into accessible, practical approaches that teachers, support staff, carers and learners can use to overcome emotional barriers to learning mathematics. However, one exception is the Mathematical Resilience Toolkit by Johnston-Wilder et al. This paper reviews the research underpinning the Mathematical Resilience Toolkit, introduces the concept of psychological safety, and presents and evaluates the results of a small-scale study. The Toolkit was used with eight mature GCSE mathematics learners in a further education college. In this exploratory study, data were collected from interviews and analysed using thematic analysis. The key themes that emerged highlight the importance of addressing emotional aspects of learning mathematics in the classroom for those returning to mathematics from adverse prior experiences. All participants rated the Mathematical Resilience Toolkit as 'extremely useful' and would advise using it as a practical strategy for any adult with anxiety in mathematics learning. This approach warrants further research to establish its efficacy in different contexts. [ABSTRACT FROM AUTHOR]

Measures of association, which typically require pairwise data, are widespread in many aspects of educational research. However, due to the need to reduce their content to equal numbers of units of analysis, they are rarely found in the analysis of textbooks. In this paper, we present two methods for overcoming this limitation, one through the use of disjoint sections and the other through the use of overlapping moving averages. Both methods preserve the temporal structure of data and enable researchers to calculate a measure of association which, in this case, is the complementary Euclidean average distance, as an indicator of the books' similarity. We illustrate these approaches by means of a comparative analysis of three commonly-used English and Swedish mathematics textbooks. Analyses were focused on individual tasks, which had all been coded according to the presence or absence of particular characteristics. Both methods produce nearly identical results and are robust with respect to both densely and sparsely occurring characteristics. For both methods, widening the aggregation window results in a slightly increased level of quantified similarity, which is the result of the 'smoothing effect'. We discuss the relation between the window width and the choice of research question. [ABSTRACT FROM AUTHOR]

This paper focusses on the process of learning mathematics in primary school from the perspectives of 62 girls aged seven to 11. For many of these Singaporean girls, English is not the dominant home language, but they all learn mathematics in English. Despite the fact that achievement in mathematics is high nationally, girls appear to be less confident than boys. Adopting notions of identity and agency at the intersection of language and gender, the paper explores how the girls oriented themselves and others to the figured world of school mathematics as successful or not through their interaction in focus group interviews. While some were confident in their mastery of the subject, for some others, the discipline, its language, and other artefacts, such as model drawing and assessment, restricted and frustrated them. Girls experienced a sense of security in their own fellowship and appreciated considerate pedagogies, such as space for individual agency and for improvisation and expression of language, through which they could achieve understanding and progress. [ABSTRACT FROM AUTHOR]

This paper aims to examine the extent to which pre-service teachers' mathematical connection skills were promoted through the course designed within the scope of pedagogies of practice (Grossman et al. [2009]. Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100. https://doi.org/10.1177/016146810911100905) in the teacher education programme. Data were collected in a course that was designed to develop pre-service mathematics teachers' (PSTs) mathematical connections skills through a classroom teaching experiment with individual contributions to the whole class learning process. Thirty-six PSTs who were enrolled in the course participated in the present study. Initial and revised lesson plans were used as primary data collection instruments. In the most general sense, the findings demonstrated that most of the PSTs improved their mathematical connection skills during the course. The results of the current study provide insight into how the courses in undergraduate education should be implemented to give PSTs opportunities to develop their mathematical connection skills. [ABSTRACT FROM AUTHOR]

Although research in mathematics education has yielded a great number of results on mathematics teachers' beliefs in recent decades, it is still an open question as to whether these teachers' beliefs are stable or not. However, since mathematics teachers' beliefs are perceived to be the default of their classroom practices, it is important to gain insight into these beliefs and into their development. In this paper, we contribute to this field of research by providing an approach designed to analyse a change in teachers' belief systems. We study a sample of 20 prospective teachers during their first practical experience. We analyse the structure of teachers' belief systems with interviews and a questionnaire set twice within one year. To analyse development of these teachers' belief systems, we assigned the young teachers of the first and second survey to clusters that were developed in a former study and re-analysed for our purposes here. Our results show considerable changes in mathematics teachers' central beliefs during their first practical experience. However, a general pattern of belief changes is not found. [ABSTRACT FROM AUTHOR]

In this paper, we aim to untangle positioning theory (Davies & Harré, 1990) and its implications for the field of mathematics education research, considering both existing use and potential use. Specific theoretical assumptions of positions or positionings in the context of learning mathematics are outlined. In this paper, a classroom-based instrumental case study illuminates examples of how students are positioned within their mathematical experiences as a means to understand some of the factors that affect how students come to exist within mathematical spaces and how classroom-based positionings impact students' opportunities to engage in learning. Our goal is to present positioning theory as a potential tool for how our teaching practices impact students' experiences in mathematical spaces. We present a moment-by-moment analysis, from an ethnographic perspective of the case, to clearly demonstrate how positioning theory may be utilized for both research and practice within mathematics education research. Implications for methodology and positioning theory through an ethnographic perspective are shared. [ABSTRACT FROM AUTHOR]

Assessment for Learning (AfL) has long been identified as effective in supporting teachers to modify their teaching and learning with the aim of improving attainment but AfL practices are rarely applied to mathematics homework. Parental involvement in learning is also a key ingredient to success. This paper explores the benefits of using AfL strategies within mathematics homework that harnessed the involvement of parents. Nine English primary schools piloted the use of mathematics homework projects that were based in the lived experiences of parents and children. A designated classroom changeover session was introduced to provide an opportunity for children, teachers and parents to practice AfL strategies within the context of mathematics homework. Findings suggest that changing the nature of the homework provided more opportunities for discussion in the home which resulted in higher quality engagement. Parents commented that there was reduced tension over homework as they were able to use their own calculation methods and children were more willing to see them as experts with this type of activity. Children more readily accepted feedback from parents and peers on how to improve their approaches. [ABSTRACT FROM AUTHOR]

In this manuscript, we discuss how we, four women scholar-practitioners of color (WSPoC), utilize their cultural intuition (CI) to navigate the work place and academia in the context of our professional roles situated within STEM-M (Science, Technology, Engineering, Mathematics-Medicine) K-16 setting. We collectively shared our testimonios through platicás in writing group sessions creating a virtual counterspace that allowed us to examine the role of CI in our lives. From that examination, we developed a conceptual model of Scholar-Practitioner Cultural Intuition (SP-CI) consisting of five tenets. The objectives of this manuscript are to describe the testimonio process, the conceptual model that emerged from the analysis of the testimonios, and the model itself. Thus, this manuscript strives to reconstruct and reimagine the understanding of how scholar practitioners (SP) navigate and advocate for themselves and students within racist educational structures and systems. [ABSTRACT FROM AUTHOR]

This study aimed to identify the means and reality of treating learning loss in mathematics at the intermediate stage. The study adopted a mixed methods approach and used the following tools: questionnaire, individual interviews, and collective interviews. There were 40 male and female teacher participants in the first stage and 25 teachers in the second. Among the many findings, the most salient were that the concept of learning loss differs among mathematics teachers and they devote part of their teaching to the treatment of learning loss using different treatment mechanisms. In particular, they reported 'always' using teaching practices supporting the affective aspect of treating learning loss and their satisfaction with their teaching practices concerning learning loss was 'average'. The study also identified several challenges that limit the treatment of learning loss related to the teacher, the student, and the family. Taking these findings into consideration, the research developed some recommendations and proposals, the most important being enhancing teachers' awareness of learning loss, showing successful experiences in treating learning loss, studying the reality of treatment in different educational stages, and adopting teaching models for treating learning loss in mathematics. [ABSTRACT FROM AUTHOR]

Teachers working to transform classrooms towards equity and justice must resist the continual press of dominant culture, which seeks to reproduce longstanding arrangements of inequity and injustice. Little is known about the learning that supports teachers in this resistance. This article offers the Teacher Learning for Transformation (TLT) framework, which is built from two theoretical pillars: Wenger's articulation of four aspects of learning in Communities of Practice: meaning, practice, identity, and community; and Holland et al.'s notion of Figured Worlds. The resulting conceptualisation of TLT is a holistic view of multiple aspects of teachers' learning, which are embedded in and mediated by socio-historical and socio-cultural contexts. I offer an illustrative example of an articulation of the framework to support research on teacher learning towards transformation in a particular context. I comment on ways in which the framework might support further research and design of professional development which aims to support transformative learning towards greater justice in classrooms. [ABSTRACT FROM AUTHOR]

Leading school mathematics is a complex task and the responsibilities and activities involved are not always clearly defined. School mathematics leaders (SML) in Australian schools are often expected to lead improvement in mathematics teaching and learning. Previous research typically focuses on the qualities of effective leaders rather than the practices of SMLs. Investigated in this study were the goals and activities of Victorian primary (elementary) and secondary SMLs and the alignment of their goals and activities. The most frequent goals focused on teams developing shared understandings and practices for improving learning and teaching. The activities of SMLs included a diverse range of activities inside and outside the classroom, irrespective of the leaders' main goal. These findings have implications for the professional learning of SMLs and highlight the importance of leaders being provided with sufficient time to undertake leadership practices that align their leadership activities with their leadership goals. [ABSTRACT FROM AUTHOR]

This article outlines the development and validation of the Mathematics Education of English Learners Scale (MEELS) to understand mathematics preservice teachers' beliefs about teaching mathematics to English learners (ELs). Nine hundred and twenty-five PSTs from 17 states across the U.S. were divided randomly into two samples for the analysis. A Principal Component Analysis was conducted with one sample of 463 respondents, which suggested a four-factor model and a five-factor model. A Confirmatory Factor Analysis with the other sample of 462 respondents suggested that the four-factor model was a better fit. The 19 item four-factor model consisted of the following factors – Classroom Strategies, Native Language, Language in Math, and Comparison with non ELs. The factors show that preservice teachers' beliefs about teaching ELs cluster around teaching moves in the mathematics classroom with ELs, the use of students' native language in the class, the role of language in mathematics, and balancing the teaching and learning of both ELs and non ELs in the mathematics class. The MEELS can be used in teacher preparation to evaluate preservice teachers' beliefs in the program. The factors of MEELS can highlight areas where preservice teachers need more focus. [ABSTRACT FROM AUTHOR]

The global pandemic has changed the mode of delivering lessons. Adult learners have missed and continue to miss the hands-on learning activity, which is a form of experiential learning. When it comes to teaching three-dimensional, geometric shapes (3D), learners often benefit from handling and manipulating concrete shapes. This study examined the use of an AR mobile application, as a learning tool for teaching geometric shapes in virtual mathematics classrooms. Data was collected from thirty learners at Functional Skills and General Certificate of Secondary Education (GCSE) levels in a Further Education college in Birmingham, UK. Learners were divided into Control and Experimental groups. The Control group used traditional learning materials, while in the Experimental group, an AR application was utilised during lessons. Qualitative data was gathered using mixed methods of one-to-one interviews and questionnaires to evaluate the learners' experience. The data was triangulated with observation and note-taking by the teacher. In this study, the content analysis method has been used to analyse the data. Results showed an improved activity and interactivity within the session, when compared to the traditional, passive, teaching and learning strategies used in the learning process. From the results of this study, we can deduce that AR-based tools are a beneficial resource in teaching mathematics and improving learner experience in virtual classrooms. Further studies are required to evaluate quantitative improvements in student performance, as well as to implement AR as a regular teaching strategy. [ABSTRACT FROM AUTHOR]

This manuscript proposes the use of the "I notice, I wonder" routine in college mathematics classrooms to address issues of diversity, equity, and inclusion. Examples are given of prompts that incorporate meaningful conversations about real-world issues affecting our students or about issues of inclusion, access, and representation in mathematics. [ABSTRACT FROM AUTHOR]

Supportive school and classroom climates can add to student achievement and compensate for the negative contribution of low-socioeconomic status (SES) to academic achievement. We tested the added contribution of school and classroom climate to Chilean students' mathematics test scores. We performed a secondary analysis of 151,015 eighth-grade students (attending 8,412 classrooms in 5,619 schools) who completed the Sistema de Medición de la Calidad de la Educación (SIMCE) test in Chile. We identified six dimensions of school climate, which we aggregated to the classroom and school level to fit three-level regression models. Students' gender (girls) and low SES were major negative predictors of test scores. School and classroom climate made an additional contribution to the explained variance in test scores. A positive school and classroom climate compensates for the detrimental effects of gender and low SES on students' mathematics achievement, which justifies investing resources to promote positive school and classroom climates. [ABSTRACT FROM AUTHOR]

The current U.S. sociopolitical climate has resurfaced long-held ideas associated with public perceptions concerning the Spanish language, Latin@s, and their portrayal in United States society. Amidst this climate, educators face the challenge of creating critical learning spaces for Latin@ bilingual children within multiple boundaries. This case study examines the pedagogical practices of an early childhood teacher who has co-constructed, with her students, a figured world where mathematics is part of everyday activities and children develop agency in their learning. Educational environments where Latin@ children use their resources as assets provide great leverage to counteract negative depictions of Latin@s in the U.S. [ABSTRACT FROM AUTHOR]

Collegiate mathematics instructors are moving away from traditional lecture-based teaching practices to accommodate the pedagogies that support more active student learning. As part of the movement, groupwork has been increasingly implemented. At the same time, mathematics classrooms have become increasingly diverse and also in the distribution of students' primary languages. In this report, we examine two students' experiences with groupwork in a collegiate mathematics course. What commonly binds these two students is that they each found themselves to be the only member of their respective groups who uses a different primary language from the other group members. After presenting the experiences, we provide instructional implications for group formation in linguistically heterogeneous classrooms. [ABSTRACT FROM AUTHOR]

Supporting students with difficulties in learning mathematics is a challenge for teachers and educational administrators. Formative assessment is considered to play a successful role in supporting at-risk students as well as students without difficulties in mathematics. There is a need for intervention programs, including formative assessment techniques, that (a) are easy to implement in the regular classroom without requiring radical changes in teachers' individual teaching style, and (b) are effective in supporting at-risk students at the earliest stage possible in their school careers. This article analyzes an effectiveness trial of a formative assessment program developed to meet these goals and conducted in the first two years of elementary school. The examination of the longitudinal dataset from Grades 1–3 (N = 2,330) revealed an effect after the implementation, which was maintained at nearly the same effect size one year after completion of the program. The findings imply that formative assessment can foster the arithmetic achievement of students at risk as well as that of the entire class without changing the curriculum or teachers' individual teaching style. [ABSTRACT FROM AUTHOR]

This study investigates differential effectiveness of teacher behaviour in relation to classroom composition by searching for the extent to which teachers exhibit the same teaching skills when they teach mathematics in different classrooms within a school year. Twenty-six teachers who taught mathematics in more than one classroom of the same age group of students participated in this study. Quality of teaching was measured through external observations and student questionnaires. Student achievement in mathematics at the beginning and at the end of the school year was measured. Data about each teacher factor of the dynamic model but orientation and dealing with student misbehaviour were generalizable at the teacher level. Multilevel structural equation modelling analysis revealed that all teacher factors had an effect on student achievement. Prior achievement (aggregated at classroom level) had an effect on the functioning of two factors (orientation and dealing with misbehaviour). Implications of findings are drawn. [ABSTRACT FROM AUTHOR]

Graphs about Us (GaU) is an activity for building classroom community within mathematics classrooms. Through the creation and analysis of graphical representations of data about the students' lives in and out of school, this activity aims to allow each student to feel seen and validated in the class, create shared knowledge of students' experiences, and to identify and challenge dominant narratives that may be unproductive for learning mathematics. By situating this activity within a mathematical context, GaU promotes students' learning about each other and about mathematics. This article describes three phases of the GaU activity, connects the activity with these goals for building classroom community, and discusses challenges that have arisen when using GaU with students. [ABSTRACT FROM AUTHOR]

Background: This study considers the moment-by-moment mathematics discourse of teachers and students and the relationship of these discourses to student learning. I focus on the discursive constructs of responsiveness to students' mathematical thinking and the intellectual work in teacher and student discourse. Responsiveness to students' mathematical thinking is the extent to which one acknowledges, elicits, takes up, or builds on student thinking in-the-moment. Intellectual work reflects the cognitive work set in motion or performed by a speaker within a given turn of talk. Methods: I developed analytic frameworks that accounted for different levels of responsiveness and intellectual work during whole-class instruction in seventh-grade mathematics classrooms. These frameworks captured variation in responsiveness and intellectual work which was linked to student achievement using MLM. Findings: Analyses revealed a significant positive relationship between teachers' responsiveness to student thinking and student learning. Additionally, the intellectual work requested by the teacher was related to the level of intellectual work students provided, acting as an upper bound on students' mathematical activity. Contributions: The analytic frameworks developed for this study identified forms of responsiveness (High Exploring moves) that were most effective for student learning and specified the relationship between a teacher's and her students' levels of intellectual work. [ABSTRACT FROM AUTHOR]